In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.
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?
Number problems at primary level that require careful consideration.
Number problems at primary level that may require resilience.
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
Find the next number in this pattern: 3, 7, 19, 55 ...
There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
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.
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?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
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 score 100 by throwing rings on this board? Is there more than way to do it?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
What is the sum of all the three digit whole numbers?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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?
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?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
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?
Resources to support understanding of multiplication and division through playing with number.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
How will you decide which way of flipping over and/or turning the grid will give you the highest total?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
Can you work out what a ziffle is on the planet Zargon?
Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?
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 combines addition, multiplication, perseverance and even proof.
This task combines spatial awareness with addition and multiplication.
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.
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. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?
The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
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,. . . .
This number has 903 digits. What is the sum of all 903 digits?
If the answer's 2010, what could the question be?