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?
Choose a symbol to put into the number sentence.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you complete this jigsaw of the multiplication square?
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?
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?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
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?
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?
Here is a chance to play a version of the classic Countdown Game.
Can you replace the letters with numbers? Is there only one
solution in each case?
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
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.
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 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.
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?
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.
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?
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!
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
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?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
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?
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?
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
These eleven shapes each stand for a different number. Can you use
the multiplication sums to work out what they are?
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?
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.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
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?
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?
What is the sum of all the three digit whole numbers?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.