Section 1:
The Language of Mathematics
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 expressions versus sentences

Section 2:
Brushing Up On Basic Arithmetic Skills
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 basic addition practice
 multiplication
 divisibility
 basic properties of zero and one
 mixed basic add/subtract/multiply/divide practice

Section 3:
The Real Numbers
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 deciding if a number is a whole number, an integer, etc.

Section 4:
Addition of Signed Numbers
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 addition of signed numbers

Section 5:
Subtraction of Signed Numbers
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 subtraction of signed numbers
 mixed addition and subtraction of signed numbers

Section 6:
Average
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 fractions with a denominator of 2 to decimal form
 average of two signed numbers
 average of signed numbers

Section 7:
The Base Ten Number System
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 identifying place values
 multiplying by powers of ten

Section 8:
Decimals
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 changing decimals to fractions
 multiplying and dividing decimals by powers of ten
 changing decimals to percents
 changing percents to decimals

Section 9:
Mathematicians are Fond of Collections
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 introduction to sets
 interval and list notation

Section 10:
Holding This, Holding That
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 introduction to variables
 reading set notation
 going from a sequence of operations to an expression
 going from an expression to a sequence of operations
 solving simple sentences by inspection
 using mathematical conventions

Section 10.5:
Solving For A Particular Variable
(important for science classes)

 ‘undoing’ a sequence of operations
 solving for a particular variable
 Getting bigger? Getting smaller?

Section 10.7:
Scientific Notation and Significant Figures
(important for science classes)

 scientific notation
 significant figures and related concepts

Section 11:
Introduction to Fractions
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 rewriting fractions as a whole number plus a fraction
 locating fractions on a number line
 fractions involving zero

Section 12:
Multiplying Fractions
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 finding reciprocals
 determining if a product is positive or negative
 multiplying and dividing fractions
 practice with the form $\,a\cdot\frac{b}{c}\,$
 more practice with the form $\,a\cdot\frac{b}{c}\,$
 renaming fractional expressions

Section 13:
Adding Fractions
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 practice with multiples
 finding least common multiples
 renaming fractions with a specified denominator
 practice with factors
 adding and subtracting fractions
 adding and subtracting simple fractions with variables
 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
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 identifying inequalities as true or false
 bigger, smaller, greater, lesser
 practice with the phrases ‘at least’ and ‘at most’
 identifying inequalities with variables as true or false
 solving equations of the form $\,xy = 0\,$

Section 15:
Numbers Have Lots of Different names!
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 recognizing zero and one

Section 16:
Exact versus Approximate
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 writing fractions in simplest form
 deciding if a fraction is a finite or infinite repeating decimal
 deciding if numbers are equal or approximately equal

Section 17:
Rounding
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 rounding decimals to a specified number of places

Section 18:
Unit Conversion
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 Tables of Unit Conversion Information
 classifying units as length, time, volume, weight/mass
 practice with unit abbreviations
 practice with unit names
 practice with unit conversion information
 onestep conversions

Section 19:
More Unit Conversion
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 multistep conversions
 rate problems
67a work problems: basic concepts
67b work problems: quickandeasy estimates
67c work problems: guided practice

Section 20:
Exponent Notation
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 exponents
 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!
 basic exponent practice with fractions

Section 21:
Exponent Laws
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 practice with $\,x^mx^n = x^{m+n}\,$
 practice with $\,(x^m)^n = x^{mn}\,$
 practice with $\,x^m/x^n = x^{mn}$
 practice with $\,x^{p} = 1/x^p$
 onestep exponent law practice
 multistep exponent law practice

Section 22:
Radicals
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 practice with radicals
 approximating radicals
78.5 renaming square roots

Section 23:
Rational Exponents
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 writing radicals in rational exponent form
 writing rational exponents as radicals
 practice with rational exponents

Section 24:
The Distributive Law
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 practice with x and x
 practice with products of signed variables
 practice with the distributive law
 mental math: addition
 Don't mix up $\,3x\,$ versus $\,x^3\,$!

