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.

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.

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

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

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....?

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

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

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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.

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

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

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?

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?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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?

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

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

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

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

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

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

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

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

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?

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

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?

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?

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

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

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Using the statements, can you work out how many of each type of rabbit there are in these pens?

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

In how many ways can you stack these rods, following the rules?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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

Investigate the different ways you could split up these rooms so that you have double the number.

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?