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Foundational Mathematics for Corequisite Courses:
Succeeding at College Mathematics
Aaron Wong
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Front Matter
Colophon
Preface
I
Main Trunk
1
Basic Algebraic Presentation
1.1
How We Write Affects How We Think
1.2
Worksheets
1.2
Worksheet 1
1.2
Worksheet 2
1.2
Worksheet 3
1.2
Worksheet 4
1.2
Worksheet 5
1.3
Deliberate Practice: Solving Equations for a Variable
1.3
Worksheet
1.4
Closing Ideas
1.5
Going Deeper: Clearing the Denominator
2
Variables in Expressions and Equations
2.1
Letters are Numbers in Disguise
2.2
Worksheets
2.2
Worksheet 1
2.2
Worksheet 2
2.2
Worksheet 3
2.2
Worksheet 4
2.2
Worksheet 5
2.3
Deliberate Practice: Solving Equations for a Variable Expression
2.3
Worksheet
2.4
Closing Ideas
2.5
Going Deeper: Sets and Solution Sets
3
Like and Unlike Terms
3.1
One of These Things is Not Like the Other
3.2
Worksheets
3.2
Worksheet 1
3.2
Worksheet 2
3.2
Worksheet 3
3.2
Worksheet 4
3.2
Worksheet 5
3.3
Deliberate Practice: Combining Like Terms
3.3
Worksheet
3.4
Closing Ideas
4
Simplifying Expressions and Solving Equations
4.1
Read the Instructions
4.2
Worksheets
4.2
Worksheet 1
4.2
Worksheet 2
4.2
Worksheet 3
4.2
Worksheet 4
4.2
Worksheet 5
4.3
Deliberate Practice: Solving Equations for a Variable (Part 2)
4.3
Worksheet
4.4
Closing Ideas
4.5
Going Deeper: Inequalities
5
Variables and Substitutions
5.1
This is a That
5.2
Worksheets
5.2
Worksheet 1
5.2
Worksheet 2
5.2
Worksheet 3
5.2
Worksheet 4
5.2
Worksheet 5
5.3
Deliberate Practice: Substitute and Solve
5.3
Worksheet
5.4
Closing Ideas
5.5
Going Deeper: Disappearing Variables
6
Exponents
6.1
Don’t Memorize These Formulas
6.2
Worksheets
6.2
Worksheet 1
6.2
Worksheet 2
6.2
Worksheet 3
6.2
Worksheet 4
6.2
Worksheet 5
6.3
Deliberate Practice: Exponents
6.3
Worksheet
6.4
Closing Ideas
6.5
Going Deeper: Radicals and Fractional Exponents
7
Products of Polynomials
7.1
Organization Will Set You Free
7.2
Worksheets
7.2
Worksheet 1
7.2
Worksheet 2
7.2
Worksheet 3
7.2
Worksheet 4
7.2
Worksheet 5
7.3
Deliberate Practice: The Distributive Property
7.3
Worksheet
7.4
Closing Ideas
7.5
Going Deeper: Algebra Tiles
7.5.1
Representing and Simplifying Algebriac Expressions
7.5.2
Solving Equations
7.5.3
Other Uses of Algebra Tiles
8
Common Factors
8.1
You All Have This in Common
8.2
Worksheets
8.2
Worksheet 1
8.2
Worksheet 2
8.2
Worksheet 3
8.2
Worksheet 4
8.2
Worksheet 5
8.3
Deliberate Practice: Factor by Grouping
8.3
Worksheet
8.4
Closing Ideas
9
Factoring Quadratic Polynomials
9.1
Lots of Methods, Not All Good
9.2
Worksheets
9.2
Worksheet 1
9.2
Worksheet 2
9.2
Worksheet 3
9.2
Worksheet 4
9.2
Worksheet 5
9.2
Worksheet 6
9.3
Deliberate Practice: Factoring Quadratic Polynomials
9.3
Worksheet
9.4
Closing Ideas
9.5
Going Deeper: Special Factorizations
10
Reading Mathematical Expressions
10.1
So Many Symbols!
