# MATH COURSE Descriptions

MathAltitude offers small classes for students in grades Pre-K through high school. In most cases students attend classes that correspond to their grade at school. However, math skills and preparation can vary significantly, and it is important to match the student’s ability with an appropriate level of challenge. Free assessment tests allow us to properly place new students.**Math-Я-Us (Offered to Students in Pre-School, Pre-K, and Kindergarten)**This is an introductory course for our youngest math wizards where in engaging and interactive form students explore the concepts of mathematics. Our students enjoy participation in creative activities, where they learn to count, compare, classify, solve problems, and have lots of fun along the way.

Students meet once a week for a

**45 minute**lesson. During that time parents can enjoy a cup of coffee in nearby cafes, or just wait in our school staying connected with our free WiFi Internet access.

**MA-K (Offered to Students in Pre-School, Kindergarten, and 1st Grade)**MathAltitude MA-K-program complements the regular Kindergarten activities, developing strong number sense, building early math skills, and learning and using math vocabulary. Instructional time in large focuses on representing and comparing whole numbers, initially with sets of objects, describing shapes and space, and working with patterns. Word problems are also introduced for the first time. Children develop logical thinking and reasoning skills through a variety of fun and engaging activities. Students meet for a

**90 minute**session once a week.

**Mathematics, MA 1 - 6 (Offered to Elementary School Students, Grades 1-6)**MathAltitude's six-year program for elementary school students spans the entire primary school curriculum. During the first two years, students develop the basic arithmetic and analytical skills. Elements of algebra and geometry are introduced. The main emphasis is on word problems and logical reasoning. As students progress through the program, they continue to expand their computational and problem solving skills. Students meet for a

**two-hour**lesson once a week.

**Pre-Algebra (Offered to Students in Grades 6-7)**Pre-Algebra provides a solid foundation for Algebra in middle and high school. The course starts with a thorough review of operations with decimals, fractions, and percent, continuing onto the study of ratios and proportions, and finally moving onto the study of linear equations, simple inequalities, and linear functions. Significant emphasis is given to solving word problems algebraically. Students meet for a

**two-hour**lesson once a week. This course is recommended to be taken concurrently with Introduction to Geometry.

**Advanced Algebra (For Current MathAltitude Students in Grades 7-9)**This is a comprehensive 3-year in-depth program that covers all topics traditionally offered in middle and high school Algebra I and II courses. The level of difficulty of our course exceeds Honors Algebra offered in middle and high school. It is recommended for students returning to MathAltitude, but may also be taken by new students based on their placement test results and teacher’s recommendation.

The* first part of the series* includes topics such as algebraic expressions, linear equations and systems of linear equations, inequalities, application of algebraic methods to solving word problems, exponents, polynomials and algebraic fractions, functions, etc. The *second year* starts with a brief review of the previous year’s topics concentrating on factoring, special products, quadratic equations. Students continue developing strong problem solving techniques. The course covers radicals and operations with radical expressions, functions, and graphs. The course concludes with an in-depth study of theory of functions, exponential and logarithmic expressions and functions, complex numbers, arithmetic and geometric sequences, combinatorics, and probability studied during the *third year*. Throughout the course, students are prepared for participation in the Center for Talented Youth (CTY) programs at Johns Hopkins University and the AMC-8, AMC-10 contests. Students meet for a **two-hour** lesson once a week.

**HS Algebra I and II (Offered to Students in Grades 8-10)**HS Algebra I and II are one year courses covering the topics offered to complement middle school Algebra I Honors or high school Algebra I and II Honors classes. Students meet for a

**two-hour**lesson once a week.

**Introduction to Geometry (Offered to Students in Grades 6-7)**Intro to Geometry is an introductory course that provides an overview of basic geometric shapes and their properties. In this course, the students will study parallel lines, angles, simple polygons (triangles, quadrilaterals, etc.), and circles as well as get the initial knowledge of simple 3D shapes like pyramids, cones, cylinders, spheres and prisms.

