Being curious

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: ×2 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?

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

There are lots of ideas to explore in these sequences of ordered fractions.

Can you maximise the area available to a grazing goat?

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

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?

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

Can you work out what step size to take to ensure you visit all the dots on the circle?