Copyright © University of Cambridge. All rights reserved.

## Let's Investigate Triangles

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths.

There are:

**yellow** strips with $3$ holes
**black** strips with $4$ holes,
**red** strips with $5$ holes and
**green** strips with $6$ holes.

There are plenty of strips of each colour.

Vincent makes a triangle with a green strip, a yellow strip and a **red** strip.

Tara makes a triangle with two **green** strips and one **red** strip and another triangle with three **black** strips.

How many different triangles can you make with these lengths?

Can you find three strips which cannot be made into a triangle when you use them together?

### Why do this problem?

This problem allows children to make important discoveries about triangles through representing the sides of triangles with strips from a construction kit. They will have the opportunity to find out which combinations of lengths cannot be made into triangles, and why this is so. They should also discover how
rigid triangles are, and that three fixed lengths can only be arranged in one way (unlike other polygons such as quadrilaterals where the angles can be changed).

This investigation requires plenty of equipment and space, so is probably best done in a small group.

### Possible approach

You could start by demonstrating with the interactivity in

this problem to show the children what can be done with three rods or sticks.

After they have been introduced to the problem, encourage the children to work on making different triangles with three lengths of strips. If they are mature enough to work in pairs, the children will gain from talking through their ideas with a partner. If they are working on a suitable plastic table the length of the rods (as numbers) can be written on the table with whiteboard markers to check
if any of the triangles made are repeats. Go on to using all four lengths when you judge the children are ready.

If you do not have access to a construction set or suitable rods,

this sheet will give you four copies of each strip in the colours in the problem. If they are printed out on card and laminated they can be
laid flat on a table to make the triangles. This sheet has uncoloured strips that can be photocopied. Paper copies can be pasted onto a backing sheet but make sure that the children have made a triangle before they have access to any glue or paste as
they will probably be frustrated on finding that the third side does not fit!
In a plenary, children can show the triangles they have made and any three lengths that will not make a triangle. Invite them to explain why the three lengths cannot make a triangle, and look out for those learners who begin to make generalisations.

### Key questions

Have you made any triangles using this length of strip?

Have you made any triangles with all the sides the same colour/length?

Have you made any triangles with all the sides different colours/lengths?

Are you sure you haven't made one like that already?

Why do you think you can't make a triangle with those three sticks/rods?

### Possible extension

Children who work quickly could be encouraged to find a way to show that they have discovered all of the possible triangles using four different lengths. They can be encouraged to compare the different triangles they have made and describe them to one another looking carefully at their characteristics.

### Possible support

Some learners might find it helpful to use just two lengths to start with. (Make sure that the longest one is shorter than two of the others put together lengthways.) You can make four different triangles with these. You can then add a third length.