ABOUT THE CAT-ON-SWING BOOK
Want a fresh start on math? View it in a totally new way?
Then read this little book.
If you're using my higher-level materials
without having gone through my
Algebra I course,
then I highly recommend that you read the cat-on-swing book. It will quickly bring
you up-to-speed with all the math language ideas you need to fully benefit
from my lessons.
You'll learn that numbers have lots of different names, and math is the renaming tool.
You'll learn that ‘$\,x\,$’ is to math as ‘cat’ is to English.
It's an easy read. If you can add, subtract, multiply and divide with numbers like 1, 2, and 3, then you can read this book.
Supplement any math class, 7th grade through college. Use for self-learners, home-schoolers, math lovers, math haters.
Reviewers and users write:
- “... wonderfully written and crafted with a care you rarely see”
- “... will do a great service to the mathematical educational world”
- “... the need for this book is immense”
- “... I found meat, potatoes, and pie on every page. It's all dessert.”
- “... never seen anything so supportive and affirming and reassuring and inspiring as the way you talk us through topics”
- “THIS IS GREAT!!!! . . . this is helping me get heads above the competition. You rock!!!! One Mathematical Cat drives me wild.”
An entire website grew from this book.
Free randomly-generated exercises. Free unlimited worksheets.
All the same style. All the same voice.
All building on the ideas in this little book.
Here's a review of the cat-on-swing book.
Here are some of my testimonials from over the years.
If you have any questions, don't hesitate to contact me (Dr. Carol JVF Burns, author and website creator):
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to try and foil spammers (sigh).
READ THE ORIGINAL CAT BOOK
GREEN ENTRIES are web exercises that support the book.
Be sure to visit these pages and click-click-click after reading each section!
Table of Contents
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 112)
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
Solutions to Exercises: Chapter 2
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
Solutions to Exercises: Chapter 3
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
Solutions to Exercises: Chapter 4
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
Solutions to Exercises: Chapter 5
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;
Solutions to Exercises: Chapter 6
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’
Solutions to Exercises: Chapter 7
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
Solutions to Exercises: Chapter 8
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
Solutions to Exercises: Chapter 9
Students at Miss Hall's School were given the following quizzes, to
test their understanding of each chapter.