Mathematics

MATHEMATICS PHILOSOPHY

Mathematical power is achieved through exploration, reasoning, problem solving, communication, and connections. Students in our mathematics classes work toward achieving the Medfield High School learner outcomes as they connect ideas within mathematics and between mathematics and other activities in their lives. MHS mathematics courses challenge students of all ability levels and encourage them to excel academically.

MATHEMATICS OBJECTIVES

The student will:

  • Explore mathematical ideas in ways that stimulate curiosity, create enjoyment of mathematics, and develop depth of understanding.
  • Explain and justify solutions to problems.
  • Recognize the relationships among different topics in mathematics and apply mathematical thinking to solve problems in other disciplines.
  • Recognize and apply sound reasoning.
  • Use multiple approaches to investigate and understand mathematical content.

CALCULATOR POLICY

The MHS mathematics department consistently integrates graphing calculators into our curriculum. All students are required to have a graphing calculator every day in class. They also need graphing calculator access in order to do homework, class work, and some assessments. The department’s instruction supports the TI-83 (plus/silver edition) and TI-84 (plus/silver edition) calculators. We look to ensure that students are able to become comfortable with certain functions of the calculator as we know that many students will use the graphing calculator beyond high school. Additionally, students will use the web- and app- based graphing calculator found at Desmos.com. This online tool has powerful graphing capabilities that may be used in place of a graphing calculator at home.

COURSE PLACEMENT

Course placement is determined by a student’s performance and learning needs. Courses are offered at college levels, designated College I and College II, and Honors/Advanced Placement levels. The curriculum in the different levels will be similar, but the pace, depth of coverage, and independent study may differ. Instructional strategies will be geared to students’ learning styles, and support personnel will be available where appropriate. Advanced Placement courses constitute a well-established national program that brings college level study to highly motivated and academically able high school students. Colleges grant either advanced standing and/or credit to students who have successfully completed an AP course, based on their performance on the AP examination. When deciding whether or not to change placement, please reach out to your teacher as well as the Mathematics Department Chair.


ALGEBRA I

Grade 9

Full year - 5 credits

Algebra I serves as a strong foundational course for all math courses in high school and beyond. Students will study algebra as a system of real numbers. Emphasis will be placed on the importance of the concept of functions in mathematics and students will use algebraic, graphical and numerical techniques in their study. Graphing technology will be used to explore mathematical ideas and concepts, verify solutions and create mathematical models. Topics covered will include linear, quadratic & exponential functions, systems of equations & inequalities and absolute value equations & inequalities. This course is aligned with the MA Math Curriculum Frameworks.

Algebra I (College I) - Course #410

Algebra I (College II) - Course #406


GEOMETRY

Grades 9 - 10

Full year - 5 credits

This course has been developed to increase an understanding of the nature of deductive and inductive reasoning. Development of critical thinking and an understanding of the relationship between algebra and geometry are the primary goals of this course. Some of the topics that will be covered include plane geometry, proofs, coordinate geometry, parallel and perpendicular lines, congruence and similarity of polygons, quadrilaterals, area, volume, transformations, right triangle trigonometry, and circles.

Geometry (College II) - Course #405

Prerequisite: Successful completion of Algebra I (Grade 9)

Geometry (College I) - Course #404

Prerequisite: A grade of C- or better in Algebra I (Grades 8 or 9)

Geometry (Honors) - Course #403

Prerequisite: Teacher Recommendation and a grade of A or better in Algebra I (Grade 8), or a grade of B- or better in Accelerated Algebra I (Grade 8).


ALGEBRA II

Grades 10-11

Full year - 5 credits

Algebra II is a continuation of the study and techniques of algebra as a system of real as well as complex numbers. Emphasis is placed on the comprehension of the function concept and its importance in mathematics and students will use algebraic, graphical and numerical techniques in their study. Students will be required to develop skills in the application of the algebraic concepts and apply them to real-life data sets. Graphing technology will be used to explore mathematical ideas and concepts, verify solutions and create mathematical models. Some of the topics that will be covered include linear functions & systems, and absolute value, polynomial, rational, root, exponential & logarithmic functions. Additionally, and sine & cosine functions will be introduced at the College 1 and Honors level. This course is aligned with the MA Math Curriculum Frameworks.

