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?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

What happens when you try and fit the triomino pieces into these two grids?

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?

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?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

What is the best way to shunt these carriages so that each train can continue its journey?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

Find your way through the grid starting at 2 and following these operations. What number do you end on?

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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?

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Can you find ways of joining cubes together so that 28 faces are visible?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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?

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

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?

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.

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

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

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

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

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

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

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

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!

Here's a simple way to make a Tangram without any measuring or ruling lines.

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

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

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.

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

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 the lobster, yacht and cyclist?

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

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

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

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