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, 2016, and 2018 US teams that won the International Math Olympiad (IMO). In this course, students study strategies needed for success on the American Mathematics Competitions 10 and 12 (AMC 10/12), the American Invitational Math Exam (AIME), the Harvard-MIT Math Tournament, and other major high school contests.

This physics course offers a hands-on introduction to Newtonian mechanics. Students will build their understanding of forces, motion, energy, and related topics and develop critical thinking skills. Students will learn to think like scientists as they design and conduct experiments and solve problems.

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 problem solvers in language arts. The course is divided into four quarters: mythology, history, theater, and storytelling. In each unit, students tackle a challenging language arts problem. As they work to solve the problem, students learn and apply deep reading, writing, and critical thinking skills. The thematic focus of the course is ancient Greece, 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.

This course prepares sixth grade and beginning middle school students for an advanced middle school language arts curriculum. The course has four units: critical thinking and persuasion, creative writing and language, research, and literary studies. In each unit, students develop new skills that contribute toward a final project that encapsulates the unit theme. Students who complete this course will be prepared for advanced middle school classes and have a competitive edge as they get ready for high school.

In this course, students will learn how to apply classic rhetorical techniques to real-world writing, speaking, and critical thinking scenarios. The course is divided into four units: Classic Rhetoric, Marketing, Literary Mystery, and Global Problem Solving. With each unit, students develop new skills that contribute toward a final project that encapsulates the unit theme. By the end of the course, students will have become savvy masters of persuasion.

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 third or fourth 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' spatial thinking abilities through explorations of symmetry, knots, plane tilings, and tessellations.

Math Beasts Camp 5 is designed for students entering a fifth grade math class in the fall. The course reviews key concepts from fourth grade, and provides some early practice with ideas they'll master in the upcoming year. Students also study strategic mathematical games to develop essential problem-solving skills such as pattern recognition, working backwards, and seeking invariance.

Math Beasts Camp 6 is designed for students entering a sixth grade math class or Prealgebra class in the fall. The course reviews key concepts from fifth 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.

Students explore middle and early high school contests such as MATHCOUNTS and the American Mathematics Competitions 8 and 10 (AMC 8 and 10). Students are introduced to important topics in number theory and geometry, and work individually or collaboratively to solve challenging problems related to these topics. Students also participate in mock individual and team competitions during the camp.

Students explore middle and early high school contests such as MATHCOUNTS and the American Mathematics Competitions 8 and 10 (AMC 8 and 10). Students are introduced to important topics in algebra, counting, and probability, and work individually or collaboratively to solve challenging problems related to these topics. Students also participate in mock individual and team competitions during the camp.

Students study strategies needed for success on the American Mathematics Competitions 10 and 12 (AMC 10/12) and other major high school contests. In addition to learning core concepts, students will participate in practice competitions during the camp, which provides the test-taking experience that will prepare them for key events in the upcoming school year.

Creative Writing is designed for students entering 3rd or 4th grade in the fall. In this fun, fast-paced course, students build their reading and writing skills by tackling creative writing projects spanning a wide range of genres.

Readers Theater is designed for students entering 4th or 5th grade in the fall. This course helps students build skills for reading, interpretation, and performance as they create their own puppet shows inspired by two novels they'll read in class.

Poetry and Performance is designed for students entering 6th or 7th grade in the fall. In this fun, expansive course, students read, discuss, and develop a new understanding of poetry in all of its forms.

Mock Trial is designed for students entering 7th or 8th grade in the fall. In this challenging and fast-paced course, students build crucial reading, writing, and public speaking skills as they participate in a simulated court case based on this year’s class novel.

Academic Essay Writing is designed for students entering 8th, 9th, or 10th grade in the fall. Featuring the popular college writing textbook, They Say / I Say: The Moves That Matter in Academic Writing, this course teaches students how to plan, draft, and revise their own academic essays.