tag:blogger.com,1999:blog-11842984067597799162024-03-13T22:39:56.856-04:00Tricky Kids MathTricky, challenging math and logic lessons for preschool/kindergarten age children. The "Year 2" lessons are more for 1st grade-age kids. Please feel free to comment and share.
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.comBlogger32125tag:blogger.com,1999:blog-1184298406759779916.post-66337818858085223752014-03-09T19:31:00.001-04:002014-03-09T19:31:11.093-04:00Year 2 - Lesson 14<div class="MsoNormal">
<span style="font-family: Georgia, Times New Roman, serif;"><i><span style="line-height: 115%;">The
kids were playing around a lot and not listening this class. They were climbing
under the table, swinging on their chairs, rolling around, poking each other…
Well it’s a good teaching experience for me, I guess </span></i><i><span style="line-height: 115%;">J</span></i><i><span style="line-height: 115%;"> <o:p></o:p></span></i></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Georgia, Times New Roman, serif;"><b><span style="line-height: 115%;">1.<span style="font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="line-height: 115%;">Which of the operations below makes the
largest odd number?<o:p></o:p></span></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Georgia, Times New Roman, serif;"><span style="line-height: 115%;">a)<span style="line-height: normal;">
</span></span><!--[endif]--><span style="line-height: 115%;">3*1+2*4<o:p></o:p></span></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Georgia, Times New Roman, serif;"><span style="line-height: 115%;">b)<span style="line-height: normal;">
</span></span><!--[endif]--><span style="line-height: 115%;">3*(1+2*4)<o:p></o:p></span></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Georgia, Times New Roman, serif;"><span style="line-height: 115%;">c)<span style="line-height: normal;">
</span></span><!--[endif]--><span style="line-height: 115%;">3* (1+2)*4<o:p></o:p></span></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Georgia, Times New Roman, serif;"><span style="line-height: 115%;">d)<span style="line-height: normal;">
</span></span><!--[endif]--><span style="line-height: 115%;">(3*1+2)*4<o:p></o:p></span></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Georgia, Times New Roman, serif;"><b><span style="line-height: 115%;">2.<span style="font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="line-height: 115%;">Kristina, Max, Dima, and Matthew had an
apple eating contest. The person who ate the most apples won. Kristina ate more
apples than Max, and Dima ate fewer apples than Matthew. We also know that Dan
did not win the contest. Who ate the most apples? <o:p></o:p></span></span></div>
<table cellpadding="0" cellspacing="0">
<tbody>
<tr>
<td height="42" style="vertical-align: top;" width="45"><!--[endif]--><!--[if !mso]--><span style="left: 0pt; mso-ignore: vglayout; position: absolute; z-index: 251661312;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></span></td></tr>
</tbody></table>
<span style="font-family: Georgia, Times New Roman, serif;">*Do a problem about backwards problem solving with shapes and adding/subtracting to get to a result*</span><div class="MsoListParagraphCxSpMiddle">
<span style="height: 42px; left: 0px; margin-left: 108px; margin-top: 19px; mso-ignore: vglayout; position: absolute; width: 45px; z-index: 251661312;"><span style="font-family: Georgia, Times New Roman, serif;"><br />
</span></span><!--[endif]--><!--[if gte vml 1]><v:group id="Group_x0020_4" o:spid="_x0000_s1028"
style='position:absolute;left:0;text-align:left;margin-left:46.5pt;
margin-top:8pt;width:321pt;height:53.25pt;z-index:251659264' coordsize="40767,6762"
o:gfxdata="UEsDBBQABgAIAAAAIQC75UiUBQEAAB4CAAATAAAAW0NvbnRlbnRfVHlwZXNdLnhtbKSRvU7DMBSF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=
">
<v:rect id="Rectangle_x0020_1" o:spid="_x0000_s1029" style='position:absolute;
top:1905;width:3619;height:3238;visibility:visible;mso-wrap-style:square;
v-text-anchor:middle' o:gfxdata="UEsDBBQABgAIAAAAIQDw94q7/QAAAOIBAAATAAAAW0NvbnRlbnRfVHlwZXNdLnhtbJSRzUrEMBDH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" filled="f" strokecolor="black [3213]" strokeweight="2pt"/>
<v:shapetype id="_x0000_t32" coordsize="21600,21600" o:spt="32" o:oned="t"
path="m,l21600,21600e" filled="f">
<v:path arrowok="t" fillok="f" o:connecttype="none"/>
<o:lock v:ext="edit" shapetype="t"/>
</v:shapetype><v:shape id="Straight_x0020_Arrow_x0020_Connector_x0020_2"
o:spid="_x0000_s1030" type="#_x0000_t32" style='position:absolute;left:4381;
top:3333;width:4382;height:0;visibility:visible;mso-wrap-style:square'
o:connectortype="straight" o:gfxdata="UEsDBBQABgAIAAAAIQD+JeulAAEAAOoBAAATAAAAW0NvbnRlbnRfVHlwZXNdLnhtbJSRzU7EIBDH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" strokecolor="black [3213]">
<v:stroke endarrow="open"/>
</v:shape><v:oval id="Oval_x0020_3" o:spid="_x0000_s1031" style='position:absolute;
left:9429;top:1905;width:4382;height:3905;visibility:visible;
mso-wrap-style:square;v-text-anchor:middle' o:gfxdata="UEsDBBQABgAIAAAAIQDw94q7/QAAAOIBAAATAAAAW0NvbnRlbnRfVHlwZXNdLnhtbJSRzUrEMBDH
74LvEOYqbaoHEWm6B6tHFV0fYEimbdg2CZlYd9/edD8u4goeZ+b/8SOpV9tpFDNFtt4puC4rEOS0
N9b1Cj7WT8UdCE7oDI7ekYIdMayay4t6vQvEIrsdKxhSCvdSsh5oQi59IJcvnY8TpjzGXgbUG+xJ
3lTVrdTeJXKpSEsGNHVLHX6OSTxu8/pAEmlkEA8H4dKlAEMYrcaUSeXszI+W4thQZudew4MNfJUx
QP7asFzOFxx9L/lpojUkXjGmZ5wyhjSRJQ8YKGvKv1MWzIkL33VWU9lGfl98J6hz4cZ/uUjzf7Pb
bHuj+ZQu9z/UfAMAAP//AwBQSwMEFAAGAAgAAAAhADHdX2HSAAAAjwEAAAsAAABfcmVscy8ucmVs
c6SQwWrDMAyG74O9g9G9cdpDGaNOb4VeSwe7CltJTGPLWCZt376mMFhGbzvqF/o+8e/2tzCpmbJ4
jgbWTQuKomXn42Dg63xYfYCSgtHhxJEM3Elg372/7U40YalHMvokqlKiGBhLSZ9aix0poDScKNZN
zzlgqWMedEJ7wYH0pm23Ov9mQLdgqqMzkI9uA+p8T9X8hx28zSzcl8Zy0Nz33r6iasfXeKK5UjAP
VAy4LM8w09zU50C/9q7/6ZURE31X/kL8TKv1x6wXNXYPAAAA//8DAFBLAwQUAAYACAAAACEAMy8F
nkEAAAA5AAAAEAAAAGRycy9zaGFwZXhtbC54bWyysa/IzVEoSy0qzszPs1Uy1DNQUkjNS85PycxL
t1UKDXHTtVBSKC5JzEtJzMnPS7VVqkwtVrK34+UCAAAA//8DAFBLAwQUAAYACAAAACEARZOIt8MA
AADaAAAADwAAAGRycy9kb3ducmV2LnhtbESPT4vCMBTE74LfITzBy6KpFty1axQRxD8X2a7u+dE8
22LzUpqo9dsbYcHjMDO/YWaL1lTiRo0rLSsYDSMQxJnVJecKjr/rwRcI55E1VpZJwYMcLObdzgwT
be/8Q7fU5yJA2CWooPC+TqR0WUEG3dDWxME728agD7LJpW7wHuCmkuMomkiDJYeFAmtaFZRd0qtR
MN2ejnt5/mw/4s1luvujuDSHWKl+r11+g/DU+nf4v73VCmJ4XQk3QM6fAAAA//8DAFBLAQItABQA
BgAIAAAAIQDw94q7/QAAAOIBAAATAAAAAAAAAAAAAAAAAAAAAABbQ29udGVudF9UeXBlc10ueG1s
UEsBAi0AFAAGAAgAAAAhADHdX2HSAAAAjwEAAAsAAAAAAAAAAAAAAAAALgEAAF9yZWxzLy5yZWxz
UEsBAi0AFAAGAAgAAAAhADMvBZ5BAAAAOQAAABAAAAAAAAAAAAAAAAAAKQIAAGRycy9zaGFwZXht
bC54bWxQSwECLQAUAAYACAAAACEARZOIt8MAAADaAAAADwAAAAAAAAAAAAAAAACYAgAAZHJzL2Rv
d25yZXYueG1sUEsFBgAAAAAEAAQA9QAAAIgDAAAAAA==
" filled="f" strokecolor="black [3213]" strokeweight="2pt"/>
<v:shape id="Straight_x0020_Arrow_x0020_Connector_x0020_5" o:spid="_x0000_s1032"
type="#_x0000_t32" style='position:absolute;left:14763;top:3524;width:4382;
height:0;visibility:visible;mso-wrap-style:square' o:connectortype="straight"
o:gfxdata="UEsDBBQABgAIAAAAIQD+JeulAAEAAOoBAAATAAAAW0NvbnRlbnRfVHlwZXNdLnhtbJSRzU7EIBDH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" strokecolor="black [3213]">
<v:stroke endarrow="open"/>
</v:shape><v:rect id="Rectangle_x0020_6" o:spid="_x0000_s1033" style='position:absolute;
left:19812;top:2190;width:7620;height:2953;visibility:visible;
mso-wrap-style:square;v-text-anchor:middle' o:gfxdata="UEsDBBQABgAIAAAAIQDw94q7/QAAAOIBAAATAAAAW0NvbnRlbnRfVHlwZXNdLnhtbJSRzUrEMBDH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" filled="f" strokecolor="black [3213]" strokeweight="2pt"/>
<v:shape id="Straight_x0020_Arrow_x0020_Connector_x0020_7" o:spid="_x0000_s1034"
type="#_x0000_t32" style='position:absolute;left:28289;top:3524;width:4381;
height:0;visibility:visible;mso-wrap-style:square' o:connectortype="straight"
o:gfxdata="UEsDBBQABgAIAAAAIQD+JeulAAEAAOoBAAATAAAAW0NvbnRlbnRfVHlwZXNdLnhtbJSRzU7EIBDH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" strokecolor="black [3213]">
<v:stroke endarrow="open"/>
</v:shape><v:shape id="_x0035_-Point_x0020_Star_x0020_8" o:spid="_x0000_s1035"
style='position:absolute;left:32670;width:8097;height:6762;visibility:visible;
mso-wrap-style:square;v-text-anchor:middle' coordsize="809625,676275"
o:gfxdata="UEsDBBQABgAIAAAAIQDw94q7/QAAAOIBAAATAAAAW0NvbnRlbnRfVHlwZXNdLnhtbJSRzUrEMBDH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" path="m1,258313r309250,2l404813,r95561,258315l809624,258313,559434,417959r95566,258314l404813,516625,154625,676273,250191,417959,1,258313xe"
filled="f" strokecolor="black [3213]" strokeweight="2pt">
<v:path arrowok="t" o:connecttype="custom" o:connectlocs="1,258313;309251,258315;404813,0;500374,258315;809624,258313;559434,417959;655000,676273;404813,516625;154625,676273;250191,417959;1,258313"
o:connectangles="0,0,0,0,0,0,0,0,0,0,0"/>
</v:shape><v:shape id="_x0000_s1036" type="#_x0000_t202" style='position:absolute;
left:34004;top:2286;width:5143;height:3333;visibility:visible;
mso-wrap-style:square;v-text-anchor:top' o:gfxdata="UEsDBBQABgAIAAAAIQDw94q7/QAAAOIBAAATAAAAW0NvbnRlbnRfVHlwZXNdLnhtbJSRzUrEMBDH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" filled="f" stroked="f">
<v:textbox>
<![if !mso]>
<table cellpadding=0 cellspacing=0 width="100%">
<tr>
<td><![endif]>
<div>
<p class=MsoNormal>
<span style='font-size:14.0pt;line-height:115%'>100<o:p></o:p></span></p>
</div>
<![if !mso]></td>
</tr>
</table>
<![endif]></v:textbox>
</v:shape></v:group><![endif]--><!--[if !vml]--><span style="height: 82px; left: 0px; margin-left: 60px; margin-top: 5px; mso-ignore: vglayout; position: absolute; width: 436px; z-index: 251659264;"><span style="font-family: Georgia, Times New Roman, serif;"><br /></span></span><!--[endif]--><span style="line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;">In 36
years, I will be 100 years old. How old am I now?</span></span></div>
<table align="left" cellpadding="0" cellspacing="0">
<tbody>
<tr>
<td height="1" width="217"></td>
<td width="45"></td>
<td width="97"></td>
<td width="45"></td>
</tr>
<tr>
<td height="7"></td>
<td colspan="2"></td>
<td height="42" rowspan="2" style="vertical-align: top;" width="45"><!--[endif]--><!--[if !mso]--><span style="left: 0pt; mso-ignore: vglayout; position: absolute; z-index: 251665408;"><span style="font-family: Georgia, Times New Roman, serif;"><br />
</span></span><!--[endif]--><!--[if !mso & !vml]--><span style="font-family: Georgia, Times New Roman, serif;"> <!--[endif]--><!--[if !vml]--></span></td>
</tr>
<tr>
<td height="35"></td>
<td height="42" rowspan="2" style="vertical-align: top;" width="45"><!--[endif]--><!--[if !mso]--><span style="left: 0pt; mso-ignore: vglayout; position: absolute; z-index: 251663360;"><span style="font-family: Georgia, Times New Roman, serif;"><br />
</span></span><!--[endif]--><!--[if !mso & !vml]--><span style="font-family: Georgia, Times New Roman, serif;"> <!--[endif]--><!--[if !vml]--></span></td>
</tr>
<tr>
<td height="7"></td>
</tr>
</tbody></table>
<div class="MsoListParagraphCxSpLast" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[endif]--><span style="line-height: 115%;"><span style="font-family: Georgia, Times New Roman, serif;"> </span></span></div>
<div class="MsoNormal">
<br /></div>
<span style="font-family: Georgia, Times New Roman, serif;"><br clear="ALL" />
</span><br />
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Georgia, Times New Roman, serif;"><b>4.<span style="font-weight: normal;"> </span></b>Othello
symmetry<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Georgia, Times New Roman, serif;"><b>5.<span style="font-weight: normal;"> </span></b><!--[endif]-->Order
R, A, and C from least to greatest. What do they spell out? <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: Georgia, Times New Roman, serif;">7-2 = R <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: Georgia, Times New Roman, serif;">1+3=A <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: Georgia, Times New Roman, serif;">10-8=C<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Georgia, Times New Roman, serif;"><b>6.<span style="font-weight: normal;"> </span></b><!--[endif]-->Mugesti
6 km left. Behaiesti 4 km left. Cripesti 2 km right. Mormaiesti 5 km right.
What’s the distance between Behaiesti and Mormaiesti? <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Georgia, Times New Roman, serif;"><b>7.<span style="font-weight: normal;"> </span></b><!--[endif]-->Vivi
said to Bibi, who is standing behind him, “Behind me, 4 coworkers are
standing”. Bibi answered “In front of me, only 3 coworkers are standing”. How
many clowns are in the line? <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Georgia, Times New Roman, serif;"><b>8.<span style="font-weight: normal;"> </span></b><!--[endif]-->Dan
has a bag of yellow, orange, red, green and brown candies. There are 20 pieces
of candy. He first eats only the yellow, red and orange ones. How many pieces
are left in the bag? <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Georgia, Times New Roman, serif;"><b>9.<span style="font-weight: normal;"> </span></b><!--[endif]-->Dan
left his home at 8:00 AM. He left school at 12:30 PM. The walk home takes 30
minutes. How long was he gone from his house?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Georgia, Times New Roman, serif;"><b>10.<span style="font-weight: normal;"> </span></b><!--[endif]-->What
number is next? 209, 902, 290…? <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin-left: .25in;">
<span style="font-family: Georgia, Times New Roman, serif;">Play mastermind and many-people
blokus – </span><i><span style="font-family: Georgia, Times New Roman, serif;">we didn’t get to this</span><o:p></o:p></i></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com1tag:blogger.com,1999:blog-1184298406759779916.post-31421342235104668372014-03-09T19:17:00.002-04:002014-03-09T19:17:53.934-04:00Year 2 - Lesson 13<div class="MsoNormal">
<span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Kangaroo problems edited from 2011 and 2010 – we’re getting
ready for the Math Kangaroo <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">1.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Fourteen children lined up in pairs. How
many pairs were there?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">The don’t
really know how to divide numbers yet, so they drew 14 dots, circled two at a
time and then counted how many circles they have. <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">2.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Today it is March 18, 2010, and I am 7
years old. How old will I be on March 18, 2020? <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">The
kids counted how many years is it from 2010 to 2020 and then added that number
to 7. <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">3.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">There were 9 four-person tables in the room
where Max had his birthday party. When Max and all his guests sat down, there
were still 7 empty seats. How many guests came to Max’s party?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">One of
the kids organized everyone to draw tables and count seats. </span></i><i><span style="font-family: Wingdings; font-size: 11.5pt; line-height: 115%; mso-ascii-font-family: Georgia; mso-char-type: symbol; mso-hansi-font-family: Georgia; mso-symbol-font-family: Wingdings;">J</span></i><i><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;"> Then he told them to subtract 7 from that
number. Wow, good management skills :) <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">4.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Sasha had $20. He bought one carton of
milk, 10 bananas, one loaf of bread and two packages of butter. With the money
he had left over, he bought lollipops. How many lollipops did he buy?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">a)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Milk: $2, <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">b)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Lollipop: $1.50, <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">c)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Bread: $2, <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">d)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Butter: $2.50, <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">e)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">10 Bananas: $5<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;"> <i> This is a relatively
simple counting problem – I presented it like a working-backwards puzzle to the
kids so that they get more familiar with working backwards in problems. <o:p></o:p></i></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">5.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Matthew has 3 pieces of candy, Katya has 2
pieces of candy less than Dima, and Dima has 4 times as many pieces of candy as
Matthew. How many pieces of candy do Matthew, Katya, and Dima have altogether?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">This
one was pretty easy they figured it out after a few moments of calculating and
scribbling. <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">6.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Today is 3/12/2011. No item can be sold
after the date shown next to it. Which of the items cannot be sold?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l1 level1 lfo3; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">a)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Cheese: 9/15/2011<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l1 level1 lfo3; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">b)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Juice: 3/4/2012<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l1 level1 lfo3; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">c)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Butter: 7/11/2011<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 1.25in; mso-add-space: auto; mso-list: l1 level1 lfo3; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">d)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Yogurt: 2/25/2011<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .5in;">
<i><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">It can
never hurt to know how the calendar works. <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">7.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">In 36 years, I will be 100 years old. How
old am I now? <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Another
backwards problem solving problem. When they solved they were like “Oh really
you’re 64? Oh we thought you were younger…” Haha for a few moments they
actually believed it <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">8.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Katya has several dogs and 4 cats. The
number of her cats’ ears is equal to the number of her dogs’ paws. How many
dogs does Katya have?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">The
thought about how many ears each cat has, then added it together for all the
cats, and then split that amount to be four legs of the dogs. <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">9.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Mr. and Mrs. Kangaroo have three daughters.
The youngest is 5 years old. The middle daughter is 4 years younger than the
oldest daughter and 6 years older than the youngest daughter. How old is the
Kangaroos’ oldest daughter? <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Another
problem where to solve the problem you first have to read the whole problem and
only then you can solve it. This is good practice. <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%; mso-bidi-font-family: Georgia; mso-fareast-font-family: Georgia;">10.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;"> Play
“I’m thinking of a domino that…” by giving hints about the domino and having
the kids rule out all the other dominoes until they get to that one. If there
is still time left, play Chocolate Fix. <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">This
was a nice cool-down game but the kids were all really tired by then (remember,
they’re coming after school </span></i><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">and<i> it’s spring now and their stored energy from sitting in school all day
long for a year is starting to escape </i></span><i><span style="font-family: Wingdings; font-size: 11.5pt; line-height: 115%; mso-ascii-font-family: Georgia; mso-char-type: symbol; mso-hansi-font-family: Georgia; mso-symbol-font-family: Wingdings;">J</span></i><i><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">)<o:p></o:p></span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "Georgia","serif"; font-size: 11.5pt; line-height: 115%;">Only a
couple kids stayed to do Chocolate Fix – the others ran off to play. This is
actually a very good mental rotation game and also it involves thinking in a
venn-diagram-y type of way – the different clues have to overlap in your mind
to solve the puzzle.<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal">
<br /></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-34360126412881614242014-03-09T18:47:00.001-04:002014-03-09T18:47:54.241-04:00Year 2 - Lesson 10<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Color a sheet of paper symmetrically,
then fold it symmetrically, and then cut it out in different ways and see if
the symmetry is still there<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Nim <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Inverse Nim<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Flip a triangle made out of poker chips
(4-3-2-1 rows) upside down by moving only three poker chips<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Color a (4-3-2-1 rows) triangle made out
of circles with three different colors so that no two matching colors touch.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span class="MsoHyperlink"><span style="color: windowtext; font-family: Symbol; font-size: 12pt; line-height: 115%;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Play </span><a href="http://www.thinkfun.com/sites/default/files/images/pdfs/HareAndHoundsBW.pdf"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">ThinkFun’s
Trap the Hare game</span></a><span class="MsoHyperlink"><span style="color: windowtext; font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%;"><o:p></o:p></span></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Play Othello<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">20 questions<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpLast" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Play bingo with addition and subtraction
(14 could be 11+3, 3 would be 4-1, etc.). If kids are younger, using smaller
numbers (only up to 10) will work better.<o:p></o:p></span></div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr style="height: 79.5pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: solid windowtext 1.0pt; height: 79.5pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">12<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 79.5pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">15<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 79.5pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">7<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 79.5pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">3<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 87.25pt; mso-yfti-irow: 1;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 87.25pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">8<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 87.25pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">9<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 87.25pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">1<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 87.25pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">11<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 65.2pt; mso-yfti-irow: 2;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 65.2pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">13<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 65.2pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">6<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 65.2pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">2<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 65.2pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">4<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 77.3pt; mso-yfti-irow: 3; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 77.3pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">10<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 77.3pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">0<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 77.3pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">5<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 77.3pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">14<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="margin-left: .25in;">
<br /></div>
<div class="MsoNormal" style="margin-left: .25in;">
<br /></div>
<div class="MsoNormal" style="margin-left: .25in;">
<br /></div>
<div class="MsoNormal" style="margin-left: .25in;">
<br /></div>
<div class="MsoNormal" style="margin-left: .25in;">
<br /></div>
<div class="MsoNormal" style="margin-left: .25in;">
<br /></div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr style="height: 79.5pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: solid windowtext 1.0pt; height: 79.5pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">9<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 79.5pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">8<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 79.5pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">2<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 79.5pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">3<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 87.25pt; mso-yfti-irow: 1;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 87.25pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">6<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 87.25pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">0<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 87.25pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">15<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 87.25pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">5<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 65.2pt; mso-yfti-irow: 2;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 65.2pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">10<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 65.2pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">14<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 65.2pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">13<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 65.2pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">11<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 77.3pt; mso-yfti-irow: 3; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 77.3pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">4<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 77.3pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">7<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 77.3pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">1<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 77.3pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">12<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<br />
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr style="height: 79.5pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: solid windowtext 1.0pt; height: 79.5pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">13<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 79.5pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">14<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 79.5pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">6<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 79.5pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">1<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 87.25pt; mso-yfti-irow: 1;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 87.25pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">0<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 87.25pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">5<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 87.25pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">4<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 87.25pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">7<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 65.2pt; mso-yfti-irow: 2;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 65.2pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">2<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 65.2pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">12<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 65.2pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">9<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 65.2pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">8<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 77.3pt; mso-yfti-irow: 3; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 77.3pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">3<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 77.3pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">11<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 77.3pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">15<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 77.3pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 114.25pt;" valign="top" width="152">
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<br /></div>
<div align="center" class="MsoNormal" style="margin: 0in 0in 0.0001pt 0.25in; text-align: center;">
<span style="font-family: "Lucida Handwriting"; font-size: 48.0pt;">1<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-59223766488918494192014-03-09T18:40:00.002-04:002014-03-09T18:40:40.212-04:00Year 2 - Lesson 11<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Some ideas are borrowed from <b><i>информатика школа 2100</i></b><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">A man walked into a hotel and went on
the elevator to the third floor. Then he went up again the same amount as last
time. What floor is he on now?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">At
first they said the 6<sup>th</sup> floor (and that’s what I expected), and then
after drawing diagrams, they counted and saw that it was actually the 5<sup>th</sup>.
