The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?
Are these statements always true, sometimes true or never true?
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.
Here are two kinds of spirals for you to explore. What do you notice?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
It starts quite simple but great opportunities for number discoveries and patterns!
This challenge asks you to imagine a snake coiling on itself.
What happens when you round these numbers to the nearest whole number?
This activity involves rounding four-digit numbers to the nearest thousand.
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.
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?
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
How many centimetres of rope will I need to make another mat just
like the one I have here?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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.
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?
This activity focuses on rounding to the nearest 10.
What happens when you round these three-digit numbers to the nearest 100?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
Can you find all the ways to get 15 at the top of this triangle of numbers?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
This challenge is about finding the difference between numbers which have the same tens digit.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
An investigation that gives you the opportunity to make and justify
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
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
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?
A game for 2 players with similaritlies to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.