Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
This task encourages you to investigate the number of edging pieces and panes in different sized windows.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
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
Can you explain the strategy for winning this game with any target?
Spotting patterns can be an important first step - explaining why it is appropriate to generalise is the next step, and often the most interesting and important.
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
Delight your friends with this cunning trick! Can you explain how it works?
Can you work out how to win this game of Nim? Does it matter if you go first or second?
Can you find sets of sloping lines that enclose a square?
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.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?
In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Can you explain how this card trick works?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
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?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?
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?
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?
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 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.
You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .
Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
It starts quite simple but great opportunities for number discoveries and patterns!
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.
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?
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?
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
Watch this animation. What do you see? Can you explain why this happens?
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
This task follows on from Build it Up and takes the ideas into three dimensions!
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
This challenge asks you to imagine a snake coiling on itself.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?