<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">How many squares are needed to make a
square double the size?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">They
had no idea how to do this at first, but after a few hints, the figured it out.<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Fold cube nets into cubes<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">For
some reason the kids loved this, even though most of their cubes looked more
like spheres :D<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Help K. get some strawberries – one jar
says “the strawberries are here” and the other one “there are no strawberries
in either of these jars”. We know that either the labels are both correct, or
both wrong. Which jar should K. open to get some strawberries?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">They
tried one option, it didn’t work, tried the other, it worked, and they were
done.<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">K, M, and D are playing ball. One of
them loses the ball. You know that one of these statements is true and one is
false:<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: .75in; mso-add-space: auto; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">1.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">K.
lost the ball<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: .75in; mso-add-space: auto; mso-list: l2 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">2.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">M.
didn’t lose the ball. <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .5in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Who lost the ball?<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .5in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Well
I think this is a good problem but it didn’t go anywhere because at this point
the kids started fooling around so I moved on.<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l1 level1 lfo3; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Number – Name (letter) codes:<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: .75in; mso-add-space: auto; mso-list: l4 level1 lfo4; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">1.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">(name
of kid)- 1234<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: .75in; mso-add-space: auto; mso-list: l4 level1 lfo4; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">2.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">(name
of kid) - 3454<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: .75in; mso-add-space: auto; mso-list: l4 level1 lfo4; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">3.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">(name
of kid) - 6454<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: .75in; mso-add-space: auto; mso-list: l4 level1 lfo4; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">4.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">(name
of kid) - 3476<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l5 level1 lfo5; text-indent: -.25in;">
<!--[if !supportLists]--><span lang="RU" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: RU; mso-fareast-font-family: "Times New Roman";">a)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">1 – letter</span><span lang="RU" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: RU;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l5 level1 lfo5; text-indent: -.25in;">
<!--[if !supportLists]--><span lang="RU" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: RU; mso-fareast-font-family: "Times New Roman";">b)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">2 – letter</span><span lang="RU" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: RU;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l5 level1 lfo5; text-indent: -.25in;">
<!--[if !supportLists]--><span lang="RU" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: RU; mso-fareast-font-family: "Times New Roman";">c)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">3 – letter</span><span lang="RU" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: RU;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l5 level1 lfo5; text-indent: -.25in;">
<!--[if !supportLists]--><span lang="RU" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: RU; mso-fareast-font-family: "Times New Roman";">d)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">4 – letter</span><span lang="RU" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: RU;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l5 level1 lfo5; text-indent: -.25in;">
<!--[if !supportLists]--><span lang="RU" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: RU; mso-fareast-font-family: "Times New Roman";">e)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">5 – letter</span><span lang="RU" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: RU;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l5 level1 lfo5; text-indent: -.25in;">
<!--[if !supportLists]--><span lang="RU" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: RU; mso-fareast-font-family: "Times New Roman";">f)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">6 – letter</span><span lang="RU" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: RU;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l5 level1 lfo5; text-indent: -.25in;">
<!--[if !supportLists]--><span lang="RU" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: RU; mso-fareast-font-family: "Times New Roman";">g)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">7 – letter</span><span lang="RU" style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: RU;"><o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Let them then decode 14, 7454, 1267, and 34674<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Figure out which number is whose name. <o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Now make your own number codes.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Have a partner figure them out. <o:p></o:p></span></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-no-proof: yes;">This was a fun and relatively simple activity. <o:p></o:p></span></i></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-no-proof: yes;">Make a drawing:<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpFirst">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-no-proof: yes;">1 – triangle<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-no-proof: yes;">2 – square<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-no-proof: yes;">3 – circle<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-no-proof: yes;">4 – green<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-no-proof: yes;">5 – blue<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-no-proof: yes;">6 – red<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-no-proof: yes;">7 – choose your
color<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l3 level1 lfo6; text-indent: -.25in;">
<!--[if !supportLists]--><b><i><span style="font-family: "Garamond","serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: Garamond; mso-fareast-font-family: Garamond; mso-no-proof: yes;">A.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-weight: normal; line-height: normal;">
</span></span></i></b><!--[endif]--><span style="font-family: "Garamond","serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-no-proof: yes;">Draw a big <b>3</b><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l3 level1 lfo6; text-indent: -.25in;">
<!--[if !supportLists]--><b><i><span style="font-family: "Garamond","serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: Garamond; mso-fareast-font-family: Garamond; mso-no-proof: yes;">B.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-weight: normal; line-height: normal;">
</span></span></i></b><!--[endif]--><span style="font-family: "Garamond","serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-no-proof: yes;">Inside the <b>3</b>, on
the left draw a <b>1 </b><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l3 level1 lfo6; text-indent: -.25in;">
<!--[if !supportLists]--><b><i><span style="font-family: "Garamond","serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: Garamond; mso-fareast-font-family: Garamond; mso-no-proof: yes;">C.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-weight: normal; line-height: normal;">
</span></span></i></b><!--[endif]--><span style="font-family: "Garamond","serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-no-proof: yes;">Inside the <b>3</b>, on
the right draw a <b>2</b> so that it
intersects with the <b>1 </b><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l3 level1 lfo6; text-indent: -.25in;">
<!--[if !supportLists]--><b><i><span style="font-family: "Garamond","serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: Garamond; mso-fareast-font-family: Garamond; mso-no-proof: yes;">D.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-weight: normal; line-height: normal;">
</span></span></i></b><!--[endif]--><span style="font-family: "Garamond","serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-no-proof: yes;">Draw a little <b>1</b>
somewhere in <b>3</b> but not in the other
shapes<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l3 level1 lfo6; text-indent: -.25in;">
<!--[if !supportLists]--><b><i><span style="font-family: "Garamond","serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: Garamond; mso-fareast-font-family: Garamond; mso-no-proof: yes;">E.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-weight: normal; line-height: normal;">
</span></span></i></b><!--[endif]--><span style="font-family: "Garamond","serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-no-proof: yes;">The part that is both <b>2</b>
and <b>1</b> color <b>6</b><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l3 level1 lfo6; text-indent: -.25in;">
<!--[if !supportLists]--><b><i><span style="font-family: "Garamond","serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: Garamond; mso-fareast-font-family: Garamond; mso-no-proof: yes;">F.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-weight: normal; line-height: normal;">
</span></span></i></b><!--[endif]--><span style="font-family: "Garamond","serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-no-proof: yes;">Color the rest of <b>1</b>
with <b>4</b><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l3 level1 lfo6; text-indent: -.25in;">
<!--[if !supportLists]--><b><i><span style="font-family: "Garamond","serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: Garamond; mso-fareast-font-family: Garamond; mso-no-proof: yes;">G.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-weight: normal; line-height: normal;">
</span></span></i></b><!--[endif]--><span style="font-family: "Garamond","serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-no-proof: yes;">Color the rest of <b>2</b>
with <b>5</b><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l3 level1 lfo6; text-indent: -.25in;">
<!--[if !supportLists]--><b><i><span style="font-family: "Garamond","serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: Garamond; mso-fareast-font-family: Garamond; mso-no-proof: yes;">H.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; font-weight: normal; line-height: normal;">
</span></span></i></b><!--[endif]--><span style="font-family: "Garamond","serif"; font-size: 14.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman"; mso-no-proof: yes;">Color the rest of the <b>3</b>
with <b>7 </b><o:p></o:p></span></div>
<br />
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-no-proof: yes;">Some of the kids did this, others ran off to play because
they were tired.<o:p></o:p></span></i></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-28127055771594423812014-02-06T14:07:00.003-05:002014-02-06T14:07:35.504-05:00Lesson 9 - Year 2<div class="MsoNormal">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%;"><i>*Sorry there are no notes on this one!</i></span></div>
<div class="MsoNormal">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Midget
Spell<o:p></o:p></span></b></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">A dragon put a curse on you (one of the kids) that
made your steps twice smaller every time you took a step. Can you get from this
side of the room to the other, with your first step being half the way to the
end of the room? Have the kids take turns and try it out and see whether they
can get to the end of the room this way. At first though, have them make a
prediction whether they will make it to the other side of the room. <o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">This is one of Zeno’s paradoxes – </span><a href="http://en.wikipedia.org/wiki/Zeno's_paradoxes#Dichotomy_paradox"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">the
Dichotomy Paradox</span></a><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> <o:p></o:p></span></div>
<div class="MsoNormal">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Folding
Paper<o:p></o:p></span></b></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">How many times can you fold a piece of paper in
half? Try to fold it in half as many times as possible. Give each of the kids a
piece of paper so they could each try it on their own. Compare results.<o:p></o:p></span></div>
<div class="MsoNormal">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Folding
Toilet Paper <o:p></o:p></span></b></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">After the kids have folded a normal piece of paper,
now have them try to fold toilet paper (I am using a long ribbon) in half as
many times as they can and see how the result differs from the number of times
they could fold a normal sheet of paper. Again, before you start the activity,
have them make predictions of what they think will happen. When they complete
the activity, they should have an idea of how exponential growth can be very
rapid, and that folding something in half one time already makes it twice
smaller. <o:p></o:p></span></div>
<div class="MsoNormal">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Splitting
Pies<o:p></o:p></span></b></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">How do you split three pies for four people evenly?
Draw three big “pies” on the board and have the kids try splitting them, and
then counting what part of a pie every person gets. <o:p></o:p></span></div>
<div class="MsoNormal">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Exploring
Fractions<o:p></o:p></span></b></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Draw circles, squares and other shapes on the white
board and have the kids explore fractions. Don’t forget to explain what
fractions are!<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpFirst" style="margin-bottom: .0001pt; margin-bottom: 0in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Are 2 out of 4 parts of a square equal
to 1 out of 2 parts of an identical square? <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-bottom: .0001pt; margin-bottom: 0in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">If you have half of a square, and you a
fourth more, how many parts out of 4 will you have? <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-bottom: .0001pt; margin-bottom: 0in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">If you have a pie, and you split it in
half, and take one of the pieces, what fraction of the pie will be left?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-bottom: .0001pt; margin-bottom: 0in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">What is bigger – one third or one half?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-bottom: .0001pt; margin-bottom: 0in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">What is one half + one half?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-bottom: .0001pt; margin-bottom: 0in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">What is one third + one third?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-bottom: .0001pt; margin-bottom: 0in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">What about one third + one third + one
third? Explain that when a fraction is x/x (same number for numerator and
denominator) that means that it is a whole (1). <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-bottom: .0001pt; margin-bottom: 0in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Explain that when the numerator is
bigger than the denominator, it means that there are more pieces than what is
available in one whole (1), which means that there is more than one of
something. <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-bottom: .0001pt; margin-bottom: 0in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">If you split one half of a cake in half,
what fraction of the cake would one of those pieces be?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-bottom: .0001pt; margin-bottom: 0in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">What is 1/2 – 1/4? <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast" style="margin-bottom: .0001pt; margin-bottom: 0in; mso-add-space: auto;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Do all of these things on the white board (the kids
can’t understand most of these unless they are visual).<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: 0.0001pt;">
<br /></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Explore! If available, use something similar to
these </span><a href="http://www.learningresources.com/product/magnetic+3-d+fraction+shapes.do?from=ac"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">3D
Magnetic Fraction Shapes</span></a><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">. <o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Play fraction Simon Says (half of you sit down, a
third of you raise your right hand, etc)<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Play opposite fraction Simon Says (if Simon says “a
third of you sit down” that third has to not do that, but the rest of the kids have
to do that)<o:p></o:p></span></div>
<br />
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-no-proof: yes;"><v:shapetype coordsize="21600,21600" filled="f" id="_x0000_t75" o:preferrelative="t" o:spt="75" path="m@4@5l@4@11@9@11@9@5xe" stroked="f">
<v:stroke joinstyle="miter">
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0">
<v:f eqn="sum @0 1 0">
<v:f eqn="sum 0 0 @1">
<v:f eqn="prod @2 1 2">
<v:f eqn="prod @3 21600 pixelWidth">
<v:f eqn="prod @3 21600 pixelHeight">
<v:f eqn="sum @0 0 1">
<v:f eqn="prod @6 1 2">
<v:f eqn="prod @7 21600 pixelWidth">
<v:f eqn="sum @8 21600 0">
<v:f eqn="prod @7 21600 pixelHeight">
<v:f eqn="sum @10 21600 0">
</v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:f></v:formulas>
<v:path gradientshapeok="t" o:connecttype="rect" o:extrusionok="f">
<o:lock aspectratio="t" v:ext="edit">
</o:lock></v:path></v:stroke></v:shapetype><v:shape id="Picture_x0020_6" o:spid="_x0000_i1025" style="height: 318.75pt; mso-wrap-style: square; visibility: visible; width: 357pt;" type="#_x0000_t75">
<v:imagedata o:title="" src="file:///C:\Users\Marie\AppData\Local\Temp\msohtmlclip1\01\clip_image001.png">
</v:imagedata></v:shape></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><o:p></o:p></span></div>
<br />
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">If there is still time left, have the kids try to
color this triangle with three different colors but no two same colors can
touch (if there are lines connecting two circles, those circles can’t have the
same color):<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-q9vDT42m2LU/UvPdUomCRzI/AAAAAAAAC_s/I_H1n3x5ddw/s1600/triangle+with+circles.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-q9vDT42m2LU/UvPdUomCRzI/AAAAAAAAC_s/I_H1n3x5ddw/s1600/triangle+with+circles.png" height="286" width="320" /></a></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div>
<br /></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-45839017065912888372013-12-13T15:05:00.000-05:002013-12-13T15:16:05.915-05:00Lesson 8 - Year 2<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">GENERAL COMMENTS: This was probably one of the best classes I've ever had! :)</span></i><br />
<b><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></b>
<b><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Talk
to the kids about system thinking and ask them questions along the way.<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></b></div>
<div class="MsoNormal">
<b><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Ask
if anybody knows what a system is, if yes, ask them to explain to everybody
else.<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Nobody
knew what a system was (except somebody who said that a system means
electricity – which is an example, but not the definition of a system), so I
just went on to the examples, so that they will learn along the way. <o:p></o:p></span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Suppose we have all the pieces to a car – the motor,
the doors, the windows, the seats, the wheels – everything. If you throw these
things in a heap, they won’t get up and drive. For this to become a system (the
car) we need to connect these things to each other. When you have a real, built
car, the different parts pass data to each other and regulate everything with
sensors. <o:p></o:p></span></div>
<div class="MsoNormal">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></b></div>
<div class="MsoNormal">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">When
one thing changes, the other parts know that and change as well in their own
way. The parts are interconnected. That’s the difference between a heap of
parts and a working system.</span></b></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The
kids are listening carefully. I asked
them whether a heap of parts from a car is a car. Half said yes, half said no.
I asked a student who said “yes” why they thought so, and same with a student
who said “no”. This was what a student who said “yes” said: “A heap of all the
parts from a car is a car because all the pieces are already there and you
wouldn’t need to add anything more to make it a car. All you would have to do
is put the parts together, and that’s easy”. A child who said “no” said: “A
heap of all the parts from a car is not a car because they are not working
together and that’s what’s needed for the car to work”. That’s precisely the
answer I was looking for. Working together, interconnected, and causing each
other to do things, are major elements of a system. For some reason they
thought it was very funny that a pile of parts from a car could get up and
drive. <o:p></o:p></span></i></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">If a human’s body is ripped into pieces (legs, feet,
hands, arms, head), will that be human? No, it will just be the pieces that a
human body is made out of. For this to be a system, the parts have to <b>connect and work together as a whole</b>. <o:p></o:p></span></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">To
check their understanding, I asked “who can now explain to everybody what a
system is?” Nobody answered. I just told
you what a system was, all I’m asking you to do is repeat what I told you! “We
forgot.” <b>Forgot… </b>I explained again,
and then each of the kids in turn, explained what a system was in their own
words. As you can see, it’s important to ask the kids to explain what they just
learned because otherwise, (like in this case), we could’ve moved on through
the lesson and I would never have known that they didn’t understand what a
system was (and that’s mainly what this lesson is about). <o:p></o:p></span></i></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<b><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">What
else is a system? <o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Nobody
could think of anything, so I gave some examples (by asking them some questions).<o:p></o:p></span></i></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Examples:<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> <i>Before giving an example, I asked the kids a
question – “do you think a friendship is a system” There was a loud chorus of
“No!!” Well then. Let me explain;<o:p></o:p></i></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l2 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l2 level1 lfo2; text-indent: -.25in;">
<!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> A friendship is a system – if you help
your friend and play with them, will your friend react in any way? (<i>Wait for the kids to respond)</i>. They will
want to be nice to you too and play with you more, right? If you are mean to
your friend and don’t share, what will they do? (<i>Again, let the kids answer!) </i>They will probably go away from you
and not want to play with you again. You and your friend are connected – your
actions influence your friend’s actions, and your friend’s actions influence
your actions. Your behavior changes depending on what your friend does and how
they act. If 1) you and your friend are connected 2) how your friend acts changes
your behavior in some way 3) you’re doing something together, is a friendship a system?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Ohh….
Now we get it. “Yess! A friendship is a system! How could we not understand
earlier”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l2 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">A family is a system – when a child
behaves badly, what do the parents do? The parents get angry, right? – The family
members’ behaviors are connected and change when others’ behaviors change. If a
child behaves well, the parents are happy, and might praise the child. This is
also a system.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">D.:
“That makes sense. If I don’t behave well, my parents get angry also”<o:p></o:p></span></i></div>
<div class="MsoNormal" style="margin-left: .25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="margin-left: .25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Also, there is a loop
here: The child behaves badly, the parents get angry, the child starts to cry
and behave worse, the parents yell more, the child behaves even worse, the
parents yell even more, until… the child smiles and starts to behave. Then it
starts to go the other way – the parents smile, the child calms down, the
parents calm down, and everything settles back down. This isn’t a very balanced
system because to stop the family from getting into a worse and worse mood,
something opposite has to happen (the child starts to behave better) for the
loop to start going the other way. <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .25in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">“Interesting...
so a lot of things are systems – that’s cool!” <o:p></o:p></span></i></div>
<div class="MsoNormal" style="margin-left: .25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="margin-left: .25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Let’s play a game <i>(‘Yay! A game!)</i>– all of you (kids) come
and stand in a circle, holding hands. When I do something, you do the same
(slightly raise a hand), the next person does the same, then the next, the
next, etc, until it comes back to me and again I slightly raise a hand (because
that’s what the previous person did), and everyone in the circle continues to
slightly raise their hands until their hands are so high that we can’t go any
higher and the system breaks. Do the same thing with a negative feedback loop –
slightly lower hands until everyone’s on the ground, and again, the system
breaks.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .25in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">They
had a lot of fun with this, especially with breaking the system at the end and
pretending to die – ok. This system is obviously not balancing.<o:p></o:p></span></i></div>
<div class="MsoNormal" style="margin-left: .25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal" style="margin-left: .25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Here are some more
examples of systems:<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l2 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l2 level1 lfo2; text-indent: -.25in;">
<span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"></span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> Imagine a forest with only wolves and
bunnies. When there become less bunnies, there become (ask - more or less?)
wolves. When there become more bunnies, there become more wolves (why?). But
when there are more wolves, there become less bunnies, and there become less
wolves. So this is a balancing system. <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">We
discussed this for a while, and the kids seemed to really enjoy it. “When there
are less bunnies, there are… more wolves because they want to eat” “No! When
there are less bunnies there are less wolves because there is less to eat” –
correct. Katya, if we didn’t feed you for a day, would you grow more or less?
“Less…oh” So now we agree that when there are less bunnies there are less
wolves. <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Me:
“But when there are less wolves are there less or more bunnies?” <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Kids
“The same amount!” <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Why?
“Uh…?”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Me:
“When there is less wolves eating the bunnies, do there become more or less
bunnies?”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Kids
“Less bunnies because there is nobody eating them.”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Me:
“What? So when there aren’t any wolves hunting you, you die? Why?”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Kids:
“OOPS! We meant to say more bunnies”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Me:
“But when there become more bunnies, do there become less or more wolves?”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Kids:
“Less because there is nothing to eat”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Me
: “But when there are less wolves there are more bunnies, right? So there become
more wolves again… or no?”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Kids:
“Yes because there are more bunnies to eat and when there is more to eat, the
wolves can lay more eggs in their nest!” <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><u><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The
parents were sitting on the couch and laughing so hard… </span></u></i><i><u><span style="font-family: Wingdings; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Wingdings;">J</span></u></i><i><u><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><o:p></o:p></span></u></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Kids
: “What’s wrong?”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Nothing…
<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Anyways,
it was a very interesting discussion.<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<b><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Can you think of any systems in
your body?<o:p></o:p></span></i></b></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Kids
“Our heart! It beats and regulates. It doesn’t just suddenly beat really fast
or really slow. It’s making sure that it’s at the right speed. Except when we
run. For some reason, when we run, our heart beats very fast. Also our heart is
a system because it makes us have blood…” <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Me:
“That’s one example. Let me give you a few more;”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l2 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l2 level1 lfo2; text-indent: -.25in;">
<!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> When you breathe in, you don’t just
continue breathing in until you burst, right? Your body regulates that you take
in the same amount of air as you breathe out. <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">“We
never thought of that…” So is that a system? “Yes.”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l2 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l2 level1 lfo2; text-indent: -.25in;">
<!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> When it’s hot outside, your body
temperature doesn’t just keep increasing and increasing until you boil, right?
Your body regulates your body temperature- when it’s cold outside, and your
temperature starts to drop, your body warms you up and raises your temperature.
When it’s hot outside, your body cools you down. This is another example of a
balancing and self-regulating system.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">When
it’s 0 degrees outside (C°), do you freeze into an icicle? When it’s hot
outside, do you melt like a sugar cube? “Oh… so our body keeps us cold, or
warm…Yay!” “So that’s a system too… there is a system inside my own body… wow!”
<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpLast">
<br /></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">In systems, there are many different processes that <b>regulate and balance the systems.<o:p></o:p></b></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Let’s play the same game as we just played except
that every person has to do the <i>opposite</i>
of what the person before them just did (I start with slightly raising my hand,
the next person does the opposite- lowers their hand, the next person raises,
and the system stays balanced). <o:p></o:p></span></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">They
loved the fact that everybody kept raising and lowering their hands and the
system still didn’t break and continued to stay balanced. <o:p></o:p></span></i></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Cause and effect are important elements of a system.
