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?
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 draw a square in which the perimeter is numerically equal
to the area?
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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
Sally and Ben were drawing shapes in chalk on the school
playground. Can you work out what shapes each of them drew using
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
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 have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
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?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Can you find all the different ways of lining up these Cuisenaire
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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
In this matching game, you have to decide how long different events take.
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?
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
How many ways can you find of tiling the square patio, using square
tiles 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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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.
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?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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?
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?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
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?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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.