Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Arrange the shapes in a line so that you change either colour or
shape in the next piece along. Can you find several ways to start
with a blue triangle and end with a red circle?
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.
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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
An activity making various patterns with 2 x 1 rectangular tiles.
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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
This activity investigates how you might make squares and pentominoes from Polydron.
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
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?
These practical challenges are all about making a 'tray' and covering it with paper.
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?
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?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
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?
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?
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?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
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?
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.
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?
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Can you draw a square in which the perimeter is numerically equal
to the area?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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?