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?
Number problems at primary level that may require resilience.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Can you work out what a ziffle is on the planet Zargon?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
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.
56 406 is the product of two consecutive numbers. What are these two numbers?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
What is the sum of all the three digit whole numbers?
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?
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?
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?
Given the products of adjacent cells, can you complete this Sudoku?
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?
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.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?
This challenge combines addition, multiplication, perseverance and even proof.
This task combines spatial awareness with addition and multiplication.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
Use the information to work out how many gifts there are in each pile.
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" .
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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. . . .
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
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?
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.
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?
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?
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?
What is happening at each box in these machines?
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 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!
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
This number has 903 digits. What is the sum of all 903 digits?
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?
Here is a chance to play a version of the classic Countdown Game.
Find the next number in this pattern: 3, 7, 19, 55 ...
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
How would you count the number of fingers in these pictures?
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?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Resources to support understanding of multiplication and division through playing with number.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Each clue in this Sudoku is the product of the two numbers in adjacent cells.