Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
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?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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!
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
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?
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.
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Find out what a "fault-free" rectangle is and try to make some of your own.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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?
Find the sum of all three-digit numbers each of whose digits is odd.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
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 is about finding the difference between numbers which have the same tens digit.
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.
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.
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?
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?
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 two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
This activity involves rounding four-digit numbers to the nearest thousand.
What happens when you round these numbers to the nearest whole number?
This activity focuses on rounding to the nearest 10.
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?
This challenge asks you to imagine a snake coiling on itself.
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
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.
What happens when you round these three-digit numbers to the nearest 100?
This is a game for two players. Can you find out how to be the first to get to 12 o'clock?
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
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.
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?