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7th Grade Math

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Overview

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Content

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Upon successful completion of this course, students will have mastered the following:

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1.
Ratios & Proportional Relationships
22 topics
1.1. Unit Rates
1.1.1. Finding Unit Prices
1.1.2. Working With Unit Prices
1.1.3. Solving Multi-Step Unit Price Problems
1.1.4. Unit Rates Associated With Ratios of Fractions
1.1.5. Unit Rates Associated With Ratios of Mixed Numbers
1.1.6. Solving Unit Rate Problems Using Ratios of Fractions
1.1.7. Solving Unit Rate Problems Using Ratios of Mixed Numbers
1.2. Proportional Relationships
1.2.1. Understanding Proportional Relationships Using Tables
1.2.2. Understanding Proportional Relationships Using Graphs
1.2.3. Understanding Proportional Relationships From Descriptions
1.2.4. Interpreting Data From Proportional Relationships
1.3. Percents
1.3.1. Applying Percentage Increases
1.3.2. Applying Percentage Decreases
1.3.3. Calculating Percentage Change
1.3.4. Finding Original Values From Percentage Increases
1.3.5. Finding Original Values From Percentage Decreases
1.3.6. Applying Percentages in Succession
1.3.7. Percentages in Commerce and Finance
1.3.8. Further Percentages in Commerce and Finance
1.3.9. Solving Multipart Commerce and Finance Percentage Problems
1.3.10. Calculating Simple Interest
1.3.11. Interpreting Percentage Change
2.
The Number System
24 topics
2.4. Addition and Subtraction of Rational Numbers
2.4.1. Subtracting a Positive Number From a Smaller Positive Number
2.4.2. Subtracting a Positive Number From a Negative Number
2.4.3. Subtracting a Positive Fraction From a Smaller Fraction
2.4.4. Subtracting a Positive Decimal From a Smaller Decimal
2.4.5. Adding a Positive Number to a Negative Number
2.4.6. Adding a Negative Number
2.4.7. Subtracting a Negative Number
2.4.8. Additive Inverses of Numbers
2.4.9. Solving Problems Using Addition and Subtraction of Rational Numbers
2.5. Multiplication and Division of Rational Numbers
2.5.1. Multiplying Positive Numbers With Negative Numbers
2.5.2. Multiplying Negative Numbers
2.5.3. Dividing With Negative Numbers
2.5.4. Equivalent Fractions With Negative Numbers
2.5.5. Dividing With Negative Decimals and Fractions
2.5.6. Reciprocals of Rational Numbers
2.5.7. Multiplying and Dividing With Zero
2.5.8. Fractions of Fractions
2.5.9. Evaluating Rational Number Expressions Without Exponents
2.5.10. Solving Problems Using the Four Operations on Rational Numbers
2.5.11. Expressing Rational Numbers as Decimals
2.6. Exponents
2.6.1. Squaring Rational Numbers
2.6.2. Cubing Rational Numbers
2.6.3. Exponents With Rational Bases
2.6.4. Evaluating Expressions With Positive Integer Exponents
3.
Expressions & Equations
41 topics
3.7. Algebraic Expressions
3.7.1. Introduction to Algebraic Expressions
3.7.2. Constructing Algebraic Expressions
3.7.3. Evaluating Linear Expressions
3.7.4. Identifying Terms in Linear Expressions
3.7.5. Identifying Coefficients and Constants
3.7.6. Identifying Like Terms in Linear Expressions
3.7.7. The Greatest Common Factor of Two Linear Expressions
3.8. Equivalent Expressions
3.8.1. Collecting Like Terms in Linear Expressions
3.8.2. Applying the Distributive Law With Linear Expressions
3.8.3. The Distributive Law With Three Terms
3.8.4. Distributing the Negative Sign in a Linear Expression
3.8.5. Simplifying Linear Expressions Using the Distributive Law
3.8.6. Simplifying Linear Expressions When a Group of Terms Is Subtracted
3.8.7. Simplifying Linear Expressions Containing Fractions
3.8.8. Factoring Numerical Expressions
3.8.9. Factoring Linear Expressions
3.9. Solving One-Step Linear Equations
3.9.1. Solving Linear Equations by Trial and Error
3.9.2. Solving One-Step Addition and Subtraction Equations
3.9.3. Solving One-Step Multiplication and Division Equations
3.10. Solving Multi-Step Linear Equations
3.10.1. Solving Two-Step Equations
3.10.2. Solving Linear Equations With Fractional Coefficients
3.10.3. Solving Linear Equations With Decimal Coefficients
3.10.4. Solving Linear Equations With Variables on Both Sides
3.10.5. Solving Linear Equations by Clearing a Rational Expression
3.11. Solving Linear Inequalities
3.11.1. Inequalities
3.11.2. Compound Inequalities
3.11.3. Verifying Solutions of Linear Inequalities
3.11.4. Solving One-Step Linear Inequalities
3.11.5. Solving Two-Step Inequalities
