How To Be Good At Math

322 Pages·043.335 MB·English

by  Carol Vorderman

How to be
good
at
maths
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How to be
T O
1
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H
5 1
L ÷
W
5 g
×
90°
0°
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How to be
good
at
maths
Peter Clarke, Caroline Clissold, Cherri Moseley
Editorial consultant Peter Clarke
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Contents
Senior editor Peter Frances
Foreword ..................................7 Comparing non-unit
Senior art editor Mabel Chan
fractions .............................50
Editors Shaila Brown, Salima Hirani, 1
Sarah MacLeod, Steve Setford, Rona Skene Numbers Using the lowest
common denominator .......51
Designers Tannishtha Chakraborty,
Louise Dick, Alison Gardner, Mik Gates,
Number symbols....................10 Adding fractions ....................52
Tessa Jordens, Shahid Mahmood,
Peter Radcliffe, Mary Sandberg, Jacqui Swan,
Place value .............................12 Subtracting fractions .............53
Steve Woosnam-Savage
Sequences and patterns ........14 Multiplying fractions ..............54
Illustrator Acute Graphics
Sequences and shapes .........16 Dividing fractions ..................56
Managing editors Lisa Gillespie, Paula Regan
Managing art editor Owen Peyton Jones
Positive and negative Decimal numbers ..................58
Senior producer, pre-production numbers .............................18
Comparing and ordering
Nikoleta Parasaki
Senior producer Mary Slater Comparing numbers ............20 decimals ............................60
Jacket editor Claire Gell Ordering numbers ...............22 Rounding decimals ................61
Jacket designers Mark Cavanagh,
Dhirendra Singh Estimating ..............................24 Adding decimals ...................62
Senior DTP designer Harish Aggarwal
Managing jackets editor Saloni Singh Rounding ...............................26 Subtracting decimals ............63
Design development manager Sophia MTT
Factors ...................................28 Percentages ..........................64
Publisher Andrew Macintyre
Art director Karen Self Multiples ................................30 Calculating percentages .......66
Design director Phil Ormerod
Publishing director Jonathan Metcalf Prime numbers .....................32 Percentage changes .............68
First published in Great Britain in 2016 by Prime factors ........................34 Ratio ...................................... 70
Dorling Kindersley Limited
80 Strand, London, WC2R 0RL Square numbers ...................36 Proportion...............................71
Copyright © 2016 Dorling Kindersley Limited Square roots ..........................38 Scaling ................................... 72
A Penguin Random House Company
10 9 8 7 6 5 4 3 2 1 Cube numbers ......................39 Different ways to describe
001–192676–July/2016
fractions ............................. 74
Fractions ................................40
All rights reserved.
No part of this publication may be reproduced, Improper fractions and 2
Calculating
stored in or introduced into a retrieval system,
mixed numbers .................42
or transmitted, in any form, or by any means
(electronic, mechanical, photocopying,
Equivalent fractions ...............44
recording, or otherwise), without the prior Addition ................................. 78
written permission of the copyright owner.
Simplifying fractions .............46
Adding with a number line ...80
A CIP catalogue record for this book
Finding a fraction of
is available from the British Library.
Adding with a number grid ...81
ISBN: 978-0-2411-8598-8 an amount ......................... 47
Addition facts ........................82
Printed and bound in China Comparing fractions with
the same denominators ....48 Partitioning for addition ........83
A WORLD OF IDEAS:
SEE ALL THERE IS TO KNOW
Comparing unit fractions ......49 Expanded column addition ...84
www.dk.com
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Column addition ...................86 More long multiplication .....122 Area ......................................168
Subtraction ............................88 Multiplying decimals ............124 Estimating area ....................169
Subtraction facts ...................90 The lattice method ...............126 Working out area with
a formula ..........................170
Partitioning for subtraction ....91 Division .................................128
Areas of triangles .................172
Subtracting with a Dividing with multiples .........130
number line .......................92 Areas of parallelograms ......173
The division grid ....................131
Shopkeeper’s addition ..........93 Areas of complex shapes ....174
Division tables ......................132
Expanded column Comparing area
Dividing with factor pairs .....134
subtraction .........................94 and perimeter ...................176
Checking for divisibility.........135
Column subtraction...............96 Capacity ...............................178
Dividing by 10, 100,
Multiplication .........................98 and 1000 ...........................136 Volume .................................179
Multiplication as scaling ......100 Dividing by multiples of 10 ...137 The volumes of solids ..........180
Factor pairs ...........................101 Partitioning for division ........138 Working out volume with
a formula ...........................181
Counting in multiples ...........102
Expanded short division .......140
Mass .....................................182
Multiplication tables .............104
Short division ........................142
Mass and weight .................183
The multiplication grid .........106
Expanded long division ........144
Multiplication patterns Calculating with mass .........184
Long division ........................146
