MATH
Our Kindergarten Enrichment Curriculum teaches students about number sense and simple equations. The math curriculum helps student understand beginning math concepts, in addition to a science component.
The Level 1 math curriculum helps students develop an understanding of whole number relationships and place value. Students will also gain understanding of addition and subtraction, the concept of time and currency, along with their application in day-to-day life. Students will also learn about geometric shapes and the concept of multiplication as repeated addition along with an introduction to the multiplication table. Basic fractions will also be covered as well.
The Level 2 math curriculum reinforces the concept of number sense, extends students’ ability to solve addition and subtraction problems with larger numbers, multiplication of one and two digit numbers, and mixed applications. Students also are introduced to division as the inverse of multiplication, the concept of equivalent fractions, and addition and subtraction of fractions. In addition to these topics, students will be introduced to the concept of probability, geometry, and will do exercises related to measurements and time
The Level 3 math curriculum focuses on reviewing arithmetic basics and developing number sense skills. Students will learn about cardinal versus ordinal numbers, Roman numerals, digit place values and expanded forms, rounding of numbers and money, inequalities and equations, division with remainders, and mixed problems, including addition subtraction multiplication and division. There is a greater focus on not only knowing how to solve math problems, but the application of math to everyday situations.
The Level 5 math curriculum includes computation and number sense, such as estimating sums, differences, and products, multiplying using the distributive property, long division, exponent operation, and geometric sequence. Students will be introduced to the concept of negative numbers using the functions of addition, subtraction, multiplication, and division, and utilize the order of operations. Students will also learn about algebra in the form of single variable equations, solve prime factorization and functions of proper fractions, improper fractions, and mixed numbers.
The Pre-Algebra curriculum focuses on advancing math concepts such as algebra in the form of variable expressions, single variable equations, and two variable equations. Students will also focus on geometry through different types of lines, perimeters and areas of polygons and circles, and surface areas and volumes of three dimensional shapes in addition to graphing. Students will also delve further into algebra and geometry with arithmetic and geometric sequences; simple and compound interest problems; algebraic equations population and variation problems; and speed time and distance problems. Also introduces students to probability and statistics, exponents and square roots, and ratio, proportion, and percentage problems.
Algebra 1 curriculum focuses on solving one/two/multi-step equations; Properties of powers; Solving Simple and Compound Inequalities; Solving Absolute value equations and Inequalities; Simplifying Roots; Solving Radical equations; Graphing Linear Equations – slope-intercept form, Point-slope form, Standard form; Functions; Linear word problems; Parallel and perpendicular lines; Graphing Linear Inequalities; Solving Linear Systems; Graphing system of Linear Inequalities; Graphing Absolute value Linear Equations; Factoring Quadratic equations; Solving Quadratic equation using Factoring; Solving Quadratic equation using Quadratic Formula; Graphing Quadratic Functions; Graphing Quadratic Inequalities.
The Geometry curriculum focuses on Points, Lines, Planes, Angles and their measures, Segment and Angle bisectors, and Angle Pair relationship; Perimeter, Circumference and Area; Proof of Perpendicular Lines, Parallel Lines, and Transversals; Interior and Exterior angles in Polygons, Apothem concept of Area of Regular Polygons; Proving Triangles Congruent -SSS, SAS, ASA, and AAS; Triangle properties, Right Triangle, Pythagorean Theorum and Special Right Triangles; Similar Triangles and Proportions; Area of Triangles; Perpendicular Bisectors, Angle Bisectors, Medians, and Altitudes of a Triangle; Locus and constructions.
Circles – Congruent Chords; Arcs of a Circle; Secants and Tangents; Angle-Arc Theorems; Inscribed and Circumscribed Polygons; Power Theorems.
Area – Areas of Parallelograms, triangles, Trapezoid, Kites and Related Figures; Areas of Circles, Sectors, and Segments; Ratios of Areas; Hero’s and Brahmagupta’s Formulas.
Surface Area and Volume – Surface Areas of Prisms, Pyramids, Circular Solids; Volumes of Prisms, Cylinders, Pyramids, Cones, and Spheres.
