08-12-2012, 02:25 PM
30 POWERFUL PRINCIPLES FOR BUILDING MATH AND NUMERACY SKILLS
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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, valueadded
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?
Snapshot
We generally cannot compare percentages to numbers unless
we know the exact numbers represented by those percentages.
Percentages, like decimals, fractions, and ratios, are relative
measures; actual numbers provide absolute measures.
Let’s presume that in a given company 10% of the employees in
department A are salespersons, whereas 20% of the employees
in department B are salespersons. Does department B have
more salespersons than department A↜? The answer, of course,
is that we cannot tell. It could be that both departments have the
same number of total employees, in which case department B
would definitely have more salespersons than department A (see
scenario 1). But there could be many more employees working
in department A than in department B. In this case, the number
of salespersons working in department A could well be greater
than the number of salespersons working in department B (see
scenario 2).