You may also like

problem icon

Tri.'s

How many triangles can you make on the 3 by 3 pegboard?

problem icon

Cutting Corners

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

problem icon

Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

Triangle Relations

Age 7 to 11 Challenge Level:

Triangle Relations


Here is an isosceles triangle and an equilateral triangle:

green isosceles triangle and yellow equilateral triangle


You will need to print off and cut out the two triangles to try this problem. (Here is a sheet of them which you could print off.)

What do the two triangles have in common?

How are they related?

Why do this problem?

The beauty of this problem is that it is completely open and therefore gives children the opportunity to approach it however they like. It is a great chance for you to observe and assess what they do, having conversations as you walk around the class.

Possible approach

It might be appropriate for children to work in pairs or small groups and they will almost certainly need a cut-out copy of each triangle. (Here is a sheet of triangles which you could use.) It would be great to have other resources available for them to use should they want - for example rulers, pencils, squared paper, triangular dotty paper etc.

Pupils will come up with a variety of different findings which might relate to side lengths, area, symmetry ... For example, some children might notice that you can halve each triangle to make two smaller triangles. The resulting four smaller triangles are in fact identical. Other children might notice that the area of each triangle is the same. You might want to bring out the fact that some of the things the triangles have in common could be exemplified in different ways.