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?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

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

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. . . .

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

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!

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?

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?

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.

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

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?

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?

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.

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

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

How would you count the number of fingers in these pictures?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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

Number problems at primary level that require careful consideration.

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?

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.

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

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

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

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

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?

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

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.

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?

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?

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

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

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

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?

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

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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

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

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

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

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?

Number problems at primary level that may require resilience.

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?

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

Resources to support understanding of multiplication and division through playing with number.