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

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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

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 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.

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?

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.

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?

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

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 moves.

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.

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?

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?

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

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

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?

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

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 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.

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

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.

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?

Find out what a "fault-free" rectangle is and try to make some of your own.

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

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

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?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

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

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?

What happens when you round these three-digit numbers to the nearest 100?

What happens when you round these numbers to the nearest whole number?

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

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

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

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

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

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

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

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?