- Topics: History of Math, Mathematicians: Mathematicians Are People, Too: Stories from the Lives of Great Mathematicians (Volume One) by L. Reimer and W. Reimer, Chapter 2 (Pythagoras).
- Topic: Algebra: Using a bunch of colored glass beads, we did some simple algebra problems. I had a chart with boxes numbered 1-8, and then by placing a stone in one of the boxes I could indicate how much that color was worth. I started with some problems where all the values were known, and asked which pile was worth more. For example, if Green = 3, Yellow = 2, and Blue = 5, which is bigger, 3G + 2Y or 3B? Then I made it a bit harder, e.g., 13G + 2Y vs. 13G + B — the goal is to introduce them to canceling equal quantities from both sides. Next, I changed the problems so that one (or sometimes two) of the values are unknown, and I give them two piles with equal values, and they have to figure out one of the unknowns. For example, if G = 2 and Y = 3, and G + B = 3Y, how much is B? Harder, if G = 1 and Y = 4, and G + B = Y + 2B, how much is Blue? Even harder, if Y = 3, and G + 4Y = G + 2B, how much is Blue?
- Topic: Decision Trees: We continued the activity from last week. First, we did a couple more tracing exercises with playing cards and more complicated trees (Tree 4 and Tree 5 from last week’s post). Next, we did more tree building using random selections of cards, but this time, instead of using playing cards, we used Pokemon TCG cards. Besides being an interesting theme, these cards are nice because they have a lot of different attributes (color, HP, damage, weight, size, and more).
How Did It Go?
We had all five kids this week
Just like last time, the kids were pretty interested in this story. It took about 15 minutes to read — I tried stopping partway through, but they insisted I finish the chapter. There wasn’t a great deal of math content — but there were good lead-ins to either the Pythagorean theorem or Platonic solids. Pythagoras definitely had an interesting life, essentially starting a cult…
I started with one shared problem for the whole table, but that didn’t work well at all — one or two kids were engaged, but the rest started drawing, writing their names in different styles, etc. I switched to having two groups each doing the same problem, which helped, but I think I should have had a copy for each kid. Also, I set up the problems each time — I probably should have had the kids make the problems themselves.
One of the kids (Kid A) already knew how to solve algebra problems such as 5X + 3 = 28, subtracting and then dividing. I didn’t ever write down the problems in this way, but a different kid (Kid B) wrote one of the earlier problems down like this, and then Kid A immediately solved it. However, Kid A wasn’t able to generalize to some of the other patterns.
For the initial problems with only given quantities, the kids quickly realized you could ignore an equal number of the same color stones from both sides — although they quickly fell back to calculation if it got more complicated. Later, when there were unknowns, they weren’t able to apply this idea without help. Perhaps the hardest problem was B=7, 4B + Y = 4Y + B — one of the kids solved it with the intuition that it would only work if B and Y were equal. I pointed out the idea of grouping one B and one Y on each side, which some of them understood, but I’m not sure they could apply it.
Tracing went well, one of the kids had been gone last week but picked it up quickly. The kids sorted quite a few cards in a short period of time. They also noticed when certain letters happened less frequently, and made some inferences about the output. The most interesting part of this section was that the kids thought the cards smelled bad, calling them stinky cheese cards (mostly they smelled like plastic).
The Pokemon theme definitely interested them. They had varying degrees of success writing down a tree. They all understood how to make a tree, but some of them had trouble making a tree that matched the cards I dealt them. The kid who missed last week didn’t understand that they weren’t supposed to rearrange the cards — their tree is the second picture above, which mentions A, B, and C even though I dealt only A and B piles. Some kids used the different attributes more effectively, finding patterns in the HP, for example. One of the kids used a range 175 lbs – 251 lbs in order to pick the middle two out of four blue Pokemon. One kid thought it was funny that Tentacool, a jellyfish pokemon, weighed 100 lbs, thus the blog post title. One of the kids finished two trees quickly (picture 1 above), each time sorting a bunch of other Pokemon after building the tree.