Polygons in the Machine
with Kim Rodgers
On Monday, we continued working with the Fabulous Function Machine by using polygons! “Polygons?” the kids asked. Yes! After suggesting many different types of polygons to put into the machine, some of them finally started seeing a pattern with the number that came out (the output was the number of edges of the polygon +1). We decided to write another T-chart next to the one we were using, substituting digits for the number of sides, along with the output. Now the lightbulbs really started going off! Once the kids saw the numbers line up, the pattern was easier to see. Using their journals, they wrote in words what they thought was going on in the Function Machine. Explaining mathematical thinking using written words is something a lot of kids don’t have experience with, but is an important skill to develop.
The next function that went into the machine had two steps to solve. Many strategies were used, one of which was focusing on numbers that were easy to work with, like: 0, 1, and 10. These numbers are small and help us see patterns, often allowing us to spot clues that are harder to see with larger, random numbers. While we were performing this function, some students thought they had it figured out, but one pair of numbers had them stumped. It didn’t fit with the pattern the other pairs were displaying. A couple of the students mentioned it, and lo and behold, I was the one who had written the wrong output! I told them it is always good to ask questions, because even adults can make mistakes!
We finished up class with a puzzle. Pairs of students were challenged to figure out a way to take 10 index cards, with one number each from 1-10, and put them in an order that would allow the cards to be dealt out in a certain way. When their stack was turned upside down the first card they flipped over had to be 1. The next card they put on the bottom of the deck. The next card they flipped had to be 2. The following card went on the bottom of the deck...and so on until they had a pile of cards in order with 1 on the bottom and 10 on the top. Each group had their own story of the strategy or strategies they used to figure this one out. A few groups got each other’s e-mail addresses to make sure they finished before class next week. At the beginning of class they will share their journey to figuring out the answer. Much of the challenge with algebra is figuring out a strategy that helps you solve the problem. If one isn’t working you switch to another! Reminding kids to break down a problem into manageable parts is one of the goals for the class.
Next week we encounter a malfunction with Professor Arbegla’s Fabulous Function Machine. Can we help her fix it?