An investigation that gives you the opportunity to make and justify
Find out about Magic Squares in this article written for students. Why are they magic?!
This activity focuses on rounding to the nearest 10.
What happens when you round these three-digit numbers to the nearest 100?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Can you substitute numbers for the letters in these sums?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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?
Can you replace the letters with numbers? Is there only one
solution in each case?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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!
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
Problem solving is at the heart of the NRICH site. All the problems
give learners opportunities to learn, develop or use mathematical
concepts and skills. Read here for more information.
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
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?
This article for teachers describes several games, found on the
site, all of which have a related structure that can be used to
develop the skills of strategic planning.
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?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
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!
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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
Let's suppose that you are going to have a magazine which has 16
pages of A5 size. Can you find some different ways to make these
pages? Investigate the pattern for each if you number the pages.
What two-digit numbers can you make with these two dice? What can't you make?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
Can you find the chosen number from the grid using the clues?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Follow the clues to find the mystery number.
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
This challenge is about finding the difference between numbers which have the same tens digit.
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?
What happens when you round these numbers to the nearest whole number?