Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
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?
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 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.
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
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
Choose a symbol to put into the number sentence.
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?
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!
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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. . . .
Twizzle, a female giraffe, needs transporting to another zoo. Which
route will give the fastest journey?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?
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?
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?
Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?
There were 22 legs creeping across the web. How many flies? How many spiders?
Number problems at primary level that require careful consideration.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
An old game but lots of arithmetic!
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
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?
Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
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?
Here is a chance to play a version of the classic Countdown Game.
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
Can you replace the letters with numbers? Is there only one
solution in each case?
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
If the answer's 2010, what could the question be?
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 clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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 work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?