Are these statements always true, sometimes true or never true?
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Here are two kinds of spirals for you to explore. 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?
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
This challenge asks you to imagine a snake coiling on itself.
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?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
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?
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?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?
Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?
Can you find all the ways to get 15 at the top of this triangle of numbers?
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
This task follows on from Build it Up and takes the ideas into three dimensions!
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
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
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.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
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.
This activity involves rounding four-digit numbers to the nearest thousand.
This challenge is about finding the difference between numbers which have the same tens digit.
Got It game for an adult and child. How can you play so that you know you will always win?
One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?
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 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.
This activity focuses on rounding to the nearest 10.
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?
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Find out what a "fault-free" rectangle is and try to make some of
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
The NRICH team are always looking for new ways to engage teachers
and pupils in problem solving. Here we explain the thinking behind
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.