Math Sampler

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description

Sampler of Math UK Version

Transcript of Math Sampler

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Copyright © Kingfisher 2010Book concept copyright © Toucan 2010Illustration copyright © Simon Basher 2010

Published in the United States by Kingfisher,175 Fifth Ave., New York, NY 10010Kingfisher is an imprint of Macmillan Children’s Books, London.All rights reserved.

Consultant: Dr. Troy P. Regis

Designed and created by Basherwww.basherbooks.com www.basherworld.com www.bebo.com/simonbasher

Dedicated to David Coleman

Distributed in the U.S. by Macmillan, 175 Fifth Ave., New York, NY 10010Distributed in Canada by H.B. Fenn and Company Ltd., 34 Nixon Road,Bolton, Ontario L7E 1W2

Library of Congress Cataloging-in-Publication data has been applied for.

ISBN: 978-0-7534-6419-9

Kingfisher books are available for special promotions and premiums. For details contact: Special Markets Department, Macmillan, 175 Fifth Ave., New York, NY 10010.

For more information, please visit www.kingfisherbooks.com

Printed in Taiwan9 8 7 6 5 4 3 2 11TR/0410/UNT/SHENS/128MA/C

Note to readers: the website addresses listed above are correct at the time of going to print. However, due to the ever-changing nature of the Internet, website addresses and content can change. Websites can contain links that are unsuitable for children. The publisher cannot be held responsible for changes in website addresses or content or for information obtained through a third party. We strongly advise that Internet searches be supervised by an adult.

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Number Bunch 4Special Sum-Things 16Shape Shifters 28Data Gang 50Index 60Glossary 62

CONTENTS Copyrighted Material

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Counting is one of the easiest things. One, two, three, four. And with ten handy counters at the end of your arms,getting to ten doesn’t take much brainpower. But what arethe Number Bunch for? Well, they’re essential if you want todo math problems. They work in groups of tens. Ten tensbecomes one hundred, ten hundreds becomes onethousand, and so on. So far so good, but math has a badhabit of getting harder. The Number Bunch is here to keepthings from becoming befuddling and boring. When itcomes to crunching numbers, they’re the ones that count!

Chapter 1Number Bunch

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Units

Zero Infinity Minus Numbers

Fraction Decimal Fraction

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Indian mathematicians first used Zero as a number 2,500 years ago.

First book to include Zero written: A.D. 628Came to Europe via Muslim scholarsThe number Zero is an even number

ZeroNumber Bunch

I am El Zero, and I can dissolve you to nothing. You knowmy sign, the round mark of Zero. So be warned! I haveextraordinary powers. Put my digit at the end of a numberand I make the number ten times larger—leaping from 1to 10 to 100 to 1,000 and so on forever. And then there’sthe curse of Zero. Divide by me and your calculator willreturn a big fat ERROR! Multiply by me and any number—no matter how large—vanishes, reduced to . . . well, Zero.

You see, I am something that stands for nothing. I amcalled nix, zip, zilch, nada, zippo . . . Hovering betweenbeing and not-being, I am one of the most importantnumbers in math. Yet I am so strange, so puzzling, that forhundreds of years even the smartest mathematicians inEurope didn’t understand or use me.

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Youngster who has two lives—as a digit and as a numberThis digit allows you to imagine huge and tiny numbersIt’s also a tricky, mysterious number that equals nothing

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Zero

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InfinityNumber Bunch

You’ll never pin me down. I’m Infinity, beyond what youcan even begin to imagine. Inconceivable! Okay, startcounting: 1, 2, 3, 4, 5, 6 . . . And keep on counting: 7, 8,9, 10, 11, 12 . . . And then count some more—and somemore and some more. Hey, you say, this could go onforever. That’s just the point! I exist, sure enough, and yetyou will never reach me. I’m that endless road thatteasingly keeps on disappearing off into the unknown.

Actually, I have a confession to make. Shh! Don’t tell theothers. I’m not a number—you can’t use me to add ormultiply or do the other things you do with numbers. ButI’m so tied up with all of them that I feel fine about beinghere. By the way, my symbol is written like this: ∞. It’s aclosed double loop, sort of like a figure 8 taking a nap.

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A mind-boggling customer that lies beyond all limits You cannot count or measure to Infinity or ever reach itNot a number, but closely involved with numbers

Georg Cantor (1845–1918) spent his life studying Infinity . . . and went crazy!

Symbol name: lemniscateSymbol introduced by: John Wallis (1655)Medieval symbol: snake biting its tail

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Infinity

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You’ll find this gang of number crunchers wherever yougo. Get the hang of them and you’re well into crackingthe mysteries of numbers. The Special Sum-Things are waysof combining numbers, finding differences between them,sharing them, and zipping up and down the numberscale with ease. They are mostly mental—not crazy—and just the sort of trick that you can do in your head.Using them can get you out of a tight spot. They will stickwith you through thick and thin, and with them on yourside, ain’t nobody gonna make a fool outta you!

