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.
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.
Ratios & Percentages
Introduction to Ratios
Writing Ratios Using Fractions
Working With Equivalent Ratios
More on Equivalent Ratios
1.2. Unit Rates
Solving Problems Using Unit Rates
Speed as a Unit Rate
Calculating Unit Rates Associated With Ratios of Fractions
Solving Unit Rate Problems Using Ratios of Fractions
1.3. Proportional Relationships
Understanding Proportional Relationships Using Tables
Understanding Proportional Relationships Using Graphs
Understanding Proportional Relationships From Descriptions
Understanding Percentages Using Models
Converting Between Percentages and Fractions
Converting Between Percentages and Decimals
Finding Part of a Number Given a Whole and a Percentage
Finding Part of a Number Given a Whole and a Percentage: Word Problems
Finding a Percentage Given Two Numbers
Finding a Percentage Given Two Numbers: Word Problems
Finding a Total Given a Part and a Percentage
Percentage Increase, Decrease, and Error
The Number System
2.5. Addition and Subtraction of Rational Numbers
Subtracting a Positive Number From a Smaller Positive Number
Subtracting a Positive Number From a Negative Number
Subtracting a Positive Fraction From a Smaller Fraction
Subtracting a Positive Decimal From a Smaller Decimal
Adding a Positive Number to a Negative Number
Adding a Negative Number
Subtracting a Negative Number
Additive Inverses of Numbers
Solving Problems Using Addition and Subtraction of Rational Numbers
2.6. Multiplication and Division of Rational Numbers
Multiplying Positive Numbers With Negative Numbers
Multiplying Negative Numbers
Dividing With Negative Numbers
Equivalent Fractions With Negative Numbers
Dividing With Negative Decimals and Fractions
Reciprocals of Rational Numbers
Multiplying and Dividing With Zero
Fractions of Fractions
Solving Problems Using the Four Operations on Rational Numbers
2.7. Number Theory
Natural Numbers, Integers, and Rational Numbers
Prime and Composite Numbers
Prime Factorization of Integers
Finding Greatest Common Factors Using Prime Factorization
Finding Lowest Common Multiples Using Prime Factorization
Divisibility of Integers
Divisibility of Integers by 3, 9 and 6
Exponents & Radicals
Squaring Rational Numbers
Cubing Rational Numbers
Exponents With Rational Bases
The Zeroth Power
Powers of Negative One
3.9. The Rules of Exponents
The Product Rule for Exponents
The Quotient Rule for Exponents
The Power Rule for Exponents
The Power of Product Rule for Exponents
The Power of Quotient Rule for Exponents
Combining the Rules of Exponents
3.10. Scientific Notation
Writing Numbers in Scientific Notation
Converting Scientific Notation to Standard Notation
Comparing Numbers in Scientific Notation
Addition and Subtraction in Scientific Notation
Addition in Scientific Notation With Different Powers of Ten
Subtraction in Scientific Notation With Different Powers of Ten
Further Addition in Scientific Notation With Different Powers of Ten
Multiplying Numbers in Scientific Notation
Dividing Numbers in Scientific Notation
3.11. Order of Operations
Evaluating Rational Number Expressions Without Exponents
Evaluating Rational Number Expressions With Positive Integer Exponents
Evaluating Rational Number Expressions With Integer Exponents