A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
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?
Can you draw a square in which the perimeter is numerically equal
to the area?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
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.
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 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?
An investigation that gives you the opportunity to make and justify
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.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?
How many models can you find which obey these rules?
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
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.
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?
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?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
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.
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?
Can you find all the different ways of lining up these Cuisenaire
These practical challenges are all about making a 'tray' and covering it with paper.
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.
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
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?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
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 you had 36 cubes, what different cuboids could you make?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
An activity making various patterns with 2 x 1 rectangular tiles.
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.
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
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?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.