The Little Green Math Book: 30 Powerful Principles for Building Math and Numeracy Skills

240 Pages·2010·1.47 MB·English

by  Brandon Royal

For Math Afi cionados from
All Walks of Life
THE LITTLE GREEN MATH BOOK reads like a collection of math recipes to
help us blend problems, principles, and approaches in creating our own lineup
of splendid math cuisine. Along with 30 of the most fundamental, recurring math
principles and rules, you’ll fi nd a three-tier system to rate problems — one chili (mild),
two chilies (hot), and three chilies (very hot).
Fine-tune your numerical mindset with a quantitative review that serves as a refresher
course and as a tool for perceiving math in a new way. Whether you’re a high school
or college student, test-prep candidate, or working professional, this book’s wealth of
explanations and insights make it a perfect learning companion.
Enjoy the benefi ts of your own self-paced math course:
• Develop a feel for how numbers behave and what makes math problems tick.
• Review the five classic formulas governing percentage increase and decrease.
• Watch for pitfalls when expressing ratios as fractions, percents, or decimals.
• Understand the strengths and weaknesses of ratios as relative, not absolute, measures.
• Employ templates to solve math problems of similar category or type.
• Use simple math to solve “business” scenarios involving price, cost, volume, profit,
and break-even, as well as how to calculate markup versus margin and efficiency.
• Be able to glance at graphs and understand their underlying math themes.
• Understand correlation: weak or strong, positive or negative, linear or nonlinear.
• Gain a newfound confidence with an increased competency with numbers.
“This book brilliantly shows the structure and subtlety of basic math. Math is a
global language that knows no borders and opens opportunities for us all.”
— Rick Frishman, author, speaker, and media expert; treasurer and secretary for the
Dr. Mark Victor Hansen Foundation, “literacy to end poverty”
$19.95 US/CDN
Math & Numeracy Skills Reference
Maven Publishing
mavenpublishing.com
THE
LITTLE GREEN
Math
Book
30 POWERFUL PRINCIPLES
FOR BUILDING MATH AND
NUMERACY SKILLS
Brandon Royal
Published by Maven Publishing
© 2010 by Brandon Royal
All rights reserved. No part of this work may be reproduced or transmitted
in any form or by any means, electronic or mechanical — including
photocopying, recording, or any information storage and retrieval
system — without permission in writing from the author or publisher.
Reviewers, however, may quote brief passages in a review, and
individuals wanting to reference material from this book for academic
or non-commercial purposes may do so provided the book, with title
and author’s name, is cited as a source.
Published by:
Maven Publishing
4520 Manilla Road
Calgary, Alberta, Canada T2G 4B7
www.mavenpublishing.com
Library and Archives Canada Cataloguing in Publication:
Royal, Brandon
The little green math book : 30 powerful principles for building math
and numeracy skills / by Brandon Royal.
ISBN 978-1-897393-50-5
Library of Congress Control Number: 2009909355
In addition to the paperback edition, this book is available as an eBook
and in the Adobe PDF file format.
Technical Credits:
Cover Design: George Foster, Fairfield, Iowa, USA
Editing: Jonathan K. Cohen, Irvine, California, USA
Illustrations: Ashley Vercekaites, Calgary, Canada
This book’s cover text was set in Minion. The interior text was set in
Scala and Scala Sans.
The beauty of math is that things
always add up. Success in math is
70 percent hard work, 30 percent
skill, and 10 percent luck.
— Anonymous

