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
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
What happens when you round these three-digit numbers to the nearest 100?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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?
An investigation that gives you the opportunity to make and justify
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
This challenge is about finding the difference between numbers which have the same tens digit.
Find the sum of all three-digit numbers each of whose digits is
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the
numbers on each circle add up to the same amount. Can you find the
rule for giving another set of six numbers?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
What happens when you round these numbers to the nearest whole number?
This activity focuses on rounding to the nearest 10.
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
While we were sorting some papers we found 3 strange sheets which
seemed to come from small books but there were page numbers at the
foot of each page. Did the pages come from the same book?
Find out what a "fault-free" rectangle is and try to make some of
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Can you continue this pattern of triangles and begin to predict how
many sticks are used for each new "layer"?
In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
How many centimetres of rope will I need to make another mat just
like the one I have here?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
How can you arrange these 10 matches in four piles so that when you
move one match from three of the piles into the fourth, you end up
with the same arrangement?
In this problem we are looking at sets of parallel sticks that
cross each other. What is the least number of crossings you can
make? And the greatest?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Ben’s class were making cutting up number tracks. First they
cut them into twos and added up the numbers on each piece. What
patterns could they see?
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
This challenge asks you to imagine a snake coiling on itself.
This activity involves rounding four-digit numbers to the nearest thousand.
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten
numbers from the bags above so that their total is 37.
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
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.