Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

Use the information to work out how many gifts there are in each pile.

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

There were 22 legs creeping across the web. How many flies? How many spiders?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

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?

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

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

Can you score 100 by throwing rings on this board? Is there more than way to do it?

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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 number has 903 digits. What is the sum of all 903 digits?

Here is a chance to play a version of the classic Countdown Game.

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

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

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

56 406 is the product of two consecutive numbers. What are these two numbers?

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

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

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

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

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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?