Is there an efficient way to work out how many factors a large number has?
Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
There are lots of ideas to explore in these sequences of ordered fractions.
A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?
If you move the tiles around, can you make squares with different coloured edges?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
Can you work out what step size to take to ensure you visit all the dots on the circle?
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...
