## The Activities

- Topic: Ratios: Book: Beanstalk: The Measure Of A Giant by A. McCallum.
- Topics: Combinations, Combinatorics: I had printouts of eggs with the top and bottom separated by a line. First, I gave them 3 colored markers and asked “If you have 3 colors, how many ways can you color the eggs?” (Answer: 9). Then I asked about 5 colors, without actually giving them 5 colors, to see if they could figure out the pattern without actually doing the coloring.
- Topic: Multiplication: I had a bag of plastic Easter eggs with a slip of paper with a number from 1-9 inside each one. At first, each kid drew out two eggs and had to figure out the product of the two. After a few rounds of this, they started drawing out three eggs and multiplying them all together.
- Topic: Tesselations: Using pattern blocks, we worked together to make this pattern:

## How Did It Go?

Four kids attended this week. Everything went pretty smoothly this week. At the end of circle, all the big kids went and voted on the birthday party activity in the little kids circle.

#### Beanstalk: The Measure of a Giant

This book was about ratios and was a good level for the kids.

#### Egg Coloring

When I asked about 3 colors, several of the kids immediately began coloring, and quickly found all the combinations. They clearly have gotten better at looking what’s missing rather than just trying random combinations. I asked how many there would be with 5 colors, the most popular answer was 15 (5 * 3). Then I arranged the eggs into a grid (as shown above) with same color tops in the rows and same color bottoms in the columns. I asked them questions about how many were there if you only had 2 colors and 1 color, and arranged the eggs in expanding “rings” to show what gets added each time you add a new color (this suggests another activity, proving that n^2 = sum of first n odd numbers). I also pointed out how each column and row corresponded to a bottom/top color. Finally, I asked what shape the chart was for each of 1, 2, 3 colors, and how many eggs on each side; at this point one of the kids saw that the pattern was to make an n x n square. When I asked about 10 colors, I still got two kids saying 3 * 10, one saying 10 * 10, and one saying “I don’t know.” After a bit more discussion they all decided it was 10 * 10. I also asked 1000 colors and 1 million colors just for fun.

#### Egg Multiplication

A couple of the kids have already memorized their multiplication tables, so the two number multiplication was very easy for them. However, three numbers was much more complicated. In particular, they definitely don’t have the idea of multiplying place by place. One of the largest multiplications was 9 * 9 * 6, quickly reduced to 81 * 6. I gave them lots of hints for what 80 * 6 was: first I asked what 8 * 6 was (immediately got 48), and then using Base Ten Blocks, I said “If 6 * 8 unit blocks is 48 unit blocks, what is 6 * 8 ten blocks?” No one ever realized the answer was 48 ten blocks — someone eventually added 80 6 times in their head to get the answer. They were able to say that 48 ten blocks was 480 once I pointed out that 6 * 8 ten blocks is 48 ten blocks.

#### Tesselation

I had come up with this pattern when experimenting (playing) with the blocks one day, and thought it was both pretty and somewhat challenging. At first, they didn’t get the rules and had trouble expanding the pattern. But once I pointed out that the yellow was surrounded by blues and whites, and the green was surrounded by blues and whites, after some practice they were able to continue expanding the pattern.