# Mathematics

Students will be placed into Algebra I or Geometry.

## ALGEBRA I

This course addresses the Common Core Standards for Algebra 1. Algebra I focuses on four critical areas: (1) deepen and extend understanding of linear and exponential relationships; (2) contrast linear and exponential relationships with each other and engage in methods for analyzing, solving, and using quadratic functions; (3) extend the laws of exponents to square and cube roots; and (4) apply linear models to data that exhibit a linear trend.

## GEOMETRY

This course transitions capable students who have successfully completed Algebra I in Grade 8 to introduce students to the Massachusetts Mathematics Curriculum Framework (2017) learning standards for Geometry. Geometry focuses on six critical areas: (1) establish criteria for congruence of triangles based on rigid motions; (2) establish criteria for similarity of triangles based on dilations and proportional reasoning; (3) informally develop explanations of circumference, area, and volume formulas; (4) apply the Pythagorean Theorem to the coordinate plane; (5) prove basic geometric theorems; and (6) extend work with probability.  As the year progresses, students explore more complex geometric situations and deepen their explanations of geometric relationships by presenting and hearing formal mathematical arguments.

Students must take Geometry or Algebra II based on their mathematics pathway. They may also choose to add Financial Literacy as an elective.

## GEOMETRY

This course addresses the Common Core Standards for Geometry. Geometry focuses on six critical areas: (1) establish criteria for congruence of triangles based on rigid motions; (2) establish criteria for similarity of triangles based on dilations and proportional reasoning; (3) informally develop explanations of circumference, area, and volume formulas; (4) apply the Pythagorean Theorem to the coordinate plane; (5) prove basic geometric theorems; and (6) extend work with probability.

## ALGEBRA II

Continuing the progression for entering Grade 10 students who successfully completed Geometry in Grade 9, this course addresses the Massachusetts Mathematics Curriculum Framework (2017) learning standards for Algebra II.  The focus is on the following four critical areas: (1) relate arithmetic of rational expressions to arithmetic of rational numbers; (2) expand understandings of functions and graphing to include trigonometric functions; (3) synthesize and generalize functions and extend understanding of exponential functions to logarithmic functions; and (4) relate data display and summary statistics to probability and explore a variety of data collection methods.  Students work closely with the expressions that define the functions, are facile with algebraic manipulations of expressions, and continue to expand and hone their abilities to model situations and to solve equations, including solving quadratic equations over the set of complex numbers and solving exponential equations using the properties of logarithms.

## FINANCIAL LITERACY

Financial Literacy is essential in meeting the financial challenge of the 21st Century with understanding and managing personal finances the key to one’s future financial success. Based on the Massachusetts Mathematics Curriculum Framework (2017) learning standards, this course teaches students to apply the knowledge and skills to various financial situations they will encounter later in life to make critical decisions regarding personal finances. Students will learn money management, savings and investing, income, and spending strategies. This course will teach students to identify and prioritize their personal money management goals, develop personal spending, savings, and investing plans, tax implications and understand the cost of using credit along with asset protection.

## Mathematics Seminar

This course is designed to help students successfully learn critical mathematics skills that they will encounter in various courses. Students will be provided with a solid understanding of the high school math content standards. Basic skills will be reviewed and reinforced, especially those involving computation. Students will learn how to analyze and solve problems using appropriate strategies. A variety of test-taking strategies will be presented to give students the tools required to successfully complete various types of assessments including district-wide and standardized tests. At the beginning of the year, an individualized plan based on diagnostic assessments will be designed for each student with ongoing benchmark measures to monitor student progress.

Students must take one of the following courses based on their mathematics pathway. They may also choose to add Introduction to Computer Science as an elective.

## Algebra II

This course is a continuation of algebraic concepts. Topics include functions and graphs and more complex problem solving, complex numbers, matrices to solve linear systems, vectors, analytic trigonometry, and relates the connections between the fundamental concepts of algebra, trigonometry and analytic geometry. Several standards in the Algebra II course were moved to the Enhanced Algebra I course which made it possible to add standards from the Pre-calculus Course to the Enhanced Algebra II course. In this way students will be prepared for Calculus after successful completion of Enhanced Algebra II. This is a course which covers material at a fast pace and in great depth, with the expectation of stronger student performance. A greater emphasis will be placed on algebraic approaches to problem-solving.

## STEAM Integration

STEAM (Science-Technology-Engineering-Arts-Mathematics) Integration is full year, double-block course that offers an interdisciplinary, standard-based mathematics and lab-based physics pathway for students who are interested in learning Algebra II through applied integration learning projects with embedded mathematical and physics content and skills. The intention of this course is for students to do highly engaging projects that deepen and extend the connections between the fundamental concepts of algebra, trigonometry, and analytic geometry connected to physics concepts of motion, energy, and electromagnetism. Content learning standards from both the Massachusetts Mathematics Curriculum Framework (2017) and the Massachusetts Science and Technology Engineering Curriculum Framework (2016) provide a foundation for allowing students to experience these standards in real-world problem learning situations.  Students will collaborate for two back-to-back blocks with two teachers, one a mathematics teacher and the other a physics teacher to build integration learning projects using problem-solving strategies, questioning, investigating, analyzing critically, gathering and constructing evidence, and communicating rigorous arguments to justify their thinking.  Co-teachers will serve as coaches to student-designed integration projects.  This course satisfies the requirements for an Algebra II and a lab-based Physics course as stipulated in MassCore. Prerequisites: Successful completion of Algebra 1 and Geometry; Enrollment in the Construction Cluster or  Manufacturing, Engineering or Technology Cluster.

