Tessellating Triangles
1 out of 3
Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?
Problem
| Equilateral triangles have three sides the same length and three angles the same. Can you make them fit together to cover the paper without any gaps between them? This is called 'tessellating'. | Image
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What about triangles with two equal sides? These are isosceles triangles.
Can you tessellate all isosceles triangles?
Now try with right angled triangles. These have one right angle or 90 degree angle.
Some triangles have sides that are all different. Can you tessellate these?
Could you tessellate any triangle?
Getting Started
Make plenty of triangles before you start (in different colours if possible).
Student Solutions
There are lots of interesting designs to be made by tessellating triangles. Have a go yourself, and if you discover anything interesting, email primary.nrich@maths.org to tell us what you've done!
Please don't worry that your solution is not "complete" - we'd like to hear about anything you have tried.
Teachers - you might like to send in a summary of your children's work.
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
This problem encourages children to use the right vocabulary when talking about shape properties. They will begin to understand that, for a shape to tessellate, the angles where they come together are important.
Possible approach
- If I took out one of the triangles, how do I know which way it fits in to make the tessellation?
- Why won't it fit if the triangle is rotated?
Possible extension
You could also challenge the children to make tessellating patterns using more than one type of shape.
Possible support
If there are children who are finding this activity difficult, give them plenty of time to manipulate the shapes practically.