Algebra II (College II) - Course #409

Prerequisite: Successful completion of Geometry (College II) and Algebra I

Algebra II (College I) - Course #408

Prerequisite: A grade of C- or better in Geometry (College I) or a grade of A or better in Geometry (College II) and an A- in Algebra I

Algebra II (Honors) - Course #407

Prerequisite: A grade of B- or better in Geometry (Honors) or a grade of A- or better in Geometry (College I) and a grade of A or better in Algebra I (College I).

FUNCTIONS AND TRIGONOMETRY (College II)

Course #423

Grades 11-12

Full year - 5 credits

This course will prepare introduce students to PreCalculus topics. Content covered will include polynomial, radical, exponential, logarithmic, rational functions and an introduction to trigonometric functions, including right triangle trigonometry. Functions will be examined from algebraic, graphical, and numerical viewpoints to bring together in a cohesive way the mathematics studied in algebra and geometry. Graphing technology will be used to explore mathematical ideas and concepts, to verify solutions and to develop mathematical models. Successful completion of this course will prepare the student for a traditional college Precalculus course.

Prerequisite: Successful completion of Algebra II (College II).

MATH ANALYSIS

Grade 11

Full year - 5 credits

This course is designed to build a strong foundation in precalculus. The essential concepts and skills of algebra and the unifying theme of functions will connect the study of trigonometric, polynomial, rational, exponential, and logarithmic functions. Students will use algebraic, graphical, and numerical techniques, as well as graphing technology in their study. Graphing technology will be used to explore mathematical ideas and concepts, to verify solutions, and to develop mathematical models. Some of the topics that will be covered include graphs and inverses, algebraic and trigonometric functions, identities, analytical trigonometry, sequences and series, probability, complex numbers, and analytic geometry. At the honors level, students will also study parametric equations, polar coordinates, and limits. Successful completion of this course will prepare the student for a Calculus course.

Math Analysis (College I) - Course # 420

Prerequisite: Successful completion of Algebra II (College I)

Math Analysis (Honors) - Course #417

Prerequisite: A grade of B- or better in Algebra II (Honors) or grade of A or better in Algebra II (College I) and approval of the math department chair, (summer work required).


PRECALCULUS

Grade 12

Full year - 5 credits

Precalculus builds on the concepts and skills studied and applied in Advance Algebra and Trigonometry. Some of the topics that will be covered include algebraic functions, probability and statistics, sequences and series, matrices and determinants, analytic geometry including conics. Applications of these topics will be emphasized throughout the course. Successful completion of this course will provide a strong background for college level work in calculus and other mathematics courses related to science and engineering programs.

Precalculus (College I) - Course #424

Prerequisite: A grade of C- or better in Advanced Algebra and Trigonometry (College I) or approval of the department chair.

Precalculus (College II) - Course #427

Prerequisite: A grade of B- or better in Functions and Trigonometry (College II) and recommendation of current teacher.

TOPICS IN MATH (College II)

Course #426

Grades 11 & 12

Full year - 5 credits

Topics in Math builds on the concepts and skills studied and applied in previous math courses. This course is designed to study mathematics through real-world applications. Some of the topics that will be covered include: Finance (personal and community based), Apportionment Theory, Voting Theory. This course will run alternate years with Applied Math.

Prerequisite: Successful Completion of Algebra II (College II) or approval of the math department chair.


APPLIED MATH (College II)

Course #429

Grades 11 & 12

Full Year - 5 credits

This is a full year 5 credit math course. Students will study mathematics through real-world application. Some of the topics that will be covered include: Finance (personal and community based), Counting Theory, Probability and Descriptive Statistics. This course will run alternate years with Topics in Math.