## Pre-Calculus (Previously Enhanced Algebra II / Pre-Calculus)

Continuing the progression for entering Grade 11 students who successfully completed Algebra II in Grade 10 and based on the Massachusetts Mathematics Curriculum Framework (2017) learning standards, this course combines the trigonometric, geometric, and algebraic techniques needed to prepare students for the study of calculus, and strengthens students’ conceptual understanding of problems and mathematical reasoning in solving problems. Facility with these topics is especially important for students intending to study calculus, physics, and other sciences, and/or engineering in college. Because the standards for this course are (+) standards, students selecting this Model Precalculus course should have met the college and career ready standards.  Instructional time will focus on four critical areas: (1) extend work with complex numbers; (2) expand understanding of logarithms and exponential functions; (3) use characteristics of polynomial and rational functions to sketch graphs of those functions; and (4) perform operations with vectors.

NOTE: Students who have not met the Competency Determination in Mathematics by earning the equivalent of a Proficient score of 240 or better on the Grade 10 Mathematics MCAS will be required to enroll in Algebra III during Grade 12.  For more information see: http://www.doe.mass.edu/ccr/epp/qa.html

## Introduction to computer science

This new math elective will introduce students to the basics of computer programming. Students will learn using Python, a relatively new and widely used programming language both in industry and academia. The concepts learned with Python are easily transferable to other popular languages such as C++ and Java. Students will use the concepts they learn to create their own programs to solve complex problems or increase the speed and efficiency of tasks performed on a computer. Topics to be covered will include basics of programming, conditional statements, loops, vectors, strings, cells, and a cursory overview of object-oriented programming. The class will be largely project-based, where students are given a problem or task that they need to create a program to solve.

Students must choose one of the following courses based on their mathematics pathway.
Students who have not met the Competency Determination in Mathematics by earning a proficient score of 240 or better on the Grade 10 Mathematics MCAS will be required to enroll in Algebra III, Pre-Calculus, or Calculus during Grade 12.

## Algebra III / Trigonometry

This course is a continuation of concepts presented in Algebra II. It will emphasize the connection between algebra, geometry and trigonometry. The focus of this course is exponential/logarithmic functions, polynomials, trigonometric functions and trigonometric identities.

Pre-Calculus
This course addresses the Learning Standards for Precalculus and focuses on four critical areas: (1) extend work with complex numbers; (2) expand understanding of logarithms and exponential functions; (3) use characteristics of polynomial and rational functions to sketch graphs of those functions; and (4) perform operations with vectors.

## Calculus

This course is for students who have successfully completed Algebra II Enhanced. The course will include a brief review of the critical concepts and skills covered in Algebra II Enhanced followed by the concepts of limit, derivative, and definite and indefinite integral. Techniques of numerical and closed form integration with applications of the definite and indefinite integrals will be studied.

A.P. Calculus AB is a full year mathematics course, structured to closely resemble a first semester Calculus course in college. It is the intent of the course to develop a conceptual understanding and computational fluency in the basics of differential and integral calculus. This course will emphasize basic techniques, problem solving skills, critical thinking, and an understanding of various applications of calculus. Technology will also be emphasized as a problem-solving tool. Students will apply the techniques learned to a variety of different types of functions as well as different representations of functions, and use these to model real-world situations. The course will also introduce basic differential equations, and use them to model growth.

# Discontinued Courses

## Enhanced Algebra I (Grade 9)

The concepts in the Algebra I course are extended in the Enhanced Algebra I course by introducing additional types of numbers, expressions, equations, and functions that naturally connect with each other (as in the case of extending finding zeros of quadratics to finding zeros of polynomials) and/or organize each other (as in the case of extending the number system to include both real and non-real numbers) and are typically seen in an Algebra II course. This is the first course on the track to reach Calculus by twelfth grade; therefore, the study of algebraic concepts of expressions, equations, polynomials, and functions are investigated in-depth and from a pre-calculus perspective. This is a fast-paced class with the expectation of strong student performance. The completion of out-of-class research and extra projects is expected.

## Math for Business and Personal Finance

Financial Literacy is essential in meeting the financial challenge of the 21st Century with understanding and managing personal finances the key to one’s future financial success. Students will apply the knowledge and skills learned in this course to various financial situations they will encounter later in life to make critical decisions regarding personal finances. Students will learn money management, savings and investing, income, and spending strategies. This course will teach students to identify and prioritize their personal money management goals, develop personal spending, savings, and investing plans, tax implications and understand the cost of using credit along with asset protection.

## Probability and Statistics (Grade 10)

This course uses a standards-based approach to the study of statistics and probability. Topics include Interpreting Categorical and Quantitative Data, Making Inferences and Justifying Conclusions, Conditional Probability and the Rules of Probability, and Using Probability to Make Decisions. Decisions or predictions are often based on data—numbers in context. These decisions or predictions would be easy if the data always sent a clear message, but the message is often obscured by variability. Statistics provides tools for describing variability in data and for making informed decisions that take it into account. Statistical applications will be used. Connections to real world and cross-curricular applications will be made (e.g., students may be asked to justify a determination of who is the best NFL quarterback using data or how best to represent data in the news to make a point).

## Financial Literacy (formerly MATH FOR BUSINESS AND PERSONAL FINANCE) (Grade 12)

Financial Literacy is essential in meeting the financial challenge of the 21st Century with understanding and managing personal finances the key to one’s future financial success. Based on the Massachusetts Mathematics Curriculum Framework (2017) learning standards, this course teaches students to apply the knowledge and skills to various financial situations they will encounter later in life to make critical decisions regarding personal finances. Students will learn money management, savings and investing, income, and spending strategies. This course will teach students to identify and prioritize their personal money management goals, develop personal spending, savings, and investing plans, tax implications and understand the cost of using credit along with asset protection.