Mathematics

MATHEMATICS

The Dennis-Yarmouth mathematics program of studies follows the recommended curriculum for college and career readiness as outlined by the Massachusetts Curriculum Frameworks.  The mathematics program follows the Integrated Pathway Model Courses for grades 9-12, Integrated Algebra I, Integrated Geometry, and Integrated Algebra II & Trigonometry.  These three courses provide a solid mathematical foundation for all students.  Additional math courses are offered to extend the students’ mathematical growth to prepare them for success in college, opportunity in the workplace, and effective participation in civic life.  

Courses in the mathematics program focus on developing students in the following areas:  

• Conceptual understanding – make sense of the math, reason about and understand math concepts and ideas  

• Procedural fluency – know mathematical facts, compute and do the math  

• Capacity – solve a wide range of problems in various contexts by reasoning, thinking, and applying the mathematics they have learned.

The Standards for Mathematical Practice describe expertise that mathematics educators at all levels seek to develop in their students. 

1. Make sense of problems and persevere in solving them. 

2. Reason abstractly and quantitatively. 

3. Construct viable arguments and critique the reasoning of others. 

4. Model with mathematics. 

5. Use appropriate tools strategically. 

6. Attend to precision. 

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Students are required to have a scientific calculator in all Level 2 courses and a graphing calculator for all Honors level courses.  (DYRHS uses the TI-83 and TI-84 series of graphing calculators).  Graphing calculators are encouraged for all students for standardized testing.    

Final course offerings are dependent upon student enrollment numbers and staffing resources. 

Faculty

Mrs. Stasia Revere - Department Chair

Ms. Alison Adams

Mrs. Katelin Crary

Ms. Marie Kade

Ms. Elizabeth Macomb

Mr. Christopher Marsh

Mr. Benjamin Thompson

Mr. Paul Tishue

8th GRADE MATH (261/262)

Grade 8:  Level 2 and Advanced

(Year) 

Advanced Prerequisites: 7th grade performance and teacher recommendation

In grade 8, instructional time focuses on three critical areas: (1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with linear equations and solving systems of linear equations; (2) grasping the concept of a function and using functions to describe relationships; and (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, congruence, and understanding and applying the Pythagorean Theorem.

Students will proceed from 8th grade math to either integrated Algebra 1 or Honors Geometry based on their performance in this course. 

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 graph linear inequalities and exponential functions. Additionally, students will be exposed to the Geometric concepts of congruence and proof writing.

INTEGRATED GEOMETRY (205)

Grades 9-12:  Level 2 and Honors

(Year) 1.50 credits

Level 2 Prerequisites: Successful completion of Integrated Algebra I

Honors Prerequisites:

1.  8th 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 Algebra I and Geometry (206):

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.

MATH ANALYSIS  (275) - NOT OFFERED 2025-2026

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 (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.

HONORS CALCULUS (233)

Grade 12:  Honors 

(Year)  1.5 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 Honors Calculus.

This course offers students the opportunity to do college level work in mathematics. Major content areas include limits, derivatives of a function and applications. Honors Calculus also covers prerequisite math topics required for successful understanding and problem solving of calculus topics. 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.

FINANCIAL ALGEBRA (259)

Grades 11-12:  Level 2 and Honors

(Semester) 1.50 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.  

Math Skills (228)

Grades 9-10;  Level 2

(Semester) 0.75 credits

The Math Skills course is designed for students in grades 9-12 who are in need of additional support and instruction in mathematics. This course provides an opportunity for credit recovery and focuses on building foundational math skills essential for success in higher-level math courses. Through personalized instruction, hands-on practice, and targeted interventions, students will reinforce key concepts, improve problem-solving abilities, and develop the confidence needed to succeed in future math classes.

Students will engage in a variety of activities, including interactive lessons, individual practice exercises, and collaborative group work, all aimed at addressing gaps in knowledge. Topics may cover basic arithmetic, algebra, geometry, and pre-algebra, with a focus on conceptual understanding and real-world applications. This course is tailored to meet students where they are and help them progress at their own pace while ensuring mastery of essential skills.

The Math Skills course provides a supportive learning environment where students can ask questions, receive individualized assistance, and track their progress toward meeting grade-level math standards. By the end of the course, students will have gained the necessary skills to succeed in future math courses and improve their overall academic performance.

STATISTICS (247/201) 

Grades 11-12: Level 2 and Honors

(Semester) 1.50 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.

AP STATISTICS (245)

Grades 11 - 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.