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?
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
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
These practical challenges are all about making a 'tray' and covering it with paper.
This activity investigates how you might make squares and pentominoes from Polydron.
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 rectangles have been torn. How many squares did each one have
inside it before it was ripped?
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?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
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?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Find out what a "fault-free" rectangle is and try to make some of
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Can you draw a square in which the perimeter is numerically equal
to the area?
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
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
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
How many trapeziums, of various sizes, are hidden in this picture?
Can you find all the different ways of lining up these Cuisenaire
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main 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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
How many models can you find which obey these rules?
What is the best way to shunt these carriages so that each train
can continue its journey?
An investigation that gives you the opportunity to make and justify
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Investigate the different ways you could split up these rooms so
that you have double the number.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.