# Middle & Upper School Mathematics

Through the study of mathematics, students discover a language for expressing the relationships that order the natural world. Our students learn to approach the study of mathematics from a conceptual angle. Even though rules, formulas, and procedures are part of studying mathematics, they are taught as tools, not as the focus of our courses. Students who gain a conceptual understanding of mathematics have the flexibility to apply their knowledge to a wide variety of problems and situations. As they progress through each level, they grow continuously in their ability to think through concepts from four different representations: numerical, graphical, algebraic, and verbal.

At Boston Trinity Academy, mathematics are tracked by ability not grade level. This is to ensure each student adequately understands the concepts before advancing to higher levels. Middle School students may test into any level, but typically begin in Transitions Math or Pre-Algebra. Upper School students are expected to begin in at least Algebra I and are required to pass at least three levels of mathematics.

## Transitions Math (Middle School Only)

Students in Transitions Math master the basic concepts of simple functions: addition, subtraction, multiplication, and division. They learn place value, decimals, positive and negative numbers, and multiplication and division of two-digit numbers without a calculator. Students also work with fractions and become proficient with common fraction/decimal equivalency. Students are also introduced to pre-algebra concepts, including percents, ratios, perimeter, and area in order to prepare students to enter Pre-Algebra.

## Pre-Algebra (Middle School Only)

In Pre-Algebra, students master mathematical operations of whole numbers, fractions, and decimals, while becoming proficient in using rate, ratio, proportions, and percentage. This course prepares students for the study of algebra by introducing the use of variables, algebraic manipulations, open sentences, equations, and inequalities.

## Algebra I

Algebra I provides students with a clear and thorough understanding of the foundational concepts of algebra. Students develop the ability to expand on mathematical operations and master algebraic manipulations of expressions, equations, polynomials, exponents, inequalities, and graphing techniques. They gain a thorough knowledge of the traditional methods for solving algebraic problems, and also the ability to use these models to solve a wide range of problems.

## Geometry

Geometry provides students with a clear and thorough understanding of geometrical concepts, as well as daily opportunities to apply them. Students use algebra to solve a wide range of geometric problems. They develop their abilities to think and plan logically as they write varying forms of geometric proofs. This course provides students with the knowledge and experience to successfully navigate through higher-level courses in mathematics.

## Algebra II

Algebra II is an honors level course that extends the content of Algebra I by advancing skills such as solving equations and inequalities, systems of equations, imaginary and complex numbers, and introducing the study of functions and their graphs including polynomial, rational, exponential, and logarithmic functions.

## Pre-Calculus

Pre-Calculus provides students with the opportunity to improve their skills in mathematical operations and algebraic manipulations of expressions and equations, and gives them mastery of the concept of functions, including trigonometric, exponential, and logarithmic functions. Students in this course also study triangle trigonometry, analytic trigonometry, and probability.

## Honors Pre-Calculus

Pre-Calculus Honors allows students to improve their skills in mathematical operations and algebraic manipulations of expressions and equations, and gives them mastery of the concept of functions and their graphs, including trigonometric, exponential, and logarithmic functions. Students in this course also study triangle trigonometry, analytic trigonometry, probability, conics, and sequence and series, and are introduced to limits and derivatives. Students who successfully complete this course are prepared for the AP Calculus AB course.

## AP Statistics

AP Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data, sampling and experimentation, anticipating patterns, and statistical inference. Students have the opportunity to earn college credit if they earn a high score on the Advanced Placement exam at the end of this course.

## AP Calculus AB

AP Calculus AB is a college-level calculus course. It covers the concepts of limit, derivative, definite integrals, and indefinite integrals; and it emphasizes a multi-representational approach to calculus, with concepts, results, and problems being expressed graphically, numerically, analytically, and verbally. Students are expected to perform high-level thinking and mathematical reasoning. Students have the opportunity to earn college credit if they earn a high score on the Advanced Placement exam at the end of this course.

## AP Calculus BC

AP Calculus BC is a college-level calculus course. This course expands on the topics covered in AP Calculus AB and also covers the concepts of convergence and divergence of functions, analysis of infinite series, various integration techniques, analysis of complex, polar, and parametric functions, and vector calculus. Students are expected to perform high-level thinking and mathematical reasoning. Students have the opportunity to earn college credit if they earn a high score on the Advanced Placement exam at the end of this course.

## AP Computer Science A

The AP Computer Science A course introduces students to computer science with fundamental topics that include problem solving, design strategies and methodologies, organization of data (data structures), approaches to processing data (algorithms), analysis of potential solutions, and the ethical and social implications, of computing. The course emphasizes both object oriented and imperative problem solving and design. Students have the opportunity to earn college credit if they earn a high score on the Advanced Placement exam at the end of this course.

### Mathematics Faculty ### Lucy Fulco

Email: ### Hillary Blakeley

Email: ### Shelby Haras

Email: ### Daniel Howard

Email: ### Kasia Weyman

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