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?
Here is a chance to play a version of the classic Countdown Game.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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.
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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 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?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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.
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
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!
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?
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?
Resources to support understanding of multiplication and division through playing with number.
Can you work out what a ziffle is on the planet Zargon?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Choose a symbol to put into the number sentence.
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
Can you replace the letters with numbers? Is there only one solution in each case?
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you complete this jigsaw of the multiplication square?
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!
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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?
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. . . .
What is happening at each box in these machines?
Put a number at the top of the machine and collect a number at the
bottom. What do you get? Which numbers get back to themselves?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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.
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?
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.
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?
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?
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?
The Man is much smaller than us. Can you use the picture of him
next to a mug to estimate his height and how much tea he drinks?
Use this grid to shade the numbers in the way described. Which
numbers do you have left? Do you know what they are called?
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,. . . .
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
An old game but lots of arithmetic!
Number problems at primary level that require careful consideration.