Resources to support understanding of multiplication and division through playing with number.
Given the products of adjacent cells, can you complete this Sudoku?
Have a go at balancing this equation. Can you find different ways of doing it?
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.
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 work out some different ways to balance this equation?
Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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 complete this jigsaw of the multiplication square?
This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
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.
Can you work out what a ziffle is on the planet Zargon?
The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?
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 replace the letters with numbers? Is there only one solution in each case?
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
Number problems at primary level that require careful consideration.
Here is a chance to play a version of the classic Countdown Game.
Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.
Choose a symbol to put into the number sentence.
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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 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.
If the answer's 2010, what could the question be?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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?
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
What is happening at each box in these machines?
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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 group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
Can you each work out the number on your card? What do you notice? How could you sort the cards?