Create a pattern on the left-hand grid. How could you extend your pattern on the right-hand grid?

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

How many loops of string have been used to make these patterns?

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

Here is your chance to investigate the number 28 using shapes, cubes ... in fact anything at all.

Can you sort these triangles into three different families and explain how you did it?

Try to picture these buildings of cubes in your head. Can you make them to check whether you had imagined them correctly?

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?

Can you split each of the shapes below in half so that the two parts are exactly the same?

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?

This interactivity allows you to sort logic blocks by dragging their images.

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.