## The Activities

**Topic: Evens and Odds, Division**: Book: Splitting the Herd by Harris. The kids will act out the book with the wooden cows we have.**Topic: Combinations**: Given a chain of 5 circles, how many different ways can you color in zero circles? 1 circle? 2 circles? 4 circles? For example, OXOOX and XXOOO are two ways to color 2 circles out of 5.**Topic: Probability**: Kids will roll two dice, compute the sum and fill in a box in a chart. We’ll end up with a 6×6 grid of all possible sums of two dice.**Topic: Sequences:**Kids arrange the story cards in order.

**How did it go?**

**How did it go?**

#### Splitting the Herd

This is a really fun book that involves Emma’s 10 cows getting into her neighbor Kirby’s pasture and mixing in with his 10 cows. The two neighbors split the cows into two groups of 10. The next night 2 cows run into the neighbor’s pasture, and they split them into two groups of 6, and send 6 back home. The kids saw no problem with this. Then again two cows run over, and they split the 8 cows. At this point one kid said “But Kirby only has 4 cows!” and the kids agreed this was unfair. Again 2 cows run over, and now there are 5 cows to split, which can’t be done so Kirby and Emma get married. I didn’t know how to explain why the cow division ended up wrong, so I talked about how Kirby and Emma should have remembered that there were still some cows in Emma’s field.

**Circle Coloring Combinations**

**Circle Coloring Combinations**

Given a chain of 5 circles, how many ways can you color in zero circles? 1 circle? 2 circles?

3 of the kids had seen this activity at an earlier circle. One of them remembered she had been able to get 8 different colorings.

This was new to the other 2 kids. I started by coloring in one circle in the chain: XOOOO. I asked Kid #1 if he could make a different chain by coloring in one bead, but he colored in the same bead as me. So I asked another kid, who found a new way: OOXOO. We continued taking turns until the kids had found 5 different ways to color in one circle. Then I asked Kid #2 to find another, and after awhile she gave up, and I suggested maybe 5 was all of the ways.

Then I gave each kid a sheet with rows of 5 circles on it, and told them to color in two beads in each chain. One kid got 7 different ways, another found 6. One kid got 5 ways…she had trouble because she felt that reflections were the same, for example: XOXOO and OOXOX.

One kid was stuck so I stood by the kid and tried that each row was a chain and we should color two beads in each. The kid colored one in each row, and sometimes seemed to think the chains should be vertical. The last kid was more interested in playing with puppets after circle and in telling me her plans to color all the circles in different colors when she got home.

Then I gave the kids a new paper and asked them to color 4 beads in each chain. 3 of the kids got 3 or more different colorings.

#### Probability Charts

By now, we’ve done probability race about 5 or 6 times. We decided the kids might be ready to learn *why* some rolls are more common than others (i.e. 7 is the most likely roll). I made a chart like this:

1 | 2 | 3 | 4 | 5 | 6 | |

1 | ||||||

2 | ||||||

3 | ||||||

4 | ||||||

5 | ||||||

6 |

The plan was to write the sum of the two dice in the appropriate box.

The kids all remembered probability race, and were happy to roll dice and count the dots. I showed them how to fill in the chart, but only one kid seemed to understand. We filled in the results of 12 rolls, and then stopped because the kids got restless.

#### Story Sequences

The kids all loved this activity. The only problem was a bit of restlessness during other people’s turns. Also, some of the kids wanted to tell the other kids how to arrange the cards. For this circle, we used a bunch of story sequences that we found on the internet and printed out.

- Kid #1 had a boy throwing a ball for a dog. At first she was intimidated because it had 6 cards, but she started organizing them and corrected herself where she was wrong.
- Kid #2 got a frog growing up from an egg. She organized them all correctly, but she had the frog with a tail as the last card. I told the story as she had arranged it and at the last card I said “then the frog grew a tail”. All the kids said that sounded good, but then I said I would change something. Kid #1 immediately swapped the adult and the tail frogs.
- Kid #3 had pictures of building a snowman, and then a melted heap of snowman parts. She put the melted heap first, and said that that was before the snowman was built. Kid #4 said she’d arrange it differently: her story was: First there’s a snowman, then all it parts disappear, then it gets a face, then it melts (she was not joking). Then I let Kid #2 have a turn and she organized them as expected with the melted picture last.
- Kid #4 had one with 3 cards: A man with a watermelon, a man with watermelon in half, man and kids eating watermelon. Kid #4’s story was: 1. watermelon in half. 2. man with whole watermelon 3. eating: “A man builds a watermelon, then he cuts it and they eat it.” Kid #1 reorganized in the expected order.
- Kid #5 had: A: A girl with dog pulling her scarf. B: Girl waving at dog with scarf. C: Boy chasing a dog with scarf. D: Boy giving scarf to girl. Kid #5 arranged it as D A B C. Everyone was tired so I ended circle here.

After circle, Kid #5 wanted to show dad the story cards and tell the story. Also several parents told me about their kids wanting to start math circles and playing pretend math circle at preschool.