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?

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

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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

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?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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

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.

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

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 is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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

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

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

"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 ...?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Can you use the information to find out which cards I have used?

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

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 possible answers?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

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

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

This problem is designed to help children to learn, and to use, the two and three times tables.

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

Here are some pictures of 3D shapes made from cubes. Can you make these shapes yourself?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

There are six numbers written in five different scripts. Can you sort out which is which?

An activity centred around observations of dots and how we visualise number arrangement patterns.

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?