Being curious

Does it make any difference how we write powers of powers? 

Investigate the family of graphs given by the equation x^3+y^3=3axy for different values of the constant a.

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?

Can you fill in the empty boxes in the grid with the right shape and colour?

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

Here's a very elementary code that requires young children to read a table, and look for similarities and differences.

Investigate what happens when you add house numbers along a street in different ways.

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.