Symmetries of Tilings
How it works
A tiling of a shape with pattern blocks is a way of covering the shape with pattern blocks without going over the edge. For a given tiling, if you can move the tiling around so it looks the same (for example, by turning it or flipping it over), you’ve found a symmetry of the tiling.
In this activity, students tile various shapes, and then they determine and compare the symmetries of their different tilings (which can be different than the symmetries of the original shape), and strategize to find tilings that have specific sets of symmetries.
Why we like this activity
- It’s fun! Students enjoy using the pattern blocks to make tilings.
- It helps students develop spatial reasoning.
It requires students to engage in mathematical habits of mind:
Making observations / looking for patterns / comparing and contrasting when exploring the symmetries of different tilings of the same shape and figuring out which groups of tilings have the same symmetries
Finding and using strategies to design tilings that have specific symmetries.
- It has a low floor and high ceiling: Students can get started making tilings and finding symmetries by trial and error, but there’s much more to explore and discover about the relationships between shapes, tilings, and symmetries.
