Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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 complete this jigsaw of the multiplication square?
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?
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?
Given the products of adjacent cells, can you complete this Sudoku?
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.
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.
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?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Here is a chance to play a version of the classic Countdown Game.
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.
A game that tests your understanding of remainders.
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?
56 406 is the product of two consecutive numbers. What are these
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Choose a symbol to put into the number sentence.
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!
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Can you replace the letters with numbers? Is there only one
solution in each case?
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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 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 group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?