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PRE-ALGEBRA ​ACADEMIC LIBRARY (MATH 800)

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Pre-Algebra Online 1st Semester (Math 800)

Pre-algebra is an introductory algebra course designed to prepare middle school students for Algebra I in high school.

The course focuses on strengthening needed skills in problem solving, integers, equations, and graphing. Students will begin to see the “big picture” of mathematics and learn how numeric, algebraic, and geometric concepts are woven together to build a foundation for higher mathematical thinking.

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Pre-Algebra Online 1St Semester (Math 800)

UNIT 1 – THE REAL NUMBER SYSTEM
  1. Course Overview
  2. Subsets of the Real Number System
    1. ​Classifying Numbers
    2. Ordering and Classifying Numbers​​
    3. Real Number System
  3. Using Variables
    1. What Is A Variable
    2. Why Aren’t We Using the Multiplication Sign
    3. Example: Evaluate a Formula Using Substitution
  4. The Number Line
    1. Number Line
  5. Comparing Rational Numbers
    1. Rational Word Problems
    2. Recognizing Rational and Irrational Numbers
  6. Decimal-Fraction Conversions
    1. ​Intro to Rational and Irrational Numbers
    2. ​​Terminating and Repeating Decimals
    3. Fraction to a Decimal
    4. ​Converting a Fraction to a Decimal
  7. Quiz 1: Relationships
  8. Alternate Quiz 1—Form A: Relationships
  9. Alternate Quiz 1—Form B: Relationships
  10. Properties of Real Numbers
    1. Commutative law of addition
    2. Commutative law of multiplication ​
    3. Associative
    4. Identity Property
    5. Distributive Property – Addition and Subtraction
  11. Exponents
    1. Introduction to Exponents
    2. Exponent Rules
  12. Scientific Notation
    1. Scientific Notation
  13. 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)
  14. Quiz 2: Other Forms
  15. Alternate Quiz 2—Form A: Other Forms
  16. Alternate Quiz 2—Form B: Other Forms
  17. Square Roots
    1. Understanding Square Roots
    2. Square Roots
  18. Order of Operations
    1. Orders of Operation
    1. Quiz 3: Simplifying
    2. Alternate Quiz 3—Form A: Simplifying
    3. Alternate Quiz 3—Form B: Simplifying
    4. Review
    5. Test
    6. Alternate Test—Form A
    7. Alternate Test—Form B
    8. Glossary and Credits
    UNIT 2 – MODELING PROBLEMS IN INTEGERS
    1. Translating Expressions and Equations
      1. Understanding Written Expressions
    2. Solving One-Step Equations
      1. One-Step Equations
    3. Solving Two-Step Equations
      1. Two-Step Equations
    4. Solving Equations with Exponents
      1. Introduction to cube roots
    5. Quiz 1: Equations with Real Numbers
    6. Alternate Quiz 1—Form A: Equations with Real Numbers
    7. Alternate Quiz 1—Form B: Equations with Real Numbers
    8. Relations and Functions
      1. Relations and Functions
    9. Functions
      1. What Is a Function
      2. Relations and Functions
    10. Analyzing Graphs
      1. Introduction to coordinate plane
    11. Quiz 2: Functions
    12. Alternate Quiz 2—Form A: Functions
    13. Alternate Quiz 2—Form B: Functions
    14. Addition of Integers
      1. Adding Negative Numbers
      2. Addition of Integers
    15. Subtraction of Integers
      1. Why Subtracting a Negative Equivalent to Adding a Positive
      2. Subtraction of Integers (Adding and Subtracting Negative Numbers)
    16. Multiplying and Dividing Integers
      1. Multiplying and Dividing Integers (Multiplying Positive and Negative Numbers)
      2. Multiplying and Dividing Integers (Multiplying and Dividing Negative Numbers)
    17. Evaluating Expressions
      1. 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)
    18. Quiz 3: Integers
    19. Alternate Quiz 3—Form A: Integers
    20. Alternate Quiz 3—Form B: Integers
    21. Graphing
      1. Graphing (Coordinate Plane)
    22. One-Step Equations
      1. One Step Equations
