A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

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

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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

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

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

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

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 cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?

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. . . .

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?

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?

A triangle ABC resting on a horizontal line is "rolled" along the line. Describe the paths of each of the vertices and the relationships between them and the original triangle.

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

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

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

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

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

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

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

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

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?

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

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

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

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

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

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

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

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

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?

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?

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

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

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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

Can you fit the tangram pieces into the outline of the child walking home from school?

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

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 watering can and man in a boat?

Each of the nets of nine solid shapes has been cut into two pieces. Can you see which pieces go together?

Which of these dice are right-handed and which are left-handed?

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

Reasoning about the number of matches needed to build squares that share their sides.

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. . . .

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

Can you fit the tangram pieces into the outlines of the candle and sundial?