animated gif by Robin Senseney, MHS Class of 2006 |

CAROL JV FISHER BURNS

Ideas for anyone, grade 7 and up,

who wants to understand mathematics

You're about to learn that

The hope is that the next time you find yourself faced with

you'll think:

and laugh a bit...

making mathematics a little less stressful,

and a little more fun.

who wants me to say everything

first

copyright 1998 Carol J.V. Fisher

This is not a true “web book”. The book contains lots of mathematics,
and at the time I put this online, mathematical typesetting was not well supported
on the web. The original book is typeset using TeX (the technical
typesetting language used by the mathematical community), and I created
“snapshots” of each page. To view and print these “snapshots”, you'll need
the ability to work with *portable document format* (pdf) file types:
Adobe Acrobat Reader is free and available for download at

```
http://www.adobe.com/products/acrobat/readstep2.html
```

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 (e.g., Geometry or Algebra II)

*without* having gone through the
Algebra I course,

then I highly recommend that you read this original cat book.

This ‘original cat book’ (below) was

If you go through that entire Algebra I course,

then you're

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

then I highly recommend that you read this original cat book.

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*.

Table of Contents

This is a printable version of the Table of Contents, with page numbers.

- 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 - THE REAL NUMBERS (pages 13–22)

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

Solutions to Exercises: Chapter 2 - MATHEMATICIANS ARE FOND OF COLLECTIONS (pages 26–37)

introduction to sets; membership in a set; finite versus infinite sets; notation used in connection with sets; the idea of "infinity"; interval notation

Solutions to Exercises: Chapter 3 - HOLDING THIS, HOLDING THAT (pages 40–55)

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

Solutions to Exercises: Chapter 4 - I LIVE TWO BLOCKS WEST OF YOU (pages 58–71)

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

Solutions to Exercises: Chapter 5 - NUMBERS HAVE LOTS OF DIFFERENT NAMES! (pages 75–91)

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

Solutions to Exercises: Chapter 6 - THESE SENTENCES CERTAINLY LOOK DIFFERENT (pages 94–109)

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"

Solutions to Exercises: Chapter 7 - TRANSFORMING TOOL #1 (the Addition Property of Equality) (pages 112–125)

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

Solutions to Exercises: Chapter 8 - TRANSFORMING TOOL #2 (the Multiplication Property of Equality) (pages 128–138)

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

Solutions to Exercises: Chapter 9

INDEX

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