Chapter 2Special Sum-Things

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Add Subtract Multiply

Divide χ

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HEAD PUZZLE You have 12 red jellybeans and 18 blue jellybeans. How many doyou have in total? Try breaking the numbers up a little. 10 + 10 = 20. Right? That’seasy to do in your head. And 2 + 8 = 10. So it’s 20 + 10, which equals 30. Hooray!

AddSpecial Sum-Things

Out of all the Special Sum-Things, I’m the one who givesyou more. Because I like putting bits and pieces together,numbers usually get bigger with me (the exception iswhen you Add a Minus Number to a positive numberand get a smaller number: 3 + (–1) = 2, for example).

I’m really simple to use—to Add numbers together, juststack one on top of another and count up each columnseparately, from right to left. You can use a calculator,an abacus, or your fingers and toes. And with me, youdon’t even have to do things in an orderly fashion: 27 + 35 + 8 is the same as 35 + 8 + 27, which is the same as 8 + 35 + 27. They all Add up to 70. The only number thatfoxes me is Zero, because he makes no difference toany of my totals. Oh well!

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With its big plus sign, this little fella joins numbers togetherThe work it does is called additionIn math, the total added together is called the sum

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Add

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HEAD PUZZLE You buy a bag of 49 gummi bears. Sally takes 14. How manydo you have left? Try counting on. From 14 to 20 is 6. Easy! From 20 to 40 is20. And then there’s the last 9. 6 + 20 + 9 = 35. So 49 – 14 = 35. Get it?

SubtractSpecial Sum-Things

People often think I’m gloomy. Okay, I admit it, I’m theexact opposite of Add, that bubbly ball of smirkingpositivity. Because I’m always taking things away, numberstend to get smaller with me around (the only exception iswhen you Subtract a bigger Minus Number from a smallerMinus Number and get a positive number: (–3) – (–5) = 2).

I have my uses, though, and some people like me. Ask anycupcake craver, fudge fiend, or jellybean junkie. With mylong-dash minus sign, I’m their favorite, because the onlyway to enjoy cake is to Subtract a slice. But if you wantyour piece of cake, you have to mind your manners—I demand order. As you know, 5 pieces of cake minus 2pieces is not the same as 2 pieces of cake minus 5 pieces(which is impossible in real life but possible in mathematics!)

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This unhappy character breaks numbers apartThe work it does is called subtractionThe total left over after subtraction is the difference

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Subtract

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Slippery! Slidy! These are the Shape Shifters, the buildingblocks of everything you see around you. Math has them and their shifty ways down to a fine art—it’s calledgeometry. Where two straight Lines meet, you get anAngle. Three straight Lines and three Angles make aTriangle. This is magic! A square has equal length andwidth, right? Give it depth as well and it can become a cube. In the world of geometric shapes, you movethrough dimensions, from 1-D to 2-D to 3-D. This is thebest building set you’ll ever have. Enjoy!

Chapter 3Shape Shifters

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Line Angle Circle Pi

Triangle Quadrilaterals Polygon 3-D Shapes

Area Volume

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In ancient times, many peoplebelieved that the Circle was divine.

CircleShape Shifters

I’m a chubby-cheeked bundle of fun. Every time youdraw a happy face, chances are it’s beaming out ofme. And of course anytime you hop on your bike andpedal down the street or do a wheelie, you’re using mycool talent for spinning, or rotating. Yes, I get thingsrolling. It’s a knack I owe to one simple fact—all pointson my perimeter (the outside line that forms my shape)are an equal distance from my center.

I’m so one of a kind that my vital statistics have their ownspecial names. My width is called my diameter (d). Thedistance from my center to my perimeter is my radius (r)—half my diameter. The length of my perimeter is that noblefella circumference (C)—“Sir Cumference.” To measuremy Area (A), you’ll need the help of my friend Pi (π).

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Perfectly rounded, this character is a real rollerAll parts of its edge are the same distance from its centerYou need a compass to draw a perfectly round Circle

Diameter: d = 2 x rCircumference: C = π x dArea: A = π x r x r

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Circle

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Pi to 20 decimal places:3.14159265358979323846

PiShape Shifters

As simple as Pi? Hmm! Up to a point. Mathematicianslove me—I’m their favorite dish (pie, get it?). But I take a bit of getting used to. How do you find me? TakeCircle’s circumference and Divide that by the diameter.It doesn’t matter how large or small the Circle is, thenumber you get will always be the same—me, Pi!

Crazy, isn’t it? And they do call me an irrational number,which could mean that I’m a bit wacky. But I’m sane,really. It’s just that you can’t capture me neatly in aFraction. So what is my magic number? 3.14159 . . . andon and on and on. The number never ends and neverrepeats. Spooky! And don’t think I’m just some funny littleoddity. No, I’m key. For example, you need me to figureout the Area of a Circle. And that’s just one of my tricks.

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A mysterious number with many math tricks up its sleeveDefined as the Ratio of a Circle’s circumference to its diameterOften written as the Greek letter π, pronounced “pie”

π = C ÷ dπ: first letter of Greek word for perimeterSurface Area of a sphere: 4 x π x r x r

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Pi

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Hot stuff, this bunch! Data is information—key statistics, suchas how tall you’ve grown over the past few months or howmany points your favorite basketball players have scored.But what’s the point of this stuff if you don’t do somethingwith it? The Data Gang will show you how. Turn those pointsinto a kind of picture (or graphic)—a multicolored BarGraph where you can see at a glance who’s scored themost. Draw a Line Graph showing how fast you’ve grown!Figure out some Averages! Calculate percentages! You’llbe so busy, you won’t know where the time has gone.

