Course Catalog

Below are the courses we offer for high-performing students in both math and language arts. We offer courses during the academic year and during the summer. Click on any course for more information about that course, and read About AoPS Academy to learn more about our educational philosophy.

Please note, course offerings may vary by campus.

Academic Year Math

Courses during the school year for high-performing math students in grades 2-12

2nd Grade Mathematics

Students expand their understanding of the number system and place value, and they develop fluency adding and subtracting multi-digit numbers. They explore the properties of special types of numbers, such as odds and evens. Problem-solving strategies are emphasized throughout the course, and each lesson includes challenging word problems and puzzles that guide students from the basics toward a deep understanding of the material.

3rd Grade Mathematics

Students develop fluency with multiplication and division, including using the distributive property to simplify calculations. They also explore two-dimensional shapes, estimation, using variables to write expressions and equations, and other topics. Students expand their understanding of numbers by learning about fractions. We use word problems to teach students how to interpret words with mathematics, and puzzles to teach higher-order strategic thinking.

4th Grade Mathematics

Students master multiplication and division of multi-digit numbers and build upon their understanding of addition and multiplication to include fractions. They also explore a wide variety of other topics, including properties of special two-dimensional shapes, symmetry, logic, factors, and probability. Students expand their understanding of numbers to include decimals and negative integers, and they encounter challenging word problems throughout to learn how to create and use mathematical models.

5th Grade Mathematics

Students complete their study of the arithmetic of fractions, decimals, and negative integers. They are also introduced to topics in geometry, number theory, statistics, and beginning algebra through lessons on three-dimensional solids, factors and multiples, statistics and data, sequences, and ratios. As with our earlier elementary school classes, we include challenging word problems and puzzles to teach students mathematical modeling and deductive reasoning.

Prealgebra

Prealgebra starts by formalizing the rules of arithmetic, so students can build on a rigorous foundation as they move into algebra. We then survey topics in number theory, algebra, geometry, counting, statistics, and probability. We place special emphasis on challenging word problems throughout the course.

Algebra 1

In Algebra 1, students learn how to work with various types of expressions both algebraically and geometrically. They learn how to solve linear and quadratic equations and how to represent various expressions in the Cartesian plane. We introduce students to the rich field of complex numbers, as well as to important common functions and concepts in discrete math. We continue the emphasis on challenging word problems from Prealgebra, so that students learn when and how to apply their new tools.

Geometry

Students learn how to think spatially in our Geometry course. We start with fundamental concepts, from which we build a rich, rigorous tapestry of relationships. Students learn how to dissect complex configurations and discover the key insights that allow them to solve difficult problems. We also teach analytic methods for tackling geometry problems by placing them on the Cartesian plane, and we introduce trigonometry, thereby laying foundations for precalculus and calculus.

Algebra 2

We review the key concepts of Algebra 1, expanding upon them to solve more difficult problems. We explore the rich field of polynomials, and lay foundations for calculus with a study of sequences and series. Students learn about a variety of common algebraic forms and important functions, and about tools for understanding new forms and functions they’ll encounter in the future. We also lay the groundwork for understanding optimization problems with a study of inequalities.

Precalculus

Our Precalculus class prepares students for a variety of college-level courses. Precalculus provides a deep exploration of trigonometry, complex numbers, and two- and three-dimensional vector spaces, with a special focus on how these areas of math are related. This gives students a solid foundation for collegiate courses in calculus, linear algebra, multi-variable calculus, complex analysis, and physics.

Calculus

Our calculus class goes well beyond the traditional AP-course emphasis on mechanics and calculators. We provide students a rigorous understanding of the fundamental operations of calculus, delivering a first-year calculus course like those students would find at a top-tier university. Students completing our calculus course will be in an excellent position to apply their new skills to physics, economics, engineering, and more advanced mathematics.