and strategies ..................107
Temperature .........................186
Converting remainders ........148
Multiplying by 10, 100,
Calculating with
Dividing with decimals .........150
and 1000 ...........................108
temperature ....................187
The order of operations .......152
Multiplying by multiples
Imperial units .......................188
of 10 ..................................109 Arithmetic laws ...................154
Imperial units of length,
Partitioning for Using a calculator ................156
volume, and mass............190
multiplication .....................110
3 Telling the time .....................192
The grid method ...................112 Measurement
Dates ....................................194
Expanded short
multiplication ....................114 Length...................................160 Calculating with time ...........196
Short multiplication ...............116 Calculating with length ........162 Money ..................................198
Expanded long Perimeter ..............................164 Using money ........................199
multiplication .....................118
Using formulas to find Calculating with money ......200
Long multiplication ...............120 perimeter ..........................166
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4 Calculating angles Averages .............................276
Geometry
inside triangles ................242
The mean ............................277
Angles inside
What is a line? .....................204 The median .........................278
quadrilaterals ..................244
Horizontal and vertical The mode ............................279
Calculating angles inside
lines .................................205
quadrilaterals ..................245 The range ............................280
Diagonal lines .....................206
Angles inside polygons .......246 Using averages ....................281
Parallel lines ........................208
Calculating the angles
Pictograms ..........................282
in a polygon .....................247
Perpendicular lines ..............210
Block graphs ......................284
Coordinates .........................248
2D shapes ............................212
Bar charts ............................285
Plotting points using
Regular and irregular
coordinates ......................249 Drawing bar charts .............286
polygons ...........................213
Positive and negative Line graphs .........................288
Triangles ...............................214
coordinates ......................250
Drawing line graphs ...........290
Quadrilaterals ......................216
Using coordinates to
Pie charts .............................292
Naming polygons ................218
draw a polygon ................251
Making pie charts ...............294
Circles ..................................220
Position and direction .........252
3D shape .............................222 Probability ...........................296
Compass directions ............254
Types of 3D shape ..............224 Calculating probability ........298
Reflective symmetry ............256
Prisms ..................................226 Rotational symmetry ...........258 6
Algebra
Nets .....................................228
Reflection .............................260
Angles .................................230
Rotation ...............................262 Equations.............................302
Degrees ................................231
Translation ...........................264 Solving equations ................304
Right angles .......................232
5 Formulas and sequences ...306
Statistics
Types of angle .....................233
Formulas .............................308
Angles on a straight line .....234
Data handling .....................268
Angles at a point .................235
Tally marks ..........................270 Glossary ...............................310
Opposite angles ..................236
Frequency tables ..................271 Index .....................................314
Using a protractor ...............238
Carroll diagrams .................272 Answers ...............................319
Angles inside triangles .......240
Venn diagrams ...................274 Acknowledgments ..............320
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Foreword
Our lives wouldn’t be the same without maths. In fact, everything would stop
without it. Without numbers we couldn’t count a thing, there would be no money,
no system of measuring, no shops, no roads, no hospitals, no buildings, no … well,
more or less “nothing” as we know it.
For example, without maths we couldn’t build houses, forecast tomorrow’s weather,
or fly a plane. We definitely couldn’t send an astronaut into space! If we didn’t
understand numbers, we wouldn’t have TV, the internet, or smartphones. In fact,
without numbers, you wouldn’t even be reading this book, because it was created
on a computer that uses a special number code based on 0s and 1s to store
information and make thousands of calculations in a second.
Understanding maths also helps us to understand the world around us. Why do
bees make their honeycombs out of hexagons? How can we describe the spiral
shape formed by a seashell? Maths holds the answers to these questions and
many more.
This book has been written to help you get better at maths, and to learn to love it.
You can work through it with the help of an adult, but you can also use it on your
own. The numbered steps will talk you through the examples. There are also
problems for you to solve yourself. You’ll meet some helpful robots, too. They’ll give
you handy tips and remind you of important mathematical ideas.
Maths is not a subject, it’s a language, and it’s a universal language. To be able
to speak it gives you great power and confidence and a sense of wonder.
Carol Vorderman
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