Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
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?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
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?
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
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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.
Can you find all the different ways of lining up these Cuisenaire
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?
These practical challenges are all about making a 'tray' and covering it with paper.
How many different triangles can you make on a circular pegboard that has nine pegs?
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 Sudoku with clues as ratios or fractions.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
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.
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?
A Sudoku with clues as ratios.
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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.
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?
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
How many triangles can you make on the 3 by 3 pegboard?
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?
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.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
A mathematician goes into a supermarket and buys four items. Using
a calculator she multiplies the cost instead of adding them. How
can her answer be the same as the total at the till?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Can you find all the different triangles on these peg boards, and
find their angles?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
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.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
Can you draw a square in which the perimeter is numerically equal
to the area?
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?