My grade 8 students have been working on some algebra basics for the last few weeks. The can write expressions using variables and evaluate expressions. They can also solve some simple equations, but in general, their approach is either intuitive or guess-and-check.

Before getting into solving equations, my co-teacher suggested that we try to build a stronger understanding of *equivalence*. We brainstormed a few ideas but couldn’t settle on anything we really liked. Later on, while walking home in the rain, the idea of Equivalence Scattergories was born.

It works like this:

- Students work in table groups
- Each group has a sheet of paper or a mini-whiteboard and marker
- In each round of the game, one number or expression is written on the board
- The object of the game is to come up with as many expressions that are equivalent to a particular number as possible
- Each equivalent expression is work 1 point
- An equivalent expression that no other team thought of is worth 5 points
- Expressions with the same terms in a different order are considered the same. For example, 1 + 2 x 5 is the same as 2 x 5 + 1

- A expression that isn’t equivalent to the particular number is -2 points

- Teams create expressions using any three digits (0-9) and any operations they choose.
- Digits can be repeated (e.g. 22 or 2 + 2)
- Digits can be used in single-digit numbers or combined in two or three digit numbers

The game starts with integers. After a few rounds, instead of integers, an expression is written on the board. Eventually, an equation is written on the board. For example, if we wrote “x +7 = 3” students would have to write an equivalent, like:

The hope is that after a few rounds with equations, students will figure out that you can create an infinite number of equivalent equations as long as apply the same operation to both sides.

Here are the slides I created to guide students through the game.

Stay tuned for an update about how it goes!

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