Lesson 4- Year 2

1)      A car is driving down a road. Draw the graph, and tell the story.

Minutes past	Distance (miles) from the house
1	1
2	2
3	5
4	7
5	7
6	8
7	9
8	9
9	9
10	5
11	3
12	0

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^th and 5^th 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).

2)      The temperature in the Arctic changes over the week. Kids: make a graph, explain how the temperature is changing.

Day 1	3
Day 2	5
Day 3	9
Day 4	9
Day 5	9
Day 6	6
Day 7	0

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?”

3)      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.

Clues:

§  Dima has a pet that has feathers.

§  Sasha and Katya have pets that don’t start with the first letter of their name.

§  Max’s pet and Dima’s pet have to be kept apart because Max’s may eat Dima’s.

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.

4)      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.

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.

http://www.education.com/worksheet/article/smiley-sudoku-second/
http://www.education.com/worksheet/article/kenken-puzzle-second-1/

Lesson 3 - Year 2

1. 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 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:

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