You can buy a paperback version of the book
For $5.00, you can buy a single pdf that contains the complete
(everything below, except the sample quizzes).
you can't sell it (or make any profit from it)
without my written permission.
If you're a teacher:
make as many copies (electronic or printed) as you need
for your students.
(Just be sure to preserve the copyright notices.)
My contact info is on my homepage
I'd love to hear from you!
(If $5.00 is a hardship, then email me, and I'll send you the pdf file.
I do not want to deny anyone these materials.)
by Robin Senseney,
MHS Class of 2006
DR. CAROL JV FISHER BURNS
Ideas for anyone
who wants to understand mathematics
You're about to learn that
x (“ex”) is to mathematics as “cat” is to English.
The hope is that the next time you find yourself faced with x,
One Mathematical Cat, Please!
and laugh a bit...
making mathematics a little less stressful,
and a little more fun.
copyright Dr. Carol JVF Burns
For a review of this book, click here!
This ‘original cat book’ (below) was filled out to become
an entire First Course in Algebra.
If you go through that entire Algebra I course,
then you're guaranteed to get everything from
the book belowplus lots more!
However, if you're trying to use my higher-level materials
without having gone through the
Algebra I course,
then I highly recommend that you read this original cat book.
TABLE OF CONTENTS
Table of Contents
This is a printable version of the Table of Contents, with page numbers.
Brief Table of Ideas, Symbols, and Notation
English versus Mathematics
This diagram summarizes the language ideas discussed in the first section,
The Language of Mathematics.
THE LANGUAGE OF MATHEMATICS (pages 110)
expressions versus sentences; sentences have verbs and state a complete
thought; conventions; definitions; simplifying an expression; connectives
Solutions to Exercises: Chapter 1
THE REAL NUMBERS (pages 1325)
the real numbers and where they live; living to the right or left of
zero; size (distance from zero) versus order (left/right positioning);
opposites; integers; averaging
MATHEMATICIANS ARE FOND OF COLLECTIONS (pages 2639)
introduction to sets; membership in a set; finite versus infinite sets;
notation used in connection with sets; the idea of ‘infinity’ interval notation
HOLDING THIS, HOLDING THAT (pages 4057)
letters used to represent other objectsvariables; variables ‘hold’
objects; variables are used to state a general principle, represent a sequence
of operations, represent an ‘unknown’ quantity; solving a sentence
I LIVE TWO BLOCKS WEST OF YOU (pages 5874)
order properties of the real numbersposition of one number relative
to another; mathematical sentences used to describe order relationships; the
phrases ‘greatest’, ‘least’, ‘at least’, ‘at most’; describing a whole class
of sentences in one fell swoop; equations versus inequalities; solution of
a sentence in one variable; graph of a sentence; reading a sentence backwards
NUMBERS HAVE LOTS OF DIFFERENT NAMES! (pages 7593)
different names can reveal various properties that a number has; theorems
are to a mathematician as tools are to a carpenter; the power of adding zero
and multiplying by one; simplifying an expression versus solving a sentence;
THESE SENTENCES CERTAINLY LOOK DIFFERENT (pages 94111)
comparing expressions versus comparing sentences; equality of expressions
versus equivalence of sentences; connectives; truth tables; synonyms for ‘is
equivalent to’; the mathematical words ‘and’ and ‘or’
TRANSFORMING TOOL #1 (the Addition Property of Equality) (pages 112127)
the Addition Property of Equality; facts versus commands; ‘for all’
sentences; translating a theorem; preferred formats for solving a sentence;
why the Addition Property of Equality is true; preferred format for
TRANSFORMING TOOL #2 (the Multiplication Property of Equality) (pages 128142)
the Multiplication Property of Equality; what goes wrong with multiplying
by zero; undoing the last operation first; why the Multiplication Property
of Equality is true
Students at Miss Hall's School were given the following quizzes, to
test their understanding of each chapter.