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OUR PROGRAM > Curriculum

Please note that the actual classes can deviate from the curricula below based on the progress of the students in the class.  Typical grade ranges are suggestions only, and students that fall outside of these ranges may benefit from a particular course

Core Program

Course 1000

Typical Grade Range: K, 1, 2

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

Prerequisite: this is our entry Course for beginners.  We accept kids as young as 6 (and advanced 5).  To enroll, kids should be able to count to 100 and be comfortable with basic addition and subtraction

Course 1100
Typical Grade Range: 1, 2, 3, 4

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

Prerequisite: to enroll, kids should be "automatic" with the multiplication table and related division

Course 1200
Typical Grade Range: 2, 3, 4, 5

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 new appreciation for brevity and precision of the "language of math" and learn how to translate to and from this language.  Our students develop strong technique 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 topics such as inequalities, absolute value, as well as new 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
Typical Grade Range: 3, 4, 5, 6, 7

Our students develop an integrated working knowledge of Fractions, Decimals, and Percentages as they use their algebraic toolkit to tackle challenging problems involving these concepts.  Students develop a better appreciation for the taxonomy of numbers as they study transformations of repeating decimals and learn about irrational numbers.  We delve into interesting topics of speed & distance; work rate & production and scale & proportion.  Our students also learn how to "think on their feet" as they develop and practice mental math techniques.  We cover more sophisticated concepts in Geometry with a particular focus on angles and triangles as well as fundamental concepts such as similarity and congruence

Course 1400
Typical Grade Range: 4, 5, 6, 7, 8

Having been accustomed to the precision of math, our students enter the fascinating world of "uncertainty".  We begin our study of Probability, Data Analysis and Statistics.  We continue to sharpen our students' minds with an introduction to an equally fascinating and very important field of Logic.   Our students learn operations with exponents and radicals, and continue their practice with previously learned concepts (such as linear equations and word problems, fractions, decimals, percentages, concepts in Number Theory and other topics) as they solve increasingly challenging problems.  We continue to sharpen mental math skills.  In Geometry our students work to become proficient with multi-step analytical problems involving finding properties of most planar shapes such as right triangles, quadrilaterals and other polygons, and circles

Course 1500
Typical Grade Range: 5, 6, 7, 8, 9, 10, 11

We enter the world of Descartes and learn linear functions, inequalities and systems of equations as well as related concepts and word problems.  Our students solidify their working knowledge of exponents with interesting and challenging problems and real world applications.  We step up the level of Number Theory as we discover the mysteries of prime numbers and learn new concepts of modular arithmetic.  We continue our exploration of Logic as our students get more proficient with symbolic logic, negation, conditionals, sets, certainty problems, truth tables, self-reference, paradoxes and related topics, problems and solution strategies.  We cover more sophisticated concepts in Probability, Data Analysis and Statistics and the adjacent field of Combinatorics.  In Geometry, our students solve challenging problems as they add to their repertoire the skills in solid and coordinate geometry

Course 1600
Typical Grade Range: 6, 7, 8, 9, 10, 11, 12

We study polynomials and polynomial division, binomial and Pascal triangle, and expand our knowledge of functions with emphasis on the quadratic equation and related concepts of factoring, analysis and applied problems.  We add logarithms to our study of exponents and radicals.  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 and Logic.  They also tackle increasingly challenging problems in Combinatorics and learn more sophisticated concepts such as binomial probability, normal distribution, and standard deviation in the field of Probability, Data Analysis and Statistics.  Geometry at this level includes problem-solving, proofs, and introduction to Trigonometry.  Our students also get introduced to complex numbers and basic linear algebra concepts (together with Trigonometry, these concepts will be covered in-depth in our advanced program)

Advanced Program

Course 1700 - Advanced Mathematics and Trigonometry
Typical Grade Range: 10, 11, 12, AP, Honors, College

We plunge deeper into the world of Descartes and learn new fascinating functions and their behavior, and develop a powerful toolkit of analysis skills.   Our students learn many real life applications, such as exponential growth and decay, logistics curves, instantaneous compounding, and many others.  They study conic sections, general equations and properties as well as applications (for example, in astronomy).  We cover more advanced topics in Sequences and Series.  Our students take their geometric analysis skills to a new level with the study of an amazing field of Trigonometry.  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.  We also study the mysterious world of imaginary and complex numbers, including their trigonometric and exponential forms

Course 1800 - Calculus
Typical Grade Range: 10, 11, 12, AP, Honors, College

Mathematical concepts that previously seemed unrelated come together, and the beauty of math itself shines when one learns Calculus.  Our students begin in the familiar territory of functions and develop understanding and visual sense of limits, average and instantaneous rate of change.  We learn the concept of a derivative and derivatives of various functions, as well as concepts of continuity and differentiability.  We learn implicit differentiation, together with important rules and techniques.  We apply these powerful concepts to functional analysis, and many interesting and challenging real world problems.  We proceed with integrals and learn Reimann sums to develop a visual sense and understanding of integrals and anti-differentiation.  We learn important theorems and rules of integration and solve many interesting problems of area, area between the curves, volume, growth and decay, as well as differential equations.  Our students build critical skills that, at a minimum, should be sufficient to take the AP Calculus AB exam

Squared School LLC
425 Angell Street, Providence, RI 02906
Tel. 401-339-6725