Chapter 4Data Gang

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Line Graph

Average Ratio Percent

Bar Graph Pie Chart

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The Greek letter μ (mu) is sometimes used for the mean.

AverageData Gang

It’s Captain Average to you. My name may be Average,but there is nothing ordinary or “plain vanilla” about me.Yes, I drive down the middle of the road so no one canpass me. But that’s my job—figuring out the exact midwaypoint among a set of two or more numbers.

Take my “mean” trick. Your aunt Mary—every time youvisit her, she gives you a bag of candy, bless her! Lasttime, the bag had 19 pieces in it. The time before, it had 16 pieces, and the time before that, seven.What’s the Average (or mean) number of pieces she’sgiven you per visit? Add up the total number of pieces: 19 + 16 + 7 = 42. Divide your total by the number of visits:42 ÷ 3 = 14. Over three visits, she’s given you an Averageof 14 pieces per visit. Not bad, really. She’s not mean!

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There’s nothing ordinary about this Average JoeIts special skills are finding midpoints among numbersHas three forms: the mode, the median, and the mean

Mean: Average of a set of numbersMode: most common number in a setMedian: the middle value in a set

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Average

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Aacute Angle 32Add 18algebra 26, 62Angle 28, 30, 32, 38, 40,

42, 57arc 30, 32, 62Area (A) 34, 36, 44, 46Average 50, 52, 62

BCBar Graph 50, 56, 57capacity 48, 62Circle 34, 36, 57circumference (C) 34, 36compasses 34cone 44, 48coordinates 58, 62cube 44, 48cylinder 48

DEdata 12–15, 50–58Decimal Fraction 13, 36 diameter (d) 34, 36difference 20, 62digit 6, 62Divide 24, 62, 64equilateral Triangle 38

FGFraction 12, 24, 55geometry 28–49, 63graph 50, 56, 57, 58grids 56–59

Hhexagon 42hypotenuse 38

IInfinity 8isosceles Triangle 38

KLkite 40Line 28, 30, 44Line Graph 50, 58

Mmean 52, 63median 52, 63Minus Numbers 10, 18, 20mode 52, 63Multiply 22, 24

Nnegative numbers 10number scale 16

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Oobtuse Angle 32

Pparallel Lines 30parallelogram 40, 63pentagon 42Percent (%) 55perimeter 34, 36, 63Pi (π) 34, 36, 48Pie Chart 57Polygon 42polyhedron 44prime number 64protractor 32pyramid 44, 64Pythagorean theorem 38, 64

QQuadrilaterals 40, 42, 63

Rradius 34, 36Ratio 36, 54rectangle 40reflex Angle 32rhombus 40right Angle 32right Triangle 38

Sscalene Triangle 38segment 30, 57shapes

1-D 28, 302-D 28, 30, 34, 38, 40, 42,

46, 63, 643-D Shapes 28, 30, 44,

48, 62–64SI Units 14, 64sphere 36, 44, 48square 40Subtract 20symmetry 40, 64

Ttrapezoid 40Triangle 28, 38, 42

UVUnits 14vertex 44, 64Volume 44, 48

XYZχ 26x-axis 58, 62y-axis 58, 62Zero 6, 10, 22

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Glossary

Perpendicular Lines that meet each other at right angles.Prime number A number that can be divided only by itselfand 1, such as 5, 7, 11, and 13. 1 is not a prime number.Pyramid A 3-D shape with either a triangular base andthree triangular faces or a square base and fourtriangular faces.Pythagorean theorem Named after the Greekmathematician Pythagoras (c. 580 B.C.–c. 500 B.C.). Hecame up with a formula to solve the length of a righttriangle’s hypotenuse (the longest side): a2 + b2 = c2.SI The International System of Units—a metric system useful inmath and science—based on seven defined units, includingkilogram (weight), meter (length), and second (time).Sum The result from adding numbers.Symmetry A property of a 2-D or 3-D shape that can be reflected or rotated to “match” or fit with itself inanother orientation. For example, the letter “A” has oneline of symmetry, and an equilateral triangle has three.Transformation To change a shape in one of three ways:flip (reflect), slide (translate), or turn (rotate).U.S. customary system A system of measurement derivedfrom units historically used in Great Britain, such as the foot.Vertex (pl. Vertices) A corner of a 3-D shape. For example,a cube has eight vertices.Whole number A number that you can use to count—somewhere from zero to infinity.

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Meet Zero, a bubbly fellow who will dissolve you to

nothing, and say hello to the all-action Units, who just

love to measure. Get a load of greedy Multiply, a big

guy who hoards numbers together, and stand amazed by

mysterious Pi, who goes on and on and on . . . to Infinity!

Multiply your number know-how with Basher’s unique one-stop guide to the

building blocks of mathematics. Packed with top tips and memorable

characters, this is an essential book for students.

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