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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?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
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.
If the answer's 2010, what could the question be?
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 happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
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.
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 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?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Use the information to work out how many gifts there are in each pile.
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.
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
Here is a picnic that Chris and Michael are going to share equally. Can you tell us what each of them will have?
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?
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?
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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 making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
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 happening at each box in these machines?
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?
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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?
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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!
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
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?
Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.
How would you count the number of fingers in these pictures?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?