Pre-Algebra: A Skills Mastery Approach

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Teacher: Alexander
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Unit 1: Expressions, Variables, and Integers

0 Course Introduction 06:24

1 Lesson 1-1: Expressions and Variables 12:34

2 Assignment 1-1 16:34

Solution to Assignment 1-1

3 Lesson 1-2: Exponents and Prime Factorization 19:03

4 Assignment 1-2 20:09

Solution to Assignment 1-2

5 Lesson 1-3: Order of Operations 13:07

6 Assignment 1-3 15:01

Solution to Assignment 1-3

7 Quiz 1-1 00:00

Quiz 1-1

8 Quiz 1-1 Solution 12:43

Quiz 1-1 Solution

9 Lesson 1-4: Negatives, Absolute Values, and Opposites 12:35

10 Assignment 1-4 19:06

Solution to Assignment 1-4

11 Lesson 1-5: Adding Negative Numbers 12:58

12 Assignment 1-5 10:24

Solution to Assignment 1-5

13 Lesson 1-6: Subtracting Negative Numbers 13:08

14 Assignment 1-6 14:38

Solution to Assignment 1-6

15 Lesson 1-7: Multiplying and Dividing Negative Numbers 11:39

16 Assignment 1-7 15:36

Solution to Assignment 1-7

17 Lesson 1-8: The Coordinate Plane 12:55

18 Assignment 1-8 12:49

Solution to Assignment 1-8

19 Quiz 1-2 00:00

Quiz 1-2

20 Quiz 1-2 Solution 19:29

Solution to Quiz 1-2

Unit 2: Solving Equations

21 Lesson 2-1: Properties and Unit Conversions 20:20

22 Assignment 2-1 23:58

Solution to Assignment 2-1

23 Lesson 2-2: The Distributive Property 11:36

24 Assignment 2-2 17:13

Solution to Assignment 2-2

25 Lesson 2-3: Simplifying Expressions 17:38

26 Assignment 2-3 13:53

Solution to Assignment 2-3

27 Quiz 2-1 00:00

Quiz 2-1

28 Quiz 2-1 Solution 10:28

Solution to Quiz 2-1

29 Lesson 2-4: Solutions to Equations 11:37

30 Assignment 2-4 16:51

Solution to Assignment 2-4

31 Lesson 2-5: Solving Equations with Addition and Subtraction 10:21

32 Assignment 2-5 14:28

Solution to Assignment 2-5

33 Lesson 2-6: Solving Equations with Multiplication and Division 12:21

34 Assignment 2-6 13:02

Solution to Assignment 2-6

35 Test 2-1 00:00

Test 2-1

36 Test 2-1 Solution 26:19

Solution to Test 2-1

37 Test 2-2 00:00

Test 2-2

38 Test 2-2 Solution 18:15

Solution to Test 2-2

Unit 3: Multi Step Equations and Inequalities

39 Lesson 3-1: Solving Two Step Equations 14:00

40 Assignment 3-1 18:53

Solutions to Assignment 3-1

41 Lesson 3-2: Solving Equations with Variables on Both Sides 11:34

42 Assignment 3-2 20:39

Solution to Assignment 3-2

43 Lesson 3-3: Solving Literal Equations 14:59

44 Assignment 3-3 17:43

Solution to Assignment 3-3

45 Quiz 3-1 00:00

Quiz 3-1

46 Quiz 3-1 Solution 15:12

Solution to Quiz 3-1

47 Lesson 3-4: Solving One Step Inequalities 14:13

48 Assignment 3-4 18:55

Solution to Assignment 3-4

49 Lesson 3-5: Solving Multi Step Inequalities 11:56

50 Assignment 3-5 11:56

Solution to Assignment 3-5

51 Test 3-1 00:00

Test 3-1

52 Test 3-1 Solution 21:46

Test 3-1 Solution

53 Test 3-2 00:00

Test 3-2

54 Test 3-2 Solution 20:16

Solution to Test 3-2

Unit 4: Factors, Fractions, and Exponents

55 Lesson 4-1: Factoring Monomials 10:50

56 Assignment 4-1 18:26

Solution to Assignment 4-1

57 Lesson 4-2: Greatest Common Factor 14:25

58 Assignment 4-2 27:03

Solution to Assignment 4-2

59 Lesson 4-3: Equivalent Fractions with Monomials 15:56

60 Assignment 4-3 16:16

Solution to Assignment 4-3

61 Lesson 4-4: Least Common Multiple 13:21

62 Assignment 4-4 25:38

Solution to Assignment 4-4

63 Quiz: 4-1 00:00

Quiz 4-1

64 Quiz 4-1 Solution 14:05

Quiz 4-1 Solution

65 Lesson 4-5: Rules of Exponents 11:38

66 Assignment 4-5 18:19

