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Three Squares

What is the greatest number of squares you can make by overlapping three squares?

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Chain of Changes

Arrange the shapes in a line so that you change either colour or shape in the next piece along. Can you find several ways to start with a blue triangle and end with a red circle?

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Halving

These pictures show squares split into halves. Can you find other ways?

Tangrams

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

The tangram is based on the dissection of a square into seven pieces.
Can you make other squares using some, not all, of the pieces?
Can you make five different squares?
What is the smallest square you can make?
What is the largest?
Tangram Image

You might find it helpful to print and cut out one of the tangrams on this sheet .

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.