Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
Can you work out some different ways to balance this equation?
56 406 is the product of two consecutive numbers. What are these
This problem is designed to help children to learn, and to use, the two and three times tables.
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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.
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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?
On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
There were 22 legs creeping across the web. How many flies? How many spiders?
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Can you complete this jigsaw of the multiplication square?
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?
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?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
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?
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.
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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.
Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
What is the sum of all the three digit whole numbers?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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?
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?
Can you replace the letters with numbers? Is there only one
solution in each case?
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 triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
This activity focuses on doubling multiples of five.
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?
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
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house