Solution to Assignment 4-5

67 Lesson 4-6: Negative Exponents 12:11

68 Assignment 4-6 16:38

Solution to Assignment 4-6

69 Lesson 4-7: Scientific Notation 12:58

70 Assignment 4-7 19:51

Solution to Assignment 4-7

71 Test 4-1 00:00

Test 4-1

72 Test 4-1 Solution 22:33

Test 4-1 Solution

73 Test 4-2 00:00

Test 4-2

74 Test 4-2 Solution 22:12

Test 4-2 Solution

Unit 5: Ratio, Proportion, and Probability

75 Lesson 5-1: Ratios and Rates 13:13

76 Assignment 5-1 18:09

Solution to Assignment 5-1

77 Lesson 5-2: Proportions 11:56

78 Assignment 5-2 18:08

Solution to Assignment 5-2

79 Lesson 5-3: Similar and Congruent Figures 14:28

80 Assignment 5-3 27:08

Solution to Assignment 5-3

81 Lesson 5-4: Similarity and Measurement 10:56

82 Assignment 5-4 20:19

Solution to Assignment 5-4

83 Lesson 5-5: Scale Diagrams and Models 12:15

84 Assignment 5-5 19:30

Solution to Assignment 5-5

85 Quiz 5-1 00:00

Quiz 5-1

86 Quiz 5-1 Solution 20:43

Solution to Quiz 5-1

87 Lesson 5-6: Probability and Odds 10:39

88 Assignment 5-6 28:09

Solution to Assignment 5-6

89 Lesson 5-7: The Multiplication Principle 11:28

90 Assignment: 5-7 25:12

Solution to Assignment 5-7

91 Test 5-1 00:00

Test 5-1

92 Test 5-1 Solution 26:29

Solution to Test 5-1

93 Test 5-2 00:00

Test 5-2

94 Test 5-2 Solution 28:18

Solution to Test 5-2

Unit 6: Percents

95 Lesson 6-1: Percents, Fractions, Decimals, and Proportions 20:27

96 Assignment 6-1 16:14

Solution to Assignment 6-1

97 Lesson 6-2: The Percent Equation 10:33

98 Assignment 6-2 18:37

Solution to Assignment 6-2

99 Lesson 6-3: Percent Change 14:01

100 Assignment 6-3 14:09

Solution to Assignment 6-3

101 Lesson 6-4: Simple and Compound Interest 17:03

102 Assignment 6-4 19:01

Solution to Assignment 6-4

103 Test 6-1 00:00

Test 6-1

104 Test 6-1 Solution 29:21

Test 6-1 Solution

105 Test 6-2 00:00

Test 6-2

106 Test 6-2 Solution 28:29

Solution to Test 6-2

Unit 7: Linear Equations

107 Lesson 7-1: Relations and Functions 14:32

108 Assignment 7-1 13:04

Solution to Assignment 7-1

109 Lesson 7-2: Linear Equations with Two Variables 14:00

110 Assignment 7-2 12:04

Solution to Assignment 7-2

111 Lesson 7-3: Using Intercepts 13:47

112 Assignment 7-3 17:31

Solution to Assignment 7-3

113 Lesson 7-4: Slope of a Line 11:40

114 Assignment 7-4 10:14

Solution to Assignment 7-4

115 Lesson 7-5: Slope Intercept Form 12:46

116 Assignment 7-5 13:28

Solution to Assignment 7-5

117 Quiz 7-1 00:00

Quiz 7-1

118 Quiz 7-1 Solution 16:17

Solution to Quiz 7-1

119 Lesson 7-6: Writing Equations 11:16

120 Assignment 7-6 17:04

Solution to Assignment 7-6

121 Lesson 7-7: Function Notation 12:08

122 Assignment 7-7 15:26

Assignment 7-7 Solution

123 Lesson 7-8: Systems of Linear Equations 15:47

124 Assignment 7-8 29:02

Solution to Assignment 7-8

125 Lesson 7-9: Graphing Linear Inequalities 11:01

126 Assignment 7-9 25:37

Solution to Assignment 7-9

127 Test 7-1 00:00

128 Test 7-1 Solution 29:22

Solution to Test 7-1

129 Test 7-2 00:00

130 Test 7-2 Solution 27:39

Solution to Test 7-2

Course Description

As a Pre-Algebra course, the first goal of this course is to provide a presentation of the foundational concepts necessary for students to proceed into Algebra. For this purpose, the course is divided into ten units with 4-8 lectures each that present the most essential skills that help students start to transition from thinking about math in terms of arithmetic and start thinking about it in a more abstract, algebraic sense.

