Reasoning about the number of matches needed to build squares that share their sides.

Can you visualise what shape this piece of paper will make when it is folded?

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

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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

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

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

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?

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

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

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 candle and sundial?

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

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

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

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

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

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.

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

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

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

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

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

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!

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

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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?

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?

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?

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.

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 ...

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

Can you fit the tangram pieces into the outline of Mai Ling?

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

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

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

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

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

Make a flower design using the same shape made out of different sizes of paper.

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

Can you fit the tangram pieces into the outline of Little Fung at the table?

This article for teachers describes a project which explores thepower of storytelling to convey concepts and ideas to children.

Can you fit the tangram pieces into the outline of this plaque design?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?

Square It game for an adult and child. Can you come up with a way of always winning this game?