An early introduction to the systematic study of Geometry allows students to avoid anxiety and complications later in high school when they are often overwhelmed with this and other subjects. The course is also helpful for students who want to advance in middle school and are planning to participate in the Center for Talented Youth (CTY) programs at Johns Hopkins University and the AMC-8 contests. Students meet for a **one hour** lesson once a week.

**Geometry I and II (Offered to Students in Grades 7-9)**We strongly believe that Geometry should be taught early and thoroughly. Our 2-year course is offered to students in grades 7 through 9 and will serve as a solid foundation for high school Geometry Honors.

During the first year, students will expand on the topics studied in the Introduction to Geometry course, such as parallel and perpendicular lines, angles, congruency of triangles, and polygons. We cover the most important postulates and theorems and teach our students how to apply them to solve more difficult problems.

The second part of the course includes topics such as similarity, circles, trigonometry of right triangles, and inequalities in geometry. Throughout the course, our students learn the importance of proofs and how to apply deductive reasoning to write proofs in a 2-column statement-reasoning format. Indirect reasoning and proofs are also introduced in this course. Constructions with a straight edge and compass are integral parts of the course. The course provides additional benefits to students planning to participate in the Center for Talented Youth (CTY) programs at Johns Hopkins University and the AMC-8, AMC-10 contests. Students meet for a **two-hour** lesson once a week.

**Geometry III / Trigonometry (Offered to Students in Grades 9-10)**This course can be considered an extension of the two-year Geometry sequence, or a stand-alone course for the students who want to learn more advanced topics of Geometry. It provides a comprehensive study of trigonometry, solids, coordinate geometry, vector algebra, and transformations. Students meet for a

**two-hour**lesson once a week.

**HS Geometry (Offered to Students in Grades 9-10)**HS Geometry is a one-year course covering the topics offered to complement high school Geometry Honors classes. Students meet for a

**two-hour**lesson once a week.

**Pre-Calculus (Grades 9-11)**As part of this

**two-hour**per week class students review the key topics from Advanced Algebra, part 3 and study more advanced topics of Pre-Calculus. This course complements high school Pre-Calculus Honors class.

**AP Calculus AB, AP Statistics (Grades 10-12)**

Prerequisites: Pre-calculus

This course covers, at a minimum, the theory and applications of differential and integral calculus as outlined in the AP Calculus AB syllabus for the College Board Advanced Placement program.

Topics include limits and continuity, definition and computation of derivatives, applications of derivatives (related rates, maxima and minima, one-dimensional motion, L'Hopital's Rule), definition and computation of integrals (including substitution and integration by parts), and applications of integrals (accumulated rate of change, volumes of revolution, differential equations, one-dimensional motion, average of a function). Important theorems, such as the Intermediate Value Theorem, Mean Value Theorem, Extreme Value Theorem, and Fundamental Theorem are covered.

A graphing calculator is required. Students learn how to use calculators to perform calculations that cannot be done by hand.

All students enrolled in the course are recommended to take the Advanced Placement examination in May.

Students meet once per week for 3 hours; 32-week course. Total instructional time 96 hours

**AP Calculus BC (Grades 10-12)**Prerequisites: Pre-calculus

A more rigorous and extensive course than the AP Calculus AB, this course will follow the syllabus for the AP Calculus BC examination of the Advanced Placement program. This course covers the theory and applications of differential and integral calculus, as well as polar coordinates, parametric equations, infinite sequences and series, and differential equations.

Topics include limits and continuity, definition and computation of derivatives, applications of derivatives (related rates, maxima and minima, one-dimensional motion, L'Hopital's Rule derivatives of polar, parametric, and vector equations), definition and computation of integrals (including substitution, integration by parts, and partial fractions), applications of integrals (accumulated rate of change, volumes of revolution, differential equations, one-dimensional motion, average of a function, arc length, improper integrals, and integrals related to parametric, vector, and polar equations), convergence tests for series, power series, Taylor and Maclaurin series, and Taylor polynomials. Important theorems, such as the Intermediate Value Theorem, Mean Value Theorem, Extreme Value Theorem, and Fundamental Theorem are covered.

