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.

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

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?

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

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

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.

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.

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

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?

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

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

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

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.

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

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?

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

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

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

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

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?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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

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

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

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

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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

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

Can you find all the ways to get 15 at the top of this triangle of numbers?

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

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?

An investigation that gives you the opportunity to make and justify predictions.

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.

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

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

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

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.

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 happens?

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

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

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

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

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?

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.