What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
You have 5 darts and your target score is 44. How many different
ways could you score 44?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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!
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?
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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!
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?
Can you draw a square in which the perimeter is numerically equal
to the area?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
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 task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
An investigation that gives you the opportunity to make and justify
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.
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
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Can you use this information to work out Charlie's house number?
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?
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
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?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Number problems at primary level that require careful consideration.
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
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?
Can you substitute numbers for the letters in these sums?
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?