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Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Counting Factors

Is there an efficient way to work out how many factors a large number has?

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Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Alison's Quilt

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


Alison joins together nine squares with side lengths $1, 4, 7, 8, 9, 10, 14, 15$ and $18$ cm with no gaps and no overlaps, to form a rectangular quilt.

Can you find the dimensions of the finished quilt, and show how Alison fitted the squares together?


Alison wants to make a second quilt from ten squares with side lengths $3, 5, 6, 11, 17, 19, 22, 23, 24$ and $25$ cm.

Can you find the dimensions of this quilt?