Have a go at balancing this equation. Can you find different ways of doing it?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

Can you work out some different ways to balance this equation?

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

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

Can you replace the letters with numbers? Is there only one solution in each case?

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

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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?

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

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

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

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?

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

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?

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

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?

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?

On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?

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

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.

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

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

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.

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?

Can you complete this jigsaw of the multiplication square?

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

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,. . . .

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

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

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

A game that tests your understanding of remainders.

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

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

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

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?

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

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!

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

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.

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

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

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?

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.

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?