When one thing happens, the other parts of the system change depending on what
just happened.<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">For example, where are the causes and effects here;<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l1 level1 lfo3; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The boy laughed because his friend told
him a funny story<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l3 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The teacher was tired of the students
because they were behaving badly<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast" style="mso-list: l3 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The girl tripped because her shoe lace
was untied, and she got hurt.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: .25in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">One
of the girls gave a lecture to the girl who tripped because her shoelace was
untied. </span></i><i><span style="font-family: Wingdings; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Wingdings;">J</span></i><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> <o:p></o:p></span></i></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Now that you know what a system is, can you think of
any more?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo4; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; line-height: 115%;"><span style="font-size: small;">·</span><span style="font-family: 'Times New Roman'; line-height: normal;"><span style="font-size: 7pt;"> </span><b><i>Take a break for systems and do a fun activity;</i></b></span></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo4; text-indent: -.25in;">
<span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"></span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> Take a huge loop of yarn (the size of
half a room) and ask the kids to hold it at any place (make sure that there is
nothing else in the room or at least a lot of space!) Then tell them to close
their eyes and that if they peeks, the game will not work and they will have to
sit out. Then, tell them that with their eyes closed, they have to make a
square with the yarn (they are allowed to communicate with each other). Try it
multiple times and see what happens!<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast" style="mso-list: l0 level1 lfo4; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; line-height: 115%;"><span style="font-size: small;">·</span><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span><span style="font-family: 'Times New Roman'; line-height: normal;"> <i>We only had a couple of minutes to play, but it came out very funny with everybody tangled. Almost all of them were cheating (their eyes were open) and they still couldn't make a square (or even get untangled). :)</i></span></span></div>
<div class="MsoListParagraphCxSpLast" style="mso-list: l0 level1 lfo4; text-indent: -.25in;">
<span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"><br /></span></span></div>
<div class="MsoListParagraphCxSpLast" style="mso-list: l0 level1 lfo4; text-indent: -.25in;">
<!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> Continue playing with the </span><a href="http://britton.disted.camosun.bc.ca/jbhandcuff.htm"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Handcuff
Puzzle</span></a><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> for 5-10 minutes and then show the kids the
solution. If there is still time left, play Othello. <o:p></o:p></span></div>
<br />
<div class="MsoNormal">
<br /></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com1tag:blogger.com,1999:blog-1184298406759779916.post-53892221788143249252013-11-08T21:24:00.002-05:002013-11-08T21:24:49.086-05:00Lesson 6 - Year 2<div class="MsoNormal">
<b><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Introduce
the concept of x as an unknown</span></i></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">– <o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">3 + <b><i>?</i></b> = 5 <b><i>–</i></b> How do we call <b><i>?</i></b>
in math? How can we solve this? <o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">What about <b><i>?</i></b> – 2 =4<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The
kids can easily solve these, but they can’t explain how they do it “We have
done a lot of these in school already so we know the answers” Me: “But what if
I gave you one that you haven’t already solved, then how would you solve it?”
Kids: “We know how to do all of them (equations) already so you won’t be able
to give us one that we don’t know!” Hmm… Anyway, since they can’t explain, life
examples are always good. They have to learn that if the equation starts “balanced
(equal on both sides)” then if they do the same operation to both sides then
the balance will stay (because they didn’t think so at first).<o:p></o:p></span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Show with a problem:<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">*pretending that all apples weigh the same, all
bananas weigh the same, all oranges weigh the same<o:p></o:p></span></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">“If
you had a scale with an apple and an orange on each side, and it was balanced,
then if I take an orange off of each side, will it still be balanced?” Kids: “NO!
Of course not!” <b>Well, we’ll need to work
on that…</b></span></i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">2 apples and 1 orange on one side of a scale, 3
oranges on the other side <b><i>–</i></b> in this example, are 2 apples
equal to 2 oranges? How do you know?<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Play with a balance scale and small cubes – taking
the same amount away from both sides<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Come back to the problem and try it again with new
understanding and do a couple more of the same type<o:p></o:p></span></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">By
the end of this part of the lesson, the kids should understand that if you take
the same amount (of the same thing) away (or add the same amount) to/from each
side of an equation, it will stay equal. If the kids still don’t understand,
have them do a few more equation examples of the same type, and let them
experiment with adding/subtraction amounts from each side and checking if it
still stays equal. That should most likely be enough for them to understand. <o:p></o:p></span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoNormal">
<b><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Try
a few substitution problems:<o:p></o:p></span></i></b></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">What is apple + apple + apple if apple = 2?<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">What is orange + apple + banana if orange = 2, apple
= 3, and banana = 4<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">With those same numbers, what is 2 apple + 3 orange?<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">What about apple+apple-apple+banana?<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> <i>This is pretty easy and not too interesting but it is good practice and will be useful later on when it gets a lot more complex.</i></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Show the kids a “magic trick” and have the kids
figure it out and then do it themselves (every person should get a turn)<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Take 10 cards- lay them down slowly one after
another until your partner says stop. When they say stop, show them the card
that you were going to put down next but haven’t put down yet (and DON’T LOOK AT IT YOURSELF), and then put
that card on top of all of those cards that you have already laid down. Then,
put that stack of cards under the rest of the 10 cards (whatever’s left). Find
your partner’s card. <o:p></o:p></span></div>
<div class="MsoNormal">
<b><i><u><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">I
used cards that had pictures on them<o:p></o:p></span></u></i></b></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The
kids thought that it was amazing and said that they will show it to all their
friends </span></i><i><span style="font-family: Wingdings; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Wingdings;">J</span></i><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> The trick is really just that you
count how many cards you put down before your partner said stop, and then you
subtract that number from ten, and the number of cards that you go through from
the top of the deck will be that number. Example: Let’s say you put down 3
cards and then your partner said stop. You know that you are showing them the <b>fourth</b> card. 10-4=6, so after putting
the cards you have already put down+your partners card under the rest of the
pile, you count 6 cards from the top, and that card will be your partner’s. It
actually involves more math than it seems like, and for a kindergarten-age child,
is pretty complicated. Anyways, it’s an activity that the kids are enthusiastic
to do, and that in itself is already very good</span></i><i><span style="font-family: Wingdings; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Wingdings;">J</span></i><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">. <o:p></o:p></span></i></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoListParagraphCxSpFirst">
<br /></div>
<div class="MsoListParagraphCxSpLast">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><a href="http://britton.disted.camosun.bc.ca/jbhandcuff.htm">Handcuff puzzle</a>-
escape!<o:p></o:p></span></b></div>
<div class="MsoNormal">
<b><i><u><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">I
made the handcuffs out of rubber bands tied together with yarn.<o:p></o:p></span></u></i></b></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">They
LOVED it! They were completely tangled up with their partner, stepping under
and over the string (and of course giggling). After a couple of minutes, the
parents got involved, wanting to try it themselves, and trying to help their
kids (and not succeeding). </span></i><i><span style="font-family: Wingdings; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Wingdings;">J</span></i><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> I asked if they wanted me to show them
the solution, and the parents said that “no”, they would need to think about it
for another week until next class, and then, after <b>they</b> get to play around with it, then I can show them the answer</span></i><i><span style="font-family: Wingdings; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Wingdings;">J</span></i><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">.
It was a complete mess. This is really an <b>awesome
</b>activity.<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal">
<br /></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-415410765609281052013-11-08T20:42:00.002-05:002013-11-08T20:42:20.166-05:00Lesson 5 - Year 2<table cellpadding="0" cellspacing="0">
<tbody>
<tr>
<td height="33" style="vertical-align: top;" width="298"><!--[endif]--><!--[if !mso]--><span style="mso-ignore: vglayout; position: absolute; z-index: 251661312;">
<table cellpadding="0" cellspacing="0" style="width: 100%px;">
<tbody>
<tr>
<td><!--[endif]-->
<div class="shape" style="padding: 3.6pt 7.2pt 3.6pt 7.2pt;" v:shape="Text_x0020_Box_x0020_2">
<div class="MsoNormal">
Move three matchsticks to make 5 triangles</div>
<div class="MsoNormal">
<o:p></o:p></div>
</div>
<!--[if !mso]--></td>
</tr>
</tbody></table>
</span><!--[endif]--><!--[if !mso & !vml]--> <!--[endif]--><!--[if !vml]--></td>
</tr>
</tbody></table>
<div class="MsoNormal">
<!--[if gte vml 1]><v:shapetype id="_x0000_t202"
coordsize="21600,21600" o:spt="202" path="m,l,21600r21600,l21600,xe">
<v:stroke joinstyle="miter"/>
<v:path gradientshapeok="t" o:connecttype="rect"/>
</v:shapetype><v:shape id="Text_x0020_Box_x0020_2" o:spid="_x0000_s1026"
type="#_x0000_t202" style='position:absolute;margin-left:270pt;margin-top:38.45pt;
width:220.5pt;height:21.75pt;z-index:251661312;visibility:visible;
mso-wrap-style:square;mso-width-percent:0;mso-height-percent:0;
mso-wrap-distance-left:9pt;mso-wrap-distance-top:0;mso-wrap-distance-right:9pt;
mso-wrap-distance-bottom:0;mso-position-horizontal:absolute;
mso-position-horizontal-relative:text;mso-position-vertical:absolute;
mso-position-vertical-relative:text;mso-width-percent:0;mso-height-percent:0;
mso-width-relative:margin;mso-height-relative:margin;v-text-anchor:top'
o:gfxdata="UEsDBBQABgAIAAAAIQC75UiUBQEAAB4CAAATAAAAW0NvbnRlbnRfVHlwZXNdLnhtbKSRvU7DMBSF
dyTewfKKEqcMCKEmHfgZgaE8wMW+SSwc27JvS/v23KTJgkoXFsu+P+c7Ol5vDoMTe0zZBl/LVVlJ
gV4HY31Xy4/tS3EvRSbwBlzwWMsjZrlprq/W22PELHjb51r2RPFBqax7HCCXIaLnThvSAMTP1KkI
+gs6VLdVdad08ISeCho1ZLN+whZ2jsTzgcsnJwldluLxNDiyagkxOquB2Knae/OLUsyEkjenmdzb
mG/YhlRnCWPnb8C898bRJGtQvEOiVxjYhtLOxs8AySiT4JuDystlVV4WPeM6tK3VaILeDZxIOSsu
ti/jidNGNZ3/J08yC1dNv9v8AAAA//8DAFBLAwQUAAYACAAAACEArTA/8cEAAAAyAQAACwAAAF9y
ZWxzLy5yZWxzhI/NCsIwEITvgu8Q9m7TehCRpr2I4FX0AdZk2wbbJGTj39ubi6AgeJtl2G9m6vYx
jeJGka13CqqiBEFOe2Ndr+B03C3WIDihMzh6RwqexNA281l9oBFTfuLBBhaZ4ljBkFLYSMl6oAm5
8IFcdjofJ0z5jL0MqC/Yk1yW5UrGTwY0X0yxNwri3lQgjs+Qk/+zfddZTVuvrxO59CNCmoj3vCwj
MfaUFOjRhrPHaN4Wv0VV5OYgm1p+LW1eAAAA//8DAFBLAwQUAAYACAAAACEAAdOA6sUCAAAeBgAA
HwAAAGNsaXBib2FyZC9kcmF3aW5ncy9kcmF3aW5nMS54bWysVH9P2zAQ/X/SvoPl/yFpaPlRkSLo
AE0Chih8gKvjNBaOndlH2vLpd3ZSWnXaJm1rpcTOPT+/e3f2+cWq1qyVzitrcj44TDmTRthCmUXO
X55vDk458wimAG2NzPlaen4x+fzpHMYLB02lBCMG48eQ8wqxGSeJF5WswR/aRhqKldbVgDR1i6Rw
sCTmWidZmh4nNSjDJ1uqL4DA3pz6CyptxasspmBa8ESpxXj3S69Ri39nhrFpb10zax5dUC4e2kfH
VJFzcs5ATRbxpA/0MJome6sWW4JV6eqAt2XJVjkfHtE/Ja41VWOYZieDUccnV8gEAbLTND0aEUAQ
Ijs5zrIeIKpvf6AQ1fXvSUhmJ4cGOxJ9EwSa9uecjzY5Pwd5V3bFso/sA5rhij5SJrHKvrmjKnlm
7LQCs5CXztllJaHwAdHZRH5220TLNjv6wDVf3tuC/IU3tJHvP1n3kTWMG+fxVtqahUHOnRQYd4L2
zmMncAOJltgbpXUstzZsmfOzEVVjL1IrlI5pVeecSke/zqGQ97Up4mIEpbsxadEm9ktIOTDhahbt
D04W6/BlTm+yw1lSSH1Ah5cGlXXvnC3pSObcf38DJznTXw05ezYYDgmGcTIcnWQ0cbuR+W4EjCCq
nCNn3XCKNEv7pC7J+lL1TnQ6giLtcYZrLWMyUW2oVw3uLiqkwdOGQ5tZI8Ia34hHgawFTcUfjHpf
Yv5bxJUsN1j0HTbaRzBav41elriPG2wZCRoBtKo3NTrrSKOmPsy5NAcvM7rn3oMUKlDgkmVJ1e/K
ThkCKsNw3cgSBPXgFLSaO9UfTfhVRPidyLOqpWcPcsmebA2mb3hSEbbDyb1tJcPKSUnOoag8qnBY
0NL0VbIRQ6dIrZY+XCeULz1paUgqPrcN8ublrHki9V3Hdh1EuHCOk72bMS7tb/Jw/e7OJz8AAAD/
/wMAUEsDBBQABgAIAAAAIQCcTl4h4gYAADocAAAaAAAAY2xpcGJvYXJkL3RoZW1lL3RoZW1lMS54
bWzsWU9vG0UUvyPxHUZ7b+P/jaM6VezYDbRpo9gt6nG8Hu9OM7uzmhkn9Q21RyQkREEcqMSNAwIq
tRKX8mkCRVCkfgXezOyud+I1SdsIKmgO8e7b37z/782b3ctX7kUMHRIhKY87XvVixUMk9vmExkHH
uzUaXFj3kFQ4nmDGY9Lx5kR6Vzbff+8y3vAZTcYci8koJBFBwCiWG7jjhUolG2tr0gcylhd5QmJ4
NuUiwgpuRbA2EfgIBERsrVaptNYiTGNvEzgqzajP4F+spCb4TAw1G4JiHIH0m9Mp9YnBTg6qGiHn
sscEOsSs4wHPCT8akXvKQwxLBQ86XsX8eWubl9fwRrqIqRVrC+sG5i9dly6YHNSMTBGMc6HVQaN9
aTvnbwBMLeP6/X6vX835GQD2fbDU6lLk2RisV7sZzwLIXi7z7lWalYaLL/CvL+nc7na7zXaqi2Vq
QPaysYRfr7QaWzUHb0AW31zCN7pbvV7LwRuQxbeW8INL7VbDxRtQyGh8sITWAR0MUu45ZMrZTil8
HeDrlRS+QEE25NmlRUx5rFblWoTvcjEAgAYyrGiM1DwhU+xDTvZwNBYUawF4g+DCE0vy5RJJy0LS
FzRRHe/DBMdeAfLy2fcvnz1Bx/efHt//6fjBg+P7P1pGzqodHAfFVS++/ezPRx+jP5588+LhF+V4
WcT/+sMnv/z8eTkQymdh3vMvH//29PHzrz79/buHJfAtgcdF+IhGRKIb5Ajt8wgMM15xNSdj8Wor
RiGmxRVbcSBxjLWUEv59FTroG3PM0ug4enSJ68HbAtpHGfDq7K6j8DAUM0VLJF8LIwe4yznrclHq
hWtaVsHNo1kclAsXsyJuH+PDMtk9HDvx7c8S6JtZWjqG90LiqLnHcKxwQGKikH7GDwgpse4OpY5f
d6kvuORThe5Q1MW01CUjOnayabFoh0YQl3mZzRBvxze7t1GXszKrt8mhi4SqwKxE+RFhjhuv4pnC
URnLEY5Y0eHXsQrLlBzOhV/E9aWCSAeEcdSfECnL1twUYG8h6NcwdKzSsO+yeeQihaIHZTyvY86L
yG1+0AtxlJRhhzQOi9gP5AGkKEZ7XJXBd7lbIfoe4oDjleG+TYkT7tO7wS0aOCotEkQ/mYmSWF4l
3Mnf4ZxNMTGtBpq606sjGv9d42YUOreVcH6NG1rl868flej9trbsLdi9ympm50SjXoU72Z57XEzo
29+dt/Es3iNQEMtb1Lvm/K45e//55ryqns+/JS+6MDRoPYvYQduM3dHKqXtKGRuqOSPXpRm8Jew9
kwEQ9TpzuiT5KSwJ4VJXMghwcIHAZg0SXH1EVTgMcQJDe9XTTAKZsg4kSriEw6Ihl/LWeBj8lT1q
NvUhxHYOidUun1hyXZOzs0bOxmgVmANtJqiuGZxVWP1SyhRsex1hVa3UmaVVjWqmKTrScpO1i82h
HFyemwbE3Jsw1CAYhcDLLTjfa9Fw2MGMTLTfbYyysJgonGeIZIgnJI2Rtns5RlUTpCxXlgzRdthk
0AfHU7xWkNbWbN9A2lmCVBTXWCEui96bRCnL4EWUgNvJcmRxsThZjI46XrtZa3rIx0nHm8I5GS6j
BKIu9RyJWQBvmHwlbNqfWsymyhfRbGeGuUVQhVcf1u9LBjt9IBFSbWMZ2tQwj9IUYLGWZPWvNcGt
52VASTc6mxb1dUiGf00L8KMbWjKdEl8Vg12gaN/Z27SV8pkiYhhOjtCYzcQ+hvDrVAV7JlTC6w7T
EfQNvJvT3jaP3OacFl3xjZjBWTpmSYjTdqtLNKtkCzcNKdfB3BXUA9tKdTfGvboppuTPyZRiGv/P
TNH7Cbx9qE90BHx40Ssw0pXS8bhQIYculITUHwgYHEzvgGyB97vwGJIK3kqbX0EO9a+tOcvDlDUc
ItU+DZCgsB+pUBCyB23JZN8pzKrp3mVZspSRyaiCujKxao/JIWEj3QNbem/3UAipbrpJ2gYM7mT+
ufdpBY0DPeQU683pZPnea2vgn558bDGDUW4fNgNN5v9cxXw8WOyqdr1Znu29RUP0g8WY1ciqAoQV
toJ2WvavqcIrbrW2Yy1ZXGtmykEUly0GYj4QJfAOCel/sP9R4TP7BUNvqCO+D70VwccLzQzSBrL6
gh08kG6QljiGwckSbTJpVta16eikvZZt1uc86eZyTzhba3aWeL+is/PhzBXn1OJ5Ojv1sONrS1vp
aojsyRIF0jQ7yJjAlH3J2sUJGgfVjgdfkyDQ9+AKvkd5QKtpWk3T4Ao+MsGwZL8Mdbz0IqPAc0vJ
MfWMUs8wjYzSyCjNjALDWfoNJqO0oFPpzybw2U7/eCj7QgITXPpFJWuqzue+zb8AAAD//wMAUEsD
BBQABgAIAAAAIQCcZkZBuwAAACQBAAAqAAAAY2xpcGJvYXJkL2RyYXdpbmdzL19yZWxzL2RyYXdp
bmcxLnhtbC5yZWxzhI/NCsIwEITvgu8Q9m7SehCRJr2I0KvUBwjJNi02PyRR7Nsb6EVB8LIws+w3
s037sjN5YkyTdxxqWgFBp7yenOFw6y+7I5CUpdNy9g45LJigFdtNc8VZ5nKUxikkUigucRhzDifG
khrRykR9QFc2g49W5iKjYUGquzTI9lV1YPGTAeKLSTrNIXa6BtIvoST/Z/thmBSevXpYdPlHBMul
FxagjAYzB0pXZ501LV2BiYZ9/SbeAAAA//8DAFBLAQItABQABgAIAAAAIQC75UiUBQEAAB4CAAAT
AAAAAAAAAAAAAAAAAAAAAABbQ29udGVudF9UeXBlc10ueG1sUEsBAi0AFAAGAAgAAAAhAK0wP/HB
AAAAMgEAAAsAAAAAAAAAAAAAAAAANgEAAF9yZWxzLy5yZWxzUEsBAi0AFAAGAAgAAAAhAAHTgOrF
AgAAHgYAAB8AAAAAAAAAAAAAAAAAIAIAAGNsaXBib2FyZC9kcmF3aW5ncy9kcmF3aW5nMS54bWxQ
SwECLQAUAAYACAAAACEAnE5eIeIGAAA6HAAAGgAAAAAAAAAAAAAAAAAiBQAAY2xpcGJvYXJkL3Ro
ZW1lL3RoZW1lMS54bWxQSwECLQAUAAYACAAAACEAnGZGQbsAAAAkAQAAKgAAAAAAAAAAAAAAAAA8
DAAAY2xpcGJvYXJkL2RyYXdpbmdzL19yZWxzL2RyYXdpbmcxLnhtbC5yZWxzUEsFBgAAAAAFAAUA
ZwEAAD8NAAAAAA==
" filled="f" stroked="f"/><![endif]--><!--[if !vml]--><span style="height: 33px; margin-left: 360px; margin-top: 51px; mso-ignore: vglayout; position: absolute; width: 298px; z-index: 251661312;">
</span><!--[endif]--><b><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Warm
up: </span></i></b></div>
<div class="separator" style="clear: both; text-align: center;">
<b><i><a href="http://3.bp.blogspot.com/-6vJEIA9A3Sk/Un2R00i--8I/AAAAAAAAAz0/hDmAFR-XE0U/s1600/three-to-five+triangle+puzzle.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="132" src="http://3.bp.blogspot.com/-6vJEIA9A3Sk/Un2R00i--8I/AAAAAAAAAz0/hDmAFR-XE0U/s320/three-to-five+triangle+puzzle.jpg" width="320" /></a></i></b></div>
<b><i> </i></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-no-proof: yes;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600"
o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f"
stroked="f">
<v:stroke joinstyle="miter"/>
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0"/>
<v:f eqn="sum @0 1 0"/>
<v:f eqn="sum 0 0 @1"/>
<v:f eqn="prod @2 1 2"/>
<v:f eqn="prod @3 21600 pixelWidth"/>
<v:f eqn="prod @3 21600 pixelHeight"/>
<v:f eqn="sum @0 0 1"/>
<v:f eqn="prod @6 1 2"/>
<v:f eqn="prod @7 21600 pixelWidth"/>
<v:f eqn="sum @8 21600 0"/>
<v:f eqn="prod @7 21600 pixelHeight"/>
<v:f eqn="sum @10 21600 0"/>
</v:formulas>
<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
<o:lock v:ext="edit" aspectratio="t"/>
</v:shapetype><v:shape id="Picture_x0020_2" o:spid="_x0000_i1027" type="#_x0000_t75"
style='width:203.25pt;height:84.75pt;visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\Marie\AppData\Local\Temp\msohtmlclip1\01\clip_image001.jpg"
o:title=""/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><b><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><o:p></o:p></span></i></b><br />
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoNormal">
<br /></div>
<div class="separator" style="clear: both; text-align: center;">
<i><a href="http://2.bp.blogspot.com/-lTETasDTCKM/Un2SOtSi11I/AAAAAAAAAz8/yIXpJ9qu40o/s1600/solution+triangle+puzzle.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="186" src="http://2.bp.blogspot.com/-lTETasDTCKM/Un2SOtSi11I/AAAAAAAAAz8/yIXpJ9qu40o/s200/solution+triangle+puzzle.jpg" width="200" /></a></i></div>
<br />
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">This
was a good warm-up even though it’s pretty easy (all you need to do is move
either the left or right triangle to the top (so that two of its vertices would
be touching the two other triangles’ vertices). I set up a couple of these so
that the kids could work in pairs. Then, I had a pair come up and explain what
they did. At some point, the kids had the right solution, but they didn’t
understand that it was the right solution because they thought they only made 4
triangles (they didn’t count the big one).<o:p></o:p></span></i></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">When I was walking to the Orange Village, I met 5
parents. Each parent had three children. Each child had a friend with them. What
was the minimum number of people walking to Orange Village?<o:p></o:p></span></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">After
a bit of thinking and discussing, they realized that the “I” could’ve been the
only one walking there (since everyone else could be walking the other way)<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">1)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> Pretend
that a policeman came and told you that someone stole a gold chain from a
museum. Facts:<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">- There are only three people who
could’ve done it- Max, Dima, and Sasha (they could’ve done it together with one
of the other suspects but those are the only people that could’ve done it)<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">- Max never does anything bad without
Dima<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpLast">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">- Sasha can’t drive (let’s say they
got there by car)<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Was Dima involved?<o:p></o:p></span></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Thinking…discussing…arguing…
After a couple of minutes, they thought of some possibilities of what could’ve
happened;<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l1 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">1)<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; line-height: normal;">
</span></span></i><!--[endif]--><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">If
Max did it, then Dima did it also – in that case, Dima did it<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpLast" style="mso-list: l1 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">2)<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; line-height: normal;">
</span></span></i><!--[endif]--><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">If
Sasha did it, then someone would have to be with him because he can’t drive, so
it could either be Max (who would be with Dima) or only Dima, which, in both
cases, involves Dima<o:p></o:p></span></i></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">OR…<o:p></o:p></span></i></div>
<div class="MsoListParagraph" style="mso-list: l1 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">3)<span style="font-family: 'Times New Roman'; font-size: 7pt; font-style: normal; line-height: normal;">
</span></span></i><!--[endif]--><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Dima
did it alone, in which case, well… Dima did it. <o:p></o:p></span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Deep
thinking… “These seem to be no other options except the ones we thought of, and
in all the ones we thought of, Dima was involved…” Suddenly the kids’ faces
brighten up “Now the policeman knows who to arrest! Ha!”<o:p></o:p></span></i></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Play </span><a href="http://www.hasbro.com/common/instruct/Mancala.pdf"><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">mancala</span></a><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">
with paper plates and poker chips (that way it is more “hands on” because it
bigger than the usual mancala game board)<o:p></o:p></span></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Very
fun, and it involves math and strategy. We slip up into teams- two kids with
me, three kids against us. The kids took turns moving, and we played a couple
rounds, and mixed up the teams (the kids liked it, but they soon got tired of
it). <o:p></o:p></span></i></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Make a rectangle out of these pieces (solutions are
included in white/gray):<o:p></o:p></span></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-no-proof: yes;"><!--[if gte vml 1]><v:shape id="Picture_x0020_7"
o:spid="_x0000_i1026" type="#_x0000_t75" style='width:223.5pt;height:156pt;
visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\Marie\AppData\Local\Temp\msohtmlclip1\01\clip_image003.jpg"
o:title=""/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--><!--[if gte vml 1]><v:shape id="Picture_x0020_1"
o:spid="_x0000_i1025" type="#_x0000_t75" style='width:231.75pt;height:171.75pt;
visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\Marie\AppData\Local\Temp\msohtmlclip1\01\clip_image004.jpg"
o:title=""/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><o:p></o:p></span></div>
<br />
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">They
played around with these for a little while, and <b>solved it</b>, afterwards announcing that since they solved it one way
already there was no point in continuing (oh well.)<o:p></o:p></span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://2.bp.blogspot.com/-7fA1LFILbKo/Un2S0IlstbI/AAAAAAAAA0M/x757WvfwGHI/s1600/make+a+rectangle.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" height="238" src="http://2.bp.blogspot.com/-7fA1LFILbKo/Un2S0IlstbI/AAAAAAAAA0M/x757WvfwGHI/s320/make+a+rectangle.jpg" width="320" /></a><a href="http://3.bp.blogspot.com/-cEzQhidaV3s/Un2SvX82WPI/AAAAAAAAA0E/JZ98m2X1iy0/s1600/rectangles.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-cEzQhidaV3s/Un2SvX82WPI/AAAAAAAAA0E/JZ98m2X1iy0/s1600/rectangles.jpg" /></a></div>
<br />
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-32270885674777955872013-10-22T16:00:00.002-04:002013-10-22T16:00:30.263-04:00Lesson 4- Year 2<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">1)<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal;"> </span></span></b><!--[endif]--><span style="font-family: "Times New Roman","serif";">A car is driving down a road.
