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,. . . .
A game that tests your understanding of remainders.
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you complete this jigsaw of the multiplication square?
Choose a symbol to put into the number sentence.
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.
Imagine a pyramid which is built in square layers of small cubes.
If we number the cubes from the top, starting with 1, can you
picture which cubes are directly below this first cube?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
Here is a chance to play a version of the classic Countdown Game.
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
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?
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?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Given the products of adjacent cells, can you complete this Sudoku?
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
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.
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?
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?
Can you replace the letters with numbers? Is there only one
solution in each case?
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Use your logical-thinking skills to deduce how much Dan's crisps
and ice-cream cost altogether.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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.
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
A game for 2 or more players with a pack of cards. Practise your
skills of addition, subtraction, multiplication and division to hit
the target score.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
56 406 is the product of two consecutive numbers. What are these
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
These eleven shapes each stand for a different number. Can you use
the multiplication sums to work out what they are?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
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?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Unmultiply is a game of quick estimation. You need to find two
numbers that multiply together to something close to the given
target - fast! 10 levels with a high scores table.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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?
Can you work out what a ziffle is on the planet Zargon?
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?
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.