Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .

It is possible to dissect any square into smaller squares. What is the minimum number of squares a 13 by 13 square can be dissected into?

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?

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

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

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

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

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

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

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

How can you make an angle of 60 degrees by folding a sheet of paper twice?

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

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

Can you fit the tangram pieces into the outline of the telescope and microscope?

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?

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

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

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

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

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

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?

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

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

In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .

Can you fit the tangram pieces into the outline of this sports car?

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

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?

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?

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.

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

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

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

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 these convex shapes?

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

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

Here's a simple way to make a Tangram without any measuring or ruling lines.

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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?

Can you fit the tangram pieces into the outline of this goat and giraffe?

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

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 Ming and Little Fung dancing?