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

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

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

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?

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

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

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 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?

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

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

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

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

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 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?

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

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

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

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 outline of Mai Ling?

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.

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

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?

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

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

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

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?

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

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 Granma T?

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!

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

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

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 the child walking home from school?

On which of these shapes can you trace a path along all of its edges, without going over any edge twice?

Can you fit the tangram pieces into the outline of these rabbits?

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Can you work out what is wrong with the cogs on a UK 2 pound coin?

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?

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

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

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

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

Exchange the positions of the two sets of counters in the least possible number of moves