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Prealgebra 1

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: 16 Weeks

Our weekly live Prealgebra 1 course brings together eager young problem solvers from around the world for 75-minute classes with an experienced instructor and multiple assistants. Students also learn from our Prealgebra textbook and videos, while honing their skills on several types of homework problems. Furthermore, they can use the class message board to collaborate with their peers and receive help from instructors outside of class time.

Live Online Course Features

16 weekly live class sessions taught by one of our outstanding faculty
Weekly homework assignments with challenging short-answer problems and practice on our adaptive online learning system, Alcumus
Detailed instructor evaluation of students' written solutions to open-response problems designed to strengthen mathematical writing skills
Class message board where students can ask instructors questions and collaborate with their classmates
Office hours every day during which AoPS instructors and teaching assistants provide live help to students on the class message board
Weekly assigned readings in our Prealgebra textbook
Over 80 videos by AoPS founder and Prealgebra co-author Richard Rusczyk
Detailed reporting that allows students and parents to track progress and performance throughout the course

Why AoPS?

Extraordinary Live Instruction from Accomplished Faculty

Our teachers were outstanding math students themselves, and many were winners of major math awards as well as recipients of degrees from schools like MIT, Harvard, Stanford, and Princeton. Our instructors understand from their personal experiences how to inspire and challenge eager learners, and they serve as role models for our students who aspire to similar success.

Active Learning

Learning is not a spectator sport. Students best learn by tackling hard problems themselves, not by watching others do the work. In our classes, instructors start with questions, challenging the students to find the key insights on their own. This helps students learn how to generate new ideas as required, and to develop new skills as needed. When students inevitably get stuck, teachers and assistants provide hints and more direct instruction. After students have solved a problem, instructors reinforce important concepts and strategies. Then–it's 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 live classes, 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.

Schedule: Prealgebra 1

The current and upcoming sections of our weekly live Prealgebra 1 course are listed below. All sections cover the same course material.

Sunday
Nov 3 - Mar 9
7:30 - 8:45
PM ET
Nov 3 - Mar 9
7:30 - 8:45 PM Eastern
6:30 - 7:45 PM Central
5:30 - 6:45 PM Mountain
4:30 - 5:45 PM Pacific
Click here to see more time zones
$445 (~$28/lesson)
$504 w/books
$445 (~$28/lesson)
$504 w/books
ENROLL
Tuesday
Nov 5 - Mar 11
7:30 - 8:45
PM ET
Nov 5 - Mar 11
7:30 - 8:45 PM Eastern
6:30 - 7:45 PM Central
5:30 - 6:45 PM Mountain
4:30 - 5:45 PM Pacific
Click here to see more time zones
$445 (~$28/lesson)
$504 w/books
$445 (~$28/lesson)
$504 w/books
ENROLL
Sunday
Jan 5 - Apr 20
7:30 - 8:45
PM ET
Jan 5 - Apr 20
7:30 - 8:45 PM Eastern
6:30 - 7:45 PM Central
5:30 - 6:45 PM Mountain
4:30 - 5:45 PM Pacific
Click here to see more time zones
$445 (~$28/lesson)
$504 w/books
$445 (~$28/lesson)
$504 w/books
ENROLL
Wednesday
Jan 15 - Apr 30
7:30 - 8:45
PM ET
Jan 15 - Apr 30
7:30 - 8:45 PM Eastern
6:30 - 7:45 PM Central
5:30 - 6:45 PM Mountain
4:30 - 5:45 PM Pacific
Click here to see more time zones
$445 (~$28/lesson)
$504 w/books
$445 (~$28/lesson)
$504 w/books
ENROLL
Monday
Feb 3 - May 19
7:30 - 8:45
PM ET
Feb 3 - May 19
7:30 - 8:45 PM Eastern
6:30 - 7:45 PM Central
5:30 - 6:45 PM Mountain
4:30 - 5:45 PM Pacific
Click here to see more time zones
$445 (~$28/lesson)
$504 w/books
$445 (~$28/lesson)
$504 w/books
ENROLL
Sunday
Mar 2 - Jun 22
7:30 - 8:45
PM ET
Mar 2 - Jun 22
7:30 - 8:45 PM Eastern
6:30 - 7:45 PM Central
5:30 - 6:45 PM Mountain
4:30 - 5:45 PM Pacific
Click here to see more time zones
$445 (~$28/lesson)
$504 w/books
$445 (~$28/lesson)
$504 w/books
ENROLL
Friday
Mar 28 - Jul 18
7:30 - 8:45
PM ET
Mar 28 - Jul 18
7:30 - 8:45 PM Eastern
6:30 - 7:45 PM Central
5:30 - 6:45 PM Mountain
4:30 - 5:45 PM Pacific
Click here to see more time zones
$445 (~$28/lesson)
$504 w/books
$445 (~$28/lesson)
$504 w/books
ENROLL
Sunday
Apr 13 - Aug 10
7:30 - 8:45
PM ET
Apr 13 - Aug 10
7:30 - 8:45 PM Eastern
6:30 - 7:45 PM Central
5:30 - 6:45 PM Mountain
4:30 - 5:45 PM Pacific
Click here to see more time zones
$445 (~$28/lesson)
$504 w/books
$445 (~$28/lesson)
$504 w/books
ENROLL
Don't see a schedule option that works for you? Check out the self-paced version of this class.

