Can you put these shapes in order of size? Start with the smallest.

These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

What is the largest cuboid you can wrap in an A3 sheet of paper?

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

If I print this page which shape will require the more yellow ink?

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

Can you find the area of a parallelogram defined by two vectors?

How much peel does an apple have?

An inequality involving integrals of squares of functions.

Several of you from different schools clearly explained how you used the charts to sort out the data.

Ken has solved the first part of this problem. Can anyone now suggest a general rule?

Samantha from Hamlin used the Find & Replace feature in Word and then some sharp thinking to unpick the cipher text

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain why the pattern occurs.

This article for teachers gives some food for thought when teaching ideas about area.

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

This article, written for teachers, discusses the merits of different kinds of resources: those which involve exploration and those which centre on calculation.