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 split each of the shapes below in half so that the two parts are exactly the same?

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

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

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

What does the overlap of these two shapes look like? Try picturing it in your head and then use some cut-out shapes to test your prediction.

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

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

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?

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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 work out what shape is made when this piece of paper is folded up using the crease pattern shown?

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

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

How many different triangles can you make on a circular pegboard that has nine pegs?

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

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?

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?

Can you fit the tangram pieces into the outlines of Mah Ling and Chi Wing?

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

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

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

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 outline of the clock?

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

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

Can you logically construct these silhouettes using the tangram pieces?

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

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

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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?

Can you fit the tangram pieces into the silhouette of the junk?

Can you fit the tangram pieces into the outline of the plaque design?

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.

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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

Why do you think that the red player chose that particular dot in this game of Seeing Squares?

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

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

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

Can you fit the tangram pieces into the outlines of Little Ming and Little Fung dancing?

Can you fit the tangram pieces into the outline of Little Ming?

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 telescope and microscope?

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