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

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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

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?

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

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?

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

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

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.

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

Can you use this information to work out Charlie's house number?

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

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?

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.

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

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

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?

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?

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?

If you had 36 cubes, what different cuboids could you make?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

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

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

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

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.

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?

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

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?

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?

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.

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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?

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?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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?

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

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?

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?

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

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?

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?

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?

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?

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?

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.