Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Choose a symbol to put into the number sentence.
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
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.
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?
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 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,. . . .
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!
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
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?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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!
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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.
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Use the information to work out how many gifts there are in each
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 group activity will encourage you to share calculation
strategies and to think about which strategy might be the most
Find the next number in this pattern: 3, 7, 19, 55 ...
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.
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
This number has 903 digits. What is the sum of all 903 digits?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
If the answer's 2010, what could the question be?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
What is happening at each box in these machines?
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?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.