Math - Senior

INTEGRATED ALGEBRA I (203)

Grades 9-12: Level 2

(Year) 1.50 credits

The fundamental goal is to extend the mathematics that students learned in 8th Grade. Integrated Algebra focuses on standards within four conceptual categories: (1) Expressions & Equations, (2) Statistics, (3) Linear & Exponential Functions, and (4) Congruence. In Integrated Algebra 1, students will continue to build on linear equations in one and two variables and further their understanding to graphing linear inequalities and exponential functions. Additionally, students will be exposed to the Geometric concepts of congruence and proof writing.

INTEGRATED GEOMETRY (205/206)

Grades 9-12: Level 2 and Honors

(Year) 1.50 credits

Level 2 Prerequisites: Successful completion of Integrated Algebra I

Honors Prerequisites:

1. 8^th grade performance and teacher recommendation

2. A- or higher in Integrated Algebra I or teacher recommendation

The focus is on quadratic expressions, equations, and functions; comparing their characteristics and behavior to those of linear and exponential relationships from Integrated Algebra I.

Instructional time will focus on six critical areas: (1) Similarity, Proof, and Trigonometry, (2) Polynomial and Quadratic Expressions, Equations, and Functions, (3) Circles, With and Without Coordinates, (4) Extending to Three Dimensions, (5) Connecting Algebra and Geometry Through Coordinates, (6) Inferences and Conclusions From Data

Honors Option: Students who have met the prerequisites and are able to commit the time and effort to move through the basic concepts at a deeper level of understanding may select the Honors option.

Instructional time will focus on nine critical areas: (1) Solving and Graphing Linear Functions, (2) Descriptive Statistics, (3) Comparing Linear and Exponential Functions, (4) Congruence, Proof, and Constructions, (5) Similarity, Proof, and Trigonometry, (6) Extending to Three Dimensions (7) Connecting Algebra and Geometry Through Coordinates, (8) Circles, With and Without Coordinates, (9) Polynomial and Quadratic Expressions, Equations, and Functions

INTEGRATED ALGEBRA II & TRIGONOMETRY (207/209)

Grades 10-12: Level 2 and Honors

(Year) 1.50 credits

Level 2 Prerequisite: Successful completion of Integrated Geometry

Honors Prerequisites: B- in Integrated Geometry Honors or an A- or higher in Integrated

Geometry Level 2

Students will integrate and apply the mathematics they have learned from their earlier courses. Instructional time will focus on four critical areas: (1) Develop an ability to model, graph and algebraically solve Quadratic Functions (2) Develop an ability to model, graph and algebraically solve Polynomial, Rational Functions (3) Develop an ability to model and algebraically solve Logarithmic Functions. (3) Develop an ability to model and algebraically solve Coordinate Geometry (4) Develop an ability to model, graph and algebraically solve right triangle trigonometry.

Honors Option: The honors option includes focused work on deriving equations and deeper understanding of coordinate geometry and right triangle trigonometry.

SPORTS STATISTICS (252)

Grades 9-10: Level 2

(Semester) .50 credits

Students will explore real world sports data by describing data visually and numerically, observing patterns and departures from patterns; planning a study, deciding what to measure and how to measure it; anticipating patterns in advance, introducing probability and simulation. Students will be using real time sports data based on the current sports season. Students will be graded through a variety of projects, classwork and online assessments.

MATH ANALYSIS (249/250)

Grades 11-12: Level 2

(Semester) 0.75 credits

Prerequisites: C or higher in Integrated Algebra II & Trigonometry level 2 or Honors

This course is designed as a 4th year mathematics course to prepare students for college and careers in the fields of social sciences (non-STEM). Through this course, students are encouraged to continue their study of mathematical ideas in the context of real-world problems and decision making through the analysis of information, modeling change, and mathematical relationships.

Instructional time will focus on three critical areas: (1) investigate and apply various mathematical models (2) explore and apply concepts of vectors and matrices to model and solve real-world problems such as networks and group population trends and (3) use probability to find expected values for discrete random variables such as lottery winnings and life insurance.

