What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.

Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?

Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

There were lots of patterns to notice and explain in this problem. Have a look at the solutions we received.

In this article for teachers, Alan Parr looks at ways that mathematics teaching and learning can start from the useful and interesting things can we do with the subject, including modelling scientific enquiry.

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.