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Reasoning about the number of matches needed to build squares that share their sides.

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In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.

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Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.

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Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.

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Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

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Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

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Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

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Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?

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In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

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Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

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When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

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Can you complete this jigsaw of the multiplication square?

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We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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Susie took cherries out of a bowl by following a certain pattern. How many cherries had there been in the bowl to start with if she was left with 14 single ones?

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A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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These alphabet bricks are painted in a special way. A is on one brick, B on two bricks, and so on. How many bricks will be painted by the time they have got to other letters of the alphabet?

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These grids are filled according to some rules - can you complete them?

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Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

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Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

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Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

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What's the greatest number of sides a polygon on a dotty grid could have?

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Can you find a way to identify times tables after they have been shifted up or down?