Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
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?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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?
An old game but lots of arithmetic!
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
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!
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?
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?
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.
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
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?
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?
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Choose a symbol to put into the number sentence.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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!
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?
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?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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.
Can you replace the letters with numbers? Is there only one
solution in each case?
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.
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
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?
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.
Can you complete this jigsaw of the multiplication square?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
There were 22 legs creeping across the web. How many flies? How many spiders?
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
At the beginning of May Tom put his tomato plant outside. On the
same day he sowed a bean in another pot. When will the two be the
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?
How would you count the number of fingers in these pictures?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
Number problems at primary level that require careful consideration.
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?
Can you design a new shape for the twenty-eight squares and arrange
the numbers in a logical way? What patterns do you notice?