In how many ways can you fit all three pieces together to make shapes with line symmetry?

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

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?

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

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

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

What is the minimum number of squares a 13 by 13 square can be dissected into?

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

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?

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

Can you work out how these polygon pictures were drawn, and use that to figure out their angles?

How many different symmetrical shapes can you make by shading triangles or squares?

See if you can anticipate successive 'generations' of the two animals shown here.

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

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

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

A huge wheel is rolling past your window. What do you see?

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

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

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

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

When dice land edge-up, we usually roll again. But what if we didn't...?

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

Can you find a way of representing these arrangements of balls?

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

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

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?

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

Can you mark 4 points on a flat surface so that there are only two different distances between them?

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.

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.

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

If you move the tiles around, can you make squares with different coloured edges?

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. . . .

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

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?

A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

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

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.

Can you describe this route to infinity? Where will the arrows take you next?

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

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

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