A graphing calculator is required. Students learn how to use calculators to perform calculations that cannot be done by hand.

All students enrolled in the course are recommended to take the Advanced Placement examination in May.

Students meet once per week for 4 hours; 32-week course. Total instructional time 128 hours.

**AP Statistics**Prerequisites: Honor Algebra 2

This course will follow the curriculum of the College Board AP Statistics course and prepare students for the Advanced Placement examination. This course covers the foundations of descriptive and inferential statistics. Topics include describing and summarizing data, normal distributions, scatterplot and linear regression, sampling and experiments, probability, random variables (including binomial and geometric distributions), sampling distributions, confidence intervals and hypothesis testing (for means, proportions, and regression slopes), and chi-squared testing.

A graphing calculator is required. Students learn how to use graphing calculators to help analyze data.

All students enrolled in the course are recommended to take the Advanced Placement examination in May.

Students meet once per week for 3 hours; 32-week course. Total instructional time 96 hours.

**Multivariable Calculus (Grades 11-12)**

**An advanced calculus course for students who have completed AP Calculus BC.**This course will cover material typically seen in a freshman/sophomore college course for math or science majors. Topics covered include the geometry of 3D and higher dimensional space, derivatives and integrals of scalar functions of several variables, and their applications; the derivative of vector-valued functions of one variable; parametrized surfaces; vector fields and related concepts (divergence, curl, line integrals); and Green's Theorem, Stokes' Theorem, and the Divergence Theorem. Students meet once per week for 2 hours.

**Linear Algebra (Grades 11-12)**An advanced calculus course for students who have completed AP Calculus BC. This course will cover material typically seen in a freshman/sophomore college course for math or science majors. Topics covered include matrix arithmetic, methods of solving linear systems, vector spaces, linear transformations, null and column spaces, determinants, change of basis, orthogonal projection, eigenvalues and eigenvectors, differential equations, Markov chains, and least-squares approximations. Students meet once per week for 2 hours.

**ACT / SAT - I (Grades 9-12)**All ACT/SAT courses cover linear equations and inequalities, systems of linear equations and inequalities, interpreting coefficients in a linear model, ratios and percents, unit conversions, quadratic functions, exponential functions, rational exponents, polynomials and rational expressions, complex number arithmetic, volume and area, right triangle trigonometry, the Pythagorean Theorem, radians, sector area and arc length, angle measures with transversals and triangles, similarity, equations of circles, scatterplots, linear and exponential models, basic inferential statistics, two-way tables, and describing measures of a data set.

**ACT/SAT 6-Week Extended Summer Course**- Students meet 8-hours per week. This course provides an in-depth review of the topics covered on the SAT Math section, and is recommended for students who would like extensive review of SAT math topics.

**ACT/SAT 6-Week Summer Course**- Students meet 4-hours per week. This course moves quicker than the 8-hour per week course; it is recommended for students who need less extensive review of topics, and who want to refresh and sharpen their SAT math skills.

*We recommend that all students who plan to take SAT Math take a free diagnostic SAT Math test prior to the beginning of classes and choose the 4- or 8-hour course based on the result.*

**ACT/SAT 12-Week Fall and Spring Courses**- Students meet once per week for a 2 hour lesson.

**Private Tutoring**Private tutoring for all of the above courses is also available. Please

**contact us**or call

**(860) 37-LEARN**to discuss your particular needs.

**Participation in Math Olympiads: Math Kangaroo, AMC, NLMC**Parents often ask us whether their children should participate in math competitions. To quote Richard Rusczyk, the founder of The Art of Problem Solving (AoPS) Inc. and a co-author of The Art of Problem Solving textbooks, “the most immediate value of math contests is obvious – they pique students’ interest in mathematics and encourage them to value intellectual pursuits”. He continues, “Beyond encouraging interest in mathematics, contests help prepare students for competition. For better or worse, much of life is competition, be it for jobs or resources or whatever”. We agree with Richard wholeheartedly and prepare our students for a great experience with the well-known mathematical contests.