Exploring and noticing

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

Explore the relationship between resistance and temperature

Alison and Charlie are playing a game. Charlie wants to go first so Alison lets him. Was that such a good idea?

How would you sort out these integrals?

Which numbers can we write as a sum of square numbers?

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?