Why do this problem?
There are two main reasons for using this problem
in the classroom. The first is to encourage children to develop a systematic approach to solving problems. The second is to enable them to understand that rotating a shape does not change the shape itself, it just puts it in a different place (or orientation). Both these ideas can be touched
upon as you introduce the problem.
To begin with, explore just two triangles. This might be best done by having cut out triangles on an OHP, or by using the interactivity. Suggest to the group that one of the triangles could be kept still while you look at the different positions of the second triangle. This will encourage them to move the second triangle around the first in a particular direction i.e. having a system so that
no possibilities are left out. Then, by looking at each of the different shapes and rotating them, children can be asked what they notice. (They are all the same.)
In this way, the class can conclude that in fact there is only one way to put two triangles together. This initial exploration and discussion will equip them for tackling the problem itself.
Have you decided what is the same and what is different?
How do you know that you have them all?
Children could have a go at Tri-Five
. They could also see what happens if they use two or three isoceles triangles. Are their results different? Why? Again the focus should be on developing the use of accruate descriptive language and beginning to introduce the correct mathematical vocabulary of vertices, sides and angles.
Having lots of cut-out triangles for children to stick down will help them access this challenge. You could use this sheet
of equilateral triangles for printing and cutting (and possibly laminating too).