Pool Party

How it works

Imagine that you shoot a ball at a 45 degree angle from the bottom left corner of a 4 x 6 pool table. The ball will bounce around the table until it ends up in one of the corner pockets. (The table only has pockets in the corners.) What will the path of the ball look like? What about on a 3 x 6 table? A 5 x 6 table? Other tables?

In this activity, students start by tracing the paths of the ball on a variety of different tables. Next, they try to find tables where the path has specific shapes; in particular, given one table where the path has a certain shape, they try to find other tables where the path has the same shape, and they explore the connections between these different tables where the path has the same shape.

Warmup Tables handout

Path Shapes handout

Square Counting handout

Why we like this activity

  • It’s fun! Students enjoy tracing the paths of the ball and finding tables where the path makes specific shapes.
  • It helps students develop geometric reasoning.
  • It helps students develop numerical reasoning.

  • It requires students to engage in mathematical habits of mind:

    • Using logic, looking for patterns, and finding and using strategies when trying to find different tables with the same path shape
  • It has a low floor and a high ceiling: Students can get started drawing paths without too much difficulty, but finding tables where the path has a specific shape requires more careful strategizing, and there's lots more to explore and discover about the paths for different tables.