Draw the graph, and tell the story.<o:p></o:p></span></div>
<table align="left" border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; margin-left: 6.75pt; margin-right: 6.75pt; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-table-anchor-horizontal: margin; mso-table-anchor-vertical: page; mso-table-left: center; mso-table-lspace: 9.0pt; mso-table-rspace: 9.0pt; mso-table-top: 92.3pt; mso-yfti-tbllook: 1184; width: 538px;">
<tbody>
<tr style="height: 22.6pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: solid windowtext 1.0pt; height: 22.6pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270">
<div align="center" class="MsoListParagraphCxSpMiddle" style="margin: 0in 0in 0.0001pt; text-align: center;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Minutes past <o:p></o:p></span></b></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 22.6pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269">
<div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">Distance
(miles) from the house<o:p></o:p></span></b></div>
</td>
</tr>
<tr style="height: 14.35pt; mso-yfti-irow: 1;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 14.35pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270">
<div align="center" class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">1<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 14.35pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269">
<div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">1<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 13.0pt; mso-yfti-irow: 2;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 13.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270">
<div align="center" class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">2<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 13.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269">
<div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">2<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 11.65pt; mso-yfti-irow: 3;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 11.65pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270">
<div align="center" class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">3<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 11.65pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269">
<div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">5<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 13.9pt; mso-yfti-irow: 4;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 13.9pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270">
<div align="center" class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">4<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 13.9pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269">
<div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">7<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.25pt; mso-yfti-irow: 5;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 15.25pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270">
<div align="center" class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">5<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.25pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269">
<div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">7<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.25pt; mso-yfti-irow: 6;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 15.25pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270">
<div align="center" class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">6<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.25pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269">
<div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">8<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.25pt; mso-yfti-irow: 7;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 15.25pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270">
<div align="center" class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">7<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.25pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269">
<div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">9<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.25pt; mso-yfti-irow: 8;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 15.25pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270">
<div align="center" class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">8<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.25pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269">
<div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">9<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.25pt; mso-yfti-irow: 9;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 15.25pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270">
<div align="center" class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">9<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.25pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269">
<div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">9<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.25pt; mso-yfti-irow: 10;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 15.25pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270">
<div align="center" class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">10<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.25pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269">
<div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">5<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.25pt; mso-yfti-irow: 11;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 15.25pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270">
<div align="center" class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">11<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.25pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269">
<div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">3<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.25pt; mso-yfti-irow: 12; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 15.25pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270">
<div align="center" class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">12<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.25pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269">
<div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt;">0<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif";">We drew a graph for this on the
white board. The story they told went like this- “for the first 2 minutes the
car was driving slowly because there was a police car behind it. Then, the
police car drove away in the other direction. The car sped up because there was
the parent had to get a child to day care. Then for the 4<sup>th</sup> and 5<sup>th</sup>
minute, the car wasn’t moving because it stopped at the day care and the
parents was talking to the instructor. Then the parent drove to the store, and
bought a few things, so the car stood in place, and then started driving home.
In 3 minute, the car was home.” I had them think about what it means when the
time is changing but the distance isn’t (I made a mistake of making it in
miles, because none of the kids knew what miles were). <o:p></o:p></span></i></div>
<div class="MsoListParagraph" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">2)<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal;"> </span></span></b><!--[endif]--><span style="font-family: "Times New Roman","serif";">The temperature in the Arctic
changes over the week. Kids: make a graph, explain how the temperature is
changing.<o:p></o:p></span></div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184;">
<tbody>
<tr>
<td style="border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" valign="top" width="319">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif";">Day
1<o:p></o:p></span></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" valign="top" width="319">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif";">3<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" valign="top" width="319">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif";">Day
2<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" valign="top" width="319">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif";">5<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" valign="top" width="319">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif";">Day
3<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" valign="top" width="319">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif";">9<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" valign="top" width="319">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif";">Day
4<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" valign="top" width="319">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif";">9<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" valign="top" width="319">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif";">Day
5<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" valign="top" width="319">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif";">9<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" valign="top" width="319">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif";">Day
6<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" valign="top" width="319">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif";">6<o:p></o:p></span></div>
</td>
</tr>
<tr>
<td style="border-top: none; border: solid windowtext 1.0pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" valign="top" width="319">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif";">Day
7<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 239.4pt;" valign="top" width="319">
<div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="font-family: "Times New Roman","serif";">0<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif";">They can’t draw the graph on
their own yet, but they can plot the points and connect them with line
segments. Ask: “If the temperature changes, but the day doesn’t?” “What if the
day changes but the temperature doesn’t?”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpFirst">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; tab-stops: 56.25pt; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">3)<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Times New Roman","serif";">Dima,
Sasha, Max, and Katya have different pets. Each of them has a kangaroo, a squirrel,
a cat, or a bird. Who has which pet? Make a table. <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.5in; mso-add-space: auto; tab-stops: 56.25pt;">
<i><span style="font-family: "Times New Roman","serif";">Clues: <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.5in; mso-add-space: auto; mso-list: l1 level3 lfo2; tab-stops: 56.25pt; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Wingdings; mso-bidi-font-family: Wingdings; mso-fareast-font-family: Wingdings;">§<span style="font-family: 'Times New Roman'; font-size: 7pt;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif";">Dima
has a pet that has feathers.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.5in; mso-add-space: auto; mso-list: l1 level3 lfo2; tab-stops: 56.25pt; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Wingdings; mso-bidi-font-family: Wingdings; mso-fareast-font-family: Wingdings;">§<span style="font-family: 'Times New Roman'; font-size: 7pt;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif";">Sasha
and Katya have pets that don’t start with the first letter of their name.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 1.5in; mso-add-space: auto; mso-list: l1 level3 lfo2; tab-stops: 56.25pt; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Wingdings; mso-bidi-font-family: Wingdings; mso-fareast-font-family: Wingdings;">§<span style="font-family: 'Times New Roman'; font-size: 7pt;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif";">Max’s
pet and Dima’s pet have to be kept apart because Max’s may eat Dima’s. <o:p></o:p></span></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif";">I had the kids draw
a chart and put Xs were things can’t be and color the square in when there is
surely something there (find the intersection of the name and the animal). It
was a good problem for building charts.<o:p></o:p></span></i></div>
<div class="MsoListParagraph" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">4)<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal;"> </span></span></b><!--[endif]--><span style="font-family: "Times New Roman","serif";">There are two villages- one
always lies, one always tell the truth. They visit each other sometimes. You
come into a village, but you don’t know which one it is. You ask a villager
walking by “do you live in this village?” Make a chart of possible
answers/liar/truth-teller/lying village/truth-telling village. <o:p></o:p></span></div>
<br />
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif";">They got kind of confused by this
one because there were many options of what the villager could answer, but it
was still a good exercise for them to think about.<o:p></o:p></span></i></div>
<br />
<a href="http://www.education.com/worksheet/article/smiley-sudoku-second/">http://www.education.com/worksheet/article/smiley-sudoku-second/</a><br />
<a href="http://www.education.com/worksheet/article/kenken-puzzle-second-1/">http://www.education.com/worksheet/article/kenken-puzzle-second-1/</a>Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-44097406408714084732013-10-11T13:13:00.000-04:002013-12-13T15:39:48.175-05:00Lesson 3 - Year 2<div class="MsoListParagraphCxSpFirst" style="text-indent: -0.25in;">
</div>
<ol>
<li><span style="font-family: 'Times New Roman', serif; text-indent: -0.25in;"><b>Consider this:</b></span></li>
</ol>
<!--[if !supportLists]--><br />
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1in; text-indent: -0.25in;">
<!--[if !supportLists]--><b><span style="font-family: Symbol;">·<span style="font-family: 'Times New Roman';">
</span></span><!--[endif]--><span style="font-family: 'Times New Roman', serif;">All
mice are small. <o:p></o:p></span></b></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1in; text-indent: -0.25in;">
<!--[if !supportLists]--><b><span style="font-family: Symbol;">·<span style="font-family: 'Times New Roman';">
</span></span><!--[endif]--><span style="font-family: 'Times New Roman', serif;">Ants
are small. <o:p></o:p></span></b></div>
<div class="MsoListParagraphCxSpLast" style="margin-left: 1in; text-indent: -0.25in;">
<!--[if !supportLists]--><b><span style="font-family: Symbol;">·<span style="font-family: 'Times New Roman';">
</span></span><!--[endif]--></b><span style="font-family: 'Times New Roman', serif;"><b>Therefore,
ants are mice. </b><o:p></o:p></span></div>
<div class="MsoNormal" style="margin-left: 0.75in;">
<i><span style="font-family: 'Times New Roman', serif;">The kids started to talk about how ants aren’t mice
because ants don’t have whiskers and ears (the kids thought this was really
funny…). I asked them how it was possible that both facts were true (all mice
are small and ants are small) and the conclusion was false, and they said “Ants
aren’t mice, and that’s all.” I couldn’t get them to tell me anything
productive, so whatever with this problem…</span></i></div>
<div class="MsoNormal" style="margin-left: 0.75in;">
<span style="font-family: 'Times New Roman', serif; text-indent: -0.25in;"><br /></span></div>
<div class="MsoNormal" style="margin-left: 0.75in;">
<span style="font-family: 'Times New Roman', serif; text-indent: -0.25in;"><b>There is a
grandpa, a grandma, a mom, a dad, a son, and a daughter in a room. What is the
least number of people possibly in this room.</b></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: 'Times New Roman', serif;">First, I drew stick figures on the board to
represent the grandpa, the grandma, a mom, a dad, a son, and a daughter. Then I
asked them if there was any possible way the some of these could be the same
people. First they said no. Then I asked them “can a grandpa be a dad?” They
said maybe. I asked them if they knew who a grandpa was. <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: 'Times New Roman', serif;">They said “Yes! Of course we know! It’s an old man
with a cane and a long white beard!” <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: 'Times New Roman', serif;">“Really? That’s interesting. Who’s an old man then?”
<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: 'Times New Roman', serif;">“Um… Oh… A grandpa is the dad of my dad”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: 'Times New Roman', serif;">“Or?”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: 'Times New Roman', serif;">“Or my mom” Good. <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: 'Times New Roman', serif;">Then we slowly started to combine the stick figures
into less and less until there was only two people left- a grandpa and a
grandma (it took them some time that their grandparents are also sons and daughters
of someone and that they didn’t just appear out of nowhere). <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-indent: -0.25in;">
<!--[if !supportLists]--><b><span style="font-family: 'Times New Roman', serif;">3.<span style="font-family: 'Times New Roman'; font-weight: normal;"> </span><span style="font-family: 'Times New Roman';"> </span></span></b><!--[endif]--><span style="font-family: 'Times New Roman', serif;"><b>Katya is slowly
walking from her house to Kristina’s. Kristina is running from her house to
Katya’s. At the point where they meet, who is closer to Katya’s house?</b><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: 'Times New Roman', serif; line-height: 115%;">Again
I repeated a problem from last year (about trains going from United States and
Canada) and again the kids had no idea how to solve it. For the first few
minutes they all said that Kristina was closer to Katya’s house because she was
running faster</span></i><i><span style="font-family: Wingdings; line-height: 115%;">J</span></i><i><span style="font-family: 'Times New Roman', serif; line-height: 115%;"> .
I was trying to get them to understand;<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: 'Times New Roman', serif; line-height: 115%;">Me:
“They were standing together, holding hands.”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: 'Times New Roman', serif; line-height: 115%;">Kids:
“But Kristina was running faster!”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: 'Times New Roman', serif; line-height: 115%;">Me:
“They were in the same spot, when they met.”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: 'Times New Roman', serif; line-height: 115%;">Kids:
“Kristina was running faster!”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: 'Times New Roman', serif; line-height: 115%;">I
had to explain multiple times for them to understand, and then I showed them. I
(pretended to be Kristina) started at the white board (Kristina’s house) and
ran to the chair (Katya’s house- and in this version Katya was waiting for me
at the porch). When I (pretend Kristina) got to Katya at the chair (Katya’s house),
me and Katya were the same distance away from the white board, right?<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle" style="text-indent: -0.25in;">
<!--[if !supportLists]--><b><span style="font-family: 'Times New Roman', serif;">4.<span style="font-family: 'Times New Roman'; font-weight: normal;"> </span><span style="font-family: 'Times New Roman';"> </span></span></b><!--[endif]--><span style="font-family: 'Times New Roman', serif;"><b>Talk about
graphs- explain what they are (a graph is a diagram that relates one thing to
another in some way- when one changes, the other changes)</b><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpLast" style="text-indent: -0.25in;">
<!--[if !supportLists]--><b><span style="font-family: 'Times New Roman', serif;">5.<span style="font-family: 'Times New Roman'; font-weight: normal;"> </span></span></b><!--[endif]--><span style="font-family: 'Times New Roman', serif;"><b>Give them a few
graphs to look at and have them tell you what’s going on.</b><o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoListParagraphCxSpFirst" style="text-indent: -0.25in;">
<!--[if !supportLists]--><b><span style="font-family: 'Times New Roman', serif;">6.<span style="font-family: 'Times New Roman'; font-weight: normal;"> </span><span style="font-family: 'Times New Roman';"> </span></span></b><!--[endif]--><span style="font-family: 'Times New Roman', serif;"><b>Take a string,
hang it over the table, with both sides hanging over opposite edges of the
table, and pull on side down- the other goes up- when one goes up, the other
goes down. Then take the string and move it side to side- when one moves one
way, the other follows it. The two variables in a graph change together- or... don't change.</b><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast">
<br /></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal" style="margin-left: 0.25in;">
<b><span style="font-family: 'Times New Roman', serif;">Bar graph- Dima, Katya, Matvei, Sasha- Dima ate 4
nuts, Katya ate 6 nuts, Matvei ate 5 nuts, and Sasha ate 3 nuts. Explain what a
bar graph is.<o:p></o:p></span></b></div>
<div class="MsoNormal">
<span style="font-family: 'Times New Roman', serif;"><i><b>Questions:<o:p></o:p></b></i></span></div>
<div class="MsoListParagraphCxSpFirst" style="text-indent: -0.25in;">
<!--[if !supportLists]--><i><b><span style="font-family: 'Times New Roman', serif;">1.<span style="font-family: 'Times New Roman';">
</span></span><!--[endif]--><span style="font-family: 'Times New Roman', serif;">Who
ate the most nuts and how many did they eat?<o:p></o:p></span></b></i></div>
<div class="MsoListParagraphCxSpMiddle" style="text-indent: -0.25in;">
<!--[if !supportLists]--><i><b><span style="font-family: 'Times New Roman', serif;">2.<span style="font-family: 'Times New Roman';">
</span></span><!--[endif]--><span style="font-family: 'Times New Roman', serif;">Who
ate the least nuts and how many did they eat?<o:p></o:p></span></b></i></div>
<div class="MsoListParagraphCxSpMiddle" style="text-indent: -0.25in;">
<!--[if !supportLists]--><i><b><span style="font-family: 'Times New Roman', serif;">3.<span style="font-family: 'Times New Roman';">
</span></span><!--[endif]--><span style="font-family: 'Times New Roman', serif;">How
many people ate nuts in this graph?<o:p></o:p></span></b></i></div>
<div class="MsoListParagraphCxSpLast" style="text-indent: -0.25in;">
<!--[if !supportLists]--><i><b><span style="font-family: 'Times New Roman', serif;">4.<span style="font-family: 'Times New Roman';">
</span></span><!--[endif]--></b></i><span style="font-family: 'Times New Roman', serif;"><i><b>How
many nuts did Matvei and Sasha eat together?</b></i><o:p></o:p></span></div>
<div class="MsoNormal">
<i><span style="font-family: 'Times New Roman', serif;">I
drew the grid/lines for the bar graph, but I had the kids draw the bars. I
didn’t mean for this to be HARD; I just wanted to <b>somehow</b> introduce them to graphs.<o:p></o:p></span></i></div>
<div class="MsoNormal">
<b><span style="font-family: 'Times New Roman', serif;">Pie
graph: 4 cats, 3 birds, 2 fish and 2 dogs are in the house. Explain what a pie
chart is.<o:p></o:p></span></b></div>
<div class="MsoNormal">
<span style="font-family: 'Times New Roman', serif;"><b><i>Questions:<o:p></o:p></i></b></span></div>
<div class="MsoListParagraphCxSpFirst" style="text-indent: -0.25in;">
<!--[if !supportLists]--><b><i><span style="font-family: 'Times New Roman', serif;">1.<span style="font-family: 'Times New Roman';">
</span></span><!--[endif]--><span style="font-family: 'Times New Roman', serif;">How
many different types of animals were there?<o:p></o:p></span></i></b></div>
<div class="MsoListParagraphCxSpMiddle" style="text-indent: -0.25in;">
<!--[if !supportLists]--><b><i><span style="font-family: 'Times New Roman', serif;">2.<span style="font-family: 'Times New Roman';">
</span></span><!--[endif]--><span style="font-family: 'Times New Roman', serif;">How
many cats were there in the house?<o:p></o:p></span></i></b></div>
<div class="MsoListParagraphCxSpMiddle" style="text-indent: -0.25in;">
<!--[if !supportLists]--><b><i><span style="font-family: 'Times New Roman', serif;">3.<span style="font-family: 'Times New Roman';">
</span></span><!--[endif]--><span style="font-family: 'Times New Roman', serif;">How
many more birds were there than dogs?<o:p></o:p></span></i></b></div>
<div class="MsoListParagraphCxSpMiddle" style="text-indent: -0.25in;">
<!--[if !supportLists]--><b><i><span style="font-family: 'Times New Roman', serif;">4.<span style="font-family: 'Times New Roman';">
</span></span><!--[endif]--><span style="font-family: 'Times New Roman', serif;">How
many legs did the birds and fish have together?<o:p></o:p></span></i></b></div>
<div class="MsoListParagraphCxSpMiddle" style="text-indent: -0.25in;">
<!--[if !supportLists]--><b><i><span style="font-family: 'Times New Roman', serif;">5.<span style="font-family: 'Times New Roman';">
</span></span><!--[endif]--><span style="font-family: 'Times New Roman', serif;">Is
the number of fish and dogs together greater than the number of cats?<o:p></o:p></span></i></b></div>
<div class="MsoListParagraphCxSpMiddle" style="text-indent: -0.25in;">
<!--[if !supportLists]--><b><i><span style="font-family: 'Times New Roman', serif;">6.<span style="font-family: 'Times New Roman';">
</span></span><!--[endif]--></i></b><span style="font-family: 'Times New Roman', serif;"><b><i>If
one of the cats left the house, would the size of each section of the pie chart
get bigger, smaller, or stay the same?</i></b><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: 'Times New Roman', serif;">I asked them a few follow-up questions to some of
these just to make sure they understand and I explained how pie graphs (parts
of a whole, etc) work. I used the pie graph below:<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpLast">
<span style="font-family: Georgia, Times New Roman, serif;"><b><i>Blue = 4 cats, </i></b></span></div>
<div class="MsoListParagraphCxSpLast">
<span style="font-family: Georgia, Times New Roman, serif;"><b><i>Red = 2 fish</i></b></span></div>
<div class="MsoListParagraphCxSpLast">
<span style="font-family: Georgia, Times New Roman, serif;"><b><i>Green = 2 dogs</i></b></span></div>
<div class="MsoListParagraphCxSpLast">
<span style="font-family: Georgia, Times New Roman, serif;"><b><i>Purple = 3 birds.</i></b></span></div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: Georgia, Times New Roman, serif;"> </span><span style="font-family: Helvetica Neue, Arial, Helvetica, sans-serif; font-size: x-small;">I inserted pictures into each of the segments, but I couldn't save it as a picture, so I can't insert it here.</span></i></div>
<div class="MsoNormal">
<b><span style="font-family: 'Times New Roman', serif;"><br /></span></b></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-axvVzttO_1w/Ulgvv_49-kI/AAAAAAAAARY/y0cfIwZzYpo/s1600/pie+graph.png" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://2.bp.blogspot.com/-axvVzttO_1w/Ulgvv_49-kI/AAAAAAAAARY/y0cfIwZzYpo/s400/pie+graph.png" height="275" width="400" /></a></td></tr>
<tr><td class="tr-caption" style="text-align: center;"><br /></td></tr>
</tbody></table>
<div class="MsoNormal">
<b><span style="font-family: 'Times New Roman', serif;">Graphs:
<o:p></o:p></span></b></div>
<div class="MsoListParagraphCxSpFirst" style="text-indent: -0.25in;">
<!--[if !supportLists]--><b><i><span style="font-family: 'Times New Roman', serif;">a<span style="font-family: 'Times New Roman'; font-style: normal; font-weight: normal;"> </span></span></i></b></div>
<div class="MsoListParagraphCxSpFirst" style="text-indent: -0.25in;">
<b><i><span style="font-family: 'Times New Roman', serif;"><span style="font-family: 'Times New Roman'; font-style: normal; font-weight: normal;"></span></span></i></b><!--[endif]--><b><span style="font-family: 'Times New Roman', serif;"> Katya measured
how fast her hair grows. When she was born, she had 2 cm hair. When she was 1,
she had 3 cm of hair. When she was 2, she had 4 cm of hair. When she was 3, she
had 5 cm of hair, etc. </span></b><span style="font-family: 'Times New Roman', serif;">Draw a line graph. How fast does Katya’s hair grow?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: 'Times New Roman', serif; line-height: 115%;">Again
I drew the “base” for the graph (the grid) and I had the kids put the points on
the graph by finding the intersections between for example, Katya’s age when
she was three, and the length of her hair at the time. Then I erased the chart
with the numbers, and I had them find one more point on the graph and then
connect all the points on the graph with a line. I also explained how a line
graph is used to show how things change over time, etc.<o:p></o:p></span></i></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoListParagraphCxSpFirst" style="text-indent: -0.25in;">
<!--[if !supportLists]--><b><i><span style="font-family: 'Times New Roman', serif;">b<span style="font-family: 'Times New Roman'; font-style: normal; font-weight: normal;"> </span></span></i></b><!--[endif]--><b><span style="font-family: 'Times New Roman', serif;">A car is driving
down a road. After 1 minute, it drove 1 mile. After 2 minutes, it drove 2
miles. After 3 minutes, it drove 5 miles. At 4 minutes, it had driven 7 miles.
