If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

This challenge is about finding the difference between numbers which have the same tens digit.

My coat has three buttons. How many ways can you find to do up all the buttons?

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

What two-digit numbers can you make with these two dice? What can't you make?

What could the half time scores have been in these Olympic hockey matches?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

How many possible necklaces can you find? And how do you know you've found them all?

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Can you fill in the empty boxes in the grid with the right shape and colour?

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

Try this matching game which will help you recognise different ways of saying the same time interval.

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?

Ben has five coins in his pocket. How much money might he have?

Investigate the number of faces you can see when you arrange three cubes in different ways.

Find a great variety of ways of asking questions which make 8.

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?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

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?

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

Are these statements relating to odd and even numbers always true, sometimes true or never true?

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?