Contents
Introduction 7
Quiz 11
Chapter 1: Basic Numeracy Ingredients
Percentages 15
Ratios and Proportions 33
Reciprocals 46
Order of Operations 48
Chapter 2: Wonderful Math Recipes
Overlap Scenarios 53
Matrix Scenarios 60
Mixture Scenarios 65
Weighted Average Scenarios 69
Chapter 3: Favorite Numeracy Dishes
Markup vs. Margin 81
Price, Cost, Volume, and Profit 85
Break-Even Point 90
Aggregate Costs vs. Per-Unit Costs 94
Efficiency 96
Distribution and Allocation 99
Chapter 4: Special Math Garnishments
Translating Basic Graphs 105
Line Graphs, Pie Charts, and Bar Charts 109
Correlation 116
Measures of Average and Dispersion 122
Statistical Significance 126
Appendix I – Numeracy Principles 1 to 30 133
Appendix II – The World of Numbers 139
Answers and Explanations 153
Quiz – Answers 229
Selected Bibliography 231
Index 233
About the Author
Introduction
Of the three primary symbols by which we communicate — letters,
numbers, and pictures — this book focuses on numbers and, in
particular, on “numeracy” skills. Numeracy combines the science
of math with the art of numbers. For the everyday student or
businessperson, this translates to developing a feel for how
numbers work — knowing both the “how” and “why” of problem
solving. The ability to perform calculations accurately is one
thing; knowing how numbers behave and what makes problems
tick is another.
The Little Green Math Book provides a compilation of the most
useful academic and real-life math concepts. The secret recipe
used in preparing material for this book is a blend of classic
problems and relevant tips. Classic problems are recurring, value-
added problems which give you, the reader, maximum return for
your time and effort spent. Tips serve as principles that underlie
math problems; they represent the themes that bind categories of
related problems. In addition to presenting 100 classic problems
and introducing 30 tips, this book lends a three-tier chili rating
system to help readers gauge a given problem’s difficulty level. A
single chili indicates that the difficulty level of a given problem is
“mild,” two chilies spell “hot,” and three chilies signal “very hot.”
Good math, like good cuisine, starts with good ingredients.
Chapter 1 — Basic Numeracy Skills — highlights the importance
of reviewing the basic building blocks of math, which lie at
the foundation of superior problem-solving skills. With these
skills come the knowledge and confidence to easily answer
the following questions: What are the five different percentage
formulas as they relate to percentage increase and decrease?
What pitfalls exist in working with ratios and proportions? Does
the order of mathematical operations really matter?
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Good math, like good cuisine, often comes with a recipe.
Chapter 2 — Wonderful Math Recipes — highlights the importance
of knowing the “best” approach. The “group formula” for solving
overlap scenarios, the “nine box” table for handling matrix
problems, the “barrel method” for solving mixture problems, and
the “weighted average” formula for tackling weighted average
problems are all examples of tools and techniques that greatly
aid problem solving.
Good math, like good cuisine, is practical.
Chapter 3 — Favorite Numeracy Dishes — highlights math in
action. With a focus on business and commerce, the topics
addressed include markup versus margin, cost-price-volume-
profit analysis, break-even point, efficiency, and distribution and
allocation scenarios.
Good math, like good cuisine, has good presentation.
Chapter 4 — Special Math Garnishments — highlights math from
a graphical perspective. Charts and graphs are “math pictures”
insofar as they are visual representations of numerical data.
Learning how to read graphical information is partly a function
of understanding how the type of graph used for presentation
purposes — line graph, pie chart, or bar chart — links to the type of
data we are trying to summarize. A brief exploration of statistics
helps us understand how two variables may be related, why the
term “average” can mean different things, and what it means if a
finding is considered to be statistically significant.
The primary target audience for this book is the everyday student:
the high school, community college, and college or university
student. Students studying for the math or quantitative sections of
College Board tests and standardized entrance exams — including
the SAT, ACT, GRE, and GMAT — will find this material especially
useful. Given the pervasive nature of math and numeracy skills,
this book is also suitable for any person seeking an on-the-job
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refresher course, particularly professionals pursuing work in
banking and management consultancy, accounting, law, and
government.
What’s special about The Little Green Math Book? Teachers and
employers frequently complain that students or employees
are weak in the basics of math or lacking in numeracy skills.
Unfortunately, there exists neither a definable, concrete list as
to what constitutes the basics nor an efficient method to acquire
such skills. This book helps address this deficiency. It provides
an answer to two key questions: “What are the math basics?”
and “How might a person build basic math and numeracy skills
within a reasonable time frame?”
With reference to the material chosen for inclusion in this book,
the term “basics” refers to “simple but insightful math” or, more
poetically, “the point at which a person starts to dance with math.”
A rudimentary level of math knowledge is required to solve the
majority of problems in this book. Apart from the ability to add,
subtract, multiply, and divide, a reader may be called upon to
perform basic algebra, including solving for a single variable.
That said, even if a reviewer can’t recall the formal techniques
used to solve basic math problems, the explanations provided for
those problems should provide a helpful bridge.
Although the purpose of this material is to help individuals
secure a numerical mindset, the greatest benefit to be gained
from this book is likely the inspiration to want to continue
learning — regardless of the skill area. The satisfaction gained
from those “aha” learning moments, coupled with a sense of
confidence from taking “ownership” in the material at hand, is a
wondrous yet real by-product of the learning process.
Let’s get started.
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