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

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?

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.

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

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

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

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

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

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

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

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

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!

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?

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?

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

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?

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?

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

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.

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

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

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?

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.

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.

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

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!

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?

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

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?

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?

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.

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?

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

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.

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

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?

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

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

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?

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

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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?

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

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

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

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?

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?

How could you arrange at least two dice in a stack so that the total of the visible spots is 18?