 Consider this:
·
All
mice are small.
·
Ants
are small.
·
Therefore,
ants are mice.
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…
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.
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.
They said “Yes! Of course we know! It’s an old man
with a cane and a long white beard!”
“Really? That’s interesting. Who’s an old man then?”
“Um… Oh… A grandpa is the dad of my dad”
“Or?”
“Or my mom” Good.
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).
3. 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?
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 fasterJ .
I was trying to get them to understand;
Me:
“They were standing together, holding hands.”
Kids:
“But Kristina was running faster!”
Me:
“They were in the same spot, when they met.”
Kids:
“Kristina was running faster!”
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?
4. 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)
5. Give them a few
graphs to look at and have them tell you what’s going on.
6. 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.
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.
Questions:
1.
Who
ate the most nuts and how many did they eat?
2.
Who
ate the least nuts and how many did they eat?
3.
How
many people ate nuts in this graph?
4.
How
many nuts did Matvei and Sasha eat together?
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 somehow introduce them to graphs.
Pie
graph: 4 cats, 3 birds, 2 fish and 2 dogs are in the house. Explain what a pie
chart is.
Questions:
1.
How
many different types of animals were there?
2.
How
many cats were there in the house?
3.
How
many more birds were there than dogs?
4.
How
many legs did the birds and fish have together?
5.
Is
the number of fish and dogs together greater than the number of cats?
6.
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 asked them a few followup 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:
Blue = 4 cats,
Red = 2 fish
Green = 2 dogs
Purple = 3 birds.
I inserted pictures into each of the segments, but I couldn't save it as a picture, so I can't insert it here.
Graphs:
a
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. Draw a line graph. How fast does Katya’s hair grow?
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.
b 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.
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.
Graphs, b):
Minutes past

Miles driven

1

1

2

2

3

5

4

7

5

7

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