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# Prealgebra

Our fully accredited, Common Core-aligned Prealgebra course serves as a critical stepping stone between 5th Grade Math and our comprehensive high-school math curriculum, providing students with the necessary skills to understand more advanced mathematical concepts.

## Content

Students will extend their foundations in arithmetic to include ratios, unit rates, negative and rational numbers, radicals, and exponents. After mastering these areas, students begin exploring algebraic expressions and equations, including two-variable equations and systems of equations. Students then apply these skills to geometric settings where mastery of algebraic manipulations is key. Finally, students learn new concepts in descriptive statistics and data analysis.

After completing the course, students will have a solid foundation in Prealgebra, preparing them for success in Algebra 1, Integrated Math I, and beyond.

Upon successful completion of this course, students will have mastered the following:
• Solving problems involving ratios, percentages, unit rates, and proportional relationships, including solving real-world problems using these concepts.
• Addition, subtraction, multiplication, and division with negative and rational numbers, and solving related real-world and mathematical problems.
• Understanding and applying fundamental concepts from number theory, such as divisibility rules, the fundamental theorem of arithmetic, and connecting primes and prime factorization to previously understood concepts, such as greatest common factors and lowest common multiples.
• Manipulating expressions involving exponents and radicals, including fractional and negative exponents, the rules of exponents and radicals, and scientific notation.
• Applying the order of operations to complex expressions containing negative and rational numbers, fractional and negative exponents, and radicals.
• Constructing, evaluating, simplifying, and factoring algebraic expressions, including some manipulations with simple rational expressions.
• Solving one-step and multi-step linear equations and inequalities, including cases involving rational expressions, cross-multiplication, and multiple variables.
• Graphing linear equations, calculating and describing a graphâ€™s key features, and slope-intercept form.
• Solving systems of equations using the substitution method and explaining how the solutions relate to the intersection of two lines.
• Understanding and applying basic geometry concepts, including segments, angles and their properties, triangles and their classifications, polygons and quadrilaterals, and area and perimeter calculations for various shapes.
• Summarizing and representing data through concepts such as centrality, spread, skew, and outliers and using frequency tables, dot plots, box plots, and histograms to visualize data and interpret distributions.
1.
Ratios & Percentages
24 topics
1.1. Ratios
 1.1.1. Introduction to Ratios 1.1.2. Equivalent Ratios 1.1.3. Writing Ratios Using Fractions 1.1.4. Working With Equivalent Ratios 1.1.5. More on Equivalent Ratios 1.1.6. Ratio Tables 1.1.7. Graphing Ratios
1.2. Unit Rates
 1.2.1. Unit Rates 1.2.2. Solving Problems Using Unit Rates 1.2.3. Speed as a Unit Rate 1.2.4. Calculating Unit Rates Associated With Ratios of Fractions 1.2.5. Solving Unit Rate Problems Using Ratios of Fractions
1.3. Proportional Relationships
 1.3.1. Understanding Proportional Relationships Using Tables 1.3.2. Understanding Proportional Relationships Using Graphs 1.3.3. Understanding Proportional Relationships From Descriptions
1.4. Percentages