Coordinate Geometry – Graphing Equations and Inequalities; Equations of Lines; Systems of Equations
The Algebra 2 and Trigonometry curriculum focuses on – Review of Basic Concepts of Algebra, Solving Compound Inequalities, Solving Absolute value Sentences Graphically
Linear Equations and Functions – Solving System of Linear Equations and Linear Inequalities; Functions and Relations
Products and factors of Polynomials – Factoring Quadratic Polynomials; Solving Polynomial Equations; Solving Polynomial Inequalities
Rational Expressions – Laws of Exponents; Sums & Differences, Products & Quotients of Rational Expressions, Complex Fractions; Problem Solving Using Fractional Equations;
Irrational and complex numbers – Properties of Radicals, Rational and Irrational Numbers, The Imaginary number i, Complex Numbers
Quadratic Equations and Functions – Completing the Square, The Quadratic formula, The discriminant; Quadratic functions and Their Graphs
Variation and Polynomial Equations – Direct variation and proportion, Inverse and Joint Variation; Dividing Polynomials, Synthetic Division, The Remainder and factor Theorem; Finding Rational Roots, Approximating Irrational Roots, Linear Interpolation
Conic Sections – Circles, Parabolas, Ellipses, and hyperbolas
Exponential and Logarithmic Functions – Rational and Real Number Exponents; Laws of Logarithms, Applications of Logarithms; The Natural Logarithm function; Problem Solving: Exponential Growth and Decay
Sequences and Series – Arithmetic, Geometric Sequences; Series and Sigma Notation; Sums of Arithmetic and Geometric Series; Infinite Geometric Series; Binomial Expansions
Triangle Trigonometry – Trigonometric Functions; Solving Right Triangles, The Law of Cosines, The Law of Sines, Areas of Triangles
Trigonometric Graphs and Identities -Radian Measure, Circular functions, Periodicity and Symmetry, Graphs of all Trigonometric functions; Trigonometric Addition Formulas, Double-Angle and half-Angle Formulas
Trigonometric Applications – Vectors in a Plane, Polar Coordinates, De Moivre’s Theorem; Inverse functions
Matrices and determinants – Addition and Scalar Multiplication, Matrix Multiplication, Applications of Matrices; Determinants, Inverses of Matrices; Expansion of Determinants by Minors, Properties of Determinants, Cramer’s Rule
The Pre-Calculus curriculum focuses on – Review of Graphing Equations
Functions and Their Graphs – Finding Domain and Range of a Function; Properties of Functions, Determine Even and Odd Functions, Locate Local Maxima & Local Minima, and Absolute Maxima & Absolute Minima; Piecewise-defined Functions, Transformations, and Applications.
Linear and Quadratic Functions – Properties of Linear Functions and Linear Models, Building Linear Models, Linear and Nonlinear Relations; Quadratic Functions and Their Properties, Transformations, Building Quadratic Models; Solving Quadratic Inequalities
Polynomial and Rational Functions – Identifying Polynomial Functions, Properties of Power Functions
The Real Zeros of a Polynomial Function – Remainder and Factor Theorem, Descartes’ Rule of Signs, Rational Zeros Theorem: Complex Zeros; Fundamental Theorem of Algebra, Conjugate Pairs Theorem; Properties of Rational Functions; Finding Asymptotes
Exponential and Logarithmic Functions – Inverse Functions, Graphing Exponential Functions Using Transformations; Define the Number e, Solve Exponential Equation; Changes in Exponential to Logarithmic and vice versa; Graphing Logarithmic Function and its Inverse, Solve Logarithmic Equations, Properties of Logarithms; Financial Models; Compound Interest, Continuous Compounding; Exponential Growth and Decay Models; Newton’s Law of Cooling; Uninhibited Radioactive Decay.
Trigonometric Functions – Unit Circle, Angles, Quadrantal Angles; Properties of Trigonometric Functions; Finding Domain and range, Period of a Function, Determine Signs and Values of Trigonometric Functions; Even-Odd Properties; Graphs of All Trig Functions; Amplitude, Period, and Graphing of Sinusoidal Functions; Phase Shift, and Sinusoidal Curve Fitting.
Analytic Trigonometry – Inverse Trigonometric Functions; Trigonometric Identities; Solving Trig Equations; Sum and Difference Formulas; Double and Half Angle Formulas; sum-to-product and product-to-sum Formulas
Applications of Trigonometric Functions – Right triangle Trigonometry Applications; The Law of Sines; The Law of Cosines; Area of a Triangle; Simple Harmonic Motion.
Polar Coordinates – Polar Equations and graphs; Complex Plane, De Moivre’s Theorem; Vectors; The Dot Product; Vectors in Space; The Cross Product.
Analytic Geometry – The Parabola; The Ellipse; The Hyperbola; Polar Equations of Conics.
Systems of Equations and Inequalities; Sequences; Induction; the Binomial Theorem; Counting and Probability
The AP Calculus curriculum focuses on:
Differential Calculus Essentials – Limits; Continuity; The definition of Derivative; Basic Differentiation; Implicit Differentiation
Differential Calculus Applications – Basic Applications of Derivative; Maxima, Minima, and Curve Sketching; Motion; Derivatives of Exponential and Logarithmic Functions; Derivative of an Inverse function; Linearization; L ‘HOPITAL’s Rule
Integral Calculus Essentials – The Integral, The Anti-Derivative, Integrals of Trig Functions, u-Substitution; Definite Integrals, Area Under A Curve, Riemann Sums, Fundamental Theorem of Calculus, The Mean Value Theorem for Integrals, Accumulation Functions; Integrals of Exponential, Logarithmic, and Trig Functions, Inverse Trig Functions.
Integral Calculus Applications – The Area between Two Curves, Vertical Slices, Horizontal slices; The Volume of a Solid of Revolution, Washers and Disks, Cylindrical Shells.
Differential Equations – Separation of Variables, Slope Fields