# PRE-ALGEBRA ACADEMIC LIBRARY (MATH 800)

## Pre-Algebra Online 1St Semester (Math 800)

##### UNIT 1 – THE REAL NUMBER SYSTEM

- Course Overview
- Subsets of the Real Number System
- Classifying Numbers
- Ordering and Classifying Numbers
- Real Number System

- Using Variables
- What Is A Variable
- Why Aren’t We Using the Multiplication Sign
- Example: Evaluate a Formula Using Substitution

- The Number Line
- Number Line

- Comparing Rational Numbers
- Rational Word Problems
- Recognizing Rational and Irrational Numbers

- Decimal-Fraction Conversions
- Intro to Rational and Irrational Numbers
- Terminating and Repeating Decimals
- Fraction to a Decimal
- Converting a Fraction to a Decimal

- Quiz 1: Relationships
- Alternate Quiz 1—Form A: Relationships
- Alternate Quiz 1—Form B: Relationships
- Properties of Real Numbers
- Commutative law of addition
- Commutative law of multiplication
- Associative
- Identity Property
- Distributive Property – Addition and Subtraction

- Exponents
- Introduction to Exponents
- Exponent Rules

- Scientific Notation
- Scientific Notation

- Operations with Scientific Notation (Use videos in the curriculum, the Resources 800 and the supplementary video in the previous assignment and work with your teacher)
- Quiz 2: Other Forms
- Alternate Quiz 2—Form A: Other Forms
- Alternate Quiz 2—Form B: Other Forms
- Square Roots
- Understanding Square Roots
- Square Roots

- Order of Operations
- Orders of Operation

- Quiz 3: Simplifying
- Alternate Quiz 3—Form A: Simplifying
- Alternate Quiz 3—Form B: Simplifying
- Review
- Test
- Alternate Test—Form A
- Alternate Test—Form B
- Glossary and Credits

##### UNIT 2 – MODELING PROBLEMS IN INTEGERS

- Translating Expressions and Equations
- Understanding Written Expressions

- Solving One-Step Equations
- One-Step Equations

- Solving Two-Step Equations
- Two-Step Equations

- Solving Equations with Exponents
- Introduction to cube roots

- Quiz 1: Equations with Real Numbers
- Alternate Quiz 1—Form A: Equations with Real Numbers
- Alternate Quiz 1—Form B: Equations with Real Numbers
- Relations and Functions
- Relations and Functions

- Functions
- What Is a Function
- Relations and Functions

- Analyzing Graphs
- Introduction to coordinate plane

- Quiz 2: Functions
- Alternate Quiz 2—Form A: Functions
- Alternate Quiz 2—Form B: Functions
- Addition of Integers
- Adding Negative Numbers
- Addition of Integers

- Subtraction of Integers
- Why Subtracting a Negative Equivalent to Adding a Positive
- Subtraction of Integers (Adding and Subtracting Negative Numbers)

- Multiplying and Dividing Integers
- Multiplying and Dividing Integers (Multiplying Positive and Negative Numbers)
- Multiplying and Dividing Integers (Multiplying and Dividing Negative Numbers)

- Evaluating Expressions
- Evaluating Expressions and Variables – (There are a series of presentations on this topic. Complete as many as needed to understand the concepts covered in the lesson)

- Quiz 3: Integers
- Alternate Quiz 3—Form A: Integers
- Alternate Quiz 3—Form B: Integers
- Graphing
- Graphing (Coordinate Plane)

- One-Step Equations
- One Step Equations

- Two-Step Equations
- Why We Do the Same Things to Both Sides of Simple Equations

- Problem Solving
- Writing Equations from Word Problems
- Writing Equations from Word Problems

- Quiz 4: Modeling with Integers
- Alternate Quiz 4—Form A: Modeling with Integers
- Alternate Quiz 4—Form B: Modeling with Integers
- Review
- Test
- Alternate Test—Form A
- Alternate Test—Form B
- Glossary and Credits

##### UNIT 3 – MODELING PROBLEMS WITH RATIONAL NUMBERS

- Prime Factorization and the GCF
- Prime Factorization
- Greatest Common Factor

- Simplifying Fractions
- Simplifying Fractions

- The LCM and the LCD
- Greatest Common Factor Word Problem
- Finding Common Denominators

- Quiz 1: Number Theory
- Alternate Quiz 1—Form A: Number Theory
- Alternate Quiz 1—Form B: Number Theory
- Adding and Subtracting Like Fractions
- Adding Fractions with Like Denominators
- Adding Fractions With Different Signs

- Adding and Subtracting Unlike Fractions
- Adding Fractions with Unlike Denominators

- Adding and Subtracting Decimal Numbers
- Adding and Subtracting Decimals Example 1

- Multiplying and Dividing Fractions
- Multiplying Negative and Positive Fractions
- Multiplying Fractions and Whole Numbers

- Multiplying and Dividing Decimal Numbers
- Intro to multiplying decimals
- More intuition on multiplying decimals
- Multiplying decimals
- Dividing a decimal by a whole number
- Dividing a whole number by a decimal

- Irrational Numbers
- Intro to rational and irrational numbers

- Quiz 2: Solving Problems with Rational Numbers
- Alternate Quiz 2—Form A: Solving Problems with Rational Numbers
- Alternate Quiz 2—Form B: Solving Problems with Rational Numbers
- One-Step Addition and Subtraction Equations
- Examples of one-step equations like ax = b and x + a = b

- One-Step Multiplication and Division Equations
- Examples of one-step equations like ax = b and x + a = b
- One-step equations with multiplication
- One step equations with division

