What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Can you draw a square in which the perimeter is numerically equal
to the area?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
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?
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.?
An investigation that gives you the opportunity to make and justify
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
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?
This activity investigates how you might make squares and pentominoes from Polydron.
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
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?
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
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Sally and Ben were drawing shapes in chalk on the school
playground. Can you work out what shapes each of them drew using
Find out what a "fault-free" rectangle is and try to make some of
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
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.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
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.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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.
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
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?
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!
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
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
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
What happens when you round these numbers to the nearest whole number?
How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?
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
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?