This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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

Number problems at primary level that require careful consideration.

It's Sahila's birthday and she is having a party. How could you answer these questions using a picture, with things, with numbers or symbols?

How will you work out which numbers have been used to create this multiplication square?

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?

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

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

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?

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

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

This task combines spatial awareness with addition and multiplication.

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?

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

Number problems at primary level that may require resilience.

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

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

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

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

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

Find the next number in this pattern: 3, 7, 19, 55 ...

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

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

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?

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

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?

How would you find out how many football cards Catrina has collected?

There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

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

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

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

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.

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?

This challenge combines addition, multiplication, perseverance and even proof.

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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?

Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?

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

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?

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?

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

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

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