In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

Can you draw a square in which the perimeter is numerically equal to the area?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

Can you find all the different ways of lining up these Cuisenaire rods?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

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?

Try out the lottery that is played in a far-away land. What is the chance of winning?

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

How many ways can you find of tiling the square patio, using square tiles of different sizes?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

These practical challenges are all about making a 'tray' and covering it with paper.

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?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

In this matching game, you have to decide how long different events take.

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

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?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

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 is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?