Section 25:
Revisiting Exponents
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 equal or opposites?
 recognizing the patterns $\,x^n\,$ and $\,(x)^n\,$
 writing expressions in the form kx^{n}
 writing more complicated expressions in the form kx^{n}
 writing quite complicated expressions in the form kx^{n}

Section 26:
FOIL and more
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 identifying variable parts and coefficients of terms
 combining like terms
 simplifying expressions like a(3b  2c  d)
 basic FOIL
 more complicated FOIL
 simplifying $\,(a+b)^2\,$ and $\,(ab)^2\,$

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!
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 practice with the mathematical words and, or, and is equivalent to

Section 28:
Introduction to Factoring
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 recognizing products and sums; identifying factors and terms
 identifying common factors
 factoring simple expressions

Section 29:
Greatest Common Factor
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 listing all the factors of a whole number
 finding the greatest common factor of 2 or 3 numbers
 finding the greatest common factor of variable expressions
 factoring out the greatest common factor

Section 30:
Transforming Tool #1
(the Addition Property of Equality)
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 the Addition Property of Equality

Section 31:
Transforming Tool #2
(the Multiplication Property of Equality)
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 the Multiplication Property of Equality

Section 32:
Solving Linear Equations in One Variable
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 solving simple linear equations with integer coefficients
 solving more complicated linear equations with integer coefficients
 solving linear equations involving fractions
 solving linear equations, all mixed up

Section 32.5:
Applications and More

 simple word problems resulting in linear equations

Section 33:
Solving Linear Inequalities in One Variable
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 solving simple linear inequalities with integer coefficients
 solving linear inequalities with integer coefficients
 solving linear inequalities involving fractions
 solving linear inequalities, all mixed up

Section 34:
Introduction to Absolute Value
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 simplifying basic absolute value expressions
 determining the sign (plus or minus) of absolute value expressions
 solving simple absolute value sentences
 solving sentences involving ‘plus or minus’

Section 35:
Solving Absolute Value Equations
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 solving absolute value equations

Section 36:
Solving Absolute Value Inequalities Involving ‘Less Than’
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 solving absolute value inequalities involving ‘less than’

Section 37:
Finishing Up Absolute Value Sentences
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 solving absolute value inequalities involving ‘greater than’
 solving absolute value sentences (all types)

Section 38:
Factoring a Difference of Squares

 identifying perfect squares
 writing expressions in the form A^{2}
 factoring a difference of squares

Section 39:
Solving Equations Involving Perfect Squares

 solving simple equations involving perfect squares
 solving more complicated equations involving perfect squares
 translating simple mathematical phrases
 word problems involving perfect squares

Section 40:
Factoring Trinomials

 basic concepts involved in factoring trinomials
 factoring $\,x^2 + bx + c\,$, $\,c > 0\,$
 factoring $\,x^2 + bx + c\,$, $\,c < 0\,$
 factoring trinomials, all mixed up

Section 41:
Solving Quadratic Equations by Factoring

 identifying quadratic equations
 writing quadratic equations in standard form
 solving simple quadratic equations by factoring

Section 42:
More on Quadratic Equations

 factoring $\,ax^2 + bx + c\,$
 solving more complicated quadratic equations by factoring

Section 42.5:
Arithmetic with Fractions Involving Variables

 multiplying and dividing fractions with variables
 adding and subtracting fractions with variables

Section 43:
Percent Increase and Decrease

 writing expressions involving percent increase and decrease
 calculating percent increase and decrease
 problems involving percent increase and decrease
 more problems involving percent increase and decrease

Section 44:
Introduction to the Coordinate Plane

 locating points in quadrants and on axes
 practice with points
 the Pythagorean Theorem
 the distance formula
 the midpoint formula
 introduction to equations and inequalities in two variables

Section 45:
Lines

 introduction to the slope of a line
 practice with slope
 graphing lines
 finding equations of lines

Section 46:
More On Lines

 pointslope form
 horizontal and vertical lines
 parallel and perpendicular lines
160.5 linear inequalities in two variables

Section 47:
Functions

 introduction to functions
 introduction to function notation
 more practice with function notation
 domain and range of a function
