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?
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.
An investigation that gives you the opportunity to make and justify
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
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Place the 16 different combinations of cup/saucer in this 4 by 4
arrangement so that no row or column contains more than one cup or
saucer of the same colour.
Can you draw a square in which the perimeter is numerically equal
to the area?
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
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?
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?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
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?
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?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
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.
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
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?
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?
Given the products of adjacent cells, can you complete this Sudoku?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
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?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
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?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?