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 task encourages you to investigate the number of edging pieces and panes in different sized windows.

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.

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

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

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

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

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.

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.

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 challenge asks you to imagine a snake coiling on itself.

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

Stop the Clock game for an adult and child. How can you make sure you always win this game?

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

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?

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

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

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

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.

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

Can you find a way of counting the spheres in these arrangements?

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

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

Are these statements relating to odd and even numbers always true, sometimes true or never true?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

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?

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

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

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

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

Are these statements always true, sometimes true or never true?

Think of a number, square it and subtract your starting number. Is the number youâ€™re left with odd or even? How do the images help to explain 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?

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?

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?

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

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

Watch this animation. What do you see? Can you explain why this happens?

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?