What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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 arrange 5 different digits (from 0 - 9) in the cross in the
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
An investigation that gives you the opportunity to make and justify
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
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!
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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 find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
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!
Can you draw a square in which the perimeter is numerically equal
to the area?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
Can you substitute numbers for the letters in these sums?
Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Number problems at primary level that require careful consideration.
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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?
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
Can you use this information to work out Charlie's house number?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you make square numbers by adding two prime numbers together?
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?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
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?
Investigate all the different squares you can make on this 5 by 5
grid by making your starting side go from the bottom left hand
point. Can you find out the areas of all these squares?
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.