Got It game for an adult and child. How can you play so that you know you will always win?
Can all unit fractions be written as the sum of two unit fractions?
The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
This challenge asks you to imagine a snake coiling on itself.
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.
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Can you explain the strategy for winning this game with any target?
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.
Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
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?
We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
A game for 2 players with similarities 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 each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
A collection of games on the NIM theme
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
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?
Find out what a "fault-free" rectangle is and try to make some of your own.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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.
The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 × 1 [1/3]. What other numbers have the sum equal to the product and can this be so for. . . .
Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
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?
An investigation that gives you the opportunity to make and justify predictions.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.
Here are two kinds of spirals for you to explore. What do you notice?
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
How many centimetres of rope will I need to make another mat just like the one I have here?
This activity involves rounding four-digit numbers to the nearest thousand.
Watch this animation. What do you see? Can you explain why this happens?
Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
This task follows on from Build it Up and takes the ideas into three dimensions!