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.
Play this game and see if you can figure out the computer's chosen number.
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
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?
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?
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.
Here is a chance to play a version of the classic Countdown Game.
Given the products of adjacent cells, can you complete this Sudoku?
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?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
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?
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?
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?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Resources to support understanding of multiplication and division through playing with number.
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?
Can you work out what a ziffle is on the planet Zargon?
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?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Find the number which has 8 divisors, such that the product of the divisors is 331776.
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?
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.
When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.
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?
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.
Number problems at primary level that may require resilience.
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Can you find different ways of creating paths using these paving slabs?
When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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!
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?