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Four Triangles Puzzle

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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Transformations on a Pegboard

How would you move the bands on the pegboard to alter these shapes?

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Inside Seven Squares

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

Cutting Corners

Stage: 2 Challenge Level: Challenge Level:1

There are lots of answers to this problem, depending on what questions you choose to ask.

Have a go yourself, and if you discover anything interesting, e-mail us to tell us what you've done! Please don't worry that your solution is not "complete" - we'd like to hear about anything you have tried. Teachers - you might like to send in a summary of your children's work.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.