In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

What fractions can you divide the diagonal of a square into by simple folding?

The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?

Can you find the area of the central part of this shape? Can you do it in more than one way?

Match the charts of these functions to the charts of their integrals.

We had some interesting explanations and comments on this unusual way of representing division.

Ideas to support mathematics teachers who are committed to nurturing confident, resourceful and enthusiastic learners.

Hilbert's Hotel has an infinite number of rooms, and yet, even when it's full, it can still fit more people in!