Chameleons
How it works
Imagine we have a bunch of chameleons in a row. Each chameleon is either blue or red.
These chameleons change color in a very specific way:
They only change color in pairs.
Two chameleons have to be next to each other in order to change color.
So if there are two blue chameleons next to each other, they can both change to red. If there are two red chameleons next to each other, they can both change to blue. If there are a blue and a red chameleon next to each other, they can both change color so the one that's blue becomes red and the one that's red becomes blue.
Given an initial arrangement of blue and red chameleons, is it possible to get all the chameleons to be blue? What about red?
In this activity, students start by exploring whether this is possible for various different arrangements of chameleons. The more arrangements they see, the more they start to notice patterns that help them to predict when it will be possible to get all the chameleons to be a specific color and when it won't.
Students also explore what happens when there are 3 colors — blue, red, and yellow. Now the chameleons are grouped by color rather than in a line. Chameleons still change color in pairs, but now they don't have to be next to each other, and the rules for changing color are different:
- Two chameleons of the same color will change so each becomes one of the other two colors (so two blue chameleons will change color so one is red and the other is yellow).
- Two chameleons of different colors will change so they both become the third color (so a blue and a red chameleon will change color so both are yellow).
Why we like this activity
- It’s fun! Students enjoy trying to get all the chameleons to be the same color.
- It helps students develop algorithmic reasoning.
- It helps students develop numerical reasoning.
It requires students to engage in mathematical habits of mind:
- Finding and using strategies to solve different arrangements.
- Making observations / comparing and contrasting / looking for patterns / making and testing predictions / understanding and explaining when exploring which arrangements are solvable and which ones aren't.
- It has a low floor and a high ceiling: It's easy for students to get started trying to solve different arrangements, but figuring out a general rule to help predict which arrangements are solvable and which aren't is more challenging.