RepTiles
How it works
Tiling is the process of using a specific shape or collection of shapes to cover an area. When you use identical copies of a shape to tile a larger version of the original shape, we call this a RepTiling (since you’re using replicas of the shape for your tiling).
Given a shape, is it possible to find a RepTiling for that shape? If so, how many copies of the original shape do you need to use? How does this number change depending on the size of the larger shape you're trying to tile?
In this activity, students use cutouts and geoboards to make RepTilings for different shapes, exploring the questions described above.
Why we like this activity
- It’s fun! Students enjoy using the cutouts and the geoboards to make RepTiles.
- It helps students develop spatial reasoning.
- It helps students develop numerical reasoning.
It requires students to engage in mathematical habits of mind:
Finding and using strategies to make RepTiles for different shapes.
Making observations / looking for patterns / comparing and contrasting / understanding and explaining when exploring how many copies you need to make a RepTile of a given size.
- It has a low floor and a high ceiling: Students can get started making RepTiles by trial and error, but there is a lot to explore and discover.
