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.

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.

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.

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 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.

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.

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.

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.

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.

Our calculus class goes well beyond mechanics and calculators, and provides 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.

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 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.

Our second grade class helps students develop an excitement for language arts. Each week, students learn tools to help them become better writers, expand their vocabularies to use advanced words in their own writing, and deepen their reading comprehension skills to become critical thinkers. Through class readings, discussions, and creative writing activities, students gain independence and confidence in their language arts abilities.

Our third grade class builds the foundation students need to become independent readers, writers, and critical thinkers. The course is divided into four quarters: the craft of narrative, informative nonfiction, logic-based persuasive speaking, and theater. Each week's lesson is built around reading a challenging text and practicing writing and grammar skills related to that text. The thematic focus of the course is ancient Greek mythology and history, giving students a rich introduction to characters and stories that are central to the Western literary tradition.

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.

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.

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. 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.

This class focuses on strengthening and deepening students’ language arts skills as they begin the transition into serious academic writing and developing skills in research, critical thinking, argumentation, and effective rhetoric. The class is structured around three writing projects: an exploratory essay, an evaluation of academic ideas, and a research paper. Additionally, students will review grammar concepts in greater depth and study challenging vocabulary words and roots.

Our 8th grade class prepares students for high-school level academic writing. There are three long-term writing projects: a position paper, an analysis essay, and a research paper. Students will begin to think critically about their topics and evaluating their sources. Additionally, students study grammatically complex sentences from classic literature and continue their rigorous study of advanced vocabulary containing Greek and Latin roots. These lessons help improve students’ writing mechanics for implementation in their multi-week writing projects.

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.

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 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 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.

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.

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 topics in number theory and geometry, and will work individually or collaboratively to solve challenging problems related to these topics. In addition, students will also participate in mock individual and team competitions during the camp.

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 topics in algebra, counting, and probability, and will work individually or collaboratively to solve challenging problems related to these topics. In addition, students will also participate in mock individual and team competitions during the camp.

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.

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.

Students explore books that know you're reading them in Middle School Book Club. 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.

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.