These eleven shapes each stand for a different number. Can you use
the multiplication sums to work out what they are?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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?
In this game, you can add, subtract, multiply or divide the numbers
on the dice. Which will you do so that you get to the end of the
number line first?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
Use the information to work out how many gifts there are in each
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 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 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!
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
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?
The value of the circle changes in each of the following problems.
Can you discover its value in each problem?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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!
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
Choose a symbol to put into the number sentence.
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Can you complete this jigsaw of the multiplication square?
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.
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.
Annie and Ben are playing a game with a calculator. What was
Annie's secret number?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you replace the letters with numbers? Is there only one
solution in each case?
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?
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?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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?
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.
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
On a calculator, make 15 by using only the 2 key and any of the
four operations keys. How many ways can you find to do it?
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?
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,. . . .
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
Can you each work out the number on your card? What do you notice?
How could you sort the cards?