AoPS Pre-Algebra


Lessons


Module 1: Properties of Arithmetic, Exponents, and Number Theory

Why Start with Arithmetic?
Addition and Multiplication
Negation and Subtraction
Reciprocals
Division
Squares
Higher Exponents
Zero as an Exponent
Negative Exponents
Multiples
Divisibility Tests
Prime Numbers and Prime Factorization
Least Common Multiple
Divisors
Greatest Common Divisor
Test 1 Review
Test 1

Module 2: Fractions, Equations and Inequalities, Decimals, and Ratios, Conversions, and Rates

Definition of a Fraction
Multiplying Fractions and Dividing by a Fraction
Raising Fractions to Powers
Simplest Form of a Fraction
Comparing Fractions
Adding and Subtracting Fractions
Mixed Numbers
Expressions
Solving Linear Equations Part 1
Solving Linear Equations Part 2
Word Problems
Inequalities
Arithmetic with Decimals
Rounding
Decimals and Fractions
Repeating Decimals
Definition of a Ratio
Multi-way Ratios
Proportions and Conversions
Speed and Other Rates
Test 2 Review
Test 2
Midterm Review
Midterm

Module 3: Percents, Square Roots, and Angles

Definition of a Percent
Word Problems
Percent Increase and Decrease
Quiz 1 Review
Quiz 1
From Squares to Square Roots
Square Roots of Non-square Integers
Arithmetic with Square Roots
Quiz 2 Review
Quiz 2
Measuring Angles
Parallel Lines
Angles in Polygons
Test 3 Review
Test 3

Module 4: Perimeter and Area, Right Triangles and Quadrilaterals, and Data and Statistics

Measuring Segments
Area and Circles
Quiz 3 Review
Quiz 3
The Pythagorean Theorem
Some Special Triangles
Types of Quadrilaterals
Quiz 4 Review
Quiz 4
Basic Statistics
Limits of Basic Statistics
Tables, Graphs, and Charts
Test 4 Review
Test 4

Module 5: Counting and Problem-Solving Strategies

Counting with Addition and Subtraction
The Multiplication Principle
Casework
Counting Pairs
Probability
Quiz 5 Review
Quiz 5
Finding Patterns
Making Lists
Drawing Pictures
Working Backwards
Test 5 Review
Test 5
Final Exam Review
Final Exam

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