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?

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?

Join pentagons together edge to edge. Will they form a ring?

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 fit the tangram pieces into the outline of the house?

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.

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.

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

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 ...

Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.

Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?

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

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

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

ABC is an equilateral triangle and P is a point in the interior of the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP must be less than 10 cm.

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

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

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

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?

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

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?

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

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

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

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

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?

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

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

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

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

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

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

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

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.

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?

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?

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 sports car?

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 Mah Ling and Chi Wing?