[ 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 their own graphing calculator every day in class. They also need graphing calculator access in order to do homework, class work, and some assessments. Please reach out to the Math Department Chair if you have any questions. The department’s instruction supports the TI-84 (CE/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 based graphing calculator found at Desmos.com.
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, verbal 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
Geometry is a course designed 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: Teacher recommendation and a grade of C- or better in Algebra I (Grade 9)
Geometry (Honors) - Course #403
Prerequisite: Successful completion of Algebra I (Grade 8) and teacher recommendation or teacher recommendation and a grade of A- or better in Algebra I (Grade 9)
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, trigonometric 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: Teacher recommendation and a grade of C- or better in Geometry (College I) or teacher recommendation a grade of A or better in Geometry (College II) and an A- or better in Algebra I
Algebra II (Honors) - Course #407
Prerequisite: Teacher recommendation and a grade of B- or better in Geometry (Honors) or teacher recommendation and a grade of A- or better in Geometry (College I) and a grade of A or better in Algebra I (College I).
PRECALCULUS
Grades 11 & 12
Full year - 5 credits
Precalculus is a continuation of the concepts from algebra I and II. 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.
Precalculus (College II) - Course #427
Prerequisite: A grade of B- or better in Algebra II (College II) and teacher recommendation.
Precalculus (College I) - Course # 424
Prerequisite: A grade of C- or better in Algebra II (College I) or grade of A or better in Algebra II (College II) and approval of the math department chair.
Precalculus (Honors) - Course #428
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).
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.
Prerequisite: Successful Completion of Algebra II (College II) or approval of the math department chair.
ADVANCED ALGEBRA WITH FINANCIAL APPLICATIONS (College II)
Course #429
Grades 11 & 12
Full Year - 5 credits
Advanced Algebra with Financial Applications offers students in 11th and 12th grade an opportunity to view the world of finance through a mathematical lens. The mathematical formulas, functions, and pictorial representations used assist students in making sense of the financial world around them and equip them with the ability to make sound financial decisions. The overarching purpose of the course is to develop mathematically proficient students who can apply mathematics to solve real world problems that arise at home, at school, in society, and in the workplace.
Prerequisite: Successful Completion of Algebra II (College II) and teacher recommendation 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 PreCalculus (Honors). This will be a fundamental course providing techniques of 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 (College I) - Course # 412
Prerequisite: Successful completion of PreCalculus (College I)
Calculus (Honors) - Course #413
Prerequisite: A minimum grade of B- in PreCalculus (Honors) or a grade of A- or better in PreCalculus (College I)
Advanced Placement Calculus AB - Course #414
Prerequisite: A minimum grade of A- in PreCalculus (Honors)
Advanced Placement Calculus BC - Course #415
Prerequisite: A minimum grade of A- in PreCalculus (Honors)
ADVANCED PLACEMENT STATISTICS
Course #416
Grades 11 & 12
Full year - 5 credits
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 PreCalculus (Honors or College I), B or better in Algebra II Honors, or B- or better in an 11th grade (College I) Algebra-based math course
SEMESTER ELECTIVE COURSES
ACCOUNTING & FINANCE
Course #433
Grades 9 - 12
Semester - 2.5 credits
Accounting and Finance offers an opportunity to learn methods of recording business transactions. Students become familiar with the accounting cycle and learn how to keep simple, effective records for a small business using a double entry system. This course is recommended for those students planning to enter a business career, operate their own business, or attend college majoring in business or accounting.
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.
STATISTICS
Grades 11 & 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.
STATISTICS IN OUR WORLD
Course #432
Grades 10 - 12
Semester - 2.5 credits
Ever wonder how a professional team decides who they want to draft? Want to know more about how a medicine is deemed effective? Curious about all those polls before an election? Ever see a statistic and wonder how it was calculated and if it's accurate? If you answered yes to any of these, then this course is for you! Statistics are everywhere and this course will help give you an insight into where they come from and how they can be used. Statistics in our World is an introductory course designed for students to learn about the many applications of statistics in our everyday lives. Students will explore statistics in sports, science, politics, and many other areas of our society.