This activity investigates how you might make squares and pentominoes from Polydron.
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
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
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?
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.
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
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?
On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
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.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
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?
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?
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?
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
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 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
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Can you find all the different ways of lining up these Cuisenaire
What is the best way to shunt these carriages so that each train
can continue its journey?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
What happens when you try and fit the triomino pieces into these
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
Can you cover the camel with these pieces?
How many trains can you make which are the same length as Matt's, using rods that are identical?
How many models can you find which obey these rules?
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
Find out what a "fault-free" rectangle is and try to make some of
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?
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?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
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.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?