This problem is designed to help children to learn, and to use, the two and three times tables.
After training hard, these two children have improved their
results. Can you work out the length or height of their first
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
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?
56 406 is the product of two consecutive numbers. What are these
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.
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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?
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 work out what a ziffle is on the planet Zargon?
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?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Grandma found her pie balanced on the scale with two weights and a
quarter of a pie. So how heavy was each pie?
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?
The triangles in these sets are similar - can you work out the
lengths of the sides which have question marks?
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?
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.
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?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
On Friday the magic plant was only 2 centimetres tall. Every day it
doubled its height. How tall was it on Monday?
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?
This activity focuses on doubling multiples of five.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Bernard Bagnall recommends some primary school problems which use
numbers from the environment around us, from clocks to house
What is the sum of all the three digit whole numbers?
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?
Can you work out some different ways to balance this equation?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
Go through the maze, collecting and losing your money as you go.
Which route gives you the highest return? And the lowest?
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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.
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Find the next number in this pattern: 3, 7, 19, 55 ...
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.