 1.4.1. Understanding Percentages Using Models 1.4.2. Converting Between Percentages and Fractions 1.4.3. Converting Between Percentages and Decimals 1.4.4. Finding Part of a Number Given a Whole and a Percentage 1.4.5. Finding Part of a Number Given a Whole and a Percentage: Word Problems 1.4.6. Finding a Percentage Given Two Numbers 1.4.7. Finding a Percentage Given Two Numbers: Word Problems 1.4.8. Finding a Total Given a Part and a Percentage 1.4.9. Percentage Increase, Decrease, and Error
2.
The Number System
25 topics
2.5. Addition and Subtraction of Rational Numbers
 2.5.1. Subtracting a Positive Number From a Smaller Positive Number 2.5.2. Subtracting a Positive Number From a Negative Number 2.5.3. Subtracting a Positive Fraction From a Smaller Fraction 2.5.4. Subtracting a Positive Decimal From a Smaller Decimal 2.5.5. Adding a Positive Number to a Negative Number 2.5.6. Adding a Negative Number 2.5.7. Subtracting a Negative Number 2.5.8. Additive Inverses of Numbers 2.5.9. Solving Problems Using Addition and Subtraction of Rational Numbers
2.6. Multiplication and Division of Rational Numbers
 2.6.1. Multiplying Positive Numbers With Negative Numbers 2.6.2. Multiplying Negative Numbers 2.6.3. Dividing With Negative Numbers 2.6.4. Equivalent Fractions With Negative Numbers 2.6.5. Dividing With Negative Decimals and Fractions 2.6.6. Reciprocals of Rational Numbers 2.6.7. Multiplying and Dividing With Zero 2.6.8. Fractions of Fractions 2.6.9. Solving Problems Using the Four Operations on Rational Numbers
2.7. Number Theory
 2.7.1. Natural Numbers, Integers, and Rational Numbers 2.7.2. Prime and Composite Numbers 2.7.3. Prime Factorization of Integers 2.7.4. Finding Greatest Common Factors Using Prime Factorization 2.7.5. Finding Lowest Common Multiples Using Prime Factorization 2.7.6. Divisibility of Integers 2.7.7. Divisibility of Integers by 3, 9 and 6
3.
35 topics
3.8. Exponents
 3.8.1. Squaring Rational Numbers 3.8.2. Cubing Rational Numbers 3.8.3. Exponents With Rational Bases 3.8.4. The Zeroth Power 3.8.5. Powers of Negative One 3.8.6. Negative Exponents
3.9. The Rules of Exponents
 3.9.1. The Product Rule for Exponents 3.9.2. The Quotient Rule for Exponents 3.9.3. The Power Rule for Exponents 3.9.4. The Power of Product Rule for Exponents 3.9.5. The Power of Quotient Rule for Exponents 3.9.6. Combining the Rules of Exponents
3.10. Scientific Notation
 3.10.1. Writing Numbers in Scientific Notation 3.10.2. Converting Scientific Notation to Standard Notation 3.10.3. Comparing Numbers in Scientific Notation 3.10.4. Addition and Subtraction in Scientific Notation 3.10.5. Addition in Scientific Notation With Different Powers of Ten 3.10.6. Subtraction in Scientific Notation With Different Powers of Ten 3.10.7. Further Addition in Scientific Notation With Different Powers of Ten 3.10.8. Multiplying Numbers in Scientific Notation 3.10.9. Dividing Numbers in Scientific Notation
3.11. Order of Operations
 3.11.1. Evaluating Rational Number Expressions Without Exponents 3.11.2. Evaluating Rational Number Expressions With Positive Integer Exponents 3.11.3. Evaluating Rational Number Expressions With Integer Exponents
 3.12.1. The Square Root of a Perfect Square 3.12.2. Squaring a Square Root 3.12.3. The Cube Root of a Perfect Cube 3.12.4. Surds 3.12.5. Simplifying Expressions With Surds 3.12.6. Evaluating Numerical Expressions Containing Radicals 3.12.7. Adding and Subtracting Radicals 3.12.8. Rationalizing Denominators
 3.13.1. Radicals as Fractional Exponents 3.13.2. The Product Rule for Radicals 3.13.3. The Quotient Rule for Radicals
4.
Algebraic Expressions
17 topics
4.14. Algebraic Expressions
 4.14.1. Introduction to Algebraic Expressions 4.14.2. Constructing Algebraic Expressions 4.14.3. Evaluating Linear Expressions 4.14.4. Evaluating Rational Expressions 4.14.5. Identifying Terms in Linear Expressions 4.14.6. Identifying Coefficients and Constants in Linear Expressions 4.14.7. The Greatest Common Factor of Two Linear Expressions
