A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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?
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?
Can you draw a square in which the perimeter is numerically equal
to the area?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
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?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
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
How many models can you find which obey these rules?
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
Can you find all the different ways of lining up these Cuisenaire
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
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?
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
Sally and Ben were drawing shapes in chalk on the school
playground. Can you work out what shapes each of them drew using
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Here are four cubes joined together. How many other arrangements of
four cubes can you find? Can you draw them on dotty paper?
An investigation that gives you the opportunity to make and justify
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?
Suppose there is a train with 24 carriages which are going to be
put together to make up some new trains. Can you find all the ways
that this can be done?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
If you had 36 cubes, what different cuboids could you make?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
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?
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?
In this investigation, you must try to make houses using cubes. If
the base must not spill over 4 squares and you have 7 cubes which
stand for 7 rooms, what different designs can you come up with?
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
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.
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
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?
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?
There are seven pots of plants in a greenhouse. They have lost
their labels. Perhaps you can help re-label them.
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?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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?