PRE-CALCULUS for MATH & SCIENCES (249/250)

Grades 11-12: Level 2 and Honors

(Year) 1.50 credits

Level 2 Prerequisite: C or higher in Integrated Algebra II & Trigonometry level 2 or Honors

Honors Prerequisite: B- or higher in Integrated Algebra II & Trigonometry Honors, or A- or higher in Integrated Algebra II & Trigonometry Level 2

Precalculus 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 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.

Honors Option: Students who have met the prerequisites are able to move through the basic concepts at a faster pace and are able to and want to go into more depth may select the honors option. This option includes a wider scope of mathematics including the development and derivation of specific formulas.

FINANCIAL ALGEBRA (239)

Grades 11 -12: Level 2 and Honors

(Semester) 0.75 credits

Level 2 Prerequisite: Successful completion of or enrollment in Integrated Algebra II & Trigonometry

Honors Prerequisite: Completion of Integrated Algebra II & Trigonometry

This course combines algebraic and graphical approaches with personal finance applications. The course uses basic algebraic formulas with variables, equations, linear and exponential functions. The algebra found in finance related topics translates into powerful real world problems. Instructional time will focus on the areas of knowledge and understanding that are fundamental to personal finance (1) Income and Expenses (2) Saving (3) Credit (4) Loans (5) Financial Investing (6) Protecting and Insuring.

Students will explore each topic algebraically, performing calculations and making mathematical connections. A student who masters the knowledge embodied in the standards should be able to avoid making poor financial decisions, understand the economic reasons behind the trade-offs between financial choices, and know the basis for their own decisions.

Honors Option: For students who have met the prerequisites and desire to learn the mathematics of Finance. Students will use algebraic skills to calculate loan repayment, including credit cards and student loans. Financial applications include linear, exponential, logarithmic functions, and systems of equations. A student who masters the knowledge embodied in the standards should be able to avoid making poor financial decisions, understand the economic reasons behind the trade-offs between financial choices, and know the basis for their own decisions. A graphing calculator is required.

ALGEBRA & COMPUTER SCIENCE (214)

Grades 11-12: Level 2

(Semester) 0.75 credits

Prerequisite: Successful completion of Integrated Geometry and completion or enrollment in Integrated Algebra II & Trigonometry.

This course is for students new to computer programming. This course teaches algebraic and geometric concepts through computer programming at code.org. It is a project based course culminating in a final, fully functioning programmed computer app. Students will explore the intersection of Math and CS by studying topics such as order of operations, the Cartesian plane, functions, boolean logic, piecewise functions, and collision detection with the Pythagorean Theorem using a graphical programming language. Students will use these concepts to build programming functions and write apps that will eventually drive the logic in their final project – a video app.

DATA SCIENCE (215)

Grades 11-12: Level 2

(Semester) 0.75 credits

Prerequisite: Successful completion of Integrated Algebra II & Trigonometry

This curriculum will introduce students to the main ideas in data science through tools such as Google Sheets, Python, Data Commons and Tableau. Students will learn to be data explorers in project-based units, through which they will develop their understanding of data analysis, sampling, correlation/causation, bias and uncertainty, probability, modeling with data, making and evaluating data-based arguments, the power of data in society, and more! At the end of the course students will have a portfolio of their data science work to showcase their newly developed abilities.

STATISTICS (251)

Grades 11-12: Level 2 and Honors

(Semester) 0.75 credits

Prerequisite: Successful completion of Integrated Algebra II & Trigonometry

Honors Prerequisite: B- or higher in Integrated Algebra II & Trigonometry or teacher

recommendation

This course will address the Common Core State Standards for High School Statistics and Probability. Students must be willing to work independently and have an interest in statistics. It is a non-calculus based introduction to statistics exposing students to four broad conceptual themes: exploring data, observing patterns and departures from patterns; planning a study, deciding what to measure and how to measure it; anticipating patterns in advance, introducing probability and simulation. Students will understand how data are used by professionals to address real-world problems. Students will analyze statistical graphs to identify patterns to relate to the real world. Students will understand that by treating photos, words, numbers, and sounds as data, they can gain insight in the real world.

