Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
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?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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 put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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
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.
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 draw a square in which the perimeter is numerically equal
to the area?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
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?
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
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
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
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
How many ways can you find of tiling the square patio, using square
tiles 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?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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 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?
In this matching game, you have to decide how long different events take.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
These practical challenges are all about making a 'tray' and covering it with paper.
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
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?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
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.
How many triangles can you make on the 3 by 3 pegboard?
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?
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?
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?
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.