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Technology. STEM - physical world. Cubes & cuboids. 2D shapes and their properties. Regular polygons and circles. Visualising. Maths Supporting SET. Generalising. Pythagoras' theorem. Interactivities.There are 143 results
Broad Topics > Thinking Mathematically > Generalising
2001 Spatial Oddity
Age 11 to 14 Challenge Level:
With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.
Christmas Chocolates
Age 11 to 14 Challenge Level:
How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
Tourism
Age 11 to 14 Challenge Level:
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.
Tilted Squares
Age 11 to 14 Challenge Level:
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Cubes Within Cubes Revisited
Age 11 to 14 Challenge Level:
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?
Picturing Triangular Numbers
Age 11 to 14 Challenge Level:
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Shear Magic
Age 11 to 14 Challenge Level:
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Frogs
Age 11 to 14 Challenge Level:
How many moves does it take to swap over some red and blue frogs? Do you have a method?
Go Forth and Generalise
Age 11 to 14
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.
Hidden Rectangles
Age 11 to 14 Challenge Level:
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Dotty Triangles
Age 11 to 14 Challenge Level:
Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
More Number Pyramids
Age 11 to 14 Challenge Level:
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Circles, Circles
Age 5 to 11 Challenge Level:
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?
Picturing Square Numbers
Age 11 to 14 Challenge Level:
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Sliding Puzzle
Age 11 to 16 Challenge Level:
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.
Overlap
Age 11 to 14 Challenge Level:
A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .
Cuboid Challenge
Age 11 to 16 Challenge Level:
What's the largest volume of box you can make from a square of paper?
Route to Infinity
Age 11 to 14 Challenge Level:
Can you describe this route to infinity? Where will the arrows take you next?
Mindreader
Age 11 to 14 Challenge Level:
A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you. . . .
Generalising
Age 5 to 11
These tasks give learners chance to generalise, which involves identifying an underlying structure.
Crossings
Age 7 to 11 Challenge Level:
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?
Arithmagons
Age 11 to 16 Challenge Level:
Can you find the values at the vertices when you know the values on the edges?
More Twisting and Turning
Age 11 to 16 Challenge Level:
It would be nice to have a strategy for disentangling any tangled ropes...
Always, Sometimes or Never?
Age 5 to 11 Challenge Level:
Are these statements relating to odd and even numbers always true, sometimes true or never true?
Seven Squares - Group-worthy Task
Age 11 to 14 Challenge Level:
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
Sums of Pairs
Age 11 to 16 Challenge Level:
Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
Walking the Squares
Age 7 to 11 Challenge Level:
Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
Strike it Out for Two
Age 5 to 11 Challenge Level:
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Konigsberg Plus
Age 11 to 14 Challenge Level:
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.
Number Pyramids
Age 11 to 14 Challenge Level:
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Winning Lines
Age 7 to 16
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
Build it up More
Age 7 to 11 Challenge Level:
This task follows on from Build it Up and takes the ideas into three dimensions!
Build it Up
Age 7 to 11 Challenge Level:
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Always, Sometimes or Never? Shape
Age 7 to 11 Challenge Level:
Are these statements always true, sometimes true or never true?
Tumbling Down
Age 7 to 11 Challenge Level:
Watch this animation. What do you see? Can you explain why this happens?
Odd Squares
Age 7 to 11 Challenge Level:
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?
Domino Numbers
Age 7 to 11 Challenge Level:
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Nim-7 for Two
Age 5 to 14 Challenge Level:
Nim-7 game for an adult and child. Who will be the one to take the last counter?
Steps to the Podium
Age 7 to 14 Challenge Level:
It starts quite simple but great opportunities for number discoveries and patterns!
Egyptian Fractions
Age 11 to 14 Challenge Level:
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.
Magic Letters
Age 11 to 14 Challenge Level:
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Button-up Some More
Age 7 to 11 Challenge Level:
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Play to 37
Age 7 to 11 Challenge Level:
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.
Handshakes
Age 11 to 14 Challenge Level:
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
Sums and Differences 1
Age 7 to 11 Challenge Level:
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
How Much Can We Spend?
Age 11 to 14 Challenge Level:
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
Strike it Out
Age 5 to 11 Challenge Level:
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Keep it Simple
Age 11 to 14 Challenge Level:
Can all unit fractions be written as the sum of two unit fractions?
Triangle Pin-down
Age 7 to 11 Challenge Level:
Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
NRICH is part of the family of activities in the Millennium Mathematics Project.