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?

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

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

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

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?

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

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?

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

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?

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?

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

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.

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

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?

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

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

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?

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

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.

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

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

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

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

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

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

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.

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

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?

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

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

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

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

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

Complete the squares - but be warned some are trickier than they look!

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

Noah saw 12 legs walk by into the Ark. How many creatures did he see?

How could you estimate the number of pencils/pens in these pictures?

Sort the houses in my street into different groups. Can you do it in any other ways?

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

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

This investigates one particular property of number by looking closely at an example of adding two odd numbers together.

"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 ...?

This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?