Triangle animals
Problem
I can join two equilateral triangles together along their edges like this:
How many different ways are there to join three equilateral triangles together? (You must match an edge to an edge.)
How do you know you have got them all? You may find it useful to print out and cut up triangles from this sheet.
Have you got a system for checking that you have them all?
For a further challenge, you might like to look at Tri-Five.
Getting Started
What is the same?
What is different?
How do you know that you have them all?
You might like to print off this sheet of equilateral triangles and cut them out.
Student Solutions
Grace and Brittany from Stradbroke Primary both made the problem simpler to start with (this is often a good way of starting a problem, so good thinking!). Grace wrote:
$1$ triangle makes $1$ shape
Jonathan from Brick Street Public School explained how he found the three different ways for 4 triangles, starting with the shape made from three triangles:
Here is a picture of the three shapes that Jonathan sent:
Teachers' Resources
Triangle Animals
I can join two equilateral triangles together along their edges like this:
How many different ways are there to join three equilateral triangles together? (You must match an edge to an edge.)
How do you know you have got them all? You may find it useful to print out and cut up triangles from this sheet.
Have you got a system for checking that you have them all?
For a further challenge, you might like to look at Tri-Five.
Why do this problem?
Possible approach
Key questions
Possible extension
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.
Possible support
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).