At 5 minutes, it was still at 7 miles. <o:p></o:p></span></b></div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: 'Times New Roman', serif;">We didn’t have time to do this but I will do it next
class because I want to get back to graphs anyway because two kids were absent
this class.<o:p></o:p></span></i></div>
<div class="MsoNormal">
<b><span style="font-family: 'Times New Roman', serif;"> <i>Graphs, b): <o:p></o:p></i></span></b></div>
<table border="1" cellpadding="0" cellspacing="0" class="MsoTableGrid" style="border-collapse: collapse; border: none; margin-left: .5in; mso-border-alt: solid windowtext .5pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184; width: 538px;">
<tbody>
<tr style="height: 22.6pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border: solid windowtext 1.0pt; height: 22.6pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270"><div align="center" class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0.0001pt; text-align: center;">
<b><span style="font-family: 'Times New Roman', serif;">Minutes past <o:p></o:p></span></b></div>
</td>
<td style="border-left: none; border: solid windowtext 1.0pt; height: 22.6pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269"><div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<b><span style="font-family: 'Times New Roman', serif;">Miles driven<o:p></o:p></span></b></div>
</td>
</tr>
<tr style="height: 23.15pt; mso-yfti-irow: 1;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 23.15pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270"><div align="center" class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: 'Times New Roman', serif;">1<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 23.15pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269"><div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: 'Times New Roman', serif;">1<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 23.9pt; mso-yfti-irow: 2;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 23.9pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270"><div align="center" class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: 'Times New Roman', serif;">2<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 23.9pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269"><div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: 'Times New Roman', serif;">2<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 23.9pt; mso-yfti-irow: 3;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 23.9pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270"><div align="center" class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: 'Times New Roman', serif;">3<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 23.9pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269"><div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: 'Times New Roman', serif;">5<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 25.3pt; mso-yfti-irow: 4;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 25.3pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270"><div align="center" class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: 'Times New Roman', serif;">4<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 25.3pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269"><div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: 'Times New Roman', serif;">7<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 23.9pt; mso-yfti-irow: 5; mso-yfti-lastrow: yes;">
<td style="border-top: none; border: solid windowtext 1.0pt; height: 23.9pt; mso-border-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 202.25pt;" valign="top" width="270"><div align="center" class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: 'Times New Roman', serif;">5<o:p></o:p></span></div>
</td>
<td style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 23.9pt; mso-border-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 201.4pt;" valign="top" width="269"><div align="center" class="MsoListParagraphCxSpLast" style="margin: 0in 0in 0.0001pt; text-align: center;">
<span style="font-family: 'Times New Roman', serif;">7<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<br />
<div class="MsoNormal">
<br /></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-55365751915580299722013-09-26T18:12:00.004-04:002013-12-13T15:31:07.703-05:00Lesson 2- Year 2<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: 'Times New Roman', serif; font-size: 11.5pt; line-height: 115%; text-indent: -0.25in;">1.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> <b> </b></span></span><span style="font-family: 'Times New Roman', serif; font-size: 11.5pt; line-height: 115%; text-indent: -0.25in;"><b>(name
of student) (animal) is always sneezing before
it rains. Today it is sneezing. “It is going to rain” – thinks (name of student).
Is he/she correct? </b></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<i style="text-indent: -0.25in;"><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;"> First
I asked who had a pet, and nobody did, except Katya, who said she had a horse
(she had a play horse). So I used the horse as an example. It took them some
time, and they argued a little with each other (which I think is very good for
them, as long as it’s peaceful arguing). Since they didn’t solve it for some
time at first, I “simplified” the problem for them by saying that it’s Dima who
is yawning before it rains. Katya said “If he is yawning, he should be going to
sleep, not predicting rain.” </span></i><i style="text-indent: -0.25in;"><span style="font-family: Wingdings; font-size: 11.5pt; line-height: 115%; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Wingdings;">J</span></i><i style="text-indent: -0.25in;"><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;"> We did the same problem last year except with
Dima eating chocolate and being happy (they obviously didn’t remember it).</span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">2.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> <b> </b></span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;"><b>Put
8 toys around a rectangular table so that each of the sides has 3 toys.</b><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;">We
had a small table and we did this problem by placing 8 poker chips around the perimeter
of the table. After a few minutes, they figured out that they could put the
poker chips in the corners and that would count for two sides instead of one. <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://2.bp.blogspot.com/-HjOYuzCiAU8/UkSxyZVla5I/AAAAAAAAAQ0/5S5JE_HMq5M/s1600/dominoe+arrange.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-HjOYuzCiAU8/UkSxyZVla5I/AAAAAAAAAQ0/5S5JE_HMq5M/s200/dominoe+arrange.png" height="197" width="200" /></a><a href="http://3.bp.blogspot.com/--3g2k6jPMCE/UkSxyR2SoCI/AAAAAAAAAQw/OXDoRn7Uak4/s1600/dominoes+puzzle.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/--3g2k6jPMCE/UkSxyR2SoCI/AAAAAAAAAQw/OXDoRn7Uak4/s320/dominoes+puzzle.png" height="131" width="320" /></a></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: 'Times New Roman', serif; line-height: 115%;"><span style="font-size: 11.5pt;">3.</span><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> <b> </b></span><span style="font-family: 'Times New Roman'; line-height: normal;"><b>Arrange the dominoes how it is done above (grey) so the sum of every side is the same. </b></span></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;">I
cut out these dominoes (you can use really ones also) and asked them to solve
it by putting it in the formation above with every side having the same sum. But
they are still very little, and counting to numbers like 15 AND having to
figure out how to add the other ones together to get that number is too hard
for them, so after a few minutes I told them that each side had to add up to
12, and then in a minute or two they figured it out.</span></i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;"><br />
<!--[if !supportLineBreakNewLine]--><br />
<!--[endif]--><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">4.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> <b> </b></span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;"><b>There
is a power outage, and everything is dark. I know there is a drawer in the
room. There are 8 blue and 8 red gloves in the drawer. How many gloves should I
pick to get at least one pair of alike (in color) gloves? What if there were 12
blue gloves and 12 red gloves? </b><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;">We
did this problem last year too, and it looks like they didn’t remember/understand
a lot of the problems from last year, because now when I gave them similar
problems to the ones we had last year, they don’t remember it at all and have
to think again and solve it afresh (which is good for them). But they grew up noticeably
since last year so they solved the problem faster than they did last year just
because they’re older now, and they go to school, and have to do some type of
math there too.</span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">5.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;"><b>Each
pair is given red and blue poker chips. Players sit back to back, so they do
not see each other’s move. The players are NOT allowed to communicate! If both
play a red chip, they get 2 points each. If they play different colors, the one
who plays the blue gets 3 points, and the one who plays the red gets nothing.
If both play blue, both get 1 coin each. The purpose is to get as many points as possible. What is
the safer choice to make? What choice gets you more points?</b><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;">For
this problem, I asked them to work with a partner and I recorded the points
that they got. Then after a couple minutes of playing I asked them what was the
safest choice to make. They all answered “blue because in any case you get some
points, and unlike with the red chips, you don’t have the risk of getting zero”.
Correct.<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">6.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> <b> </b></span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;"><b>Play
robot (opposite). The kids have to get me from one point of the room to another
while giving me instructions (I’m the robot), but I do everything <i>opposite</i> from what they say.</b><o:p></o:p></span></div>
<br />
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;">I
asked them if they remembered backwards Simon Says, and they said “YES! That
was so fun!”! Then I asked them if they remembered “robot” and they yelled “YES!
That’s our favorite game!” Then I asked them if they wanted to try playing “backwards
robot”- a mix of their two favorite games. They were so happy! They took turns
controlling me from one spot of the room to another (this was a good cool-down
activity). <o:p></o:p></span></i></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-10734648043908753572013-09-25T13:23:00.003-04:002013-12-13T15:27:09.080-05:00Lesson 1- Year 2<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">1.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><b><span style="font-family: 'Times New Roman', serif; font-size: 11.5pt; line-height: 115%; text-indent: -0.25in;">1.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 11.5pt; line-height: 115%; text-indent: -0.25in;">Mr.
and Mrs. Boo have two sons. Each of them has a sister. How many kids are there
in Boo’s family?</span></b></div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;">This
took SO long for them to understand (even though I think it was a good warm-up
and exercise because it made them think- I try to make all the problems like
that, but that doesn’t always work out). Even after I hinted them for so long
that we got to the answer, they took some time to understand. To check their
understand, I asked “If there were 1000 brothers and each one had a sister, how
many sisters would there </span></i><i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;">be?”
and I found out that they didn’t really understand the first problem, because
at first, they again yelled “1000!” but after a couple of minutes they
understood. <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpLast">
<br /></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: 'Times New Roman', serif; line-height: 115%;"><span style="font-size: 11.5pt;">1.</span><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span><span style="font-family: 'Times New Roman'; line-height: normal;"> <b>2. </b></span></span><!--[endif]--><span style="font-family: 'Times New Roman', serif; line-height: 115%;"><b>Construct
three non-intersecting routes from the gates to the houses. Each gate should be
connected to a house with the same number as the number on the gate. </b><span style="font-size: 11.5pt;"><o:p></o:p></span></span></div>
<div class="MsoListParagraphCxSpLast">
</div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;">I
think that this was a good exercise because they had to think about what they
were going to do before they did it, and they had to visualize where the paths
were going to be. They actually found three different solutions to this puzzle,
which was surprising, because I only found one when I was solving it (not that
I spent too much time on it, but still). </span></i><br />
<div class="separator" style="clear: both; text-align: center;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;"><a href="http://2.bp.blogspot.com/-17B45ahIRkk/Uqts8EFqKwI/AAAAAAAACT4/Yapx1DBEq1k/s1600/houses.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-17B45ahIRkk/Uqts8EFqKwI/AAAAAAAACT4/Yapx1DBEq1k/s1600/houses.png" height="200" width="180" /></a></span></i></div>
<div class="separator" style="clear: both; text-align: center;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;"><br /></span></i></div>
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;"><o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoListParagraphCxSpLast">
<span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin;"><b>3. Continue the pattern. </b></span></div>
<div class="MsoListParagraph">
<div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-zupBbQSV1Q4/UqttMIaHG9I/AAAAAAAACUA/NPilWzBPINA/s1600/continue+pattern.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-zupBbQSV1Q4/UqttMIaHG9I/AAAAAAAACUA/NPilWzBPINA/s1600/continue+pattern.png" /></a></div>
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;">Since
this was the first class of this year, I think that this was a good problem to
make the kids think back to what we did the previous year with patterns, and it
took like 5-10 minutes for them to solve this problem. I think the kids grew up
a lot since last year (a year is a lot for them, since they are only 5-6 years
old) because when somebody didn’t understand the problem, instead of me having to
go and explain it to them, other kids went and helped (without being told to do
so). Also, they didn’t fool around as much (even though a couple were a little
shy because they haven’t done this in a while or seen any of the kids (and me)
in some time.<o:p></o:p></span></i><br />
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoListParagraph">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoListParagraph">
<b><span style="font-family: 'Times New Roman', serif; font-size: 11.5pt; line-height: 115%;">4. </span><span style="font-family: 'Times New Roman', serif; font-size: 11.5pt; line-height: 115%; text-indent: -0.25in;"><span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><span style="font-family: 'Times New Roman', serif; font-size: 11.5pt; line-height: 115%; text-indent: -0.25in;">There
are 6 fish in a fish tank– 4 blue fish, 3 green fish and 1 purple fish. How
many of these fish can each say that it is the same color as another one?</span></b></div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;">After
a minute or two they figured it out (I actually used poker chips of different
colors for this problem to represent the fish. A nice joke when they solved the
problem “Actually, I was tricking you all along. The answer’s zero! Have you
ever heard of talking fish?!”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: 'Times New Roman', serif; line-height: 115%;"><span style="font-size: 11.5pt;">1.</span><span style="font-family: 'Times New Roman'; line-height: normal;"><span style="font-size: 7pt;"> </span><b>5. </b></span></span><span style="font-family: 'Times New Roman', serif; line-height: 115%;"><b>What
do you see?</b><span style="font-size: 11.5pt;"><o:p></o:p></span></span></div>
<div class="MsoListParagraphCxSpLast">
</div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;">This
was nice because the kids were all starting to get tired and their attention
was drifting, and I passed this picture around the table and asked very person
to describe what they saw (and then I explained it was an illusion so it can
look like two things at once, and I explained how it was made/how it worked),
so every person had to pay attention. <o:p></o:p></span></i><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-jOUhxwoOKeQ/Uqtth5r0PdI/AAAAAAAACUI/PGQIMjnYJWA/s1600/faces.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-jOUhxwoOKeQ/Uqtth5r0PdI/AAAAAAAACUI/PGQIMjnYJWA/s1600/faces.png" /></a></div>
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: 'Times New Roman', serif; line-height: 115%;"><span style="font-size: 11.5pt;">1.</span><span style="font-family: 'Times New Roman'; line-height: normal;"><span style="font-size: 7pt;"> </span><b>6. </b></span></span><span style="font-family: 'Times New Roman', serif; line-height: 115%;"><b>2
penguins were sitting on ice – a big penguin and a little penguin. The little
penguin was the son of the big penguin, but the big penguin was not his father.
How do you explain this?</b><span style="font-size: 11.5pt;"><o:p></o:p></span></span></div>
<div class="MsoListParagraphCxSpLast">
</div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;">It
took them a couple of minutes to solve this problem (they clearly didn’t
understand the problem at first because they said that the big penguin might be
an older sister or brother). This surprised me, because actually, <b>we did the same exact problem last year</b>,
except it was with dentists instead of penguins (I guess those are two
completely different problems for the kids). I kind of used this problem to
check how much the kids remember from the previous year. After they solved the
problem, I asked them “Do you remember doing this same problem last year with
the dentists?” And they answered “Dentists?! Are you crazy? How are dentists
and penguins at all similar</span></i><i><span style="font-family: Wingdings; font-size: 11.5pt; line-height: 115%; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Wingdings;">J</span></i><i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;">?” <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;"><b>General Notes:</b></span></i></div>
<div class="MsoListParagraph">
<i><span style="font-family: "Times New Roman","serif"; font-size: 11.5pt; line-height: 115%;">I
thought we would fit in many more problems in this class (I prepared about
twice more), but since it was the first class of the year, I guess it took some
time for them to adjust back to this type of thinking ( now that they are going
to school, they are getting used to straightforward thinking). <o:p></o:p></span></i></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-30027578688400773092013-05-12T19:30:00.004-04:002013-05-12T19:30:28.458-04:00Lesson 19- Everything Math
<br />
<div class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0pt 1in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -0.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">By overlapping two circles, you can make
three different areas </span><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">. How many different
areas can you make with two squares?<o:p></o:p></span></div>
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin: 0in 0in 0pt 1in; mso-add-space: auto;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">I gave each of the kids
a piece of paper and let them play around with the problem for a few minutes,
and the kids found a way of making nine different areas by overlapping two
squares. <o:p></o:p></span></i></div>
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin: 0in 0in 0pt 1in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -0.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Do a very easy Sudoku puzzle (below)<o:p></o:p></span></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://3.bp.blogspot.com/-dS5PEyhC3Bs/UZAlwi4AjCI/AAAAAAAAANU/vcyyRtToYao/s1600/sudoku+puzzle.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://3.bp.blogspot.com/-dS5PEyhC3Bs/UZAlwi4AjCI/AAAAAAAAANU/vcyyRtToYao/s320/sudoku+puzzle.gif" width="320" /></a></div>
<div class="MsoListParagraphCxSpMiddle" style="margin: 0in 0in 0pt 1in; mso-add-space: auto;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">I made a big mistake
here. I should’ve brought Sudoku puzzles that are 4x4, or instead, Sudoku
puzzles that have pictures instead of numbers. I didn’t realize that these kids
are still very little! They can’t solve Sudoku puzzles this hard (especially
that some of the kids didn’t know how to do Sudoku puzzles) unless they get a
lot of help from somebody else. <o:p></o:p></span></i></div>
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin: 0in 0in 0pt 1in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -0.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Play Mastermind<o:p></o:p></span></div>
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin: 0in 0in 0pt 1in; mso-add-space: auto;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">This is a little too
hard for them for now. It’s possible to play this game with the kids, but they
need a lot of hints and explanations during the game, which is fine, but don’t
expect them to be able to figure it out on their own. <o:p></o:p></span></i></div>
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin: 0in 0in 0pt 1in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -0.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">10 adult people are trying to crowd
under one small umbrella, but nobody gets wet. How is this possible?<o:p></o:p></span></div>
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin: 0in 0in 0pt 1in; mso-add-space: auto;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">“They can stand on each
other’s shoulders and the top person can hold the umbrella” – THIS IS THE
SOLUTION THAT ALL LITTLE KIDS OFFER AT FIRST (even I solved it this way when I
was solving it when I was 5 or 6). I don’t know what is so obvious about that
solution, but all little kids seem to think that it’s the best way to solve
this problem. Later, a few kids realized that the 10 people could be in a house
or under something- that’s a good solution. Then they couldn’t think of any
more solutions, so I asked “Where/when can you get wet?” and they said “in the
rain”. So, then I gave them a minute or so to think, and then they realized “wait,
you never said that it was raining outside!” <o:p></o:p></span></i></div>
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin: 0in 0in 0pt 1in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -0.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";"> </span></span></span><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://3.bp.blogspot.com/-LLdtMpgBFMg/UZAltfT_6uI/AAAAAAAAANM/f_6k0mL4lWU/s1600/cat+figures.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"></a> </div>
<br />
<!--[endif]--><span style="font-size: 14pt; line-height: 115%; mso-no-proof: yes;"><!--[if gte vml 1]><v:shape id="Picture_x0020_2" o:spid="_x0000_i1027"
type="#_x0000_t75" alt="ris05" style='width:145.5pt;height:28.5pt;
visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\Marie\AppData\Local\Temp\msohtmlclip1\01\clip_image003.png"
o:title="ris05"/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">- What should
the next picture in the pattern be? <o:p></o:p></span><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-XsyIv_61QBM/UZAlrxvuykI/AAAAAAAAANE/ezoSwH6Hsjc/s1600/pattern+numbers.png" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="62" src="http://4.bp.blogspot.com/-XsyIv_61QBM/UZAlrxvuykI/AAAAAAAAANE/ezoSwH6Hsjc/s320/pattern+numbers.png" width="320" /></a></div>
<div class="MsoListParagraphCxSpMiddle" style="margin: 0in 0in 0pt 1in; mso-add-space: auto;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">I first let them look
at it for a little bit and try to figure out what the pattern is. Then after
seeing that they weren’t getting anywhere I covered half of each of the terms,
and asked them what it looked like. Then, when they realized the pattern, I
asked them to continue the pattern for the next 2 terms.<o:p></o:p></span></i></div>
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin: 0in 0in 0pt 1in; mso-add-space: auto; mso-list: l0 level1 lfo1; text-indent: -0.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;"><span style="mso-list: Ignore;">·<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span><!--[endif]--><span style="mso-no-proof: yes;"><!--[if gte vml 1]><v:shape
id="Picture_x0020_4" o:spid="_x0000_i1026" type="#_x0000_t75" alt="EX41"
style='width:69pt;height:87.75pt;visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\Marie\AppData\Local\Temp\msohtmlclip1\01\clip_image005.png"
o:title="EX41"/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Which of these
shapes does this cat not have <o:p></o:p></span></div>
<br />
<!--[if !supportLists]--><div class="MsoListParagraphCxSpLast" style="margin: 0in 0in 10pt 2.75in; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -0.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="mso-list: Ignore;"><a href="http://3.bp.blogspot.com/-LLdtMpgBFMg/UZAltfT_6uI/AAAAAAAAANM/f_6k0mL4lWU/s1600/cat+figures.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="http://3.bp.blogspot.com/-LLdtMpgBFMg/UZAltfT_6uI/AAAAAAAAANM/f_6k0mL4lWU/s200/cat+figures.png" width="156" /></a></span></span></div>
<div class="MsoListParagraphCxSpLast" style="margin: 0in 0in 10pt 2.75in; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -0.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="mso-list: Ignore;">a)<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";"> </span></span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Rectangles
b) Squares c) Circles d) Triangles<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">They
didn’t understand this problem, so to make it easier, I rounded the tips of the
cats ears too, and then the saw that there weren’t any triangles in the cat. <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="mso-fareast-font-family: "Times New Roman"; mso-no-proof: yes;"><!--[if gte vml 1]><v:shape id="_x0000_i1025" type="#_x0000_t75"
alt="http://www.sudokucollection.com/sp/VE001/IMAG0003.GIF" style='width:355.5pt;
height:355.5pt;visibility:visible'>
<v:imagedata src="file:///C:\Users\Marie\AppData\Local\Temp\msohtmlclip1\01\clip_image007.gif"
o:href="http://www.sudokucollection.com/sp/VE001/IMAG0003.GIF"/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"><o:p></o:p></span><br /></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<o:p><span style="font-family: Calibri;"> </span></o:p></div>
</div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-6049248803710736812013-05-12T19:21:00.001-04:002013-05-12T19:21:21.796-04:00Lesson 17- Basic Proofs
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Everybody
needs a mouth:<o:p></o:p></span></i></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">If we didn’t have a mouth, we wouldn’t be able to
eat.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">If we weren’t able to eat, we wouldn’t get energy.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">If we didn’t have any energy, we would die.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Therefore, everybody needs a mouth. <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Does this make sense? Is it correct?<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Actually,
for this problem, I asked the kids to prove why we need a mouth instead of
telling them myself. It’s always better to have the kids doing something or
figuring something out instead of just sitting there and listening (or in some
cases, not listening). <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">How
can you prove that you breathe with your nose and not your fingers?<o:p></o:p></span></i></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">They
couldn’t quite figure out how to prove it at first, but then they closed their
noses and said that they couldn’t breathe, and then they made fists and
squeezed their fingers and they could still breathe. <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Circular
Reasoning- Do these make sense?<o:p></o:p></span></i></b></div>
<br />
<div class="MsoListParagraph" style="margin: 0in 0in 10pt 0.5in; mso-list: l0 level1 lfo1; text-indent: -0.25in;">
<!--[if !supportLists]--><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="mso-list: Ignore;">1.<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";"> </span></span></span></i></b><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">“This is a dinosaur bone!”<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">“How do you know?”<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">“Because it was stuck in this billion year old
sand.”<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">“How do you know the sand was a billion years old?”<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">“Because there was a dinosaur bone inside it.” <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">At
first, they thought that this made perfect sense, but then I drew them a
diagram, and they realized that the reasoning was going in circles. <o:p></o:p></span></i></div>
<br />
<div class="MsoListParagraph" style="margin: 0in 0in 10pt 0.5in; mso-list: l0 level1 lfo1; text-indent: -0.25in;">
<!--[if !supportLists]--><b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="mso-list: Ignore;">2.<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";"> </span></span></span></i></b><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"><span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">“I am not a monster. I don’t even know what a
monster is.”<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">“How do you know that you are not a monster if you
don’t know what a monster is?”<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">“Because if I was a monster, I would know.”<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">I
prompted them with a few hints which were actually questions AFTER I LET THEM
THINK A LITTLE BIT ON THEIR OWN. I asked them questions like “Can somebody know
that they are something (or in this case, not something) if they don’t even
know what that thing is?” Soon they realized that was I was saying was correct.