10.2
Worksheets
10.2
Worksheet 1
10.2
Worksheet 2
10.2
Worksheet 3
10.2
Worksheet 4
10.2
Worksheet 5
10.3
Deliberate Practice: Solving for Variables and Function Expressions
10.3
Worksheet
10.4
Closing Ideas
10.5
Going Deeper: Your Calculator and You
11
Reflection
11.1
A Pause for Reflection
11.2
Worksheets
11.2
Worksheet 1: Questions about the Content
11.2
Worksheet 2: Questions about You
II
Linear Equations and the Coordinate Plane
12
Lines and the Coordinate Plane
12.1
Get it Straight
12.2
Worksheets
12.2
Worksheet 1
12.2
Worksheet 2
12.2
Worksheet 3
12.2
Worksheet 4
12.2
Worksheet 5
12.3
Deliberate Practice: Graphing Lines
12.3
Worksheet
12.4
Closing Ideas
12.5
Going Deeper: Graphing Functions
13
Slope-Intercept Form
13.1
The Line in the Sand
13.2
Worksheets
13.2
Worksheet 1
13.2
Worksheet 2
13.2
Worksheet 3
13.2
Worksheet 4
13.2
Worksheet 5
13.3
Deliberate Practice: Slope-Intercept Form
13.3
Worksheet
13.4
Closing Ideas
13.5
Going Deeper: Average Rate of Change
14
Point-Slope Form
14.1
Start Here, Go There
14.2
Worksheets
14.2
Worksheet 1
14.2
Worksheet 2
14.2
Worksheet 3
14.2
Worksheet 4
14.2
Worksheet 5
14.3
Deliberate Practice: Point-Slope Form
14.3
Worksheet
14.4
Closing Ideas
15
The Method of Substitution
15.1
Replace This With That
15.1.1
Brief Fraction Review
15.2
Worksheets
15.2
Worksheet 1
15.2
Worksheet 2
15.2
Worksheet 3
15.2
Worksheet 4
15.2
Worksheet 5
15.3
Deliberate Practice: Solving by Substitution
15.3
Worksheet
15.4
Closing Ideas
16
The Method of Elimination
16.1
Make it Go Away
16.2
Worksheets
16.2
Worksheet 1
16.2
Worksheet 2
16.2
Worksheet 3
16.2
Worksheet 4
16.2
Worksheet 5
16.3
Deliberate Practice: Solving by Elimination
16.3
Worksheet
16.4
Closing Ideas
16.5
Going Deeper: Three Dimensional Systems
16.5.1
Solving Three Dimensional Systems by Substitution
16.5.2
Solving Three Dimensional Systems by Elimination
III
Fractions and Decimals
17
Fraction Basics
17.1
Facing Your Fear
17.2
Worksheets
17.2
Worksheet 1
17.2
Worksheet 2
17.2
Worksheet 3
17.2
Worksheet 4
17.2
Worksheet 5
17.3
Deliberate Practice: Reducing Fractions
17.3
Worksheet
17.4
Closing Ideas
17.5
Going Deeper: Reducing Rational Expressions
17.5.1
A Collection of Errors
17.5.2
Factoring Out the Constant (Including the Negative)
18
Fraction Addition and Subtraction
18.1
Find the Common Denominator
18.2
Worksheets
18.2
Worksheet 1
18.2
Worksheet 2
18.2
Worksheet 3
18.2
Worksheet 4
18.2
Worksheet 5
18.3
Deliberate Practice: Adding and Subtracting Fractions
18.3
Worksheet
18.4
Closing Ideas
18.5
Going Deeper: Adding and Subtracting Rational Expressions
19
Fraction Multiplication
19.1
Multiply Straight Across
19.2
Worksheets
19.2
Worksheet 1
19.2
Worksheet 2
19.2
Worksheet 3
19.2
Worksheet 4
19.2
Worksheet 5
19.3
Deliberate Practice: Multiplying Fractions
19.3
Worksheet
19.4
Closing Ideas
19.5
Going Deeper: Additional Factoring Techniques
20
Fraction Division
20.1
Multiply by the Reciprocal
20.2
Worksheets
20.2
Worksheet 1
20.2
Worksheet 2
20.2
Worksheet 3
20.2
Worksheet 4
20.2
Worksheet 5
20.3
Deliberate Practice: Dividing Fractions
20.3
Worksheet
20.4
Closing Ideas
20.5
Going Deeper: Fractions Inside of Fractions
21
Decimal Addition and Subtraction
21.1
Making Sense with Dollars and Cents
21.2
Worksheets
21.2
Worksheet 1
21.2
Worksheet 2
21.2
Worksheet 3
21.2
Worksheet 4
21.2
Worksheet 5
21.3
Deliberate Practice: Adding and Subtracting Decimals
21.3
Worksheet
21.4
Closing Ideas
22
Multiplying Decimals and Percents
22.1
What Percent Do You Understand?
