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

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

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

Can you visualise what shape this piece of paper will make when it is folded?

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

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

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 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.

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. . . .

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

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 ...

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?

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

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

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?

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

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

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

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?

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

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

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

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

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

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?

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

Make a flower design using the same shape made out of different sizes of paper.

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?

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 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?

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?

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?

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

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

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

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

Can you cut up a square in the way shown and make the pieces into a triangle?

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?

How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 cube that is green all over AND a 2 x 2 cube that is yellow all over?

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

Exploring and predicting folding, cutting and punching holes and making spirals.

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

What shape is made when you fold using this crease pattern? Can you make a ring design?

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

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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

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