    23. Two-Step Equations
      1. Why We Do the Same Things to Both Sides of Simple Equations
    24. Problem Solving
      1. Writing Equations from Word Problems
      2. Writing Equations from Word Problems
    25. Quiz 4: Modeling with Integers
    26. Alternate Quiz 4—Form A: Modeling with Integers
    27. Alternate Quiz 4—Form B: Modeling with Integers
    28. Review
    29. Test
    30. Alternate Test—Form A
    31. Alternate Test—Form B
    32. Glossary and Credits
    UNIT 3 – MODELING PROBLEMS WITH RATIONAL NUMBERS
    1. Prime Factorization and the GCF
      1. Prime Factorization
      2. Greatest Common Factor
    2. Simplifying Fractions
      1. Simplifying Fractions
    3. The LCM and the LCD
      1. Greatest Common Factor Word Problem
      2. Finding Common Denominators
    4. Quiz 1: Number Theory
    5. Alternate Quiz 1—Form A: Number Theory
    6. Alternate Quiz 1—Form B: Number Theory
    7. Adding and Subtracting Like Fractions
      1. Adding Fractions with Like Denominators
      2. Adding Fractions With Different Signs
    8. Adding and Subtracting Unlike Fractions
      1. Adding Fractions with Unlike Denominators
    9. Adding and Subtracting Decimal Numbers
      1. Adding and Subtracting Decimals Example 1
    10. Multiplying and Dividing Fractions
      1. Multiplying Negative and Positive Fractions
      2. Multiplying Fractions and Whole Numbers
    11. Multiplying and Dividing Decimal Numbers
      1. Intro to multiplying decimals
      2. More intuition on multiplying decimals
      3. Multiplying decimals
      4. Dividing a decimal by a whole number
      5. Dividing a whole number by a decimal
    12. Irrational Numbers
      1. ​Intro to rational and irrational numbers
    13. Quiz 2: Solving Problems with Rational Numbers
    14. Alternate Quiz 2—Form A: Solving Problems with Rational Numbers
    15. Alternate Quiz 2—Form B: Solving Problems with Rational Numbers
    16. One-Step Addition and Subtraction Equations
      1. Examples of one-step equations like ax = b and x + a = b
    17. One-Step Multiplication and Division Equations
      1. Examples of one-step equations like ax = b and x + a = b
      2. One-step equations with multiplication
      3. One step equations with division
    18. Two-Step Equations
      1. Solving simple equations
    19. One-Step Inequalities
      1. One-step inequalities
      2. One-step inequality involving addition
      3. Multiplying and dividing with inequalities example
    20. Two-Step Inequalities
      1. Solving a two-step inequality
    21. Quiz 3: Solving Equations and Inequalities
    22. Alternate Quiz 3—Form A: Solving Equations and Inequalities
    23. Alternate Quiz 3—Form B: Solving Equations and Inequalities
    24. Review
    25. Test
    26. Alternate Test—Form A
    27. Alternate Test—Form B
    28. Glossary and Credits
    UNIT 4 – PROPORTIONAL REASONING
    1. Perimeter
      1. Writing proportions
      2. Proportion word problem: hot dogs
      3. Proportion word problem: cookies
    2. Linear Applications
      1. Finding unit rates
      2. Finding unit prices
    3. Direct Variation
      1. Direct variation 1
    4. Quiz 1: Proportions
    5. Alternate Quiz 1—Form A: Proportions
    6. Alternate Quiz 1—Form B: Proportions
    7. Fraction, Percent and Decimal Equivalents
      1. Representing a number as a decimal, percent, and fraction
    8. Solving Percent Problems
      1. Solving percent problems
      2. Solving Percent Problems Using The Percent Proportion
      3. Solving Percent Problems using Proportions
    9. Applications of Ratios and Percent
      1. Percent word problems
      2. Another percent word problem
    10. More Applications with Percent
      1. Solving Percent Problems Using The Percent Proportion
      2. Solving Percent Problems using Proportions
    11. Quiz 2: Percents
    12. Alternate Quiz 2—Form A: Percents
    13. Alternate Quiz 2—Form B: Percents
    14. Unit Conversion within Customary Units
