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Resources tagged with Generalising similar to Factor Lines:

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Broad Topics > Using, Applying and Reasoning about Mathematics > Generalising

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More Magic Potting Sheds

Age 11 to 14 Challenge Level:

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?

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Round and Round the Circle

Age 7 to 11 Challenge Level:

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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Got It

Age 7 to 14 Challenge Level:

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.

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Have You Got It?

Age 11 to 14 Challenge Level:

Can you explain the strategy for winning this game with any target?

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Broken Toaster

Age 7 to 11 Short Challenge Level:

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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Three Dice

Age 7 to 11 Challenge Level:

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

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Surprising Split

Age 7 to 11 Challenge Level:

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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Dotty Circle

Age 7 to 11 Challenge Level:

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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Adding in Rows

Age 11 to 14 Challenge Level:

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

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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.

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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?

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Centred Squares

Age 7 to 11 Challenge Level:

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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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 ...?

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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?

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Repeaters

Age 11 to 14 Challenge Level:

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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Make 37

Age 7 to 14 Challenge Level:

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.

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Number Tracks

Age 7 to 11 Challenge Level:

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?

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Special Sums and Products

Age 11 to 14 Challenge Level:

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

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Sitting Round the Party Tables

Age 5 to 11 Challenge Level:

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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Three Times Seven

Age 11 to 14 Challenge Level:

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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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!

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Got it for Two

Age 7 to 14 Challenge Level:

Got It game for an adult and child. How can you play so that you know you will always win?

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One O Five

Age 11 to 14 Challenge Level:

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. . . .

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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.

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Sums and Differences 2

Age 7 to 11 Challenge Level:

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?

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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.

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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.

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Doplication

Age 7 to 11 Challenge Level:

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?

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Winning Lines

Age 7 to 16

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.

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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.

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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?

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Snake Coils

Age 7 to 11 Challenge Level:

This challenge asks you to imagine a snake coiling on itself.

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Always, Sometimes or Never? Number

Age 7 to 11 Challenge Level:

Are these statements always true, sometimes true or never true?

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Up and Down Staircases

Age 7 to 11 Challenge Level:

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

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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?

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Bundles of Cubes

Age 7 to 11 Challenge Level:

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

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Enclosing Squares

Age 11 to 14 Challenge Level:

Can you find sets of sloping lines that enclose a square?

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Truth or Lie

Age 7 to 11 Challenge Level:

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

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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.

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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?

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Journeys in Numberland

Age 7 to 11 Challenge Level:

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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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?

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Spirals, Spirals

Age 7 to 11 Challenge Level:

Here are two kinds of spirals for you to explore. What do you notice?

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Fault-free Rectangles

Age 7 to 11 Challenge Level:

Find out what a "fault-free" rectangle is and try to make some of your own.

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Tiling

Age 7 to 11 Challenge Level:

An investigation that gives you the opportunity to make and justify predictions.

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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.

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Roll over the Dice

Age 7 to 11 Challenge Level:

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?

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Division Rules

Age 7 to 11 Challenge Level:

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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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?

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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.