I gave them a couple more variations of this problem after they solved just to
make sure that they understood. For example, I said “If you were an apple, and
somebody came up to you and said, “you are an apple” and you said “ I am not an
apple. I don’t even know what an apple is”, would that make sense?” <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Chairs:<o:p></o:p></span></i></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">In a rectangular room, put 8 chairs around the walls
so that there are 3 chairs at each wall.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">We
did a few easier examples before this one. For example, I asked them to put 12
chairs around a <u>square</u> room so that there would be an equal number of
chairs at each side. Then I asked them to figure out a strategy for placing an
equal number of chairs at each wall to add up to a certain number (the solution
was to keep adding one chair to each wall in a circle until there is enough
chairs). Then, after a few tries, most of the kids figured out the answer to
the problem and THE KIDS THAT FIGURED IT OUT ALREADY EXPLAINED IT TO THE KIDS
THAT DIDN’T UNDERSTAND. <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Estimate:<o:p></o:p></span></i></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">a)<span style="mso-tab-count: 1;"> </span>How
many people are in the house<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">b)<span style="mso-tab-count: 1;"> </span>How
many poker chips I am holding<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">c)<span style="mso-tab-count: 1;"> </span>How
many poker chips are in this bag<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">d)<span style="mso-tab-count: 1;"> </span>How
many people live on this street<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">e)<span style="mso-tab-count: 1;"> </span>How
many apples equal the weight of you<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif";">The answers varied wildly. Some
people said that there were a thousand poker chips in the bag, and some said
that there were 5 (there were actually about 50 of them). Also, before we did
“how many apples equal the weight of you” we did “how many apples equal the
weight of a cat” because that was an easier variation.<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif";">General Comments:<o:p></o:p></span></i></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif";">I was planning to fit in a lot
more things in this lesson, but we spent a lot of time on each problem (which
is actually a good thing, because it’s better to have all of the kids
completely understand only a couple of problems instead of having the kids have
no clue what’s going on in many problems). <o:p></o:p></span></i></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-5594099787969448662013-05-12T19:18:00.004-04:002013-05-12T19:18:46.434-04:00Lesson 18- Math
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Colors:<o:p></o:p></span></i></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Kristina, Katya, and Max are standing in a line.
They all are holding either a blue or green bouncy ball. Two people are holding
a green bouncy ball, and one is holding a blue bouncy ball. We also know that
some of these people always lie and some only tell the truth.<span style="mso-spacerun: yes;"> </span>Kristina says, “I have a blue bouncy ball.”
Katya says, “I have a blue bouncy ball”. Max says, “I have a green bouncy
ball.” Kristina says, “Katya is lying.” Katya says, “Kristina is lying.” Max
says, “Katya is telling the truth.” Who is holding which color bouncy ball? Who
are the truth tellers, and who are the liars? <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">For
this problem, I drew a diagram on the white board which showed which person was
holding which color bouncy ball. Also, the diagram had arrows pointing from one
person to the other with Xs and checkmarks at the ends (depending on whether
that specific person was saying that the other was a liar or a truth teller).
We checked the possibilities for who could’ve been the liar or the truth
teller, and the diagram helped a lot. This problem wasn’t too hard, but it
wasn’t very easy either, so it was a good warm up. <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Handshake
Puzzle:<o:p></o:p></span></i></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">If there are: 1, 2, 3, 4, 5, or 6 people in a room,
and every person shakes hands with every other person, how many handshakes will
happen? Can you find any patterns? <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">ACT
IT OUT. Ask a few kids to come to the front of the room, and have them shake
each other’s hands, and count how many handshakes would happen in all. We
recorded our results in a table, and we also recorded how many handshakes<o:p></o:p></span></i></div>
<br />
<div class="MsoListParagraphCxSpFirst" style="margin: 0in 0in 0pt 0.5in; mso-list: l0 level1 lfo1; text-indent: -0.25in;">
<!--[if !supportLists]--><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="mso-list: Ignore;">a)<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span></i><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">The
person that shook everyone’s hands first<o:p></o:p></span></i></div>
<br />
<div class="MsoListParagraphCxSpMiddle" style="margin: 0in 0in 0pt 0.5in; mso-list: l0 level1 lfo1; text-indent: -0.25in;">
<!--[if !supportLists]--><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="mso-list: Ignore;">b)<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span></i><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">The
person that shook everyone’s hands second<o:p></o:p></span></i></div>
<br />
<div class="MsoListParagraphCxSpLast" style="margin: 0in 0in 10pt 0.5in; mso-list: l0 level1 lfo1; text-indent: -0.25in;">
<!--[if !supportLists]--><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";"><span style="mso-list: Ignore;">c)<span style="font-size-adjust: none; font-stretch: normal; font: 7pt/normal "Times New Roman";">
</span></span></span></i><!--[endif]--><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">The
person that shook everyone’s hands third, etc. <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">They
found a few different patterns while solving this problem.<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Knots:<o:p></o:p></span></i></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Dima has a string. He is holding the ends of the
string with his hands. How can Dima tie a knot in the string without switching
the ends of the string with different hands? <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">I
brought a scarf so that each child would get a chance to try doing this
problem. After each child had a turn and nobody figured out yet, I gave them
the hint that your hands can be crossed in any way when you start, as long as
your hands are holding the ends of the scarf, and that they stay there for the
whole time while solving the problem. After about 5-10 minutes of them trying
to solve it (with me giving more and more hints every time), I showed them how
to do it. Then I let a few kids try repeating what I did to show them that it
was actually possible (they thought that I was cheating, because it was
obviously impossible). <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Toothpick
puzzle:<o:p></o:p></span></i></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">There are 4 squares joined together to make a bigger
square (out of toothpicks). How can you move just two toothpicks to make seven
squares? <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">I
brought popsicle sticks (toothpicks are too sharp and small) and they solved
the problem using them. I let each child try, and they figured out after a few
minutes that the popsicle sticks could be crossed over each other. <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Try
making a magic square (3x3)<o:p></o:p></span></i></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">I
drew a 3x3 square on the white board, and gave them two numbers to start with
(in random places in the square). They tried to solve it from there, but many
of the times it ended up not working (obviously, since I just placed the
numbers in randomly). Then, I let them try and figure out on their own how to
start (and finish) the puzzle. This is actually a pretty hard puzzle.<o:p></o:p></span></i></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-34525320715450600632013-05-04T20:07:00.003-04:002013-05-04T20:08:35.162-04:00Lesson 14- Logic Puzzles<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
This lesson includes a few problems from: <i style="mso-bidi-font-style: normal;">The Moscow Puzzles book</i>, and from <i style="mso-bidi-font-style: normal;">Julia Brodsky</i> <span style="color: blue;">(<a href="http://www.artofinquiry.net/">Art of Inquiry</a></span> math circle)<o:p></o:p></div>
<br />
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<i style="mso-bidi-font-style: normal;">General comments: the
kids seemed to love this lesson- they paid attention, they didn’t fool around,
and they seemed to enjoy the problems. Two of the parents stayed in the room,
and made sure that the kids were behaving themselves. The kids were very focused.
<o:p></o:p></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<b style="mso-bidi-font-weight: normal;">Dentist<o:p></o:p></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
A boy went to the dentist to have his cavity filled. The boy
was the dentist’s son, but the dentist was not his father. How can this be?<o:p></o:p></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<i style="mso-bidi-font-style: normal;">“Oh, that’s
impossible! Hmmm… Wait! Maybe it was his mom!” Everybody was paying attention
and thinking. <o:p></o:p></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<b><o:p></o:p></b> </div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<b>Glasses<o:p></o:p></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt 22.5pt;">
<b><span style="font-family: "Arial","sans-serif";"><o:p> </o:p></span></b></div>
<em><strong>*Sorry, I couldn't get the image into the post. I will add it to the post later.</strong></em> <b><span style="font-family: "Arial","sans-serif";"><br style="mso-special-character: line-break;" />
<!--[if !supportLineBreakNewLine]--></span></b><br />
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt 22.5pt;">
<span style="mso-bidi-font-weight: bold;">You may touch and move only one glass to get the following:<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt 22.5pt;">
<b><o:p> </o:p></b></div>
<strong><em>*Sorry, I couldn't get the image into the post. I will add it to the post later.</em></strong> <br />
<div class="MsoNormal" style="margin: 0in 0in 0pt 22.5pt;">
<b><o:p> </o:p></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt 22.5pt;">
<i style="mso-bidi-font-style: normal;"><span style="mso-bidi-font-weight: bold;">This problem can be presented
in a couple different ways; either there can be actual paper/plastic cups used
and toys or something similar put inside them, or you could draw it on a
whiteboard (which is how I did it). The kids were focused, and in their seats,
and after trying different strategies of switching around the cups, they
realized that water can also be poured from one cup to another. After their discovery,
they soon figured out the solution to the problem.<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<b><o:p> </o:p></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<b>Paper clip problem<o:p></o:p></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt 22.5pt;">
<span style="mso-bidi-font-weight: bold;">If you drop a paper clip, it will land flat on its side. What can you do
so when you drop it, it will land balanced on edge?<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt 22.5pt;">
<i style="mso-bidi-font-style: normal;"><span style="mso-bidi-font-weight: bold;">The kids seemed to enjoy
solving a problem that had science incorporated into it. I was just trying to
have the kids solve a problem where they have to figure out a creative way of
doing something, or of using random materials to complete a task. They thought
of many ways of solving this problem; stick it into a crack, squeeze it between
two books/boxes, putting two magnets on the sides of it, and multiple other
ideas. <o:p></o:p></span></i></div>
<br />
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<b>The bathroom scale problem<o:p></o:p></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt 31.5pt;">
<span style="mso-bidi-font-weight: bold;">What happens if you stand on a bathroom scale and lift one foot up? What
will the scale read? What if you put one foot on one scale, and another foot on
another scale?<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt 31.5pt;">
<i style="mso-bidi-font-style: normal;"><span style="mso-bidi-font-weight: bold;">This took some explanation, but
the kids realized that their foot wouldn’t be disappearing anywhere- it would
still be there, it’s just that it was in a different place. I explained to them
that the weight still “flows” into the scale- it’s just that it all goes
through one foot. They seemed to understand, and to check, I asked one of the
kids to clarify why a person’s weight stays the same on a scale when they lift
one foot up. When I asked them whether the weight would still be the same if
they put a foot on a different scale, and they said that they weight would be
about equal on both scales. Maybe, if there aren’t too many kids, after some
exploring and thinking, the kids could actually try standing on a<span style="mso-spacerun: yes;"> </span>scale and lifting their foot up and checking
if there would be a difference- just a suggestion.<o:p></o:p></span></i></div>
<br />
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<b style="mso-bidi-font-weight: normal;">Discuss: If halves are
equal, then wholes are equal.<span style="mso-spacerun: yes;"> </span><o:p></o:p></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
Example 1: If half-length of one road is equal to
half-length of another road, then road lengths are equal. Right?<o:p></o:p></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
Example 2: Consider a glass below. Half empty glass is the
same as half full glass. Does it mean that an empty glass is a full glass?<b style="mso-bidi-font-weight: normal;"> <o:p></o:p></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<i style="mso-bidi-font-style: normal;">“Hahaha! No! The
second example isn’t right! Probably the rule doesn’t work for everything…”<o:p></o:p></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<b style="mso-bidi-font-weight: normal;"><o:p> </o:p></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<b style="mso-bidi-font-weight: normal;">Two camels<o:p></o:p></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
Two camels in the middle of the desert were facing in
opposite directions.<span style="mso-spacerun: yes;"> </span>One was facing east
and another west. How could they manage to see each other without walking,
turning around or even moving their heads?<o:p></o:p></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<i style="mso-bidi-font-style: normal;">We acted it out,
because the kids had trouble imagining this in their head- they soon realized
that looking in different directions didn’t necessarily have to mean looking
away from each other.<span style="mso-spacerun: yes;"> </span><o:p></o:p></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p></o:p> </div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<b style="mso-bidi-font-weight: normal;">Moving Checkers:<o:p></o:p></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
6 checkers lay in a row, alternating in color (black, white,
black, white, black, etc.). There are four empty spaces on the left. Checkers
can only be moved in pairs together with an adjacent checker. Move the checkers
in such a way that all of the white checkers end up on the left, with the black
ones following them. <o:p></o:p></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<i style="mso-bidi-font-style: normal;">The kids loved this
exercise- and to my amazement, figured it out after only a few tries (we went
around in a circle, and every child got to move a pair of poker chips (that is
what we used instead of checkers) on their turn. They even re-did the activity
multiple times because they wanted to. <o:p></o:p></i></div>
<br />
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<b style="mso-bidi-font-weight: normal;">Combinations: <o:p></o:p></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
If you have two colors, how many combinations can you find
of coloring in three empty circles? Now try it with four empty circles? What
about if you have three colors? How many combinations for three empty circles
then? Try to get the most possible number of combinations. <o:p></o:p></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<i style="mso-bidi-font-style: normal;">They really liked
finding the combinations, and watching the pace at which the number of
combinations grew.<o:p></o:p></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<b>Coloring Activity<o:p></o:p></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="color: black;"><o:p> </o:p></span></div>
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<span style="color: black;">Using 3/4/5 different colors, color
the picture so that neighboring parts differ by color. <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<i style="mso-bidi-font-style: normal;"><span style="color: black;">We didn’t have time to get to this, but after the class,
the kids stayed colored this (following the instructions)- I gave them the
sheet.<o:p></o:p></span></i></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://2.bp.blogspot.com/-kmGKPaUB5jA/UWWg_wd_heI/AAAAAAAAAMo/7HGDNSjnAUw/s1600/math+coloring+activity.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="239" src="http://2.bp.blogspot.com/-kmGKPaUB5jA/UWWg_wd_heI/AAAAAAAAAMo/7HGDNSjnAUw/s320/math+coloring+activity.jpg" width="320" /></a></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p> </o:p></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 0pt;">
<o:p> </o:p></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-18063555530843575432013-05-04T20:06:00.000-04:002013-05-04T20:06:05.792-04:00Lesson 15- Math Mix<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: Calibri;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 12pt; line-height: 115%;">Heads and Legs</span></b><span style="font-size: 12pt; line-height: 115%;">:<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: Calibri;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 12pt; line-height: 115%;"><span style="mso-spacerun: yes;"> </span></span></b><span style="font-size: 12pt; line-height: 115%;">In a garden, there are five horses. On each of the first
three horses, sits a rooster. On each of the last two horses, sits a fish. How
many heads and legs are there all together?<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Calibri;">“Fish and chickens ride on horses?
Haha!” The kids solved the problem by making a little diagram with little
circles representing heads, and lines from those circles representing the
number of legs that animal has (the animals who sat on top of the horses were
drawn above the horses, and the kids thought that doing that really mattered to
solve the problem). <span style="mso-spacerun: yes;"> </span>I offered the kids
to draw the animals sitting on the horses in columns, with the animals under
the horses, but the kids refused to do that, since it was “not following the
rules of the problem”. It is good that they pay attention to the directions of
the problem, but I think that <b style="mso-bidi-font-weight: normal;">I should
spend some more time discussing the importance of various parts of a problem</b>.
<o:p></o:p></span></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<span style="font-family: Calibri;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 12pt; line-height: 115%;">Fill in the blanks</span></b><span style="font-size: 12pt; line-height: 115%;">: </span><b><span style="font-size: 14pt; line-height: 115%;"><o:p></o:p></span></b></span></div>
<span style="line-height: 115%;"><o:p><span style="font-family: Calibri;"><em><strong><span style="font-size: x-small;">*sorry, the image was not inserted correctly. It will be posted later.</span></strong></em> </span></o:p></span><br />
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-weight: bold;"><span style="font-family: Calibri;">The kids figured out what had to be in each row, and then solved the
problem easily. Give everybody a chance to share what they think. This didn’t
seem to be too hard for the kids, but it was a good warm-up type of problem. It
is good for the kids to recognize and figure out what figures and inner figures
had to be in each row, column, and diagonal- don’t tell them those things! Let
them think! It might not seem like it, but it is the most important part of the
problem!<o:p></o:p></span></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<b><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Calibri;">Checkers: <o:p></o:p></span></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<span style="font-size: 12pt; line-height: 115%; mso-bidi-font-weight: bold;"><span style="font-family: Calibri;">Is it possible to put 5 checkers in
such a way that each checker touches 2 others? 3 others? <span style="mso-spacerun: yes;"> </span><o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-weight: bold;"><span style="font-family: Calibri;">I gave each child some poker chips (that is what we used instead of
checkers), and they played around a bit. Most of them solved it after a little
while, others were stuck, and were explained how to do it <b>by the children
that already figured it out</b>, and NOT by me. We only had time to make the 5
checkers touch 2 others. Later we will try making each of the checkers touch
three others.</span></span></i></div>
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<b><span style="font-size: 12pt; line-height: 115%;"><o:p><span style="font-family: Calibri;"> </span></o:p></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<b><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Calibri;">Elevator Problem:<o:p></o:p></span></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<span style="font-size: 12pt; line-height: 115%; mso-bidi-font-weight: bold;"><span style="font-family: Calibri;">I know one tall building in Antarctica.
Only one person lives on the first floor, 2 people live on the second floor, 3
people live on the third floor, and 4 people live on the fourth floor. There is
an elevator in the building.<span style="mso-spacerun: yes;"> </span>On what
floor does the elevator stop most often?<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-weight: bold;"><span style="font-family: Calibri;">At first, they all thought that the elevator visits the fourth floor the
most often, which is the most obvious response. I let the kids think for a
couple of minutes, and everybody still stuck to their answer. I gave them a
hint; “is there any place in the building that all the people need to go to,
that the elevator would take them to?” Soon after this, they figured out that
everybody in the building needs to get to the exit (the door) at some point,
and that is on the first floor. “Or they can jump out the window!” said one of
the kids. I said, “Do you normally see people jumping out the window from the
fourth floor?” “Fine…” <o:p></o:p></span></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<b><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Calibri;">Flower colors:<o:p></o:p></span></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<span style="font-size: 12pt; line-height: 115%; mso-bidi-font-weight: bold;"><span style="font-family: Calibri;">Once, Sasha drew a flower. He had
blue, red and white colors.<span style="mso-spacerun: yes;"> </span>“It is not
white” – said Max. “It is blue or red” – said Kristina. “It is red” – said
Dima. It is known that at least one of the kids guessed wrong, and at least one
guessed right.<span style="mso-spacerun: yes;"> </span>What color is the flower?<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-weight: bold;"><span style="font-family: Calibri;">We checked the combinations possible for who was lying and who was
telling the truth, and we were in the middle of solving the problem, when the
kids started to fool around, so I stopped, and moved on to the next activity. I
will re-state this problem and try it again next time.<o:p></o:p></span></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<b><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Calibri;">Passing Trains: <o:p></o:p></span></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<span style="font-size: 12pt; line-height: 115%; mso-bidi-font-weight: bold;"><span style="font-family: Calibri;">A train is going from the US to
Canada, at 60 mph. Another train is heading in the opposite direction- from
Canada to the US, and it is moving at the speed of 40 mph. When the two trains
pass each other (meet), which one will be closer to Canada?<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-weight: bold;"><span style="font-family: Calibri;">The kids didn’t seem to understand what the point of the problem was-
“Wait… won’t they be in the same place when they meet?” OK… I guess I didn’t
succeed in tricking these children… </span></span></i><i style="mso-bidi-font-style: normal;"><span style="font-family: Wingdings; font-size: 12pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-weight: bold; mso-char-type: symbol; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-symbol-font-family: Wingdings;"><span style="mso-char-type: symbol; mso-symbol-font-family: Wingdings;">J</span></span></i><i style="mso-bidi-font-style: normal;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-weight: bold;"><span style="font-family: Calibri;"> <o:p></o:p></span></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<b><span style="font-size: 12pt; line-height: 115%;"><o:p><span style="font-family: Calibri;"> </span></o:p></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<b><span style="font-size: 12pt; line-height: 115%;"><span style="font-family: Calibri;">Boiling Eggs:<o:p></o:p></span></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<span style="font-size: 12pt; line-height: 115%; mso-bidi-font-weight: bold;"><span style="font-family: Calibri;">If it takes 2 minutes to boil one
egg, how long will it take to boil three eggs?<o:p></o:p></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-weight: bold;"><span style="font-family: Calibri;">“Will the eggs boil in the same pot or in different pots?” “What about
you decide?”, I answered. The kids were moving in the right direction. “Um…
usually eggs are boiled in the same pot, so… let’s have them boil in the same
pot.” The kids were getting really close. “Wait, if they’re in the same pot,
it’s not like first one will boil and then the other! They will boil at the
same time, so it will also take only 2 minutes!” These kids are smart!<o:p></o:p></span></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<span style="font-family: Calibri;"><b><span style="font-size: 12pt; line-height: 115%;">Play Pentagrams. </span></b><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-weight: bold;">Try building solid rectangles out
of them.<span style="color: teal;"><span class="msoIns"><ins cite="mailto:Marie" datetime="2013-04-02T21:11">
</ins></span><o:p></o:p></span></span></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 22.5pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-size: 12pt; line-height: 115%; mso-bidi-font-weight: bold;"><span style="font-family: Calibri;">The kids were surprisingly good at this! They built small rectangles, and
a lot of them got <b>really</b> close to making a rectangle using all the
pieces. I gave each of the kids a set of pentagrams, so they would be able to
work on their own if they wanted to. Which they did. <o:p></o:p></span></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b><span style="font-size: 14pt; line-height: 115%;"><o:p><span style="font-family: Calibri;"> </span></o:p></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b><span style="font-size: 14pt; line-height: 115%;"><o:p><span style="font-family: Calibri;"> </span></o:p></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b><span style="font-size: 14pt; line-height: 115%;"><o:p><span style="font-family: Calibri;"> </span></o:p></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b><span style="font-size: 14pt; line-height: 115%;"><o:p><span style="font-family: Calibri;"> </span></o:p></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-size: 12pt; line-height: 115%;"><o:p><span style="font-family: Calibri;"> </span></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-size: 12pt; line-height: 115%;"><o:p><span style="font-family: Calibri;"> </span></o:p></span></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-36788055718769102502013-04-16T13:52:00.000-04:002013-09-26T15:05:44.419-04:00Lesson 20- Year 1- Mixed Math<div class="MsoListParagraph" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br />Add
three toothpicks to make 5 triangles.<o:p></o:p></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> big <b><i>triangle</i></b></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Kanoodle<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">HotSpot Beginner levels <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Pyramid puzzle<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Mini Rubics cube<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Pentago<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Wooden puzzle<o:p></o:p></span></div>
<br />
<div class="MsoListParagraphCxSpLast" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Mini ring puzzle<o:p></o:p></span></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-41521348586256479372013-03-14T20:00:00.000-04:002013-04-10T13:43:05.201-04:00Lesson 16- Games, Puzzles, and Manipulatives
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Trebuchet MS","sans-serif"; font-size: 12pt; line-height: 115%; mso-bidi-font-family: "Times New Roman";"><span style="color: blue;"><a href="http://www.artofinquiry.net/bookstore/">http://www.artofinquiry.net/bookstore/</a></span></span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"> </span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Century Schoolbook","serif"; mso-bidi-font-family: "Times New Roman";">Go to “Math Games and Puzzles”</span></b><b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"> <o:p></o:p></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Hanoi
Tower <o:p></o:p></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">We
started with two rings, and then went on to three. At first, I let the kids
take turns moving one ring at a time, but that didn’t work; since each of the
kids had their own strategy for how to solve the problem, they all started
arguing with each other and saying that they were right and everybody else was
wrong. Because of this, I let each of the kids take turns solving the whole
puzzle, so that they would be able to complete their idea and strategy and so
that they would be able to try to solve it on their own. Since there were many
kids waiting to solve this puzzle (it took a few minutes for each child to
complete it), I had a few children go and do some of the other puzzles (Rush
Hour, Hoppers, and IZZI).<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span><o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Rush
Hour<span class="msoDel"><del cite="mailto:Marie" datetime="2013-04-10T12:33"><o:p></o:p></del></span></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Oops!
