This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

How many starfish could there be on the beach, and how many children, if I can see 28 arms?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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.

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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

Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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

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

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

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?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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

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?

Are you resilient enough to solve these number problems?

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

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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

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

Number problems at primary level that require careful consideration.

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

Can you find different ways of creating paths using these paving slabs?

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

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?

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

More resources to support understanding multiplication and division through playing with numbers

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?