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
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.
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
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
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?
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
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?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
This activity investigates how you might make squares and pentominoes from Polydron.
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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.
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are 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?
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.
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
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?
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?
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?
How many triangles can you make on the 3 by 3 pegboard?
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.
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.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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?
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?
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?