Recommended Grade
Grade 6-7 (or advanced Grade 4-5)
Duration
10 Weeks, 2.5 hours/week
Chapters Covered
Chapters 1-9
Class Size
4-8 Students
Course Philosophy
This syllabus outlines a 10-week schedule for mastering the foundational concepts in Art of Problem Solving: Prealgebra. 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.
Required Textbook
The Art of Problem Solving: Prealgebra
by Richard Rusczyk, David Patrick, Ravi Boppana
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 – Properties of Arithmetic
Topics:
Addition, multiplication, subtraction, negation, reciprocals, division, summary
Objectives:
- Review fundamental operations and their properties (commutativity, associativity, distributivity)
- Build fluency with negative numbers, reciprocals, division
- Understand why arithmetic rules hold
Activities:
Guided reading of sections 1.1-1.7, practice problems; end with summary 1.8
Homework:
Selected problems from chapter; emphasize proofs/explanations not just computation
Week 2 (Week of 1/12/2026): Chapter 2 – Exponents
Topics:
Squares, higher exponents, zero exponent, negative exponents, summary
Objectives:
- Grasp exponent notation and meaning
- Understand operations with exponents (including negative and zero exponents)
- Connect exponents to repeated multiplication and arithmetic properties
Activities:
Lecture + examples; short quiz on exponent laws
Homework:
Various exponent exercises; include some challenge problems
Week 3 (Week of 1/19/2026): Chapter 3 – Number Theory
Topics:
Multiples, divisibility tests, prime numbers, prime factorization, LCM, divisors, GCD, summary
Objectives:
- Introduce basic number theory concepts relevant for contest math
- Practice factorization, divisibility, greatest/least common divisor/multiple
- Begin applying these in problem-solving context
Activities:
Group work on divisibility tests, factor puzzles
Homework:
Problems emphasizing primes, GCD/LCM, factorization
Week 4 (Week of 1/26/2026): Chapter 4 – Fractions
Topics:
What is a fraction, multiply/divide fractions, raising fractions to powers, simplest form, comparing, mixed numbers, summary
Objectives:
- Master fraction arithmetic and transformations
- Explore raising fractions to powers
- Compare fractions, convert mixed numbers
Activities:
Workshop conversion and comparison of fractions; fraction puzzles
Homework:
Set of fraction problems, including proofs of rules
Week 5 (Week of 2/2/2026): Chapter 5 – Equations and Inequalities
Topics:
Expressions, solving linear equations I & II, word problems, inequalities, summary
Objectives:
- Transition from arithmetic to algebraic thinking
- Solve linear equations and inequalities; interpret word problems
- Develop reasoning for algebraic manipulation
Activities:
Solve sample word problems in pairs; class discussion of solution methods
Homework:
Mixed set of linear equations, inequalities, and word problems
Week 6 (Week of 2/9/2026): Chapter 6 – Decimals
Topics:
Arithmetic with decimals, rounding, decimals & fractions, repeating decimals, summary
Objectives:
- Work confidently with decimals and convert between decimals and fractions
- Understand repeating decimals, rounding rules
- Integrate decimal operations into problem-solving
Activities:
Hands-on exercises converting repeating decimals; rounding challenge
Homework:
Problems mixing fractions, decimals, repeating decimals
Week 7 (Week of 2/16/2026): Chapter 7 – Ratios, Conversions, and Rates (Part 1)
Topics:
Ratio fundamentals, multi-way ratios, proportions
Objectives:
- Grasp ratios and proportions in depth
- Solve conversion and rate problems (speed, unit conversions, etc.)
- Apply to real-world and contest-style situations
Activities:
Real-life rate problems (e.g., speed, work)
Homework:
Proportions and multi-way ratio problems; challenge conversion rate puzzles
Week 8 (Week of 2/23/2026): Chapter 7 – Ratios, Conversions, and Rates (Part 2)
Topics:
Conversions, speed, other rates, summary
Objectives:
- Grasp ratios and proportions in depth
- Solve conversion and rate problems (speed, unit conversions, etc.)
- Apply to real-world and contest-style situations
Activities:
More real-life rate problems (e.g., speed, work)
Homework:
More proportions and multi-way ratio problems; challenge conversion rate puzzles
Week 9 (Week of 3/2/2026): Chapter 8 – Percents
Topics:
What is a percent, word problems, percent increase/decrease, summary
Objectives:
- Understand percent concept and convert between percent, fraction, decimal
- Solve percent word problems and percent change problems
- Apply to finance/real-life contexts
Activities:
Simulate real-life percent problems (discounts, markups, taxes)
Homework:
Percent change, reverse percent, multi-step percent problems
Week 10 (Week of 3/9/2026): Chapter 9 – Square Roots
Topics:
From squares to square roots, square roots of non-square integers, arithmetic with square roots, summary
Objectives:
- Define square roots, estimate non-perfect roots
- Perform operations involving square roots
- Connect to exponent work from earlier chapters
Activities:
Estimation exercises, simplify radicals
Homework:
Simplifying square roots, arithmetic with radicals, bridging with exponents