Number problems at primary level that require careful consideration.
Resources to support understanding of multiplication and division through playing with number.
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.
Can you complete this jigsaw of the multiplication square?
Have a go at balancing this equation. Can you find different ways of doing it?
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?
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?
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?
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 why 2 by 2 could be 5? Can you predict what 2 by 10
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
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?
Can you replace the letters with numbers? Is there only one
solution in each case?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you work out what a ziffle is on the planet Zargon?
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 is a chance to play a version of the classic Countdown Game.
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
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?
Choose a symbol to put into the number sentence.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
A game that tests your understanding of remainders.
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.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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.
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?
Given the products of adjacent cells, can you complete this Sudoku?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
When the number x 1 x x x is multiplied by 417 this gives the
answer 9 x x x 0 5 7. Find the missing digits, each of which is
represented by an "x" .
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
When I type a sequence of letters my calculator gives the product
of all the numbers in the corresponding memories. What numbers
should I store so that when I type 'ONE' it returns 1, and when I
type. . . .
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.
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
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,. . . .
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
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!
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?