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.
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.
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.
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.
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 activity involves rounding four-digit numbers to the nearest thousand.
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
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.
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
A collection of games on the NIM theme
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
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.
This challenge asks you to imagine a snake coiling on itself.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
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 find all the ways to get 15 at the top of this triangle of numbers?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
An investigation that gives you the opportunity to make and justify predictions.
How many centimetres of rope will I need to make another mat just like the one I have here?
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
What happens when you round these three-digit numbers to the nearest 100?
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
It starts quite simple but great opportunities for number discoveries and patterns!
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?
This challenge is about finding the difference between numbers which have the same tens digit.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
This task follows on from Build it Up and takes the ideas into three dimensions!
Find out what a "fault-free" rectangle is and try to make some of your own.
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?
How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?
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?
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?
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.
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
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?
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
Find the sum of all three-digit numbers each of whose digits is odd.
Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?