Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
Mr. Sunshine tells the children they will have 2 hours of homework.
After several calculations, Harry says he hasn't got time to do
this homework. Can you see where his reasoning is wrong?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
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?
What is the sum of all the three digit whole numbers?
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?
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?
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
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?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
Resources to support understanding of multiplication and division through playing with number.
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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.
This problem is designed to help children to learn, and to use, the two and three times tables.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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 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?
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?
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.
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?
Use the information to work out how many gifts there are in each
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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!
Can you arrange 5 different digits (from 0 - 9) in the cross in the
EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.
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?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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?
This number has 903 digits. What is the sum of all 903 digits?
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?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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.
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? What do you think is happening to the numbers?
Can you work out what a ziffle is on the planet Zargon?
This challenge combines addition, multiplication, perseverance and even proof.