Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
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?
Number problems at primary level that require careful consideration.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Can you substitute numbers for the letters in these sums?
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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!
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
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!
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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?
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?
This challenge is about finding the difference between numbers which have the same tens digit.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
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?
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!
What happens when you round these three-digit numbers to the nearest 100?
This activity focuses on rounding to the nearest 10.
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
What two-digit numbers can you make with these two dice? What can't you make?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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 to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Can you work out some different ways to balance this equation?
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?
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 challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
What happens when you round these numbers to the nearest whole number?
Explore the different snakes that can be made using 5 cubes.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
This train line has two tracks which cross at different points. Can
you find all the routes that end at Cheston?
Can you make square numbers by adding two prime numbers together?