pre-algebra ​ACADEMIC LIBRARY (math 800) 

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.
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​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.

GO TO PRE-ALGEBRA 2nd SEMESTER

UNIT 1 - THE REAL NUMBER SYSTEM

UNIT 2 - MODELING PROBLEMS IN INTEGERS

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
   • What Is A Variable 
   • Why Aren’t We Using the Multiplication Sign  
   • Example: Evaluate a Formula Using Substitution  
4. The Number Line
   • Number Line  
5. Comparing Rational Numbers
   • Rational Word Problems  
   • 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 
    • Commutative law of addition  
    • Commutative law of multiplication ​ 
    • Associative  
    • Identity Property  
    • Distributive Property – Addition and Subtraction 
11. Exponents
    • Introduction to Exponents  
    • Exponent Rules 
12. Scientific Notation
    • 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
    • Understanding Square Roots 
    • Square Roots  
18. Order of Operations
    • Orders of Operation . 
19. Quiz 3: Simplifying
20. Alternate Quiz 3—Form A: Simplifying
21. Alternate Quiz 3—Form B: Simplifying
22. Review
23. Test
24. Alternate Test—Form A
25. Alternate Test—Form B
26. Glossary and Credits

1. Translating Expressions and Equations
   • Understanding Written Expressions 
2. Solving One-Step Equations
   • One-Step Equations 
3. Solving Two-Step Equations
   • 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
   • Relations and Functions 
9. Functions
   • What Is a Function
   • Relations and Functions  
10. Analyzing Graphs
    • 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
    • Adding Negative Numbers 
    • Addition of Integers  
15. Subtraction of Integers
    • Why Subtracting a Negative Equivalent to Adding a Positive  
    • Subtraction of Integers (Adding and Subtracting Negative Numbers) 
16. Multiplying and Dividing Integers
    • Multiplying and Dividing Integers (Multiplying Positive and Negative Numbers)  
    • Multiplying and Dividing Integers (Multiplying and Dividing Negative Numbers) 
17. 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)
18. Quiz 3: Integers
19. Alternate Quiz 3—Form A: Integers
20. Alternate Quiz 3—Form B: Integers
21. Graphing
    • Graphing (Coordinate Plane) 
22. One-Step Equations
    • One Step Equations 
23. Two-Step Equations
    • Why We Do the Same Things to Both Sides of Simple Equations   
24. Problem Solving
    • Writing Equations from Word Problems  
    • 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

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​UNIT 3 - MODELING PROBLEMS WITH RATIONAL NUMBERS

UNIT 4 - PROPORTIONAL REASONING

1. Prime Factorization and the GCF
   • Prime Factorization 
   • Greatest Common Factor  
2. Simplifying Fractions
   • Simplifying Fractions  
3. The LCM and the LCD
   • Greatest Common Factor Word Problem   
   • 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
   • Adding Fractions with Like Denominators 
   • Adding Fractions With Different Signs 
8. Adding and Subtracting Unlike Fractions  
   • Adding Fractions with Unlike Denominators 
9. Adding and Subtracting Decimal Numbers
   • Adding and Subtracting Decimals Example 1    
10. Multiplying and Dividing Fractions
    • Multiplying Negative and Positive Fractions 
    • Multiplying Fractions and Whole Numbers 
11. 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 
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
    • Examples of one-step equations like ax = b and x + a = b  
17. 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 
18. Two-Step Equations
    • Solving simple equations 
19. One-Step Inequalities
    • One-step inequalities
    • One-step inequality involving addition  
    • Multiplying and dividing with inequalities example  
20. Two-Step Inequalities
    • 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

1. Proportions
   • Writing proportions 
   • Proportion word problem: hot dogs  
   • Proportion word problem: cookies ​ 
2. Linear Applications
   • Finding unit rates  
   • Finding unit prices  
3. Direct Variation
   • 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
   • Representing a number as a decimal, percent, and fraction 
8. Solving Percent Problems
   • Solving percent problems 
   • Solving Percent Problems Using The Percent Proportion  
   • Solving Percent Problems using Proportions  
9. Applications of Ratios and Percent
   • Percent word problems  
   • Another percent word problem  
10. More Applications with Percent
    • Solving Percent Problems Using The Percent Proportion  
    • 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
    • Examples determining reasonable units 
15. Unit Conversion within Metric Units
    • Conversion between metric units 
    • ​Conversion between metric units
16. Corresponding Parts
    • Congruent triangle proof example  
17. Indirect Measure
    1. ​Indirect Measurement Using Similar Triangles ​ 
18. Models and Scales
    • 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

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UNIT 5 - MORE WITH FUNCTIONS

1. Rewriting Equations
   • Algebra 2 1.4 Examples Rewriting Equations and Formulas  
2. Combine Like Terms
   • Combining like terms  
   • Combining like terms  
   • Combining like terms and simplifying expressions  
3. Solving Equations by Combining Like Terms
   • Math Lessons : Solving Equations With Like Terms  
   • Solving an Equation by Combining Like Terms  
4. Distributive Property
   • The Distributive Property  
   • The Distributive Property 2  
   • The Distributive Property  
   • Distributive Property  
5. Solving Equations with Distributive Property
   • Solving equations with the distributive property  
   • Solving equations with the distributive property 2  
   • Equations with parentheses ​  
6. Solving Equations with Special Solutions
   • Solving Linear Equations with One Variable 
   • Solving Equations With One, Many, or No Solutions 
7. Literal Equations
   • 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
    • Slope of a line
    • Slope = Rise over Run. "You have to RISE before you RUN"  
12. Comparing Functions
    • Comparing functions rate of change  
13. Using Intercepts
    • x- and y-intercepts 
    • Graphing using x- and y-intercepts  
14. Slope-Intercept Form
    • Converting to slope-intercept form  
    • Slope-Intercept Form y=mx+b  
15. More Slope-Intercept Form
    • 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
    • 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
    • System of Equations: One Solution, No Solution, or Infinitely Many Solutions 
22. Solving Systems of Linear Equations Using Substitution
    • Algebra - Solving Using Substitution Method  
23. Solving Systems of Linear Equations Using Addition
    • 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
    • Figuring out days of the week 
    • Arithmetic sequences 
    • Arithmetic sequences 1  
29. Geometric Sequences
    • Geometric sequence or progression 
    • Geometric sequences 1  
30. Exponential Sequences
    • Exponential growth functions 
31. Recursive Sequences
    • 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

GO TO PRE-ALGEBRA 2nd SEMESTER