Academy Track

Course 1000

Our main objective is to have our students build a strong number sense and numeric fluency.  Our students learn basic arithmetic operations, numeric manipulations, word problems and problem-solving strategies.  The fundamentals of algebraic thinking are also introduced in a fun and engaging way.  We cover basic shapes and geometric properties.  Through an array of puzzles, exercises and games, our students improve the agility and the depth of their thinking and learn powerful reasoning and problem-solving skills.

Course 1100

We focus on completing the toolkit of our young mathematicians as well as increasing their analytical and problem-solving skills.  Our students learn operations with larger numbers.  We introduce Fractions as well as fundamental concepts in Number Theory, and continue our exploration of Geometry, including hands-on practice with geometric tools.  Our students deepen their mathematical intuition, algebraic thinking, pattern recognition and problem-solving skills as they work through a broad spectrum of challenging and engaging problems.

Course 1150

We review key concepts students learned in Course 1100 so they can build strong skills before proceeding to the next level.  We emphasize proficiency in operations with Fractions, more experience with solving word problems as well as reviewing fundamentals and learning new topics in Number Theory and Geometry.  We embark on exploration of Algebra and introduce a broad range of algebraic techniques and skills.  We cover many of the same topics in Algebra as we do in Course 1200 including learning the language of Algebra, working with variables, operations with negative numbers, linear equations, modeling and solving word problems. A few advanced topics will be reserved for upper levels to allow the students  to comfortably learn the material.

Course 1200

We work with students to develop a strong understanding of algebraic concepts and operations.  Traversing between the worlds of numbers and variables, our students develop a new appreciation for the brevity and precision of the "language of math", and learn how to translate to and from this language.  Our students develop strong techniques in solving linear equations and word problems with an unknown, and develop a more profound appreciation of the power of math as a modeling framework of the real world.  We cover more challenging topics in Number Theory and Fractions, and continue our exploration of Geometry, which becomes more analytical and leverages the newly acquired algebraic knowledge and skills.

Course 1300

Our students learn to use increasingly sophisticated algebraic tools and techniques to solve more challenging problems.  They develop an integrated understanding of fractions, decimals, and percentages and learn how to “fuse” these concepts with Algebra.  They learn how to work with multiple variables, use substitution and a vanishing variable, and how to solve a wide range of interesting and challenging problems.  We delve deeper into Number Theory, and our students expand their toolkit of skills and concepts that they apply to problem-solving.  We cover more sophisticated concepts in Geometry as we study angles, triangles, polygons, and circles.  We focus in particular on fundamental concepts of triangle similarity, congruence, Pythagorean Theorem and special right triangles.

Course 1400

We add Speed and Distance and Work Rate problems to the arsenal of word problems our students can solve with their algebraic skills, while they learn such new ideas as the harmonic average.  Our journey through Algebra  continues with the study of exponents and exponential growth.  The study of Number Theory goes to the next level as our students learn the technical foundations of modular arithmetic and its many applications.  We introduce the formal study of Logic, including: symbolic logic, negation, conditionals, sets, certainty problems, truth tables, self-reference, paradoxes and related topics, problems and solution strategies.  In Geometry, we learn more about triangles and the centers of concurrency, and solve a wide range of challenging problems with planar and solid shapes.

Course 1500

Our students learn to describe motion and other phenomena algebraically and geometrically -- the duality discovered by René Descartes -- as they enter the world of functions and graphing in the Cartesian plane.  We focus in particular on linear equations and inequalities as well as on the absolute value function.  Having been accustomed to the precision of math, our students get exposed to the new world of "uncertainty" as we begin our study of Probability, Data Analysis and Statistics.  We start with an exploration of Combinatorics - a fascinating area of math where “counting” is not as simple as it sounds.  We step up our study of Number Theory and explore a wide range of topics, including Euclidean Algorithm, Diophantine equations, and Cryptology.  We continue exploration of Logic, including the area of proofs and the process of proof by mathematical induction.  In Geometry, we solve very challenging problems using sophisticated methods, including coordinate geometry learned earlier in the course.

Course 1600

We explore quadratics and polynomials from an algebraic and graphing points of view to give our students a nuanced understanding of the behavior of these functions.  We cover fundamental concepts, theorems and proofs, such as factoring, deriving the quadratic formula, deriving the coordinates of the vertex of a parabola, Vieta’s formula, the Remainder Theorem, the Rational Root Theorem, and many others.  We apply these concepts to a broad range of problem solving, including the position function of a falling object, optimization, infinite fractions and infinite nested roots, and many others.  Our students also learn the sum and difference of powers, binomials and the Pascal Triangle, complex numbers, and related problems.  We add logarithms to our study of exponential functions.  We also cover sequences and series as we learn ground rules such as convergence of infinite series. Our students increase their mastery of important concepts in Number Theory where we cover such concepts as number bases, the Chinese Remainder Theorem, quadratic residues, and various Number Theory proofs.  We cover increasingly sophisticated concepts in Combinatorics, Probability, and Statistics and Data Analysis.  Geometry at this level involves a wide range of theorems with more involved proofs, and challenging problem-solving.

Course 1700

We begin this course with Trigonometry - the analytical tool for Geometry.  Starting with the basic concepts of the unit circle, radian measure, an introduction of fundamental identities and laws, we emphasize proofs to derive other important identities.  Our students work with interesting and challenging problems and learn graphing and behavior of periodic functions and their transformation, interrelations between identities, polar coordinates, and many important theorems, laws and real life applications.  The many proofs we cover include Law of Sines, Law of Cosines, Angle Addition, Heron’s Formula, and many others.  We round up our study of functions by exploring rational functions, and inverse and composite functions.  Our students enhance their knowledge of complex numbers by learning the absolute value, trigonometric and exponential forms, roots and DeMoivre’s Theorem, and other concepts and applications.  Later in the course we enter the mystical world of conic sections and learn about their fundamental properties, centers, axes, asymptotes, foci, and eccentricity.   We conclude with the exploration of Linear Algebra, focusing on vectors and matrices.

Course 1800

We enter the whole new paradigm of the infinitesimal and the instantaneous - the groundbreaking discoveries and concepts developed Newton and Leibnitz.  As our students explore this new world, they also sharpen and take to the new level their Algebra and Trigonometry skills.  Calculus unites many previously learned concepts, and our students develop a new perspective and deeper appreciation for those concepts.  We begin in the familiar territory of functions and develop understanding and visual sense of limits, the average and the instantaneous rate of change.  We learn the concept of a derivative and derivatives of various functions, together with concepts of continuity and differentiability.  Similar to our other courses, we emphasize proofs as we study important rules and techniques of differentiation, along with implicit differentiation and problems involving related rates.  We apply these powerful concepts to functional analysis, and to solving many interesting and challenging problems.  Later in the course we switch gears and tackle anti-differentiation and integrals.  Starting with the fundamentals like Riemann Sums, we visually explain the idea of integration.  We then proceed to learn how to integrate different functions and a wide range of integration techniques such as substitution, Trigonometric substitution and reducing powers of Trigonometric functions, partial fractions, integration by parts, and others.  Our students also learn improper integrals and many applications of integration.

Please note that the actual classes can deviate from the curricula above based on the progress of the students in the class or other adjustments we may make from time to time.