Prerequisite: Successful Completion of Algebra II (College II) or approval of the math department chair.


CALCULUS

Grade 12

Full year - 5 credits

This course will be offered to students who have completed Algebra I and II, Geometry and Math Analysis (Honors). This will be a fundamental course providing techniques of the differential and integral calculus. Graphical interpretation of such concepts as a slope, extreme value, differential and the definite integral will be emphasized. Additional topics in calculus, which are necessary for those taking the AP Exam, will be taught in these classes. As part of fulfilling course expectations in AP Calculus AB and BC, students will take the AP Exam in May.

Calculus (Honors) - Course #413

Prerequisite: A minimum grade of B- in Math Analysis (Honors).

Advanced Placement Calculus AB - Course #414

Prerequisite: A minimum grade of A- in Math Analysis (Honors)

Advanced Placement Calculus BC - Course #415

Prerequisite: A minimum grade of A- in Math Analysis (Honors)


ADVANCED PLACEMENT STATISTICS

Course #416

Grades 11 and 12

Full year - 5 credits

(Preference given to Grade 12; If there is room in the course for Grade 11 students, a lottery will be conducted among students who have signed up)

Students will be exposed to four broad conceptual themes in a nationally standardized curriculum: 1) Exploring Data; 2) Sampling and Experimentation; 3) Anticipating Patterns Through Probability; 4) Statistical Inference. This course is equivalent to a first year college level course and should be of interest to students pursuing areas of study that require statistical analysis such as engineering, psychology, sociology, health science, business, science, and mathematics. Students will use graphing calculators and computer statistics software throughout the course. Students taking AP Statistics must concurrently take either Precalculus or Calculus OR receive approval from the Math Department Chair. As part of fulfilling course expectations in AP Statistics, students will take the AP Exam in May. Students are required to complete a summer assignment as a component of this course.

Prerequisite: A grade of C- or better in Math Analysis (Honors), or B or better in an 11th grade (College I) Algebra-based math course


STATISTICS

Grades 11 and 12

Semester - 2.5 credits

(Preference given to Grade 12; If there is room in the course for Grade 11 students, a lottery will be conducted among students who have signed up)

Students will be exposed to four broad conceptual themes in the curriculum: 1) Exploring Data; 2) Sampling and Experimentation; 3) Anticipating Patterns Through Probability; 4) Statistical Inference. This course is an excellent overview of statistics and should be of interest to students pursuing areas of study that require statistical analysis such as engineering, psychology, sociology, health science, business, science, and mathematics. Students taking Statistics must concurrently take either Precalculus or Calculus OR receive approval from the Math Department Chair.

Statistics (College I) - Course #418

Prerequisite: A grade of C or better in Algebra II (College I), A- or better in Algebra II (College II) OR approval of the Math Department Chair.

Statistics (Honors) - Course #411

Prerequisite: Successful completion of Algebra II (Honors) or a grade of B- or better in Algebra II (College I) OR approval of the Math Department Chair.


COMPUTER SCIENCE

Course #702

Grades 9 - 12

Semester - 2.50 credits

Exploring Computer Science courses present students with the conceptual underpinnings of computer science through an exploration of human/computer interaction, web design, computer programming, and data modeling. While these courses include programming, the focus is on computational practices associated with doing computer science, rather than just a narrow focus on coding, syntax, or tools. Exploring Computer Science courses teach students the computational practices of algorithm design, problem solving, and programming within a context that is relevant to their lives.


SOPHOMORE MATH SUPPORT

Course #430

Grade 10

Semester - 2.5 credits

This class offers academic enrichment to sophomores in math. Students will be given independent assignments as well as support in their courses. Individual conferences are held frequently to discuss the student's’ academic progress and/or concerns. Special emphasis is placed on MCAS preparation and test-taking techniques. Eligible students will be selected based on their academic needs. This course is not calculated into the GPA and is graded pass/fail.