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?
There are seven pots of plants in a greenhouse. They have lost
their labels. Perhaps you can help re-label them.
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
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
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.
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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.
An activity making various patterns with 2 x 1 rectangular tiles.
This activity investigates how you might make squares and pentominoes from Polydron.
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?
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?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
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?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the
clues to work out which name goes with each face.
My coat has three buttons. How many ways can you find to do up all
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
Can you cover the camel with these pieces?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
What happens when you try and fit the triomino pieces into these
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
Can you draw a square in which the perimeter is numerically equal
to the area?
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
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!
How many models can you find which obey these rules?
An investigation that gives you the opportunity to make and justify
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
What could the half time scores have been in these Olympic hockey
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
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.
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?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake