- Topics: Numbers, Codes, Algebra: The Cat in Numberland, Chapter 3, by I. Ekeland. In this chapter the letters come to visit the numbers, and we learn about letter/number ciphers and letters standing in for numbers.
- Topic: Algebra: I made problems of the form “X + 3 = 5” using unit cubes from Base Ten Blocks and a small cardboard box. I.e., I would secretly put 2 blocks into the box and close it, put 3 blocks next to it, and then say “There are 5 blocks total, how many are in the box?”
- Topic: Primes: I introduced the idea of primes using Base Ten Blocks: a number N is a prime if the only rectangle you can make using N blocks is 1 X N. I gave different numbers to each kid and had them figure out whether it was prime or not.
- Topics: Combinations, Combinatorics: I printed a bunch of “Easter eggs” with a top and bottom section. Using five different colors of crayons, I asked the kids to make as many different eggs as they could, coloring each section in solid colors (not stripes/dots/etc.). I taped each one to the wall (stacking repeats).
How Did It Go?
We had four kids this week.
Cat In Numberland
The algebra in this chapter is tricky because it includes addition, subtraction, multiplication, and division; most of the kids don’t know multiplication or division yet.
This worked pretty well. The kids understood what was going on right away, and they were always excited when I opened the box and dumped out the blocks inside to see if their guess was correct. At the end they made a problem for me, which was something like “X + 3 = 39” (of course, they used as many blocks as they could).
We did up to about 14. I kept track of each result. The only odd composite number <= 14 is 9, so for the most part they just needed to check a 2 row rectangle. Proving something is prime is tricky, of course, and whenever a kid said that something was prime, I always asked them “did you check 3-wide”? Whoever had 9 didn’t initially check 3×3.
The kids were really into this activity and worked very hard to get all the combinations. They got all 10 two-color combinations pretty quickly and without help (first two rows in picture above) — but there was no pattern to which color was on top vs. bottom. Then one of the kids realized that you could flip the colors. They quickly got 6 more, but the next 3 took them a lot longer to find, and I had to help them find the last one. This got them to 20, but they didn’t think of having the same color on top and bottom. I suggested it to them and they quickly made the last 5. Then I rearranged them so that there were same color tops along the rows and same color bottoms along the columns. I realized afterwards that I should have made this chart before I gave them the hint about same color top/bottom, because then there would have been gaps and I could ask them what went in the gaps.