What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
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?
An investigation that gives you the opportunity to make and justify
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
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?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios 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?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
This activity investigates how you might make squares and pentominoes from Polydron.
Can you draw a square in which the perimeter is numerically equal
to the area?
Find out what a "fault-free" rectangle is and try to make some of
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
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?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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.
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
Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Can you put the numbers 1-5 in the V shape so that both 'arms' have 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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
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!
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?
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!
Can you arrange 5 different digits (from 0 - 9) in the cross in the
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
These practical challenges are all about making a 'tray' and covering it with paper.
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?
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
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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