Big mistake! I meant to let them play Rush Hour Jr., not Rush Hour! They will
only be able to actually solve the puzzles in Rush Hour in a couple of years.
Since I accidentally brought Rush Hour to the class, they were only able to
solve the first few problems (and even those were still hard for them). Rush
Hour Jr. should be at their level, though. <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Hoppers<o:p></o:p></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">The
kids liked this game, and they were good! They quickly figured out the
solutions to the problems, and on the puzzles that they couldn’t solve right
away, they worked together to think of the different possibilities- working
together is a very good skill for them to have, and so is continuing to solve a
problem after several tries, instead of giving up. <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Cathedral<o:p></o:p></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">I
explained the kids how to play this game, and they seemed to follow along, but
I think that they didn’t quite understand what I was saying. Maybe in a few
years this game would be good for them, but for now, it’s a bit too complicated.
<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">IZZI<o:p></o:p></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">This
is best to be played at the end of the class, because the kids are tired by
then, and this game really doesn’t use up any energy… It’s very simple, but the
kids seem to <b style="mso-bidi-font-weight: normal;">love</b> it. <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Othello-
kids against me<o:p></o:p></span></b></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">This
is a nice game to play with the kids; they get to team up and play <b style="mso-bidi-font-weight: normal;">against the teacher</b>. They liked it, and
they took turns adding pieces to the board. They were actually pretty good
(especially considering that this was their first time playing).<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"><o:p> </o:p></span></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0Maryland, USA39.0457549 -76.641271235.8785819 -81.8048452 42.2129279 -71.477697200000009tag:blogger.com,1999:blog-1184298406759779916.post-58519702637160946792013-03-07T21:41:00.000-05:002013-03-17T21:43:24.735-04:00Logical Fallacies and other Puzzles
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Materials:
Set (game), Hanoi Tower<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Lying
or telling the truth?<o:p></o:p></span></b></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">If I say that there are only girls in
this room, am I lying or telling the truth? How do you know? If I say that you
are a million years old, am I lying or telling the truth? How do you know? <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Kids
reply: Lying!</span></i><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"><span style="mso-tab-count: 1;"> </span><o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">If I say that you are a boy (<i style="mso-bidi-font-style: normal;">talk to everybody at once)</i>, would I be
lying or telling the truth? Wait… how is this possible? How come Kristina is
saying that I am lying, and Dima is saying that I am telling the truth?
Something can’t be true and false at the same time, can it? <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">All
of the boys say: “It isn’t both true and false; it’s true!” while all of the
girls say, “It isn’t both true and false; it’s false!” Huh? Confusion. “Oh… I
get it… it’s true for some people but not others”- very good answer.<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">“I like cats”- am I lying or telling the
truth? How do you know? Is this a fact? Or is it an opinion?<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">The
kids all had their own viewpoints; <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">“It
is true, because since you are saying that you like cats, it means that you do
like cats.” <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">“It
is true, because a lot of people like cats.”<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">“It
is false, because I don’t like cats that much; I like dogs more.”<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">“We
don’t know if it’s true or false, because we don’t know what you like and don’t
like.”<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Which
of these are facts, and which are opinions?<o:p></o:p></span></b></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">We are in a house.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">We are humans.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">I like blue.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Cats are fluffy.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">This is a big house.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">There are mermaids in the ocean. <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Dragons are real.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">The
kids needed an explanation between a fact and an opinion; they knew that were
things called facts and opinions, but they didn’t seem to know the clear
difference between them. They went through this activity quickly though, which
was what I expected. On the question, “This is a big house”, the kids couldn’t
decide whether it was a fact or an opinion. So, we concluded that opinions
weren’t really true or false, because they vary from person to person. The kids
enjoyed the fact that I thought that dragons were real, and that there were
mermaids in the ocean. </span></i><i style="mso-bidi-font-style: normal;"><span style="font-family: Wingdings; font-size: 12pt; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Wingdings;"><span style="mso-char-type: symbol; mso-symbol-font-family: Wingdings;">J</span></span></i><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"> <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"><o:p> </o:p></span></b></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Analogies:<o:p></o:p></span></b></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Bird is to nest as spider is to
___________<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Teacher is to school as doctor is to _________<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Book is to read as movie is to _________<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Paw is to claws as foot is to __________<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Cat is to “<i style="mso-bidi-font-style: normal;">meaw”</i> as dog is to _________<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Black is to white as top is to _________<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">I
explained to the kids what an analogy was, and for the first problem I had to hint
them a little, because even after the explanation, they still didn’t quite
understand what an analogy was. The hint I gave sounded like this: “A bird does
what in a nest?” Kids: “Lives!” “A bird lives in a nest; a spider lives in a…”After
they understood well what an analogy was, the rest of the problems were
relatively easy for them, and the kids seemed to enjoy doing the analogies.<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;"><o:p> </o:p></span></b></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Backwards
Simon Says- </span></b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Play
Simon Says except the kids have to do the opposite of whatever Simon says. <i style="mso-bidi-font-style: normal;"><o:p></o:p></i></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">The
kids were slowly getting tired, so I decided to play a game for a few minutes.
Anyways, the kids seemed to love playing this game, and it involved some
thought, because every round, I made the game a little harder- I didn’t just
want the kids to be sitting around. This game makes the kids think of opposites
of things, and that was something that I noticed seemed hard to them during
previous lessons.<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Generalizations:<o:p></o:p></span></b></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<u><span style="font-family: "Cambria","serif"; font-size: 12pt; mso-ascii-theme-font: major-latin; mso-bidi-font-family: "Times New Roman"; mso-hansi-theme-font: major-latin;">True or false?<o:p></o:p></span></u></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">“I came to my teacher and she got mad at
me. My sister came to her teacher and the teacher got mad at her. My friend
came to her teacher and the teacher got mad at her.” <i style="mso-bidi-font-style: normal;">Conclusion: Teachers always get mad when people come up to them.<o:p></o:p></i></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Kids:
“You don’t get mad at us when we come up to you, so the statement is false.”
“Well, let’s not focus on what is actually happening, but what is in the
problem.” Kids: “If only a few people came up to the teacher, then how do we
know if everybody does? Only if every person in the whole world comes up to the
teacher and the teacher yells at them it would be true. And since that didn’t
happen, the statement is false.”- very good.<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"><span style="mso-spacerun: yes;"> </span>“I
used to own a fish, and it fell out of its tank.” <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">Conclusion: All fish fall out of
their fish tanks.<o:p></o:p></i></b></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">“A
fish fell out of its tank? Ha-ha-ha! That is so funny!” “Ok, I’m glad that you
are having fun, but we still have to solve the problem.” Kids: “Ok. Not all
fish fall out of their tanks! If one fish fell out of its tank (how did it fall
out, by the way?), that doesn’t mean that all fish fall out of their tanks!”<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"><o:p> </o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;"><o:p> </o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">“I heard that somebody got eaten by a
lion.” <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">Conclusion: It is possible to be eaten by a lion.<o:p></o:p></i></b></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Kids:
“Well, if somebody got eaten by a lion, then the conclusion is true; it is
possible to get eaten by a lion. This time the conclusion makes sense; it’s not
like it says, “everybody gets eaten by lions”- that would be strange, because I
didn’t get eaten by a lion… well, for right now. Maybe I will…does it feel
scary when you get eaten by a lion?” <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">“I know a person from Antarctica, and he
was nice.” <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">Conclusion: All people from Antarctica are nice.<o:p></o:p></i></b></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">“You
know somebody from Antarctica?! That’s so cool! Oh, fine, back to the problem.
Um… if you knew all the people from Antarctica, and they were all nice, then
the statement would be true, but since you only know one person from Antarctica
who is nice, the statement is false.” <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">These
are actually some good answers, considering that these are little kids. <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Building Tables: <o:p></o:p></span></i></b></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Figure out who likes which sport- there
are four sports; tennis, soccer, basketball, and badminton, and there are four
kids; Dima, Kristina, Katya, and Max. <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Kristina doesn’t like basketball or
soccer.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Max used to like basketball and
badminton best, but now he changed his mind.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Neither of the boys likes soccer best. <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">As
they always do, the kids loved that they were in the problem. I called them up
to the board (make sure to let all of them solve part of the problem), and
asked each of them to figure something out and mark it on the table we drew
(sports vs. kids comparison). This took some time, and the kids were already
tired and started to roll around on the floor and play around. Again, time for
a game.<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Simplified
Set</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">:<b style="mso-bidi-font-weight: normal;"> </b><o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Take out a few cards at random, and ask
the kids to find the similarities and differences between the cards; this can
be done in the form of a game (every child gets one or two cards, and then I
put down a card from the pile, and the kids have to put down the cards that
they have, but only the ones that are similar in any way to the starting card.)<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">If
the kids don’t listen, have the child who wasn’t following directions sit on a
chair in the corner, or something similar to that, because otherwise, all of
the kids take the child’s example and stop listening to directions as well. If
a child takes the Set cards and don’t give them back, tell them that either
they give the cards back or they don’t get to play the game- easy solution;
this happened once during the class, but the kids really wanted to play the
game, so they gave back the cards.<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="line-height: normal; margin: 0in 0in 10pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">Simplified
Hanoi Tower</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12pt;">:
Play with two-three pieces; it’s a complex and at the same time interesting
activity for the kids.<span style="mso-spacerun: yes;"> </span><o:p></o:p></span></div>
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%; mso-ansi-language: EN-US; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-fareast-theme-font: minor-latin;">We only got to do this for a few minutes,
because the class ended, and we ran </span></i>Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-62482898818548143032013-02-10T12:58:00.004-05:002013-02-10T12:58:55.974-05:00Lesson 11- Logic Puzzles
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.75in;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Exclusions:</span></i><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"><o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 99pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">I will give Max,
Kristina, and Dima a shape- there are two squares, and one circle. If Dima and
Kristina have the same shape, who has which shape?<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 99pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">All
of them figured out right away, but I think it was a good warm-up. I also asked
them to explain why they thought that their answer was correct, to get them
involved- it was the beginning of the class, and they were still playing around
a bit, and haven’t gotten into “concentrating mode” yet. <span style="mso-spacerun: yes;"> </span><o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 99pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Now, I will give Katya,
Matthew, and Sasha a colored pencil-there are two red pencils, and one green
pencil. If Matthew and Sasha have different colored pencils, what color pencil
does Katya have?<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 99pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">They
also answered this one right away, and had no problem explaining their answer. <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 99pt;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">This time, I will give
Katya, Kristina, Max, and Dima a poker chip. There are three blue poker chips,
and one white chip. Katya and Dima have the same colored chip, but Dima and Max
have different colored chips. Who has the white chip? <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 99pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">They
though a little bit on this one (don’t give them hints until they thought for
some time), and soon figured out the answer. I think that these problems were a
perfect warm-up for the class, and the kids started to pay more attention after
this. This warm-up wasn’t too hard, but wasn’t extremely easy, either, so,
without having to struggle, the kids started to get more involved and
interested in the lesson.<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Dima, Kristina,
Matthew, and Katya have different pets. Each of them has a turtle, a cat, a
dog, or a bird. Who has which pet? <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.75in;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Clues:
<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Matthew has a fluffy
and fuzzy pet.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Katya has a pet that
has feathers.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Kristina has a pet with
shining green eyes. <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Dima got his pet from
the aquarium.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 99pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">I
used this problem, first of all, to get all of them thinking, but more
importantly, to show them how to make a basic table. I asked them what we could
use to mark down who has which pet, and who doesn’t have a certain pet, and
they said a table, so that is what I did. I wanted them to answer, “a chart”,
or “a table”, but I wasn’t actually expecting them to figure that out- I was
going to tell them myself. The problem itself wasn’t very hard for the kids,
but, with multiple clues, it took a little while to complete the table and to
figure out who had which pet in the end.<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 99pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">The
children saw that the table was useful in this case, but they need more
exposure to these types of problems to fully appreciate this type of
information organization.<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">A mouse, a fox, a
zebra, and a dinosaur want to see how they compare in height, but they are not
allowed to see each other. They are given these clues:<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">The mouse is taller
than the dinosaur.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">The fox is taller than
the mouse.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">The zebra is taller
than the dinosaur, but shorter than the mouse. <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.75in; tab-stops: right 6.5in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">List
them in order from tallest to shortest, or vice versa. <span style="mso-tab-count: 1;"> </span><o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.75in;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">The
kids burst out laughing when hearing that a mouse is taller than a dinosaur, a
zebra is shorter than a mouse, etc. They thought that the problem was very
silly, and they still seemed to be a bit confused with the sizes while solving
the problem. I asked the kids how I could represent that one of the animals is
taller than another, and they said to write the names of the animals from top
to bottom (taller animals on the top, shorter animals at the bottom) - a
wonderful solution. After righting down the heights of the animals compared to
each other (using their strategy), they figured out the answer very easily- all
they had to do was look at the “diagram”. <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Let’s pretend that Peter
is a cook. The first day, he makes three chocolates. The next day, he makes two
cakes, and four cookies. The next week, he makes two different types of soup,
seven pancakes, and nine meatballs. What is the name of that cook?<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.75in;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">About
a second after I asked the question, they answered- correctly. Also, if the
problem is being addressed to only one child, instead of saying that Peter is
the cook, they should be told that they are the cook. It’s more interesting
that way. <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.25in;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Basic
logic</span></i><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"><o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">A teacher told a group
of kids that zebras had stripes. Later that day, the kids went to the zoo, and they
saw an animal with stripes. A child said that it was surely a zebra, because it
had stripes. Was the child’s thinking correct?<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 99pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">The
kids thought that the child was perfectly correct, until I hinted to them about
there being other animals with stripes as well, not only a zebra. After that,
they realized that the child was wrong. Without the hint, they didn’t seem to
be able to figure it out.<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Let’s say, that every
time Dima eats a chocolate, he is happy. I just came out of my room, and I saw
that Dima was happy. Can I now say that he just ate a chocolate? <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 99pt;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Dima
really liked the fact that the problem was about the fact that he was eating
chocolate, and being happy after it. They again responded the same way as in
the previous problem, but this time I didn’t give them a hint (since this was
just a variation of the previous problem, they should be able to figure it out
now). They thought for a while, and then decided that Dima is sometimes happy
without having to eat a chocolate before it.</span></i><span style="font-family: Wingdings; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-char-type: symbol; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin; mso-symbol-font-family: Wingdings;"><span style="mso-char-type: symbol; mso-symbol-font-family: Wingdings;">J</span></span><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"><o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">A string has three cuts
made in it. How many pieces of string did that form? What about with four cuts?
Try it with a piece of paper.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.75in;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">When
there were three cuts made, they though there would be three pieces, so I
started with two cuts. The same thing happened with two cuts. Then I asked them
about zero cuts, they said, “Zero pieces!” two seconds later… “Oops! There will
be one piece!” Then I asked them, “What about one cut?” Without hesitating,
they yelled, “One piece!” “Really?”<span style="mso-spacerun: yes;"> </span>I
replied. “Let’s check”. We checked by cutting the string once. It made two
pieces. They finally understood. Later, I asked them to come up to the
whiteboard and “cut” the string in various numbers of cuts. <o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">How many corners does a
table have? Four! If one of the corners was cut off, how many corners would be
left? Try it with a piece of paper.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.75in;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">“Three!”
the kids shouted. It is understandable that people expect the numbers to go
down when you subtract/cut something. <span style="mso-spacerun: yes;"> </span>“OK. Let’s check.” I showed them with a piece
of paper, and said, “Look! I cut off a corner, and got MORE corners!” The kids
were startled, and excited. I did it again, and kept getting more corners. A
few kids said that it was impossible, and some others argued that I did it, so
it must be possible.<o:p></o:p></span></i></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">Teach the kids how to
play 20 questions. <o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin: 0in 0in 10pt 0.75in;">
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">It’s
way too hard for them. They just starting guessing- “Is it a table? Is it a
couch? Is it our planet?” The kids are too young to play twenty questions, but
they can play pretty well if the game is played only within a specific
category. For example, if I am only allowed to think of something in the
category of food. That would be a lot easier for the kids, because at this age
they do not yet understand the concept of first asking more general questions,
and slowly narrowing down to more detail. They just guess randomly, and think
that eventually they will get it right. I would suggest gradually introducing
categorizing and generalizing skills while playing this game.<o:p></o:p></span></i></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-24034746508639253412013-01-08T13:48:00.000-05:002013-09-26T15:06:12.215-04:00Lesson 12- Year 1- Symboland<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">- Discussion: </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">What
is a code? <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">They had no idea. I explained that
a code is something that takes on object or idea, and replaces it with
something different, to write secret messages, or anything that needs to be
symbolized.<o:p></o:p></span></i></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Make
a key that says that a red circle means then number 5. Then, draw a red circle.
Ask the kids what the red circle represents. Ask them what other ways they can
think of to represent numbers, words, and other symbols.<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The kids said that the red circle
represents the number 5, but they could think of no other ways of representing
or coding numbers or anything else. <o:p></o:p></span></i></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Problems: </span></i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Pretend
you were taking a walk, and you slipped and fell into a fairytale. In the
fairytale, everything is coded, but you have to get out- a dragon is wandering
around the forest, and it is soon going to find you! Here are the puzzles that
you encounter:<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">“We fell into a fairytale! Hahaha!
That is so cool… wait… it’s possible?!”<o:p></o:p></span></i></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">You
come up to a fairy, and she gives you a card. She says that the path you should
take is: right, left, left, but the card says it differently; left, left, right
(with arrows). Then she whispers in your ear, “Everything is coded around here,
and to get out, you will have to explain to the king elf how you figured out
what this card means.” How are the instructions on the card different from the
instructions that the fairy gave you? <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">First the kids started to say that
the directions are all different, but then they realized that the directions
were backwards.<o:p></o:p></span></i></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Now
that you have figured out, the fairy wants to double check that you understand;
she gives you a few more similar puzzles to solve before you are allowed to
leave: <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The kids expressed their opinion;
“Ughh… why do fairies have to be so annoying?!” </span></i><i><span style="font-family: Wingdings; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Wingdings;">J</span></i><i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> <o:p></o:p></span></i></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Play
Simon Says as a break, and then play backwards Simon Says (The kids have to do
the opposite thing of what Simon Says tells them to do). <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The kids loved the backwards Simon
Says! Don’t play the normal Simon Says for long, because, first of all, it doesn’t
teach the kids anything new, or make them think, and plus, it is pretty boring.
Even the kids agree with that. I think that it is better to play Simon Says,
first of all backwards, and, for this specific purpose, without saying Simon
Says before all of the instructions; the kids should have to listen to
everything the “Simon” says, even if the “Simon” doesn’t say, “Simon Says…” <o:p></o:p></span></i></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The message is:</span></i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">
red, red, green, blue, but the coded message is: blue, green, red, red. What is
the code? <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The kids were a bit more
concentrated because they had just played Simon Says, but it still took some
work to get their attention. <u>Don’t draw this problem on the white-board! Use
poker chips or other small colorful objects to do the problem! Let the kids
have something to play with in their hands and actually hold while solving the
problem! </u>I made a big mistake by just drawing the colors on the board, and
the kids stopped paying attention!<o:p></o:p></span></i></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Now
that the fairy sees that you understand, she tells you that you are free to go.
Finally! You are out of the forest! Oops… the dragon is waiting for you in the
forest. The dragon gives you some more problems… and he gives you a key;
turtles represent the number 1, dragons represent the number 3, princes
represent the number 4, princesses represent the number 5, and rabbits
represent the number 6. <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">They loved the story; especially
the part about the dragon. <o:p></o:p></span></i></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Turtle
+ Dragon =?<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Rabbit
- Prince + Dragon =?<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Princess
+ Turtle - Prince =?<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">This was fun for them to do, but
they weren’t paying much attention. <u>Get every child involved!</u> If even
one child starts to goof and play around, almost all of the other kids follow
them, and start to play around as well! As I mentioned before, the kids should
have something to hold in their hands. Use actual toys, stickers, game pieces…
anything, to represent the numbers in this problem, and have the kids build the
equation from those toys!<o:p></o:p></span></i></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Now,
signs are also coded! Let’s say that addition signs are cats, subtraction signs
are dogs, and equal signs are mice. <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Princess,
Cat, Turtle, Mouse, Rabbit<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Prince,
Dog, Dragon, Mouse, ?<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Rabbit,
Dog, Princess, Mouse, ?<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Now…<o:p></o:p></span></i></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Prince,
Cat, ?, Mouse, Princess<o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Turtle,
?, Dragon, Mouse, Prince <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The kids were good at this, but
since I could only call one child up to the white-board at a time (I shouldn’t
even have used a white-board), half the kids weren’t paying any attention, and
they were rolling around on the floor and running around the room. I made
another huge mistake of continuing with the lesson even though the kids were
still rolling around and not listening (I told them a few times not to, but
then I just gave up and kept going with the lesson- very bad idea). There was
only one child actually solving the problem while all the others weren’t doing
anything, and only playing around- I was literally wasting time, because nobody
was listening, and nobody had any idea about what was going on. Also, I think
the kids got really tired of repeating similar problems over and over again. <o:p></o:p></span></i></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Now
the dragon wants you to make up your own problem, with your own key. He wants
to see how smart he is, and if can solve your problem. <o:p></o:p></span></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The kids were not behaving well
enough to even calm down and do this… I had to play another game of backwards
Simon Says with them, which didn’t exactly make them pay attention more… more
like the opposite. <o:p></o:p></span></i></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<br /></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">There
are 3 envelopes (use actual envelopes). You know there is a magic wand, a key
to the dungeon, and an invisibility
ring. One envelope says “Magic wand”; another “Key to the dungeon” another “Invisibility
ring and magic wand”. We know that each label is misplaced. How can you find
out which object is where without opening any of the envelopes (split the kids
in pairs, and give each pair a goal- figure out where the invisibility ring is,
figure out where the magic wand is, etc. ) Use flash cards that have pictures
of a ring, a magic wand, and a key to place into the envelopes.<o:p></o:p></span></div>
<br />
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">I didn’t use actual envelopes, I
didn’t use flash cards, and I didn’t pair the kids up! It was a complete mess!