4.15. Simplifying Linear Expressions
 4.15.1. Identifying Like Terms in a Linear Expression 4.15.2. Collecting Like Terms in a Linear Expression 4.15.3. Applying the Distributive Law With Linear Expressions 4.15.4. The Distributive Law With Three Terms 4.15.5. Distributing the Negative Sign in a Linear Expression 4.15.6. Simplifying Linear Expressions Using the Distributive Law 4.15.7. Simplifying Linear Expressions When a Group of Terms Is Subtracted 4.15.8. Simplifying Linear Expressions Containing Fractions 4.15.9. Factoring Numerical Expressions 4.15.10. Factoring Linear Expressions
5.
Equations & Inequalities
28 topics
5.16. Solving One-Step Linear Equations
 5.16.1. Solving Linear Equations by Trial and Error 5.16.2. Solving One-Step Addition and Subtraction Equations 5.16.3. Solving One-Step Multiplication and Division Equations
5.17. Solving Multi-Step Linear Equations
 5.17.1. Solving Two-Step Equations 5.17.2. Solving Linear Equations With Fractional Coefficients 5.17.3. Solving Linear Equations With Decimal Coefficients 5.17.4. Solving Linear Equations With Variables on Both Sides 5.17.5. Solving Linear Equations by Clearing a Rational Expression 5.17.6. Solving Linear Equations Using Cross-Multiplication 5.17.7. Solving Two-Variable Equations 5.17.8. Equations With Many Solutions and No Solutions
5.18. Solving Linear Inequalities
 5.18.1. Inequalities 5.18.2. Compound Inequalities 5.18.3. Verifying Solutions of Linear Inequalities 5.18.4. Solving One-Step Linear Inequalities 5.18.5. Solving Two-Step Inequalities 5.18.6. Representing Solutions to Inequalities on Number Lines 5.18.7. Further Solving Linear Inequalities
5.19. Graphs of Linear Equations
 5.19.1. The Cartesian Coordinate System 5.19.2. The Distance Between Two Points in the Coordinate Plane 5.19.3. Two-Variable Linear Equations and Their Solutions 5.19.4. Graphing Linear Equations 5.19.5. Horizontal and Vertical Lines 5.19.6. Calculating Slopes of Straight Lines 5.19.7. Equations of Lines in Slope-Intercept Form 5.19.8. Finding Properties of Lines Given in Slope-Intercept Form
5.20. Systems of Equations
 5.20.1. Introduction to Systems of Linear Equations 5.20.2. Solving Systems of Two Linear Equations Using Substitution
6.
Geometry
47 topics
6.21. Introduction to Geometry
 6.21.1. Units of Area and Volume 6.21.2. Points, Lines, Rays, and Segments 6.21.3. Parallel and Perpendicular Lines 6.21.4. Measures of Segments 6.21.5. Congruent Segments 6.21.6. Midpoints 6.21.7. Collinear Points 6.21.8. The Segment Addition Postulate
6.22. Angles
 6.22.1. Angles and Measures of Angles 6.22.2. Connecting Angles and Circles 6.22.3. Measuring Angles Using a Protractor 6.22.4. Sums of Angles 6.22.5. Right, Straight, Full, and Null Angles 6.22.6. Acute, Obtuse, and Reflex Angles 6.22.7. Congruent Angles 6.22.8. Vertical Angles 6.22.9. Solving Problems With Angles
 6.23.1. Complementary Angles 6.23.2. Supplementary Angles 6.23.3. Corresponding Angles 6.23.4. Alternate Angles 6.23.5. Consecutive Angles 6.23.6. Angle Criteria for Parallel Lines 6.23.7. Angle Bisectors 6.23.8. Perpendicular Lines and Bisectors
6.24. Triangles
 6.24.1. Interior Angles of Triangles 6.24.2. Exterior Angles of Triangles 6.24.3. Problem Solving With Angles of Triangles 6.24.4. Classifying Triangles 6.24.5. The Triangle Inequality 6.24.6. The Isosceles Triangle Theorem 6.24.7. Heights of Triangles
6.25. Polygons
 6.25.1. Polygons 6.25.2. Interior Angles of Polygons 6.25.3. Exterior Angles of Polygons 6.25.4. Congruent Polygons 6.25.5. Regular Polygons 6.25.6. The Perimeter of a Polygon