      1. Examples determining reasonable units
    15. Unit Conversion within Metric Units
      1. Conversion between metric units​
      2. Conversion between metric units
    16. Corresponding Parts
      1. Congruent triangle proof example
    17. Indirect Measure
      1. ​Indirect Measurement Using Similar Triangles
    18. Models and Scales
      1. Interpreting a scale drawing
    19. Quiz 3: Measurement/Similar Figures
    20. Alternate Quiz 3—Form A: Measurement/Similar Figures
    21. Alternate Quiz 3—Form B: Measurement/Similar Figures
    22. 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?)
    23. Review
    24. Test
    25. Alternate Test—Form A
    26. Alternate Test—Form B
    27. Glossary and Credits
    UNIT 5 – MORE WITH FUNCTIONS
    1. Rewriting Equations
      1. Algebra 2 1.4 Examples Rewriting Equations and Formulas
    2. Combine Like Terms
      1. Combining like terms
      2. Combining like terms
      3. Combining like terms and simplifying expressions
    3. Solving Equations by Combining Like Terms
      1. Math Lessons : Solving Equations With Like Terms
      2. Solving an Equation by Combining Like Terms
    4. Distributive Property
      1. The Distributive Property
      2. The Distributive Property 2
      3. The Distributive Property
      4. Distributive Property
    5. Solving Equations with Distributive Property
      1. Solving equations with the distributive property
      2. Solving equations with the distributive property 2
      3. Equations with parentheses
    6. Solving Equations with Special Solutions
      1. Solving Linear Equations with One Variable Solving
      2. Equations With One, Many, or No Solutions
    7. Literal Equations
      1. Solving Literal Equations
    8. Quiz 1: Solving Equations
    9. Alternate Quiz 1—Form A: Solving Equations
    10. Alternate Quiz 1—Form B: Solving Equations
    11. ​Slope
      1. Slope of a line
      2. Slope = Rise over Run. “You have to RISE before you RUN”
    12. Comparing Functions
      1. Comparing functions rate of change
    13. Using Intercepts
      1. x- and y-intercepts
      2. Graphing using x- and y-intercepts
    14. Slope-Intercept Form
      1. Converting to slope-intercept form
      2. Slope-Intercept Form y=mx+b
    15. More Slope-Intercept Form
      1. Graphing Lines in Slope-Intercept form y=mx+b
    16. Applications of Linear Functions
      1. Slope Intercept Form| Real World Applications Linear Equations
      2. Real World Problems Using Linear Equations
    17. Non-Linear Functions
      1. Recognizing linear functions
    18. Quiz 2: Families of Functions
    19. Alternate Quiz 2—Form A: Families of Functions
    20. Alternate Quiz 2—Form B: Families of Functions
    21. Graphing Systems of Linear Equations
      1. System of Equations: One Solution, No Solution, or Infinitely Many Solutions
    22. Solving Systems of Linear Equations Using Substitution
      1. Algebra – Solving Using Substitution Method
    23. Solving Systems of Linear Equations Using Addition
      1. Solving Systems of Equations: The Addition Method
    24. Application of Linear Systems
      1. ​Solving Systems of Equations: Coins
    25. Quiz 3: Systems of Equations
    26. Quiz 3: Alternate Quiz A: Systems of Equations
    27. Quiz 3: Alternate Quiz B: Systems of Equations
    28. Patterns and Arithmetic Sequences
      1. Figuring out days of the week
      2. Arithmetic sequences
      3. Arithmetic sequences 1
    29. Geometric Sequences
      1. Geometric sequence or progression
      2. Geometric sequences 1
    30. Exponential Sequences
      1. Exponential growth functions
    31. Recursive Sequences
      1. Explicit and recursive definitions of sequences
    32. Quiz 4: Patterns
    33. Alternate Quiz 4—Form A: Patterns
    34. Alternate Quiz 4—Form B: Patterns
    35. Review
    36. Test
    37. Alternate Test—Form A
    38. Alternate Test—Form B
    39. Glossary and Credits