An investigation that gives you the opportunity to make and justify
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
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!
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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 help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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.
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?
The challenge here is to find as many routes as you can for a fence
to go so that this town is divided up into two halves, each with 8
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
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.
On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
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 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
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
If you have three circular objects, you could arrange them so that
they are separate, touching, overlapping or inside each other. Can
you investigate all the different possibilities?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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?
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
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?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way
to share the sweets between the three children so they each get the
kind they like. Is there more than one way to do it?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
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?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?