22.2
Worksheets
22.2
Worksheet 1
22.2
Worksheet 2
22.2
Worksheet 3
22.2
Worksheet 4
22.2
Worksheet 5
22.3
Deliberate Practice: Percent Calculations
22.3
Worksheet
22.4
Closing Ideas
22.5
Going Deeper: Proportional Reasoning
23
Reflection
23.1
Another Pause for Reflection
23.2
Worksheets
23.2
Worksheet 1: Questions about the Content
23.2
Worksheet 2: Questions about You
IV
Arithmetic
24
Rethinking Arithmetic
24.1
Visualizing Numbers
24.2
Worksheets
24.2
Worksheet 1
24.2
Worksheet 2
24.2
Worksheet 3
24.2
Worksheet 4
24.2
Worksheet 5
24.3
Deliberate Practice: Inequalities and the Number Line
24.3
Worksheet
24.4
Closing Ideas
24.5
Going Deeper: Intervals on the Number Line
25
Addition
25.1
Carry the One (or Maybe Not)
25.2
Worksheets
25.2
Worksheet 1
25.2
Worksheet 2
25.2
Worksheet 3
25.2
Worksheet 4
25.2
Worksheet 5
25.3
Deliberate Practice: Addition Practice
25.3
Worksheet
25.4
Closing Ideas
25.5
Going Deeper:Automaticity with Arithmetic
26
Subtraction
26.1
Borrowing is Overrated
26.2
Worksheets
26.2
Worksheet 1
26.2
Worksheet 2
26.2
Worksheet 3
26.2
Worksheet 4
26.2
Worksheet 5
26.3
Deliberate Practice: Subtraction Practice
26.3
Worksheet
26.4
Closing Ideas
26.5
Going Deeper: Subtraction as Displacement
27
Negatives on the Number Line
27.1
Through the Looking Glass
27.2
Worksheets
27.2
Worksheet 1
27.2
Worksheet 2
27.2
Worksheet 3
27.2
Worksheet 4
27.2
Worksheet 5
27.3
Deliberate Practice: Practice with Negatives
27.3
Worksheet
27.4
Closing Ideas
27.5
Going Deeper: The Absolute Value Function
28
Calculations with Integer Chips
28.1
When All the Chips are Down
28.2
Worksheets
28.2
Worksheet 1
28.2
Worksheet 2
28.2
Worksheet 3
28.2
Worksheet 4
28.2
Worksheet 5
28.3
Deliberate Practice: Practice with Negatives
28.3
Worksheet
28.4
Closing Ideas
28.5
Going Deeper: Mental Arithmetic
29
Arithmetic as Movement on a Number Line
29.1
Turn Around and Walk Backwards
29.2
Worksheets
29.2
Worksheet 1
29.2
Worksheet 2
29.2
Worksheet 3
29.2
Worksheet 4
29.2
Worksheet 5
29.3
Deliberate Practice: Movement on the Number Line
29.3
Worksheet
29.4
Closing Ideas
29.5
Going Deeper: Number Patterns
30
Multiplication
30.1
Making Groups of Things
30.2
Worksheets
30.2
Worksheet 1
30.2
Worksheet 2
30.2
Worksheet 3
30.2
Worksheet 4
30.2
Worksheet 5
30.3
Deliberate Practice: Multiplication Concepts
30.3
Worksheet
30.4
Closing Ideas
30.5
Going Deeper: Alternative Multiplication Techniques
30.5.1
The Lattice Method
30.5.2
The Egyptian Multiplication Method
31
Division
31.1
Breaking Down the Mantra
31.2
Worksheets
31.2
Worksheet 1
31.2
Worksheet 2
31.2
Worksheet 3
31.2
Worksheet 4
31.2
Worksheet 5
31.3
Deliberate Practice: Division
31.3
Worksheet
31.4
Closing Ideas
31.5
Going Deeper: Remainders and Decimals
32
Reflection
32.1
Yet Another Pause for Reflection
32.2
Worksheets
32.2
Worksheet 1: Questions about the Content
32.2
Worksheet 2: Questions about You
V
Applications
33
Mathematical Relationships
33.1
Key Words are (Mostly) Evil
33.2
Worksheets
33.2
Worksheet 1
33.2
Worksheet 2
33.2
Worksheet 3
33.2
Worksheet 4
33.2
Worksheet 5
33.3
Deliberate Practice: Basic Word Problems
33.3
Worksheet
33.4
Closing Ideas
34
Scientific Notation
34.1
Numbers That Are Annoyingly Big or Small
34.2
Worksheets
34.2
Worksheet 1
34.2
Worksheet 2
34.2
Worksheet 3
34.2
Worksheet 4
34.2
Worksheet 5
34.3
Deliberate Practice: Scientific Notation
34.3
Worksheet
34.4
Closing Ideas
35
Unit Conversions
35.1
Say Goodbye to the Mars Climate Orbiter
35.2
Worksheets
35.2
Worksheet 1
35.2
Worksheet 2
35.2
Worksheet 3
35.2
Worksheet 4
35.2
Worksheet 5
35.3
Deliberate Practice: Unit Conversions
35.3
Worksheet
35.4
Closing Ideas
36
Reflection
36.1
Yet Another Pause for Reflection
36.2
Worksheets
36.2
Worksheet 1: Questions about the Content
36.2
Worksheet 2: Questions about You
Back Matter
A
Definitions
B
Theorems
C
PDF Textbooks
D
PDF Worksheets
Index
Print
Worksheet
Worksheet 3
A4
US
1
.
Solve the system of equations using the method of elimination.
{
−
x
+
2
y
=
6
3
x
−
4
y
=
1
2
.
Solve the system of equations using the method of elimination.
{
−
3
x
+
5
y
=
3
−
2
x
+
3
y
=
−
2
