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Prealgebra 1 Self-Paced
Summary
In AoPS Prealgebra 1, middle school students build the foundation they need to succeed in the next course on their journey. Students explore key topics in number theory and algebra: exponents and exponent laws, common divisors and multiples, linear equations, inequalities, ratio and proportion, conversion, speed, and more.
Prealgebra 1 is available as a live course that meets online weekly for 75-minute sessions, or as a self-paced course. Our self-paced course allows students to move ahead at their preferred pace, with automated interactive instruction replacing the live class meeting times. Both course styles offer instructor feedback on student work, as well as office hours and a class message board for student support throughout the course.
Prealgebra 1: Self-Paced
Length: 50 Lessons
In our self-paced Prealgebra 1 course, students proceed at their own rate and explore new concepts independently through a series of automated, interactive mathematical conversations.
Instead of prescheduled meeting times, self-paced math classes offer live interaction through the class message board, where students can connect with peers on challenging problems and receive support from instructors. We reinforce lessons with examples from the first half of our Prealgebra textbook, engaging videos, and various types of homework problems.
While many students will complete Prealgebra 1 in 3–6 months, we offer unlimited access to the class for 9 months.
What's Included?
Why AoPS?
Innovative Interactive Instruction
In our self-paced courses, students progress through interactive lessons that engage them in mathematical conversations, guiding them step-by-step and addressing common misconceptions. Students learn in various ways, so we offer multiple learning avenues: interactive lessons, a textbook, videos, diverse homework problems, and opportunities to engage in discussions with instructors and peers on the class message board.
Active Learning
Learning is not a spectator sport, and students learn best by tackling hard problems themselves. Our lessons start with challenging questions to help students develop new mathematical strategies. If students get stuck, our learning technology supplies helpful hints and adapts lesson structure to further reinforce key concepts.
Focus on Non-Routine, Challenging Problems
To prepare our students for the challenges of tomorrow, we teach them how to apply fundamentals to different types of problems, not just variations on the same problem they’ve seen before. Building a critical problem-solving skill set, our students are prepared for the rigors of top-tier colleges and internationally competitive careers.
Who Should Take This Class?
This course is ideal for students who have completed an elementary school (grades 1-5) math curriculum and are eager for a more challenging mathematical experience.
- To determine if you’re ready for the course, students can take the diagnostic pretest.
- To determine if you need this course, students can take the diagnostic post-test.
Prealgebra 1 is also the next step for students who have completed grade 5 of our elementary school curriculum, Beast Academy. (But you don't have to be a Beast Academy student to take Prealgebra 1!)
Self-Paced vs. Weekly Live
Our self-paced class is designed for students who prefer to set their own study schedule. In this format, students can engage with peers and receive support from staff through the class message board. For students interested in a live group experience with real-time interactions in an online classroom setting, we recommend considering the weekly live version of this course.Instructional Videos
Expand your conceptual understanding with free instructional videos! Featuring AoPS Founder Richard Rusczyk, these step-by-step tutorials model problem solving strategies to help students master key ideas from almost every lesson in the prealgebra textbook.
- Rigorous definition of arithmetic basics
- Clever applications of arithmetic rules to make seemingly-complicated calculations simple
- Exponentiation and powers
- Exponent laws
- Zero as an exponent
- Negative exponents
- Multiples and divisibility
- Primes, composites, and prime factorization
- Fundamental Theorem of Arithmetic
- Least common multiple (LCM) and greatest common divisor (GCD)
- Rigorous definition of fractions
- Arithmetic with fractions and mixed numbers
- Fraction comparison and simplification
- Challenging word problems with fractions
- Expressions and equations
- Linear equations
- Applications of linear equations to word problems
- Principles of inequalities
- Linear inequalities
- Definition of decimal notation
- Rigorous exploration of arithmetic with decimals
- Decimal comparison and approximation
- Conversion between fractions and decimals
- Rational numbers and their decimal representation
- Definition of ratio and proportion
- Proportional thinking
- Problem-solving with part-to-part and part-to-whole ratios
- Variables in ratios and proportions
- Unit conversion with conversion factors
- Relationship between speed, distance, and time
- Joint work, relative speed, and average speed
Required Textbook
Related courses: Prealgebra 1 and Prealgebra 2
