Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?

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?

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?

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?

These tasks give learners chance to generalise, which involves identifying an underlying structure.

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?

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.

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.

Here are two kinds of spirals for you to explore. 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?

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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.

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?

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?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

This challenge asks you to imagine a snake coiling on itself.

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

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?

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

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 article for teachers and pupils that encourages you to look at the mathematical properties of similar games.

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?

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

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 is a game for two players. Can you find out how to be the first to get to 12 o'clock?

Nim-7 game for an adult and child. Who will be the one to take the last counter?

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 and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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?

Got It game for an adult and child. How can you play so that you know you will always win?

Can you work out how to win this game of Nim? Does it matter if you go first or second?

This article for primary teachers discusses how we can help learners generalise and prove, using NRICH tasks as examples.

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?

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Try out this number trick. What happens with different starting numbers? What do you notice?

It starts quite simple but great opportunities for number discoveries and patterns!

This activity involves rounding four-digit numbers to the nearest thousand.

This task follows on from Build it Up and takes the ideas into three dimensions!

This challenge is about finding the difference between numbers which have the same tens digit.

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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?