- K-12 Curriculum
- 0 (Registered)
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Credit Value: Full-year course 1 credit
Anticipated Grade Level(s): Grade 8
Prerequisites: Satisfactory completion of grade 7 mathematics
Course Description:
The grade 8 curriculum is designed to provide an integrated course for students of all abilities. Students enrolled in this course are assumed to have mastered those concepts outlined in the grade 7 curriculum. A thorough treatment of advanced algebraic concepts is provided. Emphasis will be placed on practical applications and modeling throughout the course of study. Oral and written communication concerning the language of algebra, logic of procedures, and interpretation of results also should permeate the course.
Graphing utilities (graphing calculators or computer graphing simulators), computers, spreadsheets, and other appropriate technology tools will be used to assist in teaching and learning. They also provide an effective tool for solving/verifying equations and inequalities. Any other available technology that will enhance student learning should be used.
Innovative Interactive Instruction
In our self-paced courses, students work their way through carefully scripted interactive lessons. These automated lessons lead students in mathematical conversations designed to engage, entertain, and educate. Each lesson reacts to student input, guiding them step-by-step through problems and tackling common misconceptions along the way. When students need extra help, they can turn to the class message board where instructors provide additional assistance.
Active Learning
Learning is not a spectator sport. Students best learn by tackling hard problems themselves, not by watching others do the work. Therefore, we start lessons with questions, challenging the students to find the key insights on their own. This teaches students how to create new mathematical strategies as needed. When students inevitably get stuck, we provide hints and more direct instruction to help them proceed. After students have solved a problem, we follow up with important concepts and strategies before moving on to the next problem.
Focus on Non-Routine, Challenging Problems
Thirty years ago, many intellectual careers consisted of repeatedly solving routine problems. Computers fill most of those roles now. Successful people in the next generation will need to develop new skills throughout their careers as their older skills become obsolete. To prepare our students for this challenging future, we go well beyond the basics in our courses, showing students how to apply fundamentals to problems that are not replicas of problems they’ve already seen. This teaches students how to learn, so they’ll be ready for the rigors of top-tier colleges and internationally competitive careers.
Multiple Learning Avenues
Students learn in many ways, so we deliver instruction in multiple forms. In addition to our automated interactive lessons, our students can read the Prealgebra textbook, watch videos, solve many different types of homework problems, and participate in mathematical conversations with instructors and other students on the class message board and during office hours.
Course Content
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Variables, Expressions, and Integers
8-
Lecture1.1Expressions and Variables
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Lecture1.2Powers and Exponents
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Lecture1.3Order of Operations
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Lecture1.4Comparing and Ordering Integers
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Lecture1.5Adding Integers
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Lecture1.6Subtracting Integers
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Lecture1.7Multiplying and Dividing Integers
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Lecture1.8The Coordinate Plane
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Solving Equations
7-
Lecture2.1Properties and Operations
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Lecture2.2The Distributive Property
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Lecture2.3Simplifying Variable Expressions
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Lecture2.4Variables and Equations
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Lecture2.5Solving Equations Using Addition or Subtraction
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Lecture2.6Solving Equations Using Multiplication or Division
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Lecture2.7Decimal Operations and Equations with Decimals
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Multi-Step Equations and Inequalities
6-
Lecture3.1Solving Two-Step Equations
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Lecture3.2Solving Equations Having Like Terms and Parentheses
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Lecture3.3Solving Equations with Variables on Both Sides
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Lecture3.4Solving Inequalities Using Addition or Subtraction
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Lecture3.5Solving Inequalities Using Multiplication or Division
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Lecture3.6Solving Multi-Step Inequalities
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Factors, Fractions, and Exponents
7-
Lecture4.1Factors and Prime Factorization
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Lecture4.2Greatest Common Factor
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Lecture4.3Equivalent Fractions
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Lecture4.4Least Common Multiple
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Lecture4.5Rules of Exponents
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Lecture4.6Negative and Zero Exponents
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Lecture4.7Scientific Notation
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Rational Numbers and Equations
7-
Lecture5.1Rational Numbers
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Lecture5.2Adding and Subtracting Like Fractions
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Lecture5.3Adding and Subtracting Unlike Fractions
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Lecture5.4Multiplying Fractions
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Lecture5.5Dividing Fractions
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Lecture5.6Using Multiplicative Inverses to Solve Equations
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Lecture5.7Equations and Inequalities with Rational Numbers
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Ratio, Proportion, and Probability
8-
Lecture6.1Ratios and Rates
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Lecture6.2Writing and Solving Proportions
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Lecture6.3Solving Proportions Using Cross Products
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Lecture6.4Similar and Congruent Figures
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Lecture6.5Similarity and Measurement
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Lecture6.6Scale Drawings
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Lecture6.7Probability and Odds
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Lecture6.8The Counting Principle
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Percents
7-
Lecture7.1Percents and Fractions
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Lecture7.2Percents and Proportions
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Lecture7.3Percents and Decimals
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Lecture7.4The Percent Equation
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Lecture7.5Percent of Change
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Lecture7.6Percent Applications
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Lecture7.7Simple and Compound Interest
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Linear Functions
9-
Lecture8.1Relations and Functions
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Lecture8.2Linear Equations in Two Variables
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Lecture8.3Using Intercepts
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Lecture8.4The Slope of a Line
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Lecture8.5Slope-Intercept Form
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Lecture8.6Writing Linear Equations
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Lecture8.7Function Notation
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Lecture8.8Systems of Linear Equations
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Lecture8.9Graphs of Linear Inequalities
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Real Numbers and Right Triangles
8-
Lecture9.1Square Roots
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Lecture9.2Simplifying Square Roots
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Lecture9.3The Pythagorean Theorem
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Lecture9.4Real Numbers
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Lecture9.5The Distance and Midpoint Formulas
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Lecture9.6Special Right Triangles
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Lecture9.7The Tangent Ratio
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Lecture9.8The Sine and Cosine Ratios
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Measurement, Area, and Volume
8-
Lecture10.1Triangles
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Lecture10.2Polygons and Quadrilaterals
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Lecture10.3Areas of Parallelograms and Trapezoids
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Lecture10.4Circumference and Area of a Circle
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Lecture10.5Surface Areas of Prisms and Cylinders
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Lecture10.6Surface Areas of Pyramids and Cones
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Lecture10.7Volumes of Prisms and Cylinders
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Lecture10.8Volumes of Pyramids and Cones
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Data Analysis and Probability
9-
Lecture11.1Stem-and-Leaf Plots and Histograms
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Lecture11.2Box-and-Whisker Plots
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Lecture11.3Using Data Displays
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Lecture11.4Collecting Data
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Lecture11.5Interpreting Data
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Lecture11.6Permutations
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Lecture11.7Combinations
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Lecture11.8Probabilities of Disjoint and Overlapping Events
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Lecture11.9Independent and Dependent Events
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Polynomials and Nonlinear Functions
8-
Lecture12.1Polynomials
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Lecture12.2Adding and Subtracting Polynomials
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Lecture12.3Multiplying Monomials and Polynomials
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Lecture12.4Multiplying Binomials
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Lecture12.5Other Rules of Exponents
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Lecture12.6Quadratic Functions
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Lecture12.7Exponential Growth and Decay
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Lecture12.8Sequences
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Angle Relationships and Transformations
7-
Lecture13.1Angle Relationships
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Lecture13.2Angles and Parallel Lines
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Lecture13.3Angles and Polygons
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Lecture13.4Translations
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Lecture13.5Reflections and Symmetry
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Lecture13.6Rotations and Symmetry
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Lecture13.7Dilations
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About the Instructor
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