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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: 50 Lessons
In our self-paced Prealgebra 1 course, students proceed at their own rate through a series of automated interactive mathematical conversations. We reinforce these lessons with our Prealgebra textbook and videos, as well as multiple types of homework problems. Our self-paced classes also offer live interaction through the class message board, on which students can collaborate with peers and receive help from instructors. 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 work their way through carefully scripted interactive lessons. These automated lessons lead students in mathematical conversations designed to engage, entertain, and educate. Each lesson reacts to student input, guiding them step-by-step through problems and tackling common misconceptions along the way. When students need extra help, they can turn to the class message board where instructors provide additional assistance.
Active Learning
Learning is not a spectator sport. Students best learn by tackling hard problems themselves, not by watching others do the work. Therefore, we start lessons with questions, challenging the students to find the key insights on their own. This teaches students how to create new mathematical strategies as needed. When students inevitably get stuck, we provide hints and more direct instruction to help them proceed. After students have solved a problem, we follow up with important concepts and strategies before moving on to the next problem.
Focus on Non-Routine, Challenging Problems
Thirty years ago, many intellectual careers consisted of repeatedly solving routine problems. Computers fill most of those roles now. Successful people in the next generation will need to develop new skills throughout their careers as their older skills become obsolete. To prepare our students for this challenging future, we go well beyond the basics in our courses, showing students how to apply fundamentals to problems that are not replicas of problems they've already seen. This teaches students how to learn, so they'll be ready for the rigors of top-tier colleges and internationally competitive careers.
Multiple Learning Avenues
Students learn in many ways, so we deliver instruction in multiple forms. In addition to our automated interactive lessons, our students can read the Prealgebra textbook, watch videos, solve many different types of homework problems, and participate in mathematical conversations with instructors and other students on the class message board and during office hours.
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. Students can try the Prealgebra 1 "Are You Ready?" diagnostic test to see if they are prepared to take this course.
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!)
Our self-paced class is designed for students who wish to set their own schedule for their studies. While this course does provide some peer interaction and live teacher support through the class message board and office hours, students wishing to have a live group experience in an online classroom with instructors and peers should consider our weekly live version of Prealgebra 1.
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
