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Colouring Triangles

Explore ways of colouring this set of triangles.


Can you make symmetrical patterns? With two colours? Three colours? More than three colours?

Can you colour the small triangles, using four colours, with no two triangles of the same colour side-by-side?

Why do this problem?

This problem will help children recognise reflective symmetry, but it offers more than that. By giving children the freedom to create their own symmetrical patterns, they will push their own understanding of symmetry further and may well suprise you! It also provides an opportunity for children to discuss what makes one symmetrical pattern different, or the same as, another.

Possible approach

You could begin by displaying two sets of the triangles, each one coloured but only one of them coloured to create a symmetrical design. (You may want to recreate the two pictures on this sheet, or display these images directly on the interactive whiteboard.) Invite the children to look carefully at the images on their own for a moment, then talk to a partner about what they see.

Take suggestions from the class about what they notice. They may talk about the shapes they see, the colours, the number of colours, the number of triangles of each colour etc etc. Welcome all suggestions and if the idea of symmetry doesn't come up naturally, you may like to ask the group to look for differences between the two pictures. You can then set them off on the activity, perhaps by giving out copies of this sheet of the triangles. After a little while, give them time to share their designs with a partner so that the two children together confirm that each way of colouring does indeed have line symmetry.

Let them work further on their designs and then encourage each child to select just one to share with everyone at the end. (You could of course make an engaging display of these for the classroom wall.) The plenary can also be a time to bring up some points for discussion that might have arisen as the children worked. For example, did anyone create a design which had more than one line of symmetry? If we turn the design round, does that make a new design or is it the same?

Key questions

Where is the line of symmetry in this design?
How do you know it is a line of symmetry?
Have you tried with fewer/more colours?
Tell me about this design.

Possible extension

Encourage children to ask their own 'what if ...?' questions. For example, what would happen if there were more triangles? What would happen if I was only allowed to colour in triangles on the bottom 'row'? What would happen if I joined two of the triangle designs together?

Possible support

Many children will be happier if they draw in the line of symmetry. You could also have mirrors available for those that want them. Some learners may want to cut out their triangles and try to fold them to check the mirror lines.