Elementary School Contest Math

Math contests allow students to review old topics and to discover and explore new topics through a variety of challenging problems. In this course, we use problems from Math Kangaroo, Math Olympiads in the Elementary and Middle Schools (MOEMS), and the American Mathematics Competitions 8 (AMC 8) to deepen student understanding of the fundamentals while developing complex critical-thinking skills.

Middle School Contest Math

This course covers middle school contests such as MATHCOUNTS and the American Mathematics Competitions 8 (AMC 8), as well as beginning high school contests like the American Mathematics Competitions 10 (AMC 10). Students are introduced to important new topics in counting, probability, and number theory, while reviewing topics in algebra and geometry and applying these concepts to advanced problems.

High School Contest Math

High school students have relied on AoPS for high school contest preparation since 1993. Over the last decade, most of the winners of the USA Mathematical Olympiad (USAMO) have been AoPS students, including the team members of the 2015 US team that won the International Math Olympiad (IMO). In this course, students study strategies needed for success on the American Mathematics Competitions 12 (AMC 12), the American Invitational Math Exam (AIME), the Harvard-MIT Math Tournament, and other major high school contests.

Academic Year Language Arts

Courses during the school year for high-performing language arts students in grades 2-12

2nd Grade Language Arts

Our second grade students will develop strong analytical thinking and comprehension skills while studying a variety of fiction, poetry, and nonfiction texts. Students will begin building advanced vocabularies, incorporating them into their writing and speaking. This course will expand on second grade reading and writing objectives for written communication, oral communication, literature, and syntax.

3rd Grade Language Arts

This course expands on third-grade reading and writing objectives for written communication, oral communication, literature, and syntax. In class, students read and analyze a wide variety of challenging texts, including selections from fiction and non-fiction sources. Through integrated grammar, vocabulary, reading, and writing lessons, students build the skills they need to craft their own insightful interpretations of a text and to convey their ideas clearly and elegantly in writing.

4th Grade Language Arts

Our fourth grade students begin a rigorous study of classic words, Latin and Greek stems, paragraph construction, and grammar analysis. This course expands on fourth grade reading and writing objectives for written communication, oral communication, literature, and syntax.

5th Grade Language Arts

In our fifth grade course, students will learn the art of research and essay writing, applying advanced grammar skills in the construction of each written piece. They will continue developing deep vocabularies through the study of classic words and Latin and Greek stems. This course will expand on fifth grade reading and writing objectives for written communication, oral communication, literature, and syntax.

6th Grade Language Arts

Our sixth-grade course guides students beyond grade level in reading, writing, and critical thinking. Through integrated grammar, vocabulary, reading, and writing lessons, students build the skills they need to craft their own insightful interpretations of a text and convey their ideas clearly and elegantly in writing. In-class lessons guide students through increasingly sophisticated selections from a variety of fiction and non-fiction sources. Along the way, students practice emulating the authors they are reading, and work closely with their teachers to learn the craft of literary analysis.

7th Grade Language Arts

Our seventh grade students begin a rigorous study of advanced words in addition to refining their knowledge of Latin and Greek stems. Students continue to hone their research, grammar, and essay-writing skills through analysis of poetry, comparison of complex subjects, evaluation of ideas, and the creation of academic theses.

8th Grade Language Arts

In our eighth grade course, students analyze the most grammatically complex sentences from classic literature. Students apply advanced research and essay-writing skills to papers about complex subjects such as artistic expressions, historical movements, great discoveries, and ancient ethics. They also continue to broaden their vocabularies with the study of advanced words and Latin and Greek stems.

Debate and Public Speaking

Effective communication is essential for success in both professional and academic environments. This course will provide high school students with the opportunity to sharpen their communication skills, focusing not only on the art of delivering their message verbally, but also on nonverbal presentation cues, such as poise, demeanor, and self-awareness.

High School Language Arts

​In this course students will develop their interpretive skills through the analysis of classic world literature about which they will craft concise, elegant essays that clearly reflect a complexity of thought and depth of understanding. Students will sharpen their understanding and application of grammar, syntax, and usage as they produce polished written works. They will learn to read with greater comprehension as they acquire a deeper understanding of literary and rhetorical techniques. As students encounter the sophisticated vocabulary in the literature, their own vocabularies will expand.