- Two-Step Equations
- Solving simple equations

- One-Step Inequalities
- One-step inequalities
- One-step inequality involving addition
- Multiplying and dividing with inequalities example

- Two-Step Inequalities
- Solving a two-step inequality

- Quiz 3: Solving Equations and Inequalities
- Alternate Quiz 3—Form A: Solving Equations and Inequalities
- Alternate Quiz 3—Form B: Solving Equations and Inequalities
- Review
- Test
- Alternate Test—Form A
- Alternate Test—Form B
- Glossary and Credits

##### UNIT 4 – PROPORTIONAL REASONING

- Perimeter
- Writing proportions
- Proportion word problem: hot dogs
- Proportion word problem: cookies

- Linear Applications
- Finding unit rates
- Finding unit prices

- Direct Variation
- Direct variation 1

- Quiz 1: Proportions
- Alternate Quiz 1—Form A: Proportions
- Alternate Quiz 1—Form B: Proportions
- Fraction, Percent and Decimal Equivalents
- Representing a number as a decimal, percent, and fraction

- Solving Percent Problems
- Solving percent problems
- Solving Percent Problems Using The Percent Proportion
- Solving Percent Problems using Proportions

- Applications of Ratios and Percent
- Percent word problems
- Another percent word problem

- More Applications with Percent
- Solving Percent Problems Using The Percent Proportion
- Solving Percent Problems using Proportions

- Quiz 2: Percents
- Alternate Quiz 2—Form A: Percents
- Alternate Quiz 2—Form B: Percents
- Unit Conversion within Customary Units
- Examples determining reasonable units

- Unit Conversion within Metric Units
- Conversion between metric units
- Conversion between metric units

- Corresponding Parts
- Congruent triangle proof example

- Indirect Measure
- Indirect Measurement Using Similar Triangles

- Models and Scales
- Interpreting a scale drawing

- Quiz 3: Measurement/Similar Figures
- Alternate Quiz 3—Form A: Measurement/Similar Figures
- Alternate Quiz 3—Form B: Measurement/Similar Figures
- Project: Proportional Reasoning (Follow the directions given in the assignment to draw from a comic picture one frame and then to reproduce the picture. Answer the following questions in more than 125 words – Write about the similarity of the original comic to the enlargement. How similar are they and how can you tell? What would cause differences in the two pictures? If you drew another comic using a grid, is there anything you would do differently? What would happen if you reduced the comic’s size rather than enlarged it? Would the process be the same? What would you do differently?)
- Review
- Test
- Alternate Test—Form A
- Alternate Test—Form B
- Glossary and Credits

##### UNIT 5 – MORE WITH FUNCTIONS

- Rewriting Equations
- Algebra 2 1.4 Examples Rewriting Equations and Formulas

- Combine Like Terms
- Combining like terms
- Combining like terms
- Combining like terms and simplifying expressions

- Solving Equations by Combining Like Terms
- Math Lessons : Solving Equations With Like Terms
- Solving an Equation by Combining Like Terms

- Distributive Property
- The Distributive Property
- The Distributive Property 2
- The Distributive Property
- Distributive Property

- Solving Equations with Distributive Property
- Solving equations with the distributive property
- Solving equations with the distributive property 2
- Equations with parentheses

- Solving Equations with Special Solutions
- Solving Linear Equations with One Variable Solving
- Equations With One, Many, or No Solutions

- Literal Equations
- Solving Literal Equations

- Quiz 1: Solving Equations
- Alternate Quiz 1—Form A: Solving Equations
- Alternate Quiz 1—Form B: Solving Equations
- Slope
- Slope of a line
- Slope = Rise over Run. “You have to RISE before you RUN”

- Comparing Functions
- Comparing functions rate of change

- Using Intercepts
- x- and y-intercepts
- Graphing using x- and y-intercepts

- Slope-Intercept Form
- Converting to slope-intercept form
- Slope-Intercept Form y=mx+b

- More Slope-Intercept Form
- Graphing Lines in Slope-Intercept form y=mx+b

- Applications of Linear Functions
- Slope Intercept Form| Real World Applications Linear Equations
- Real World Problems Using Linear Equations

- Non-Linear Functions
- Recognizing linear functions

- Quiz 2: Families of Functions
- Alternate Quiz 2—Form A: Families of Functions
- Alternate Quiz 2—Form B: Families of Functions
- Graphing Systems of Linear Equations
- System of Equations: One Solution, No Solution, or Infinitely Many Solutions

- Solving Systems of Linear Equations Using Substitution
- Algebra – Solving Using Substitution Method

- Solving Systems of Linear Equations Using Addition
- Solving Systems of Equations: The Addition Method

- Application of Linear Systems
- Solving Systems of Equations: Coins

- Quiz 3: Systems of Equations
- Quiz 3: Alternate Quiz A: Systems of Equations
- Quiz 3: Alternate Quiz B: Systems of Equations
- Patterns and Arithmetic Sequences
- Figuring out days of the week
- Arithmetic sequences
- Arithmetic sequences 1

- Geometric Sequences
- Geometric sequence or progression
- Geometric sequences 1

- Exponential Sequences
- Exponential growth functions

- Recursive Sequences
- Explicit and recursive definitions of sequences

- Quiz 4: Patterns
- Alternate Quiz 4—Form A: Patterns
- Alternate Quiz 4—Form B: Patterns
- Review
- Test
- Alternate Test—Form A
- Alternate Test—Form B
- Glossary and Credits