Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
Use the information to work out how many gifts there are in each pile.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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.
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
This challenge combines addition, multiplication, perseverance and even proof.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Can you find different ways of creating paths using these paving slabs?
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
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?
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?
This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.
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!
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 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?
What is happening at each box in these machines?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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'.
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?
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
This task combines spatial awareness with addition and multiplication.
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
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.
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?
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?
Resources to support understanding of multiplication and division through playing with number.
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
How would you count the number of fingers in these pictures?
Can you each work out the number on your card? What do you notice? How could you sort the cards?
If the answer's 2010, what could the question be?
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?
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.
During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
Number problems at primary level that require careful consideration.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Number problems at primary level that may require resilience.
This number has 903 digits. What is the sum of all 903 digits?