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Resources tagged with Generalising similar to Triangle Transformation:

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

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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?

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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?

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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. . . .

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Cut it Out

Age 7 to 11 Challenge Level:

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?

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Number Differences

Age 7 to 11 Challenge Level:

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?

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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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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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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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Counting Counters

Age 7 to 11 Challenge Level:

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

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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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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.

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Cuisenaire Rods

Age 7 to 11 Challenge Level:

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

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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. . . .

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Tumbling Down

Age 7 to 11 Challenge Level:

Watch this animation. What do you see? Can you explain why this happens?

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Pentanim

Age 7 to 16 Challenge Level:

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.

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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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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?

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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.

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Keep it Simple

Age 11 to 14 Challenge Level:

Can all unit fractions be written as the sum of two unit fractions?

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Dice Stairs

Age 7 to 11 Challenge Level:

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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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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Cuboid Challenge

Age 11 to 16 Challenge Level:

What's the largest volume of box you can make from a square of paper?

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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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Rope Mat

Age 7 to 11 Challenge Level:

How many centimetres of rope will I need to make another mat just like the one I have here?

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Searching for Mean(ing)

Age 11 to 14 Challenge Level:

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

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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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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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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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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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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?

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Consecutive Negative Numbers

Age 11 to 14 Challenge Level:

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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Partitioning Revisited

Age 11 to 14 Challenge Level:

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

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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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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?

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More Number Pyramids

Age 11 to 14 Challenge Level:

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

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Always, Sometimes or Never? Shape

Age 7 to 11 Challenge Level:

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

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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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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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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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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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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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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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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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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?

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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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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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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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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.