Recommended Grade
Grade 7-8 (or advanced Grade 5-6)
Duration
10 Weeks, 2.5 hours/week
Chapters Covered
Chapters 1-11
Class Size
4-8 Students
Course Philosophy
This syllabus outlines a 10-week schedule for mastering the foundational concepts in Art of Problem Solving: Introduction to Algebra. The pace is approximately one chapter per week, though some chapters require more time than others.
The AoPS methodology is built on learning by solving challenging problems. You should not expect to understand everything immediately. The learning happens when you get stuck and work your way out. Each weekly class follows a structured format that includes review of previous material and problem sets, introduction of new concepts, and hands-on problem-solving practice.
Required Textbook
The Art of Problem Solving: Introduction to Algebra
by Richard Rusczyk
ISBN-13: 978-1934124215
Additional reference materials will be provided by the instruction team.
Learning Approach
Read and do the Problems
Complete all "Problems" as you read through each section.
Do the Exercises
Complete all "Exercises" after reading each section.
Mastery
True understanding is demonstrated by successfully solving the Review Problems and Challenge Problems at the end of each chapter. Do not skip these!
Check Solutions
Use the Solutions Manual after you have attempted a problem and are either (1) stuck or (2) want to check your final answer and see an alternative method.
Tips for Success
Consistency is Key
Set aside dedicated time each day to work on the subject. 30-45 minutes every day is better than one 4-hour session on the weekend.
Write Everything Down
Do not do problems in your head. Write out every step, every time. This builds good habits and makes it easier to find mistakes.
Don't Be Afraid to Be Wrong
You will make mistakes. Every mistake is a learning opportunity. When you get a problem wrong, don't just fix the answer; understand why you made the mistake.
Review
Before starting a new chapter, spend 15 minutes reviewing a few problems from the previous chapter to keep the concepts fresh.
Weekly Breakdown
Schedule is tentative and may be adjusted based on class progress
Week 1 (Week of 1/5/2026): Chapter 1 - Follow the Rules and Chapter 2 - Marks the Spot
Objective:
Master the order of operations and the fundamental properties of arithmetic. Understand what a variable is and become comfortable evaluating and simplifying algebraic expressions.
Week 2 (Week of 1/12/2026): Chapter 3 - One-Variable Linear Equations
Objective:
Learn to isolate a variable using inverse operations to solve basic linear equations.
Week 3 (Week of 1/19/2026): Chapter 4 - More Variables
Objective:
Become comfortable evaluating and simplifying algebraic expressions that have more than one variable.
Week 4 (Week of 1/26/2026): Chapter 5 - Multi-Variable Linear Equations
Objective:
Master solving linear equations with more than one variable using substitution and elimination.
Week 5 (Week of 2/2/2026): Chapter 6 - Ratios and Percents
Objective:
Understand and apply ratios and percents to solve problems.
Week 6 (Week of 2/9/2026): Chapter 7 - Proportion
Objective:
Understand various proportion relationships and apply proportion to solve problems.
Week 7 (Week of 2/16/2026): Chapter 8 - Graphing Lines
Objective:
Understand the Cartesian plane and how to graph linear equations.
Week 8 (Week of 2/23/2026): Chapter 9 - Introduction to Inequalities
Objective:
Learn to solve and graph linear inequalities.
Week 9 (Week of 3/2/2026): Chapter 10 - Quadratic Equations - Part 1
Objective:
Learn to solve quadratic equations by factoring.
Week 10 (Week of 3/9/2026): Chapter 11 - Special Factorizations
Objective:
Learn the most common special factorizations and use them to solve problems.