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

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

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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?

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

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

You have 5 darts and your target score is 44. How many different ways could you score 44?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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?

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

An investigation that gives you the opportunity to make and justify predictions.

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?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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.

This task follows on from Build it Up and takes the ideas into three dimensions!

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

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Can you find all the ways to get 15 at the top of this triangle of numbers?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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?

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

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?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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

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

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

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

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

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

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

These two group activities use mathematical reasoning - one is numerical, one geometric.

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?