Activity Icon - RepTiles.png


How it works

Tiling is the process of using a set 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).

In this activity, students use cutouts and then geoboards to make RepTilings for various shapes.

How does the size of a RepTiling increase based on the number of tiles used? How much larger are each of the sides of the resulting shape compared to the original tile?

RepTiles Cutouts
RepTiles Puzzle
Geoboards RepTiles Handouts
Trapezoids 1-2-3 Handout

Why we like this activity:

  • It’s fun! Students using the cutouts and the geoboards to make RepTiles.

  • It helps to develop spatial 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 / finding similarities and differences / understanding and explaining when exploring how many pieces you need to make a RepTile of a given size.

  • It has a low floor and high ceiling: Students can get started making RepTiles by trial and error, but there is a lot to explore and discover.

To find out more about our approach to math and math education, click here.