Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
If you had 36 cubes, what different cuboids could you make?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
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 help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
Ben has five coins in his pocket. How much money might he have?
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?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
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?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
An investigation that gives you the opportunity to make and justify
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
Can you draw a square in which the perimeter is numerically equal
to the area?
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?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
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?
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
These practical challenges are all about making a 'tray' and covering it with paper.
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?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Can you find all the different ways of lining up these Cuisenaire
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?
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?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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.
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?
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
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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....?
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?
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.