Many thanks to Miss Hall's School in Pittsfield, Massachusetts for their support of this site.
This web site got started when I taught there, from 1999 to 2008.

A First Course in Algebra

This is a complete, sequenced, free course,
with unlimited, randomly-generated exercises and worksheets.
It can be used for a year-long high school course,
or a one-semester college course.

You're about to learn that
$\,x\,$ 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 $\ldots\,$
making mathematics a little less stressful,
and a little more fun.


Click here for lots more info
on my algebra book.
Buy the book at Amazon.

New!! (January 2022)

the Extra Sections

F U N   S T U F F   (for when you need a break)
Sections with the light green background are from the original ‘cat’ book.
The original ‘cat’ book was filled out to become this First Course in Algebra.

Section 1:
The Language of Mathematics

Read Section 1
  1. expressions versus sentences
Section 2:
Brushing Up On Basic Arithmetic Skills

Read Section 2
  1. basic addition practice
  2. multiplication
  3. divisibility
  4. basic properties of zero and one
  5. mixed basic add/subtract/multiply/divide practice
Section 3:
The Real Numbers

Read Section 3
  1. deciding if a number is a whole number, an integer, etc.
Section 4:
Addition of Signed Numbers

Read Section 4
  1. addition of signed numbers
Section 5:
Subtraction of Signed Numbers

Read Section 5
  1. subtraction of signed numbers
  2. mixed addition and subtraction of signed numbers
Section 6:

Read Section 6
  1. writing fractions with a denominator of 2 in decimal form
  2. average of two signed numbers
12.5 application of averaging concepts: factoring a quadratic
          (optional; for more advanced readers)
  1. average of signed numbers
Section 7:
The Base Ten Number System

Read Section 7
  1. identifying place values
  2. multiplying by powers of ten
Section 8:

Read Section 8
  1. changing decimals to fractions
  2. multiplying and dividing decimals by powers of ten
  3. changing decimals to percents
  4. changing percents to decimals
Section 9:
Mathematicians are Fond of Collections

Read Section 9
  1. introduction to sets
  2. interval and list notation
Section 10:
Holding This, Holding That

Read Section 10
  1. introduction to variables
  2. reading set notation
  3. going from a sequence of operations to an expression
  4. going from an expression to a sequence of operations
  5. solving simple sentences by inspection
  6. using mathematical conventions
Section 10.5:
Solving For A Particular Variable

(important for science classes)
  1. ‘undoing’ a sequence of operations
  2. solving for a particular variable
  3. Getting bigger? Getting smaller?
Section 10.7:
Scientific Notation and Significant Figures

(important for science classes)
  1. scientific notation
  2. significant figures and related concepts
32.5 (optional)
a conundrum: When is equal, not equal? Or, not equal, equal?
Section 11:
Introduction to Fractions

Read Section 11
  1. rewriting fractions as a whole number plus a fraction
  2. locating fractions on a number line
  3. fractions involving zero
Section 12:
Multiplying Fractions

Read Section 12
  1. finding reciprocals
  2. determining if a product is positive or negative
  3. multiplying and dividing fractions
  4. practice with the form $\,a\cdot\frac{b}{c}\,$
  5. more practice with the form $\,a\cdot\frac{b}{c}\,$
  6. renaming fractional expressions
Section 13:
Adding Fractions

Read Section 13
  1. practice with multiples
  2. finding least common multiples
  3. renaming fractions with a specified denominator
  4. practice with factors
  5. adding and subtracting fractions
  6. adding and subtracting simple fractions with variables
  7. divisibility equivalences
Section 13.5:
Prime Numbers and Related Concepts

(Short on time?
Section 13.5 can be skipped without any loss of continuity.)
   48a. prime numbers
   48b. the Prime Factorization Theorem
   48c. relatively prime numbers and related concepts
Section 14:
I Live Two Blocks West Of You

Read Section 14
  1. identifying inequalities as true or false
  2. bigger, smaller, greater, lesser
  3. practice with the phrases ‘at least’ and ‘at most’
  4. identifying inequalities with variables as true or false
  5. solving equations of the form $\,xy = 0\,$
Section 15:
Numbers Have Lots of Different Names!

Read Section 15
  1. recognizing zero and one
Section 16:
Exact versus Approximate

Read Section 16
  1. writing fractions in simplest form
  2. deciding if a fraction is a finite or infinite repeating decimal
  3. deciding if numbers are equal or approximately equal
Section 17:

Read Section 17
  1. rounding decimals to a specified number of places
Section 18:
Unit Conversion

Read Section 18
  1. Tables of Unit Conversion Information
  2. classifying units as length, time, volume, weight/mass
  3. practice with unit abbreviations
  4. practice with unit names
  5. practice with unit conversion information
  6. one-step conversions
Section 19:
More Unit Conversion

Read Section 19
  1. multi-step conversions
  2. rate problems
  67a work problems: basic concepts
  67b work problems: quick-and-easy estimates
  67c work problems: guided practice
Section 20:
Exponent Notation

Read Section 20
  1. practice with exponents
  2. practice with order of operations
   69.3 (optional) Laurel, Yanny, Cookies, Bananas, and Clocks
   69.5 taking PEMDAS too literally: don't make this mistake!
  1. basic exponent practice with fractions
Section 21:
Exponent Laws

Read Section 21
  1. practice with $\,x^mx^n = x^{m+n}\,$
  2. practice with $\,(x^m)^n = x^{mn}\,$
  3. practice with $\,x^m/x^n = x^{m-n}$
  4. practice with $\,x^{-p} = 1/x^p$
  5. one-step exponent law practice
  6. multi-step exponent law practice
Section 22:

