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?

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?

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

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

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

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

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

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?

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

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

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

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

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?

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

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

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

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?

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

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

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?

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

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

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

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

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?

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....?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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.

An activity making various patterns with 2 x 1 rectangular tiles.

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

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.

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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?

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?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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?

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

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?

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?

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

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

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.

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?