This article for teachers describes how modelling number properties
involving multiplication using an array of objects not only allows
children to represent their thinking with concrete materials,. . . .
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
Can you replace the letters with numbers? Is there only one
solution in each case?
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?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you work out some different ways to balance this equation?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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?
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!
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Can you complete this jigsaw of the multiplication square?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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.
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?
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?
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?
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
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.
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
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?
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?
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
How would you count the number of fingers in these pictures?
Mathematicians are always looking for efficient methods for solving problems. How efficient can you 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?
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Resources to support understanding of multiplication and division through playing with number.
This problem is designed to help children to learn, and to use, the two and three times tables.
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?
After training hard, these two children have improved their
results. Can you work out the length or height of their first
Here is a chance to play a version of the classic Countdown Game.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Given the products of adjacent cells, can you complete this Sudoku?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.