Being curious

Can you find the values at the vertices when you know the values on the edges?

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

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?

Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

If you move the tiles around, can you make squares with different coloured edges?

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?

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

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?