Only a couple of kids were paying attention; all of the others were still
goofing around- I had no idea how to get them to listen…</span></i></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoNormal" style="margin-bottom: .0001pt; margin-bottom: 0in;">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><b>I was going to introduce "x" into this lesson, but the kids were tired and we didn't have time. Anyway, I think that it is a little too early.</b> <o:p></o:p></span></i></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-27598868190869642012-12-20T13:45:00.000-05:002013-09-26T15:06:38.035-04:00Lesson 10- Mobeuis Strip- Year 1<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">1.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Make a normal loop (ring), just to
show the kids the difference later between a normal loop and a Mobius strip. <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">2.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Make a Mobius strip. Ask the kids
what it is. Is it just a plain loop of paper? <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">3.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">How many sides do you think it has?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">4.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Have a toy animal move around the edge
of the Mobius strip. What happened? Where did it end up? Mark the starting
point with a pencil.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">5.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Explain what a Mobius strip is, and
how it is made.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">6.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Cut down the middle of the Mobius
strip. What will happen? Did it divide into two pieces? A larger strip formed! Do
you think that we can make an even bigger strip?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">7.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Cut down the center of the larger
strip. What happens this time? The same thing? Keep repeating this, until it
forms a huge loop.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">8.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Cut down the edge of a Mobius strip.
What will happen now? It divides into two rings interlocked with each other!<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">9.<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;">
</span></span></b><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Magic trick with dice- what number
is on the other side? Let the kids guess.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">1</span></b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Matchstick
puzzles (below)</span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-zP2lOwUFOfE/UkMhCkQ6n5I/AAAAAAAAAQg/b59mAWSh3Mk/s1600/fish.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="http://4.bp.blogspot.com/-zP2lOwUFOfE/UkMhCkQ6n5I/AAAAAAAAAQg/b59mAWSh3Mk/s200/fish.gif" width="155" /></a></div>
<o:p></o:p><br />
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Flip a house upside down. How many
matchsticks do you have to move?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Turn the fish around.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: Symbol; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Symbol; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Make three triangles into four.</span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle" style="margin-left: 1.0in; mso-add-space: auto; mso-list: l1 level1 lfo2; text-indent: -.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><b><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">1<span style="font-family: 'Times New Roman'; font-size: 7pt; font-weight: normal; line-height: normal;"> </span></span></b><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Shape
Shuffle<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraph" style="margin: 0in 0in 0.0001pt 0.25in; text-indent: -0.25in;">
</div>
<div class="MsoListParagraphCxSpLast">
<br /></div>
<br />
<div class="MsoNormalCxSpMiddle" style="margin-bottom: 0.0001pt;">
<br /></div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-88849712464185521142012-12-13T08:30:00.000-05:002012-12-15T18:51:04.252-05:00Lesson 8- Perspective, Illusions, and Distance<div class="separator" style="clear: both; text-align: center;">
</div>
<i><span style="font-family: Times, Times New Roman, serif;">*A student asked a question about why the moon seems to follow you while driving, and that inspired this lesson</span></i><br />
<br />
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Materials:
toy, <u><a href="http://www.amazon.com/Incredible-Visual-Illusions-Wont-Believe/dp/1841931977">Incredible Visual Illusions- You Won’t Believe Your Eyes!</a></u> ,or just
the optical illusion pictures used in this lesson, craft sticks<o:p></o:p></span></i><br />
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i>
<i><span style="font-family: "Times New Roman","serif";"><span style="font-size: small;"><span style="line-height: 115%;">Summary: This was an unusual lesson, because a lot of kids were sick, and the ones that came weren't paying much attention. Next time, I would split this lesson into two </span></span><span style="line-height: 18.18181800842285px;">separate</span><span style="font-size: small;"><span style="line-height: 115%;"> lessons, one with optical illusions, and the other one about perspective.</span></span></span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i>
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">***</span></i></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">1.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Why
does the moon always stay in place as if it is not moving, while the trees are
always moving when we drive? <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Answer
offered by the kids: <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">“The
moon is big!” – Possible response from teacher: “What if it was something that
was small and we could barely see it, but it was very far away? Would it still seem to stay in place all
the time?”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Kids
thought after the comment, and then decided that as long as we can see the
object, if it is far enough away, it would seem to stay in place, and not go
away from us.<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i>
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">***</span></i><br />
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;"><u>A great activity on this topic suggested by <a href="http://www.moebiusnoodles.com/">Maria Droujkova</a>:</u></span><br />
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span>
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">1. Draw 2 parallel lines on a paper; add perpendicular lines (so it looks like a railroad)</span><br />
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">2. Put the paper behind the window laying down on the windowsill.</span><br />
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">3. Take a transparency; lay it against the window; use markers to trace the railroad you see through the window.</span><br />
<span style="font-family: "Times New Roman","serif"; font-size: 12pt; line-height: 115%;">4. The resulting railroad tracks will not be parallel anymore.</span><br />
<span style="font-family: Times New Roman, serif;"><span style="line-height: 18.18181800842285px;">5. Now, take two lego men and start moving them along the railroad, at the same speed.</span></span><br />
<span style="font-family: Times New Roman, serif;"><span style="line-height: 18.18181800842285px;">6. It will look like at the same time interval, the lego men cover different distances, since the distance between two railroad ties in the front seems to be bigger than the distance between the railroad tracks in the back.</span></span><br />
<span style="font-family: Times New Roman, serif;"><span style="line-height: 18.18181800842285px;">7. For the moon, which can be considered to be at in infinite distance, the speed of movement is almost negligible.</span></span><br />
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i>
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">***</span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">2.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Ask
the kids to sit right next to a toy on the floor, and see how far they can move
without turning their head. Then put a toy on the opposite side of the table,
and ask them to move until the toy comes out of their view. Can you see the toy
longer if it’s on the opposite side of the table, or if it’s right next to you?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: Times New Roman, serif; font-size: small;"><span style="line-height: 115%;">This
activity was interesting for the kids, but it was a mistake that I put a
hands-on activity at the beginning of class. DO NOT put hands-on activities at
the beginning of class. First of all, the kids get very involved in it, and
then they want to keep doing it, and also, they start to think that since </span></span><span style="font-family: Times New Roman, serif;"><span style="line-height: 18.18181800842285px;">they've</span></span><span style="font-family: Times New Roman, serif; font-size: small;"><span style="line-height: 115%;"> already done the hands-on activity, they don’t have to pay attention
anymore, because they already did the fun stuff!<o:p></o:p></span></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: Times New Roman, serif; font-size: small;"><span style="line-height: 115%;"><br /></span></span></i>
<i><span style="font-family: Times New Roman, serif; font-size: small;"><span style="line-height: 115%;">***</span></span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">3.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">How
do we measure distances? Can distances only be measured with a ruler? Measure
distances in steps, sitting people (let them sit on the floor), and toys. <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">At
first, when I asked the kids if distances can only be measured with a ruler,
they said, no, they can also be measured with a meter stick! Again, it would be
better if this would be closer to the end of class, because the kids actually
do something. Also, hands-on activities should be spread through the entire class,
not bunched up one after another, as in this lesson. <o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i>
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">***</span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">4.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">How
does an airplane look like in the sky? Is it big or small? Why do you think it
looks that way? Take a toy, and show close up in front of the kids’ faces, and
then slowly move it away. What happens? Why?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Kids
had a pretty good answer: “Airplanes look small in the sky because they are so
far away, and there are many things around us that are closer to us, and look much
larger compared to the far away airplane.” At this age, kids have an intuition that things closer to us seem larger, and things farther away seem smaller, but they don't yet know why.<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i>
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">***</span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">5.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Show the kids the illusions in the <u>Incredible Visual Illusions- You Won’t Believe Your
Eyes</u>- discuss what is going on and why.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<!--[if gte vml 1]><v:shapetype
id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t"
path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f">
<v:stroke joinstyle="miter"/>
<v:formulas>
<v:f eqn="if lineDrawn pixelLineWidth 0"/>
<v:f eqn="sum @0 1 0"/>
<v:f eqn="sum 0 0 @1"/>
<v:f eqn="prod @2 1 2"/>
<v:f eqn="prod @3 21600 pixelWidth"/>
<v:f eqn="prod @3 21600 pixelHeight"/>
<v:f eqn="sum @0 0 1"/>
<v:f eqn="prod @6 1 2"/>
<v:f eqn="prod @7 21600 pixelWidth"/>
<v:f eqn="sum @8 21600 0"/>
<v:f eqn="prod @7 21600 pixelHeight"/>
<v:f eqn="sum @10 21600 0"/>
</v:formulas>
<v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/>
<o:lock v:ext="edit" aspectratio="t"/>
</v:shapetype><v:shape id="Picture_x0020_2" o:spid="_x0000_i1030" type="#_x0000_t75"
alt="https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcQ7ys9N0k7EfXMlHtaTpcktg_8-8APW4WomA0aXaUgvROEw3ZQ29w"
style='width:132.75pt;height:85.5pt;visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\Marie\AppData\Local\Temp\msohtmlclip1\01\clip_image001.jpg"
o:title="ANd9GcQ7ys9N0k7EfXMlHtaTpcktg_8-8APW4WomA0aXaUgvROEw3ZQ29w"/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"> </span><!--[if gte vml 1]><v:shape
id="Picture_x0020_6" o:spid="_x0000_i1029" type="#_x0000_t75" alt="https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcQ4D3FExU_KlkakYmLFgF1cNQAn7yr8HGk9NLwNx1LcABJP21nqNw"
style='width:65.25pt;height:147.75pt;visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\Marie\AppData\Local\Temp\msohtmlclip1\01\clip_image003.jpg"
o:title="ANd9GcQ4D3FExU_KlkakYmLFgF1cNQAn7yr8HGk9NLwNx1LcABJP21nqNw"/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<div class="separator" style="clear: both; text-align: center;">
<a href="http://3.bp.blogspot.com/-NGtixX9aDME/UMywIhUP4FI/AAAAAAAAAJM/Tav2Ud2uiWw/s1600/same+size+circles.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" height="128" src="http://3.bp.blogspot.com/-NGtixX9aDME/UMywIhUP4FI/AAAAAAAAAJM/Tav2Ud2uiWw/s200/same+size+circles.jpg" width="200" /></a><a href="http://4.bp.blogspot.com/-Dqe8sPCRvWI/UMyxM7Hk-PI/AAAAAAAAAKE/Yj-Vq-1VPKc/s1600/moon+illustration.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="200" src="http://4.bp.blogspot.com/-Dqe8sPCRvWI/UMyxM7Hk-PI/AAAAAAAAAKE/Yj-Vq-1VPKc/s200/moon+illustration.jpg" width="88" /></a></div>
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">As
soon as I showed them those two illusions, they wanted to start seeing more,
and wouldn’t let me move on to the next activity. It was hard for the kids to
understand why the pictures were optical illusions, and how they worked, but
they still liked them.</span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i>
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">***</span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">6.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Optical
Illusions can use color, light and patterns to create images that mislead our
brains. Optical illusions occur because our brain is trying to interpret what
we see and make sense of the world around us. Optical illusions simply trick
our brains into seeing things which may or may not be real.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">This
is actually a good explanation of optical illusions, and kids understood it
well.<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i>
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">***</span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">7.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Do
the Extra Floating Finger Illusion, and the Hole in Your Hand Illusion. <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The
kids thought it was extremely cool that they themselves could make an optical
illusion. When kids just see an optical illusion on a picture, it feels fake,
but when they themselves can make an optical illusion, they prove to themselves
that optical illusions are real.<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i>
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">***</span></i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">8.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Is
this possible:<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-no-proof: yes;"><!--[if gte vml 1]><v:shape
id="Picture_x0020_1" o:spid="_x0000_i1028" type="#_x0000_t75" style='width:205.5pt;
height:138pt;visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\Marie\AppData\Local\Temp\msohtmlclip1\01\clip_image005.png"
o:title="impossible pencil triangle"/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Try making it with craft sticks to
double-check the kids’ answers.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The
kids were all certain that it was possible, but after we tried making it with
craft sticks, they realized that pencils can’t interconnect like in the
picture.<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/--vMrHC9jgGU/UMyxj-q0qzI/AAAAAAAAAKM/ZTPTFt5DGI4/s1600/impossible+pencil+triangle.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="133" src="http://4.bp.blogspot.com/--vMrHC9jgGU/UMyxj-q0qzI/AAAAAAAAAKM/ZTPTFt5DGI4/s200/impossible+pencil+triangle.png" width="200" /></a></div>
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%;">***</span><br />
<span style="font-family: 'Times New Roman', serif; font-size: 12pt; line-height: 115%;">Is it possible
that the blue trees are the same size?</span></div>
<div class="MsoListParagraphCxSpMiddle">
<!--[if gte vml 1]><v:shape
id="Picture_x0020_3" o:spid="_x0000_i1027" type="#_x0000_t75" style='width:274.5pt;
height:220.5pt;visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\Marie\AppData\Local\Temp\msohtmlclip1\01\clip_image007.jpg"
o:title="perspective 1"/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--><o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle">
<i>There were two different answers from the kids. Some kids said that the blue trees were the same size, and found it easy to explain this way. Other kids were certain that the trees were different sizes, because when they put their finger on top of the far away blue tree, it was higher than the top of the closer blue tree. This shows that some kids at this age still don't understand that the linear measurement depends on the difference between two points - final and initial, not just the final one. This was noted by A.K.Zvonkin in his book " Math from three to seven" as well.</i></div>
<div class="MsoListParagraphCxSpLast">
<br /></div>
<div align="center" class="MsoNormal" style="text-align: center; text-indent: .5in;">
<div class="separator" style="clear: both; text-align: center;">
<a href="http://2.bp.blogspot.com/-ENNQYjZt8uI/UMywM2W3wLI/AAAAAAAAAJU/jKSROwBcaPU/s1600/trees+perspective.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="161" src="http://2.bp.blogspot.com/-ENNQYjZt8uI/UMywM2W3wLI/AAAAAAAAAJU/jKSROwBcaPU/s200/trees+perspective.jpg" width="200" /></a></div>
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></div>
<div align="center" class="MsoNormal" style="text-align: center; text-indent: .5in;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span>
<br />
<div style="text-align: left;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">***</span></div>
<div style="text-align: left;">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Is
this possible? <o:p></o:p></span></div>
</div>
<div class="MsoListParagraphCxSpFirst">
<!--[if gte vml 1]><v:shape
id="Picture_x0020_4" o:spid="_x0000_i1026" type="#_x0000_t75" style='width:379.5pt;
height:253.5pt;visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\Marie\AppData\Local\Temp\msohtmlclip1\01\clip_image008.jpg"
o:title="forced-perspective-10"/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--><o:p></o:p></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">If
kids don’t understand how this is possible, this is a possible hint: “Are the
people actually standing on the man’s hand?” After this hint, the kids figured
out right away that the people are just standing behind the man, and the man is
just sticking his hand in front of them, making it look like they are standing
on his hand.<o:p></o:p></span></i><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://3.bp.blogspot.com/-nC6P4QO8c1A/UMywStmt3VI/AAAAAAAAAJk/nPhCMpTJyDQ/s1600/man+blowing+skiers+illusion.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="214" src="http://3.bp.blogspot.com/-nC6P4QO8c1A/UMywStmt3VI/AAAAAAAAAJk/nPhCMpTJyDQ/s320/man+blowing+skiers+illusion.jpg" width="320" /></a></div>
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<br />
***</div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-no-proof: yes;">The two yellow
lines are the same size!<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<!--[if gte vml 1]><v:shape
id="Picture_x0020_5" o:spid="_x0000_i1025" type="#_x0000_t75" style='width:318.75pt;
height:243.75pt;visibility:visible;mso-wrap-style:square'>
<v:imagedata src="file:///C:\Users\Marie\AppData\Local\Temp\msohtmlclip1\01\clip_image010.jpg"
o:title="moon_illusion1a"/>
</v:shape><![endif]--><!--[if !vml]--><!--[endif]--><o:p></o:p></div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-size: 12.0pt; line-height: 115%;">The kids didn’t seem amazed at this
one, and seemed to know that the lines were the same size from the really beginning.
The kids checked themselves by placing their fingers on the sides of both of
the yellow lines, and they were parallel. <o:p></o:p></span></i></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://2.bp.blogspot.com/-keqUmmeAEFg/UMywVNXMREI/AAAAAAAAAJs/gLNo8kZMSYI/s1600/moon_illusion1a.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-keqUmmeAEFg/UMywVNXMREI/AAAAAAAAAJs/gLNo8kZMSYI/s1600/moon_illusion1a.jpg" /></a></div>
<i><span style="font-family: Times, Times New Roman, serif;"><br /></span></i>
<i><span style="font-family: Times, Times New Roman, serif;"><br /></span></i>Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0tag:blogger.com,1999:blog-1184298406759779916.post-92143007147548307142012-12-06T22:00:00.000-05:002012-12-15T18:56:33.582-05:00Lesson 7- Symmetry and Snowflakes<br />
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Materials:
several papers, scissors, safe mini mirror, pencils<o:p></o:p></span></i></div>
<div class="MsoNormal">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i>
<span style="font-family: Times New Roman, serif;"><span style="line-height: 18.18181800842285px;"><i>***</i></span></span></div>
<div class="MsoListParagraphCxSpFirst" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">1.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Make
cuts in the paper:<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">If I make no folds, and 1 cut, how
many cuts will there be?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">If I make 1 fold, and 1 cut, how
many cuts will there be?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">If I make 2 folds, and 1 cut, how
many cuts will there be?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">If I make no folds, and 2 cuts, how
many cuts will there be?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">If I make 1 fold, and 2 cuts, how
many cuts will there be?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">If I cut on the side, will the cuts
be in the middle when I unfold it, or will they be on the edge?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Kids
liked this activity, even though it was a bit too hard for them. Even though these
little kids can’t imagine things in their head very well yet, it’s still a good
activity for them to do, so that they can improve their mental rotation, at an
early age.<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i>
<i style="font-family: 'Times New Roman', serif; line-height: 18.18181800842285px;">***</i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">2.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">How
can I fold a square piece of paper into a triangle? Is it possible?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The
kids figured this out really fast. “Fold it in half diagonally!”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i>
<i style="font-family: 'Times New Roman', serif; line-height: 18.18181800842285px;">***</i></div>
<div class="MsoListParagraphCxSpMiddle">
<span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">What about a triangle piece of
paper into a smaller triangle?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">This
one was a bit harder, but still, it took them almost no time. “Fold it in half
through the center again!”<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i>
<i style="font-family: 'Times New Roman', serif; line-height: 18.18181800842285px;">***</i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">3.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Take
turns going around the table, and ask every person to draw a shape on a folded
snowflake. After everyone draws a shape, cut all the shapes out, and see what
snowflake comes out. <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">This
doesn’t exactly improve kids’ mental rotation skills, but kids learn that just
from folding a piece of paper, and then cutting out pieces, can make a
beautiful design. The snowflakes end up very pretty, and it gets the kids to
pay attention more. It is a hands-on activity, and kids enjoyed it. </span></i><i><span style="font-family: "Bodoni MT","serif"; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman";">Put
the scraps from the snowflake into the recycling bin right away, because kids
start playing with the scraps, and it is very hard to stop them! Also, do not
give little kids sharp scissors! </span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Bodoni MT","serif"; font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: "Times New Roman";"><br /></span></i>
<i style="font-family: 'Times New Roman', serif; line-height: 18.18181800842285px;">***</i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">4.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Cut
a piece of paper into a circle. Will a circular snowflake work?<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The
kids were sure that a circular snowflake was impossible, (arguing that a snowflake has sharp corners, making it impossible to create from a smooth circle), until we actually made
one. It is interesting to see how kids respond to this question, and to see how
they react.<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i>
<i style="font-family: 'Times New Roman', serif; line-height: 18.18181800842285px;">***</i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">5.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Divide
the page in half by vertical line; draw a shape on one side; ask the students
to draw a mirror reflection on the other side. Check your work with a mini-mirror.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The
kids were very happy that they were allowed to draw. Let the kids draw their
own object also, and let them try drawing a mirror reflection over the line.<o:p></o:p></span></i></div>
<div class="MsoListParagraphCxSpMiddle">
<br />
<i style="font-family: 'Times New Roman', serif; line-height: 18.18181800842285px;">***</i></div>
<div class="separator" style="clear: both; text-align: center;">
</div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">6.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Easy
snowflake symmetrical designs – color symmetrically. (Snowflake designs below)<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">For
this activity, to get more teamwork, pass the design around the table, and let
every child color one specific part of the design, and after everyone is done
coloring, to see if everyone made a symmetrical design together. Teamwork is
good for little kids.<o:p></o:p></span></i></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-sC4OkC3Z8ww/UMzBhf0AuiI/AAAAAAAAAKc/u4Msxczdkbs/s1600/blue+snowflake.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" height="320" src="http://4.bp.blogspot.com/-sC4OkC3Z8ww/UMzBhf0AuiI/AAAAAAAAAKc/u4Msxczdkbs/s320/blue+snowflake.jpg" width="300" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-If3h7SGE43s/UMzBjc-F0EI/AAAAAAAAAKk/bQ5dIbzFJRk/s1600/outline+snowflake.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="http://1.bp.blogspot.com/-If3h7SGE43s/UMzBjc-F0EI/AAAAAAAAAKk/bQ5dIbzFJRk/s1600/outline+snowflake.jpg" /></a></div>
<div class="MsoListParagraphCxSpMiddle">
</div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<br /></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i>
<i style="font-family: 'Times New Roman', serif; line-height: 18.18181800842285px;">***</i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">7.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Symmetrical
movement (I raise my right arm, you raise your left, etc.)– work in pairs.<o:p></o:p></span></div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Wonderful!
Have one child act as a mirror, and one child to be a real person doing the
motions. When kids get to stand up and move around, they concentrate much
better.</span></i> </div>
<div class="MsoListParagraphCxSpMiddle" style="text-align: center;">
</div>
<div class="MsoListParagraphCxSpMiddle">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;"><br /></span></i>
<i style="font-family: 'Times New Roman', serif; line-height: 18.18181800842285px;">***</i></div>
<div class="MsoListParagraphCxSpMiddle" style="mso-list: l0 level1 lfo1; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%; mso-fareast-font-family: "Times New Roman";">8.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">Get
Othello (board game), and make symmetrical designs. <o:p></o:p></span></div>
<div class="MsoListParagraphCxSpLast">
<i><span style="font-family: "Times New Roman","serif"; font-size: 12.0pt; line-height: 115%;">The kids liked this activity, and they took turns making symmetrical designs with me, and other kids in the group. This
is very funny, but it is what I observed during the class: When I told the kids
that the problem they were solving was a game, <u>even if it wasn’t</u>, the kids
started getting much more involved in it, because they <u>thought</u> that it
was a game.</span></i><i><span style="font-family: Wingdings; font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: "Times New Roman"; mso-bidi-font-family: "Times New Roman"; mso-char-type: symbol; mso-hansi-font-family: "Times New Roman"; mso-symbol-font-family: Wingdings;">J</span></i></div>
<div class="MsoListParagraphCxSpLast">
</div>
Mashkahttp://www.blogger.com/profile/07156442645957724379noreply@blogger.com0