You can buy a paperback version of the book
at Amazon.

For $5.00, you can buy a single pdf that contains the complete cat book
(everything below, except the sample quizzes).



As per my terms of use,
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.)

Questions?
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.)
title graphic image:  One Mathematical Cat, Please! an animated mathematical cat
animated gif
by Robin Senseney,
MHS Class of 2006

BY
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,
you'll think:

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!


NOTE:
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 below—plus lots more!

However, if you're trying to use my higher-level materials
(Geometry, Algebra II, Precalculus, Calculus)
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.

Introduction

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.

  1. THE LANGUAGE OF MATHEMATICS (pages 1–10)
    expressions versus sentences; sentences have verbs and state a complete thought; conventions; definitions; simplifying an expression; connectives
    Solutions to Exercises: Chapter 1
  2. THE REAL NUMBERS (pages 13–25)
    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
  3. MATHEMATICIANS ARE FOND OF COLLECTIONS (pages 26–39)
    introduction to sets; membership in a set; finite versus infinite sets; notation used in connection with sets; the idea of ‘infinity’ interval notation
  4. HOLDING THIS, HOLDING THAT (pages 40–57)
    letters used to represent other objects—variables; variables ‘hold’ objects; variables are used to state a general principle, represent a sequence of operations, represent an ‘unknown’ quantity; solving a sentence
  5. I LIVE TWO BLOCKS WEST OF YOU (pages 58–74)
    order properties of the real numbers—position 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
  6. NUMBERS HAVE LOTS OF DIFFERENT NAMES! (pages 75–93)
    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; unit conversion
  7. THESE SENTENCES CERTAINLY LOOK DIFFERENT (pages 94–111)
    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’
  8. TRANSFORMING TOOL #1 (the Addition Property of Equality) (pages 112–127)
    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 checking solutions
  9. TRANSFORMING TOOL #2 (the Multiplication Property of Equality) (pages 128–142)
    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

INDEX

SAMPLE QUIZZES:
Students at Miss Hall's School were given the following quizzes, to test their understanding of each chapter.