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Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

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Paving the Way

A man paved a square courtyard and then decided that it was too small. He took up the tiles, bought 100 more and used them to pave another square courtyard. How many tiles did he use altogether?

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Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

Hidden Rectangles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Picture of rectangles

Rectangles are considered different if they vary in size or have different locations.

How many different rectangles can be drawn on a chessboard?

How many of the rectangles are squares?

What happens on an n by n board?


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.