ONE MATHEMATICAL CAT, PLEASE! A First Course in Algebra

This is a complete, sequenced, free course. It has randomly-generated exercises and worksheets—you'll never run out of practice. It can be used for a year-long class. Have fun with Algebra Pinball!

You're about to learn that $\,x\,$ is to mathematics as ‘cat’ is to English. Next time you see ‘$\,x\,$’, I hope you think One Mathematical Cat, Please! and laugh a bit $\ldots\,$ making mathematics a little less stressful, and a little more fun.

How to Use This Algebra Course

(1) Decide If It Will Work For You

Read the first lesson: Expressions Versus Sentences. Hear my voice (Yep! That's me!) by clicking the audio icon next to the title. See how the text is highlighted while I read. Try both Skill Practice and Concept Practice problems. Create some worksheets—they're different every time you click.

Then, click ‘Read Section 1’ from the first column below. My entire Algebra book (37 sections) is in that first column. This shows my ‘writing voice’.

Like this short experiment? Then my course should be a good fit.

(2) Old-Fashioned Paper and Pencil

You'll want to read every word and work every problem. In order, from beginning to end. Really.

Fly through parts that are easy for you, but don't skip anything. Why? This isn't a traditional Algebra course. You'll learn the language of math while you learn algebra. There are lots of things you've never seen before. If you miss them, things won't flow.

The book has ‘active reading’ exercises—loads of them, every few paragraphs. This way, you check your understanding after tiny steps. (Of course, all solutions are included!) To learn the most, do every single exercise with old-fashioned paper and pencil.

You could print out all 37 sections (close to 400 pages), punch holes, put in a binder. But, my printed book is easier and costs less (I did the math). I worked hard to publish it in an affordable way. Then, you can do all the problems right in the book. (Plus, it supports me, for which you get my deepest gratitude 😊)

(3) Keep It Going

After you finish Algebra, you can continue with Geometry, Algebra II, Precalculus, and Calculus. All the same voice. All the same style. All free. I hope you learn lots of math, and have some fun along the way!

Sections with the light green background are from the original ‘cat’ book (cat-on-swing). It was filled out to become this First Course in Algebra (which is also available as the cat-in-hammock book).

Section 1:
The Language of Mathematics
Read Section 1
Section 2:
Brushing Up On Basic Arithmetic Skills
Read Section 2
Section 3:
The Real Numbers
Read Section 3
Section 4:
Addition of Signed Numbers
Read Section 4
Section 5:
Subtraction of Signed Numbers
Read Section 5
Section 6:
Average
Read Section 6
Section 7:
The Base Ten Number System
Read Section 7
Section 8:
Decimals
Read Section 8
Section 9:
Mathematicians are Fond of Collections
Read Section 9
Section 10:
Holding This, Holding That
Read Section 10
Section 10.5:
Solving For A Particular Variable
(important for science classes)
Section 10.7:
Scientific Notation and Significant Figures
(important for science classes)
Section 11:
Introduction to Fractions
Read Section 11
Section 12:
Multiplying Fractions
Read Section 12
Section 13:
Adding Fractions
Read Section 13
Section 13.5:
Prime Numbers and Related Concepts
(Short on time? Section 13.5 can be skipped without any loss of continuity.)
Section 14:
I Live Two Blocks West Of You
Read Section 14
Section 15:
Numbers Have Lots of Different Names!
Read Section 15
Section 16:
Exact versus Approximate
Read Section 16
Section 17:
Rounding
Read Section 17
Section 18:
Unit Conversion
Read Section 18
Section 19:
More Unit Conversion
Read Section 19
Section 20:
Exponent Notation
Read Section 20
Section 21:
Exponent Laws
Read Section 21
71. Practice with $\,x^mx^n = x^{m+n}\,$
72. Practice with $\,(x^m)^n = x^{mn}\,$
73. Practice with $\,x^m/x^n = x^{m-n}$
74. Practice with $\,x^{-p} = 1/x^p$
75. One-Step Exponent Law Practice
76. Multi-Step Exponent Law Practice
Section 22:
Radicals
Read Section 22
Section 23:
Rational Exponents
Read Section 23
Section 24:
The Distributive Law
Read Section 24
Section 25:
Revisiting Exponents
Read Section 25
Section 26:
FOIL and More
Read Section 26
Section 27:
These Sentences Certainly Look Different!
Read Section 27
Section 28:
Introduction to Factoring
Read Section 28
Section 29:
Greatest Common Factor
Read Section 29
Section 30:
Transforming Tool #1
(the Addition Property of Equality)
Read Section 30
Section 31:
Transforming Tool #2
(the Multiplication Property of Equality)
Read Section 31
Section 32:
Solving Linear Equations in One Variable
Read Section 32
Section 32.5:
Applications and More
Section 33:
Solving Linear Inequalities in One Variable
Read Section 33
Section 34:
Introduction to Absolute Value
Read Section 34
Section 35:
Solving Absolute Value Equations
Read Section 35
Section 36:
Solving Absolute Value Inequalities Involving ‘Less Than’
Read Section 36
Section 37:
Finishing Up Absolute Value Sentences
Read Section 37
Section 38:
Factoring a Difference of Squares
Section 39:
Solving Equations Involving Perfect Squares
Section 40:
Factoring Trinomials
133. Basic Concepts Involved in Factoring Trinomials
134. Factoring $\,x^2 + bx + c\,,$   $\,c \gt 0\,$
135. Factoring $\,x^2 + bx + c\,,$   $\,c \lt 0\,$
136. Factoring Trinomials, All Mixed Up
Section 41:
Solving Quadratic Equations by Factoring
Section 42:
More on Quadratic Equations
Section 42.5:
Arithmetic with Fractions Involving Variables
Section 43:
Percent Increase and Decrease
Section 44:
Introduction to the Coordinate Plane
Section 45:
Lines
Section 46:
More On Lines
Section 47:
Functions