Read Section 22
  1. practice with radicals
  2. approximating radicals
  78.5   renaming square roots
Section 23:
Rational Exponents

Read Section 23
  1. writing radicals in rational exponent form
  2. writing rational exponents as radicals
  3. practice with rational exponents
Section 24:
The Distributive Law

Read Section 24
  1. practice with  x  and  -x
  2. practice with products of signed variables
  3. practice with the distributive law
  4. mental math: addition
  5. Don't mix up $\,3x\,$ versus $\,x^3\,$!
Section 25:
Revisiting Exponents

Read Section 25
  1. equal or opposites?
  2. recognizing the patterns $\,x^n\,$ and $\,(-x)^n\,$
  3. writing expressions in the form kxn
  4. writing more complicated expressions in the form kxn
  5. writing quite complicated expressions in the form kxn
Section 26:
FOIL and more

Read Section 26
  1. identifying variable parts and coefficients of terms
  2. combining like terms
  3. simplifying expressions like -a(3b - 2c - d)
  4. basic FOIL
  5. more complicated FOIL
  6. simplifying $\,(a+b)^2\,$ and $\,(a-b)^2\,$
  7. simplifying expressions like (a - b)(c + d - e)
98.5   dividing more than one term by a single term
Section 27:
These Sentences Certainly Look Different!

Read Section 27
  1. practice with the mathematical words and, or, and is equivalent to
Section 28:
Introduction to Factoring

Read Section 28
  1. recognizing products and sums; identifying factors and terms
  2. identifying common factors
  3. factoring simple expressions
Section 29:
Greatest Common Factor

Read Section 29
  1. listing all the factors of a whole number
  2. finding the greatest common factor of 2 or 3 numbers
  3. finding the greatest common factor of variable expressions
  4. factoring out the greatest common factor
Section 30:
Transforming Tool #1
(the Addition Property of Equality)

Read Section 30
  1. the Addition Property of Equality
Section 31:
Transforming Tool #2
(the Multiplication Property of Equality)

Read Section 31
  1. the Multiplication Property of Equality
Section 32:
Solving Linear Equations in One Variable

Read Section 32
  1. solving simple linear equations with integer coefficients
  2. solving more complicated linear equations with integer coefficients
  3. solving linear equations involving fractions
  4. solving linear equations, all mixed up
Section 32.5:
Applications and More

  1. simple word problems resulting in linear equations
Section 33:
Solving Linear Inequalities in One Variable

Read Section 33
  1. solving simple linear inequalities with integer coefficients
  2. solving linear inequalities with integer coefficients
  3. solving linear inequalities involving fractions
  4. solving linear inequalities, all mixed up
Section 34:
Introduction to Absolute Value

Read Section 34
  1. simplifying basic absolute value expressions
  2. determining the sign (plus or minus) of absolute value expressions
  3. solving simple absolute value sentences
  4. solving sentences involving ‘plus or minus’
Section 35:
Solving Absolute Value Equations

Read Section 35
  1. solving absolute value equations
Section 36:
Solving Absolute Value Inequalities Involving ‘Less Than’

Read Section 36
  1. solving absolute value inequalities involving ‘less than’
Section 37:
Finishing Up Absolute Value Sentences

Read Section 37
  1. solving absolute value inequalities involving ‘greater than’
  2. solving absolute value sentences (all types)
Section 38:
Factoring a Difference of Squares
  1. identifying perfect squares
  2. writing expressions in the form A2
  3. factoring a difference of squares
Section 39:
Solving Equations Involving Perfect Squares
  1. solving simple equations involving perfect squares
  2. solving more complicated equations involving perfect squares
  3. translating simple mathematical phrases
  4. word problems involving perfect squares
Section 40:
Factoring Trinomials
  1. basic concepts involved in factoring trinomials
  2. factoring $\,x^2 + bx + c\,$,   $\,c > 0\,$
  3. factoring $\,x^2 + bx + c\,$,   $\,c < 0\,$
  4. factoring trinomials, all mixed up
Section 41:
Solving Quadratic Equations by Factoring
  1. identifying quadratic equations
  2. writing quadratic equations in standard form
  3. solving simple quadratic equations by factoring
Section 42:
More on Quadratic Equations
  1. factoring $\,ax^2 + bx + c\,$
  2. solving more complicated quadratic equations by factoring
Section 42.5:
Arithmetic with Fractions Involving Variables
  1. multiplying and dividing fractions with variables
  2. adding and subtracting fractions with variables
Section 43:
Percent Increase and Decrease
  1. writing expressions involving percent increase and decrease
  2. calculating percent increase and decrease
  3. problems involving percent increase and decrease
  4. more problems involving percent increase and decrease
Section 44:
Introduction to the Coordinate Plane
  1. locating points in quadrants and on axes
  2. practice with points
  3. the Pythagorean Theorem
  4. the distance formula
  5. the midpoint formula
  6. introduction to equations and inequalities in two variables
Section 45:
  1. introduction to the slope of a line
  2. practice with slope
  3. graphing lines
  4. finding equations of lines
Section 46:
More On Lines
  1. point-slope form
  2. horizontal and vertical lines
  3. parallel and perpendicular lines
160.5   linear inequalities in two variables
Section 47:
  1. introduction to functions
  2. introduction to function notation
  3. more practice with function notation
  4. domain and range of a function