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Cut it Out

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

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Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

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Tessellating Transformations

Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?

Regular Rings 1

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Below is a picture of an unfolded piece of paper. 
Can you work out what shape is made when it’s folded up using the crease pattern shown?

Click below if you want to see the shape.

Can you make one of these shapes with a new piece of paper?

Now make several of the same shape from A4, A5 and A6 pieces of paper in two contrasting colours.

Challenge 1
Take a large and small shape made from your first colour and a medium shape made from your second colour.

Make a pattern from your shapes, by laying them on top of each other, that fits both of these rules:
You must be able to see at least part of each shape.
All three shapes must fit inside the perimeter (outline) of the largest shape.

Challenge 2
Use a new large, medium and small shape to recreate the same pattern but in opposite colours from Challenge 1.

Place these two patterns next to each other and continue to fold and add to your pattern until you’ve made a ring. 

Can you predict how many of your original Challenge 1 pattern you will need?

We would love to see photos of the ring you make.

If you enjoyed these challenges, why not have a go at Regular Rings 2?