A distinction from many other math courses is the emphasis this course places on practice of the skills that have been learned, not just immediately after following the lecture, but throughout the remainder of the course. Each homework assignment begins with a thorough Spiral Review of the most important skills for students to know. This ensures that students continue to get more and more practice with previously learned skills as they progress through the course.

Additionally, this course provides detailed video solutions to all the assignments, quizzes, and tests in which the instructor explains his thinking and approach to solving each of the problems. It’s through a review of these solutions that students will have examples of how someone experienced with these skills approaches these problems as well as a repeated demonstration for what kinds of skills are repeatedly used in mastering the subject.

Lastly, the quizzes and tests of this courses are closer to a different type of assignment rather than an opportunity for students to prove to the instructor that they have learned the content. Many of the quizzes and tests will fall into the category of Applied Problem Solving, in which the students will try to solve story problems that require the use of the Pre-Algebra skills they have been learning. There will also be a Cumulative Skills Review Test in most units, which will be a longer assignment in which students will be able to demonstrate their mastery of the skills presented throughout the course.

Course Goals

Upon completion, students will have been exposed to the most essential skills in pre-Algebra and had a great deal of opportunity to practice all of those skills repeatedly in many different assignments. Students will also gain some experience applying those skills to some real-world problems through Applied Problem Solving Assignments.

Target Audience

This course is intended primarily for those students from 7th-8th grade, particularly if there is a high emphasis on skill mastery and practice. It will also serve well as an in depth review for those students heading into their first Algebra course.

Course Requirements

Students should have a solid grasp of fraction and decimal arithmetic when entering this course.

Course Includes

  • 29+ hours of video content
  • 46 video lectures 
  • 46 worksheet assignments
  • 46 worksheet solution videos
  • 19 Quiz/Test Assignments
  • 19 Quiz/Test Review videos
  • Digital Copies of all notes instructor took in the class
  • Digital Copies of solutions to all assignments

Course Topics

  1. Expressions, Variables, and Integers
    1. Expressions and Variables
    2. Exponents and Prime Factorization
    3. order of Operations
    4. Negatives, Absolute Values, and Opposites
    5. Adding Negative Numbers
    6. Subtracting Negative Numbers
    7. Multiplying and Dividing Negative Numbers
    8. The Coordinate Plane
  2. Solving Equations
    1. Properties and Unit Conversions
    2. The Distributive Property
    3. Simplifying Expressions
    4. Solutions to Equations
    5. Solving Equations with Addition and Subtraction
    6. Solving Equations with Multiplication and Division
  3. Multi-step Equations and Inequalities
    1. Solving Two Step Equations
    2. Solving Equations with Variables on Both Sides
    3. Solving Literal Equations
    4. Solving One Step Inequalities
    5. Solving Multi Step Inequalities
  4. Factors, Fractions, and Exponents
    1. Factoring Monomials
    2. Greatest Common Factor
    3. Equivalent Fractions and Monomials
    4. Least Common Multiple
    5. Rules of Exponents
    6. Negative Exponents
    7. Scientific Notation
  5. Ratio, Proportion, and Probability
    1. Ratios and Rates
    2. Proportions
    3. Similar and Congruent Figures
    4. Similarity and Measurement
    5. Scale Diagrams and Models
    6. Probability and Odds
    7. The Multiplication Principle
  6. Percents
    1. Percents, Fractions, Decimals, and Proportions
    2. The Percent Equation
    3. Percent Change
    4. Simple and Compound Interest
  7. Linear Equations
    1. Relations and Functions
    2. Linear Equations with Two Variables
    3. Using Interecepts
    4. Slope of a Line
    5. Slope Interept form
    6. Writing Equations
    7. Function Notation
    8. Systems of Linear Equations
    9. Graphing Linear Inequalities

 

  • Teacher: Alexander
  • Areas of expertise: Physics, Science, & Mathematics
  • Education: BS Engineeering Physics Colorado Scool of Mines 2007 MS Applied Physics Colorado School of Mines 2008 MS Biophysics University of Michigan 2011
  • Interests: Education, Energy, Knowledge, Physical Activity
  • Skills: Writing/Communicating, High-level science and math tutoring, Relocating to new places
  • Associations: American Modeling Teachers Association
  • Issues I care about: Education, Energy, Philosophy

I came to education through a passion for science and more specifically physics. I've taught physics and advanced sciences at many different levels, and communicating these ideas has not only been one of the joys of my life, but has given me insight into the areas where students tend to struggle when taking on these more challenging subject. I try to prepare all the science and math courses I teach with the idea that I would like students to be prepared for the more challenging scientific and mathematical challenges they will encounter in these higher classes.

Digital Quizzes and Tests Answer Keys Document

Digital Quizzes and Tests Answer Keys Document

Test Preparation Document

Test Preparation Document

Digital Check Answer Key

Answers for all of the Digital Check questions
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