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Tessellating Triangles

Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?

Two by One

An activity making various patterns with 2 x 1 rectangular tiles.


Age 7 to 11 Challenge Level:

Why do this problem?

This problem encourages children to work together and will require some visualisation. It is a good context in which to focus on working systematically and justifying results.

It might be convenient to print off this board and tetromino pieces for pupils to use. This sheet has some copies of the other four tetrominoes which may be useful once children have discovered them for themselves. It will be helpful for squared paper to be available too.

Key questions

Which way up could that one be fitted in?
Do you need to fill the whole board to be sure?
How else could you arrange four squares to make a different tetromino?
Are you sure you have found all the tetrominoes? How do you know?
Have you tried fitting this tetromino on the board?

Possible extension

Learners will have their own ideas for further investigation, for example looking at differently sized grids, or using pentominoes.

Possible support

Using the sheets (or interactivity) will help all children access this problem.