Honors Option: Students must be willing to work independently and have an interest in statistics. Topics may include descriptive statistics, linear regression, surveys and experiments, estimating parameters and creating confidence intervals, and hypothesis testing.

HONORS COLLEGE ALGEBRA (242)

Grade 12 only: Level H

(Semester) 0.75 credits

Prerequisite: Successful completion of Pre-Calculus

This course is open to seniors who have completed Pre-Calculus and require another year of mathematics in their senior year. This course continues to work with the Massachusetts Mathematics Framework (+) Standards through grade twelve. A learning environment is provided that allows the student to continue to work towards mastering the standards. The students engage in mathematics developed around problem contexts that involve students in exploring, problem solving, generalizing mathematical concepts and algorithms and developing their capabilities to do mathematics. This course completes the progression of student performance expectations that lead to college-level work.

Topics include rational and radical equations and inequalities, polynomial functions, sequences and series, logarithmic and exponential equations, trigonometric and periodic functions, permutations, combinations and the binomial theorem. Other advanced topics may be covered based on the interest and ability of students.

AP STATISTICS (245)

Grades 10 - 12: Advanced Placement

(Year) 1.50 credits

Prerequisite: B- in Integrated Algebra II & Trigonometry Honors or A- in Integrated Algebra II & Trigonometry or A- in Honors Geometry and Teacher Recommendation

Students must be willing to work independently and have an interest in statistics. This course offers students the opportunity to do college level work in mathematics. It is a non-calculus based introduction to statistics exposing students to four broad conceptual themes: exploring data, observing patterns and departures from patterns; planning a study, deciding what to measure and how to measure it; anticipating patterns in advance, introducing probability and simulation; and statistical inference, confirming models for explanations of patterns.

Students are strongly urged to take the Advanced Placement Examination, and those who do will be exempted from the course final examination

AP CALCULUS AB (219)

Grade 11-12: Advanced Placement

(Year) 1.50 credits

Prerequisite: Successful completion of college preparatory mathematics through Precalculus and the willingness, time, and resources to put forth the effort required to learn the topics to pass AP Calculus AB.

This course offers students the opportunity to do college level work in mathematics, primarily calculus and related analytical geometry. The content follows the prescribed Advanced Placement program. Major content areas include limits, derivatives of a function and applications, the indefinite integral, the definite integral and applications, transcendental functions, and methods of integration. Students will gain insight and respect for the importance and usefulness of calculus. Students are encouraged to discover original solutions to challenging problems and give explanations of their work to the class. Explanations are provided by the teacher for new concepts and problems which have not been solved successfully by students. Students are urged to take the Advanced Placement Examination, and those who do will be exempted from the course final examination.

AP CALCULUS BC (211)

Grade 12: Advanced Placement

(Year) 1.50 credits

Prerequisite: Successful completion of college preparatory mathematics through Precalculus by the end of their junior year and the willingness, time, and resources to put forth the effort required to learn the topics to pass AP Calculus BC.

Advanced Placement Calculus BC is for students who have completed four courses in college preparatory mathematics including Pre-Calculus and wish to continue the study of mathematics. This course offers the opportunity to do college level work in mathematics, primarily calculus and related analytical geometry. Reading and problem solving are emphasized. The content follows the prescribed Advanced Placement program. Major content areas include limits, derivatives of functions and applications, the indefinite integral, the definite integral and applications, transcendental functions, and methods of integration. Additionally, parametric, polar, and vector functions and series will be studied.

Students will gain insight and respect for the importance and usefulness of calculus. Students are encouraged to discover original solutions to challenging problems and give explanations of their work to the class. Explanations are provided by the teacher for new concepts and problems which have not been solved successfully by students. Students are urged to take the Advanced Placement Examination, and those who do will be exempted from the course final examination. Content and methodology reflect practical applications and current technology.