Advanced Language Arts Seminar

This course introduces students to the craft of literary studies at the college level. Through close reading of challenging texts, students learn to form their own critical interpretations, to write and speak with sophistication, and to build well-crafted arguments one piece of evidence, one claim, and one draft at a time. Over the course of the year, students polish their style, grammar, and vocabulary as they produce creative texts, and develop the research skills integral to successful academic writing and public speaking.

Summer Math

Courses during the summer for high-performing math students entering grades 3-9

Math Beasts Camp 3-4

Math Beasts Camp 3-4 is designed for students entering a 3rd or 4th grade math class in the fall. The course keeps students' math skills sharp over the summer while introducing new avenues of mathematical discovery, with a focus on honing students' deductive reasoning and spatial thinking abilities.

Math Beasts Camp 5

Math Beasts Camp 5 is designed for students entering a 5th grade math class in the fall. The course reviews key concepts from 4th grade, provides some early practice with ideas they'll master in the upcoming year, and introduces advanced problem solving strategies through a study of strategic mathematical games.

Math Beasts Camp 6 (Prealgebra Prep)

Math Beasts Camp 6 is designed for students entering a 6th grade math class or Prealgebra class in the fall. The course reviews key concepts from 5th grade, provides some early practice with ideas they'll master in the upcoming year, and offers an early exploration of graph theory, a rich field of advanced math with many important real-world applications.

Math Beasts Camp 7-9 (Algebra and Geometry Prep)

The Math Beasts Camp 7-9 summer program is designed for students who have just completed a Prealgebra or Algebra 1 equivalent math class. The course reviews key algebraic and geometric concepts, provides some early practice with ideas they'll master in the upcoming year, and offers an exploration of cryptography, with an emphasis on important areas of number theory that make internet security possible.

Middle School Math Contests

This course covers middle school contests such as MATHCOUNTS and the American Mathematics Competitions 8 (AMC 8), as well as beginning high school contests like the American Mathematics Competitions 10 (AMC 10). Students are introduced to important new topics in areas such as counting, probability, and number theory, while reviewing topics in algebra and geometry and applying these concepts to advanced problems.

Summer Language Arts

Courses during summer for high-performing language arts students in grades 2-12

Elementary School Book Club: Animal Minds

Students explore the world from animals' perspectives in Elementary School Book Club: Animal Minds. During the course, students expand their vocabulary as they experience several different texts through both deep independent reading and guided analysis. They also hone their writing and public speaking skills with a variety of analytical activities.

Creative Writing for Elementary School

In this course, we teach students how to weave narratives that will enchant their audiences. We empower students to tell the stories they wish to tell, and we provide them with the tools to do so effectively. We begin by examining a variety of writing skills and techniques necessary to craft riveting short stories. We later reinforce these tools, as students implement what they have learned while constructing their own short stories.

Middle School Book Club: Metafiction

Students explore books that know you're reading them in Middle School Book Club: Metafiction. In addition to honing their close-reading skills, students will also participate in a wide variety of writing and public-speaking exercises that will give them much greater facility with written and spoken language. This course is designed for students entering grades 6-8.

Academic Essay Writing

For students entering grades 7-10, our Academic Essay Writing course offers an intensive study of the how and why of academic writing. In two weeks, students learn not just how to structure an academic essay, but also why such essays matter: why people write them, why people read them, and why teachers and professors care so much about them.
"AoPS Academy is truly a wonderful place to learn advanced concepts in math. The academy has highly qualified instructors who not only help kids learn rigorous math concepts in great depth, but also inspire them to achieve the lofty heights that they are capable of. The instructors are truly an inspiration for my children due to their thoughtful mentoring. Thank you for everything you do for our kids."
-Praveen T.
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