Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?
Are these statements always true, sometimes true or never true?
Here are two kinds of spirals for you to explore. What do you notice?
These tasks give learners chance to generalise, which involves identifying an underlying structure.
The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
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.
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
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.
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?
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?
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?
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?
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
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?
Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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.
I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
Got It game for an adult and child. How can you play so that you know you will always win?
A game for 2 players with similarities 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.
Stop the Clock game for an adult and child. How can you make sure you always win this game?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Watch this animation. What do you see? Can you explain why this happens?
Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
It starts quite simple but great opportunities for number discoveries and patterns!
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
This challenge asks you to imagine a snake coiling on itself.
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 article for primary teachers discusses how we can help learners generalise and prove, using NRICH tasks as examples.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
This activity involves rounding four-digit numbers to the nearest thousand.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
Can you find a way of counting the spheres in these arrangements?
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.
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.