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Foundational Mathematics for Corequisite Courses:
Succeeding at College Mathematics
Aaron Wong
Contents
Index
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Contents
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Next
Front Matter
Colophon
Preface
I
Main Trunk
1
Basic Algebraic Presentation
How We Write Affects How We Think
Worksheets
Deliberate Practice: Solving Equations for a Variable
Closing Ideas
Going Deeper: Clearing the Denominator
2
Variables in Expressions and Equations
Letters are Numbers in Disguise
Worksheets
Deliberate Practice: Solving Equations for a Variable Expression
Closing Ideas
Going Deeper: Sets and Solution Sets
3
Like and Unlike Terms
One of These Things is Not Like the Other
Worksheets
Deliberate Practice: Combining Like Terms
Closing Ideas
4
Simplifying Expressions and Solving Equations
Read the Instructions
Worksheets
Deliberate Practice: Solving Equations for a Variable (Part 2)
Closing Ideas
Going Deeper: Inequalities
5
Variables and Substitutions
This is a That
Worksheets
Deliberate Practice: Substitute and Solve
Closing Ideas
Going Deeper: Disappearing Variables
6
Exponents
Don't Memorize These Formulas
Worksheets
Deliberate Practice: Exponents
Closing Ideas
Going Deeper: Radicals and Fractional Exponents
7
Products of Polynomials
Organization Will Set You Free
Worksheets
Deliberate Practice: The Distributive Property
Closing Ideas
Going Deeper: Algebra Tiles
8
Common Factors
You All Have This in Common
Worksheets
Deliberate Practice: Factor by Grouping
Closing Ideas
9
Factoring Quadratic Polynomials
Lots of Methods, Not All Good
Worksheets
Deliberate Practice: Factoring Quadratic Polynomials
Closing Ideas
Going Deeper: Special Factorizations
10
Reading Mathematical Expressions
So Many Symbols!
Worksheets
Deliberate Practice: Solving for Variables and Function Expressions
Closing Ideas
Going Deeper: Your Calculator and You
11
Reflection
A Pause for Reflection
Worksheets
II
Linear Equations and the Coordinate Plane
12
Lines and the Coordinate Plane
Get it Straight
Worksheets
Deliberate Practice: Graphing Lines
Closing Ideas
Going Deeper: Graphing Functions
13
Slope-Intercept Form
The Line in the Sand
Worksheets
Deliberate Practice: Slope-Intercept Form
Closing Ideas
Going Deeper: Average Rate of Change
14
Point-Slope Form
Start Here, Go There
Worksheets
Deliberate Practice: Point-Slope Form
Closing Ideas
15
The Method of Substitution
Replace This With That
Worksheets
Deliberate Practice: Solving by Substitution
Closing Ideas
16
The Method of Elimination
Make it Go Away
Worksheets
Deliberate Practice: Solving by Elimination
Closing Ideas
Going Deeper: Three Dimensional Systems
III
Fractions and Decimals
17
Fraction Basics
Facing Your Fear
Worksheets
Deliberate Practice: Reducing Fractions
Closing Ideas
Going Deeper: Reducing Rational Expressions
18
Fraction Addition and Subtraction
Find the Common Denominator
Worksheets
Deliberate Practice: Adding and Subtracting Fractions
Closing Ideas
Going Deeper: Adding and Subtracting Rational Expressions
19
Fraction Multiplication
Multiply Straight Across
Worksheets
Deliberate Practice: Multiplying Fractions
Closing Ideas
Going Deeper: Additional Factoring Techniques
20
Fraction Division
Multiply by the Reciprocal
Worksheets
Deliberate Practice: Dividing Fractions
Closing Ideas
Going Deeper: Fractions Inside of Fractions
21
Decimal Addition and Subtraction
Making Sense with Dollars and Cents
Worksheets
Deliberate Practice: Adding and Subtracting Decimals
Closing Ideas
22
Multiplying Decimals and Percents
What Percent Do You Understand?
Worksheets
Deliberate Practice: Percent Calculations
Closing Ideas
Going Deeper: Proportional Reasoning
23
Reflection
Another Pause for Reflection
Worksheets
IV
Arithmetic
24
Rethinking Arithmetic
Visualizing Numbers
Worksheets
Deliberate Practice: Inequalities and the Number Line
Closing Ideas
Going Deeper: Intervals on the Number Line
25
Addition
Carry the One (or Maybe Not)
Worksheets
Deliberate Practice: Addition Practice
Closing Ideas
Going Deeper:Automaticity with Arithmetic
26
Subtraction
Borrowing is Overrated
Worksheets
Deliberate Practice: Subtraction Practice
Closing Ideas
Going Deeper: Subtraction as Displacement
27
Negatives on the Number Line
Through the Looking Glass
Worksheets
Deliberate Practice: Practice with Negatives
Closing Ideas
Going Deeper: The Absolute Value Function
28
Calculations with Integer Chips
When All the Chips are Down
Worksheets
Deliberate Practice: Practice with Negatives
Closing Ideas
Going Deeper: Mental Arithmetic
29
Arithmetic as Movement on a Number Line
Turn Around and Walk Backwards
Worksheets
Deliberate Practice: Movement on the Number Line
Closing Ideas
Going Deeper: Number Patterns
30
Multiplication
Making Groups of Things
Worksheets
Deliberate Practice: Multiplication Concepts
Closing Ideas
Going Deeper: Alternative Multiplication Techniques
31
Division
Breaking Down the Mantra
Worksheets
Deliberate Practice: Division
Closing Ideas
Going Deeper: Remainders and Decimals
32
Reflection
Yet Another Pause for Reflection
Worksheets
V
Applications
33
Mathematical Relationships
Key Words are (Mostly) Evil
Worksheets
Deliberate Practice: Basic Word Problems
Closing Ideas
34
Scientific Notation
Numbers That Are Annoyingly Big or Small
Worksheets
Deliberate Practice: Scientific Notation
Closing Ideas
35
Unit Conversions
Say Goodbye to the Mars Climate Orbiter
Worksheets
Deliberate Practice: Unit Conversions
Closing Ideas
36
Reflection
Yet Another Pause for Reflection
Worksheets
Back Matter
A
Definitions
B
Theorems
C
PDF Textbooks
D
PDF Worksheets
Index
Authored in PreTeXt
Worksheet
Worksheet 4
A4
US
1
.
Find three different point-slope forms for the given line.
2
.
Find three different point-slope forms for the given line.