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?

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

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?

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 will you go about finding all the jigsaw pieces that have one peg and one hole?

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

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

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

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

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 cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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. . . .

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

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?

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

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?

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

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

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

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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 outline of this brazier for roasting chestnuts?

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

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

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

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

Can you make a 3x3 cube with these shapes made from small cubes?

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

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 outline of Wai Ping, Wah Ming and Chi Wing?

Can you use the interactive to complete the tangrams in the shape of butterflies?

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 this goat and giraffe?

Can you fit the tangram pieces into the outline of these rabbits?

Can you logically construct these silhouettes using the tangram pieces?

Can you fit the tangram pieces into the outline of these convex shapes?

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

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 the telescope and microscope?

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

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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

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 the candle and sundial?

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

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 ...

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