3.11.6. Representing Solutions to Inequalities on Number Lines
3.12. Modeling With Linear Equations and Inequalities
3.12.1. Interpreting Linear Expressions
3.12.2. Modeling With Linear Equations
3.12.3. Introduction to Modeling With Inequalities
3.12.4. Modeling With One-Step Inequalities
3.12.5. Modeling With Two-Step Inequalities
3.12.6. Solving Geometrical Problems Using Linear Equations
3.13. Rational Expressions and Equations
3.13.1. Evaluating Rational Expressions
3.13.2. Equivalent Expressions With Fractions
3.13.3. Simplifying Rational Expressions
3.13.4. Simplifying Rational Expressions by Factoring
3.13.5. Solving Rational Equations Containing One Fractional Term
4.
Geometry
50 topics
4.14. Introduction to Geometry
4.14.1. Points, Lines, Rays, and Segments
4.14.2. Parallel and Perpendicular Lines
4.14.3. Measures of Segments
4.14.4. Congruent Segments
4.14.5. Midpoints
4.14.6. Collinear Points
4.14.7. The Segment Addition Postulate
4.14.8. Segment Bisectors and the Perpendicular Bisector Theorem
4.15. Angles
4.15.1. Angles and Measures of Angles
4.15.2. Connecting Angles and Circles
4.15.3. Measuring Angles Using a Protractor
4.15.4. Sums of Angles
4.15.5. Right, Straight, Full, and Null Angles
4.15.6. Acute, Obtuse, and Reflex Angles
4.15.7. Congruent Angles
4.16. Advanced Angles
4.16.1. Vertical Angles
4.16.2. Complementary Angles
4.16.3. Supplementary Angles
4.16.4. Angle Bisectors
4.16.5. Solving Problems With Angles
4.17. Polygons
4.17.1. Interior Angles of Triangles
4.17.2. Classifying Triangles
4.17.3. Heights of Triangles
4.17.4. Classifying Quadrilaterals
4.17.5. Properties of Rectangles and Squares
4.17.6. Properties of Trapezoids
4.17.7. Polygons
4.17.8. Congruent Polygons
4.18. Area and Perimeter
4.18.1. The Perimeter of a Polygon
4.18.2. Areas of Rectangles and Squares
4.18.3. Areas of Parallelograms
4.18.4. Areas of Triangles
4.18.5. Areas of Trapezoids
4.18.6. Areas and Perimeters of Composite Shapes
4.18.7. The Area Between Two Shapes
4.19. Scale Drawings
4.19.1. Introduction to Scale Drawings
4.19.2. Calculating Lengths From Scale Drawings
4.19.3. Calculating Perimeters and Areas of Scaled Shapes
4.20. Circles
4.20.1. Introduction to Circles
4.20.2. The Circumference of a Circle
4.20.3. The Area of a Circle
4.20.4. Composite Shapes With Circles
4.20.5. Finding Areas and Perimeters of Part-Circles
4.21. Solid Geometry
4.21.1. Volumes of Cubes
4.21.2. Surface Areas of Cubes
4.21.3. Surface Areas of Rectangular Solids
4.21.4. Volumes of Triangular Prisms
4.21.5. Surface Areas of Triangular Prisms
4.21.6. Surface Areas of Combined Rectangular Prisms
4.21.7. Cross-Sections of Three-Dimensional Shapes
5.
Statistics & Probability
38 topics
5.22. Sampling
5.22.1. Sampling
5.22.2. Estimation From Samples
5.22.3. Biased and Unbiased Samples
5.22.4. Interpreting Survey Results
5.22.5. Sampling and Margin of Error
5.23. Representing Data
5.23.1. Joint Frequency Tables
5.23.2. Cumulative Frequency
5.23.3. Calculating Means From Frequency Tables
5.23.4. Calculating Medians From Frequency Tables
5.23.5. Calculating Modes From Frequency Tables
5.23.6. Calculating Modes and Medians From Histograms
5.23.7. Calculating Means From Histograms
5.24. Comparing Data
5.24.1. Comparing Means
5.24.2. Comparing Medians
5.24.3. Comparing Modes
5.24.4. Comparing Data Sets Using Range and Quartiles
5.24.5. Comparing Data Set Visualizations Using Standard Deviation and MAD
5.24.6. Comparing Data Sets Using Standard Deviation and MAD
5.25. Probability
5.25.1. Experimental Probability
5.25.2. Sample Spaces and Events in Probability
5.25.3. Single Events in Probability
5.25.4. Analyzing Probability Models
5.26. Compound Events in Probability
5.26.1. Sample Spaces for Compound Events
5.26.2. Experimental Probability for Compound Events
5.27. Probability (To Remove)
5.27.1. Experimental Probability
5.27.2. Making Decisions Using Probability
5.27.3. Finding Probabilities Using Geometry
5.27.4. Designing Experiments to Determine Probabilities
5.27.5. Experimental Probability for Compound Events
5.27.6. Dependent and Independent Events
5.27.7. The Multiplication Law for Independent Events
5.27.8. Calculating Probabilities of Compound Events Using Information Given in Context
5.27.9. Calculating Probabilities of Compound Events Using Tables
5.27.10. Calculating Probabilities of Compound Events Using Tree Diagrams
5.28. Permutations and Combinations
5.28.1. Finding Probabilities Using the Counting Principle
5.28.2. Ordering Objects Using Factorials
5.28.3. Permutations
5.28.4. Combinations