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?

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?

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

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

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?

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

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

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?

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

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?

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?

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

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.

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?

"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?

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

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?

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

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

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.

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

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

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

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

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?

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?

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 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?

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

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 ...

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

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

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?

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

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?

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

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?

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

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?

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

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

This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

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?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?