This is deeply connected to the idea of backtracking for solving equations. The idea is that expressions are recipes of things to do to numbers, and “x” just stands for “pick a number, and number.” Explaining why some of these number tricks work (“It’s always 7!”) we can get at some serious math, and it motivates a lot of algebra. This is something that I could see coming back through the year, making connections between different topics. Here are some resources for it:
- Dan Meyer’s stuff in Week 3.
- Discovering Algebra’s online material for their Chapter 2
- CME Project’s worksheet on number tricks