This challenge is about finding the difference between numbers which have the same tens digit.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
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.
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?
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?
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?
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Got It game for an adult and child. How can you play so that you know you will always win?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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.
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.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
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
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
Find the sum of all three-digit numbers each of whose digits is
Can you work out how to win this game of Nim? Does it matter if you go first or second?
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?
It starts quite simple but great opportunities for number discoveries and patterns!
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
This activity involves rounding four-digit numbers to the nearest thousand.
This challenge asks you to imagine a snake coiling on itself.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Take a counter and surround it by a ring of other counters that
MUST touch two others. How many are needed?
Can you dissect an equilateral triangle into 6 smaller ones? What
number of smaller equilateral triangles is it NOT possible to
dissect a larger equilateral triangle into?
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?
What happens when you round these numbers to the nearest whole number?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
What happens when you round these three-digit numbers to the nearest 100?
Compare the numbers of particular tiles in one or all of these
three designs, inspired by the floor tiles of a church in
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
This challenge encourages you to explore dividing a three-digit number by a single-digit 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?
This problem challenges you to find out how many odd numbers there
are between pairs of numbers. Can you find a pair of numbers that
has four odds between them?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
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.
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.
This activity focuses on rounding to the nearest 10.
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?