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?
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?
Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?
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.
Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
This challenge asks you to imagine a snake coiling on itself.
This activity involves rounding four-digit numbers to the nearest thousand.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
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?
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?
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.
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
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.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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?
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 activity focuses on rounding to the nearest 10.
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.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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 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.
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?