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Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Cut and Make

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

Midpoint Triangle

Can you cut up a square in the way shown and make the pieces into a triangle?

Square to L

Age 7 to 11
Challenge Level

Why do this problem?

This activity is an accessible piece of spatial-awareness work and will encourage children to visualise.

Possible approach

Each child should be given the opportunity to start this with some practical resources, for example paper, card, plastic squares etc.

Key questions

How are you finding your solutions?
Show me how the cut-off piece fits so that we get an "L" shape.

Possible extension

Try other even-sized squares - and afterwards look at the Solutions !
Some pupils may like to have a go at 'near' solutions that do not work, saying precisely why they do not.

Possible support

Some pupils may need adult help in trying to cut out the shapes to see if they work.