AoPS Holidays

There are no classes November 25 ‐ December 1, December 21 ‐ January 3, May 24 ‐ 26, July 4 ‐ 6, August 29 ‐ September 1, and October 31, 2025.

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!)

Each class session is 75 minutes long, and brings together eager students with outstanding instructors for a highly interactive mathematical conversation. Students whose schedules don't allow participation in the live classes, or who wish to pursue their studies at their own pace, should consider our self-paced 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.

Lessons

Show All Topics
Lesson 1
Arithmetic Rules, Day 1
  • Rigorous rules for addition and multiplication
  • Longer, more complicated sums
  • Gauss's clever summation technique
Lesson 2
Arithmetic Rules, Day 2
  • Reciprocals
  • Rigorous definition of division to set the stage for fractions
Lesson 3
Exponents and Exponent Laws
  • Squares and higher powers
  • Products and quotients of powers
  • Power of a power
Lesson 4
Non-positive Exponents
  • Zero as an exponent
  • Negative exponents
  • Extension of exponent laws to non-positive exponents
Lesson 5
Multiples and Divisibility
  • Principles of multiples
  • Divisibility tests for 2, 3, 4, 5, 6, 8, 9
Lesson 6
Primes and Prime factorization
  • Primes and composites
  • Prime factorization
  • Problem-solving with prime factorizations
  • Infinitude of primes
Lesson 7
Least Common Multiple (LCM) and Greatest Common Divisor (GCD)
  • Common multiples and common divisors
  • Definition of LCM and GCD
  • Application of prime factorizations to LCM and GCD
Lesson 8
Fractions, Day 1
  • Formal definition of fractions
  • Fraction multiplication and division
  • Fraction simplification
Lesson 9
Fractions, Day 2
  • Fraction comparison
  • Fraction addition and subtraction
  • Word problems with fractions
Lesson 10
Linear Equations
  • Expressions and Equations
  • Expression simplification
  • One- and two-step linear equations
  • Basic word problems
Lesson 11
Advanced Linear Equations and Word Problems
  • Complicated linear equations
  • More complex word problems
  • Linear equations with no solution or with infinitely many solutions
Lesson 12
Inequalities
  • Principles of inequalities
  • Inequalities on the number line
  • Linear inequalities
  • Word problems with inequalities
Lesson 13
Decimal Arithmetic
  • Definition of decimals
  • Decimal addition, subtraction, multiplication, and division
  • Decimal comparison
Lesson 14
Decimals and Fractions
  • Decimal approximation
  • Conversion between decimals and fractions
  • Rational numbers and their decimal representation
Lesson 15
Ratio and Proportion
  • Definition of ratio and proportion
  • Proportional thinking
  • Part-to-part and part-to-whole problem-solving
  • Word problems with ratios and proportions
Lesson 16
Conversion, Speed, and Other Rates
  • Units and conversion factors
  • Relationship between speed, distance, and time
  • Joint work, relative speed, and average speed

Required Textbook

Prealgebra By Richard Rusczyk, David Patrick, Ravi Boppana
Prealgebra prepares students for the rigors of algebra and also teaches students problem-solving techniques to prepare them for prestigious middle school math contests such as MATHCOUNTS, MOEMS, and the AMC 8. The text is written to challenge students at a much deeper level than a traditional middle school prealgebra course.
Related courses: Prealgebra 1 and Prealgebra 2
View Details

I liked the way my instructor presented and taught all the topics in this course. I feel that the challenge problems were truly challenging. They really kept me thinking about how many different ways I can come up with a solution. One main thing that I have improved during this course was learning how to write a detailed explanation under the writing challenge problem. The elaborate feedback that I received for the writing challenge problem was helpful and I was able to find an easier way to do the problem. I also learned how to use LaTeX. Overall I can't explain in words how much I truly enjoyed this course.