Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
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.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Here is a chance to play a version of the classic Countdown Game.
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?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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!
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
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.
56 406 is the product of two consecutive numbers. What are these two numbers?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
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.
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,. . . .
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.
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?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
Ben’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?
What is the sum of all the three digit whole numbers?
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?
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?
Resources to support understanding of multiplication and division through playing with number.
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?
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 clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
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.
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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?
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 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!
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?
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?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
What is happening at each box in these machines?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Can you find different ways of creating paths using these paving slabs?
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?
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?
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?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.