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

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

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 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?

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 ...

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

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

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

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!

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

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

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

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.

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

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?

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?

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

What shape is made when you fold using this crease pattern? Can you make a ring design?

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?

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

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Can you fit the tangram pieces into the outlines of the convex shapes?

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 outlines of the lobster, yacht and cyclist?

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

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

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

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

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?

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?

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

Can you fit the tangram pieces into the outline of the house?

Can you fit the tangram pieces into the outline of the butterfly?

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

Can you fit the tangram pieces into the outlines of Wai Ping, Wu Ming and Chi Wing?

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 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?

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

Can you fit the tangram pieces into the outline of the clock?

Can you fit the tangram pieces into the outline of the playing piece?

Can you fit the tangram pieces into the outlines of the camel and giraffe?

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.