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?
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?
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?
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.
Make a flower design using the same shape made out of different sizes of paper.
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?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
What is the greatest number of squares you can make by overlapping three squares?
Make a cube out of straws and have a go at this practical challenge.
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?
How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
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.
Reasoning about the number of matches needed to build squares that share their sides.
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?
Can you fit the tangram pieces into the outline of Little Ming?
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 kind of rotation produced this pattern of pegs in our pegboard?
Can you fit the tangram pieces into the outline of Granma T?
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 fit the tangram pieces into the outlines of these people?
Exchange the positions of the two sets of counters in the least possible number of moves
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outline of the rocket?
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 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 outline of Little Fung at the table?
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?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Try this interactive strategy game for 2
Exploring and predicting folding, cutting and punching holes and making spirals.
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!
Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?
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 ...
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
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 work out what is wrong with the cogs on a UK 2 pound coin?
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.
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?
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.