Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Can you draw a square in which the perimeter is numerically equal
to the area?
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
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
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?
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.
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?
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
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?
Can you use this information to work out Charlie's house number?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
If you had 36 cubes, what different cuboids could you make?
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?
How many triangles can you make on the 3 by 3 pegboard?
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
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?
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?
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?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
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
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
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?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
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.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using 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!
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?