In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

Can you complete this jigsaw of the multiplication square?

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

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

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

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?

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?

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

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

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

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?

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

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

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?

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

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.

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.

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

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?

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

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

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

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

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!

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

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

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

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

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

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

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

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

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?

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

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 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?

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

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

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,. . . .