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

What can you see? What do you notice? What questions can you ask?

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?

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

Here are four tiles. They can be arranged in a 2 by 2 square so that this large square has a green edge. If the tiles are moved around, we can make a 2 by 2 square with a blue edge... Now try to. . . .

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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?

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

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?

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?

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?

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. . . .

Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?

Is it true that any convex hexagon will tessellate if it has a pair of opposite sides that are equal, and three adjacent angles that add up to 360 degrees?

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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 fit the tangram pieces into the outline of these rabbits?

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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

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?

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

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

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

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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

A game for 2 people. Take turns joining two dots, until your opponent is unable to move.

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

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

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.

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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?

What is the shape of wrapping paper that you would need to completely wrap this model?

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

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

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?

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .

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

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

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

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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 Ming and Little Fung dancing?

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

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