Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
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?
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?
What is the greatest number of squares you can make by overlapping three squares?
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?
Can you cut up a square in the way shown and make the pieces into a triangle?
Try this interactive strategy game for 2
Exploring and predicting folding, cutting and punching holes and making spirals.
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 Mai Ling?
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
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 shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
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.
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.
What is the best way to shunt these carriages so that each train can continue its journey?
10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
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.
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.
Can you work out what is wrong with the cogs on a UK 2 pound coin?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of Granma T?
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 the child walking home from school?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
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 ...
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 this shape. How would you describe it?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of Little Ming playing the board game?
Can you fit the tangram pieces into the outline of this plaque design?
Exchange the positions of the two sets of counters in the least possible number of moves
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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 flower design using the same shape made out of different sizes of paper.
Can you fit the tangram pieces into the outline of this telephone?
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!
Can you fit the tangram pieces into the outline of Little Ming?
Make a cube out of straws and have a go at this practical challenge.
Can you work out what kind of rotation produced this pattern of pegs in our pegboard?
This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .
Here's a simple way to make a Tangram without any measuring or ruling lines.
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.