Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

Think of a number, square it and subtract your starting number. Is the number youâ€™re left with odd or even? How do the images help to explain this?

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

How many moves does it take to swap over some red and blue frogs? Do you have a method?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

Can you cut up a square in the way shown and make the pieces into a triangle?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Exploring and predicting folding, cutting and punching holes and making spirals.

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

How many different triangles can you make on a circular pegboard that has nine pegs?

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 cube that is green all over AND a 2 x 2 cube that is yellow all over?

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

Can you fit the tangram pieces into the outlines of the candle and sundial?

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

What is the greatest number of squares you can make by overlapping three squares?

Which of these dice are right-handed and which are left-handed?

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

Make a cube out of straws and have a go at this practical challenge.

Can you fit the tangram pieces into the outlines of the chairs?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outline of Little Ming?

Can you fit the tangram pieces into the outline of Granma T?

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

In how many ways can you fit all three pieces together to make shapes with line symmetry?

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

Can you fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outlines of these clocks?

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.

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

Can you fit the tangram pieces into the outline of this telephone?

Can you fit the tangram pieces into the outline of Little Ming playing the board game?