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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
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 |
Orianne Luo |
$430
(~$27/lesson)
$489 w/books
|
$430
(~$27/lesson)
ENROLL
$489 w/books
|
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 |
Josh Zucker |
$430
(~$27/lesson)
$489 w/books
|
$430
(~$27/lesson)
ENROLL
$489 w/books
|
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 |
James Sheldon |
$430
(~$27/lesson)
$489 w/books
|
$430
(~$27/lesson)
ENROLL
$489 w/books
|
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 |
Julie Zhu |
$430
(~$27/lesson)
$489 w/books
|
$430
(~$27/lesson)
ENROLL
$489 w/books
|
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 |
Andrea Knapp |
$430
(~$27/lesson)
$489 w/books
|
$430
(~$27/lesson)
ENROLL
$489 w/books
|
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 |
Dan Kneezel |
$430
(~$27/lesson)
$489 w/books
|
$430
(~$27/lesson)
ENROLL
$489 w/books
|
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 |
James Sheldon |
$430
(~$27/lesson)
$489 w/books
|
$430
(~$27/lesson)
ENROLL
$489 w/books
|
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 |
Laura Pierson |
$430
(~$27/lesson)
$489 w/books
|
$430
(~$27/lesson)
ENROLL
$489 w/books
|
AoPS Holidays
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.
- Rigorous rules for addition and multiplication
- Longer, more complicated sums
- Gauss's clever summation technique
- Reciprocals
- Rigorous definition of division to set the stage for fractions
- Squares and higher powers
- Products and quotients of powers
- Power of a power
- Zero as an exponent
- Negative exponents
- Extension of exponent laws to non-positive exponents
- Principles of multiples
- Divisibility tests for 2, 3, 4, 5, 6, 8, 9
- Primes and composites
- Prime factorization
- Problem-solving with prime factorizations
- Infinitude of primes
- Common multiples and common divisors
- Definition of LCM and GCD
- Application of prime factorizations to LCM and GCD
- Formal definition of fractions
- Fraction multiplication and division
- Fraction simplification
- Fraction comparison
- Fraction addition and subtraction
- Word problems with fractions
- Expressions and Equations
- Expression simplification
- One- and two-step linear equations
- Basic word problems
- Complicated linear equations
- More complex word problems
- Linear equations with no solution or with infinitely many solutions
- Principles of inequalities
- Inequalities on the number line
- Linear inequalities
- Word problems with inequalities
- Definition of decimals
- Decimal addition, subtraction, multiplication, and division
- Decimal comparison
- Decimal approximation
- Conversion between decimals and fractions
- Rational numbers and their decimal representation
- Definition of ratio and proportion
- Proportional thinking
- Part-to-part and part-to-whole problem-solving
- Word problems with ratios and proportions
- Units and conversion factors
- Relationship between speed, distance, and time
- Joint work, relative speed, and average speed
Required Textbook
Related courses: Prealgebra 1 and Prealgebra 2