A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
Can you draw a square in which the perimeter is numerically equal
to the area?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Sally and Ben were drawing shapes in chalk on the school
playground. Can you work out what shapes each of them drew using
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
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?
An investigation that gives you the opportunity to make and justify
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?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
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
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 models can you find which obey these rules?
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 we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
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.
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
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?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
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?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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.
Place the 16 different combinations of cup/saucer in this 4 by 4
arrangement so that no row or column contains more than one cup or
saucer of the same colour.
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?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
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?
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
Here are four cubes joined together. How many other arrangements of
four cubes can you find? Can you draw them on dotty paper?
If you had 36 cubes, what different cuboids could you make?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
What could the half time scores have been in these Olympic hockey
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
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?
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
Can you use the information to find out which cards I have used?
This activity investigates how you might make squares and pentominoes from Polydron.
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Investigate the different ways you could split up these rooms so
that you have double the number.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates