Try to picture these buildings of cubes in your head. Can you make them to check whether you had imagined them correctly?
Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?
Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?
How many pieces of string have been used in these patterns? Can you describe how you know?
How many loops of string have been used to make these patterns?
Can you describe a piece of paper clearly enough for your partner to know which piece it is?
Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.
This second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.
Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!
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 Mah Ling?
How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 x 2 cube that is green all over AND a 2 x 2 x 2 cube that is yellow all over?
Here are shadows of some 3D shapes. What shapes could have made them?
Can you fit the tangram pieces into the outline of this teacup?
Can you fit the tangram pieces into the outline of the butterfly?
Can you cut up a square in the way shown and make the pieces into a triangle?
Move four sticks so there are exactly four triangles.
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 fit the tangram pieces into the outlines of the people?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Exploring and predicting folding, cutting and punching holes and making spirals.
Can you fit the tangram pieces into the outline of the house?
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?
This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?
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.
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.
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.
You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
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 convex shapes?
How many balls of modelling clay and how many straws does it take to make these skeleton shapes?
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
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.
Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?
Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?
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?
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 candle?
This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.
We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?
Can you fit the tangram pieces into the outline of the brazier for roasting chestnuts?
Can you fit the tangram pieces into the outline of the telephone?
One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?
Can you fit the tangram pieces into the outlines of the camel and giraffe?
Read about the adventures of Granma T and her grandchildren in this series of stories, accompanied by interactive tangrams.
Can you fit the tangram pieces into the outlines of Wai Ping, Wu Ming and Chi Wing?
Can you fit the tangram pieces into the outline of the dragon?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of the rabbits?