Mathematics Department

Ms. Jean-Marie Johnson, Director

Phone: 508-841-8806 Email: jmjohnson@shrewsbury.k12.ma.us

An understanding of mathematics is vitally important to developing critical thinking and problem-solving skills and, therefore, students are encouraged to take a rigorous course of high school math. Algebra and Geometry are the foundation for all other mathematics studies, so it is important for students to work diligently to achieve a sound understanding of these subjects. Our program is designed to meet the diverse needs of the learners at SHS to provide all students with the opportunity for success. All of the math courses in our programs are college preparatory courses based on the standards set forth by the Massachusetts Frameworks and will ensure students an opportunity to be successful on statewide assessments. Senior electives include advanced placement courses in Calculus (AB and BC) and Statistics. Other electives for seniors include Mathematical Modeling Honors, Advanced Quantitative Reasoning (A-level & Honors), Calculus Honors, and Functions & Trigonometry. We also offer an enrichment opportunity in the Math Internship for advanced juniors and seniors to work as teacher assistants in underclassmen classes.

The SHS Mathematics Department curriculum connects the Standards for Mathematical Practice to the Standards for Mathematical Content as set by the Massachusetts Frameworks. Reading, writing & speaking in mathematical terms are important aspects of all courses. Students are taught to read mathematical explanations and are encouraged to communicate in mathematical terms, both orally and in writing, to justify & explain solutions. Problem-solving is the central focus and is discussed in real-world context. This involves posing and defining problems, considering different strategies and finding appropriate mathematical models that make sense in the situation. Skills are taught through applications and connections to other curriculum areas, as well as through the integration of mathematical topics. Technology is incorporated into all courses through the use of various software applications & graphing calculators. Our goal is to empower students to develop as practitioners of math through thinking, reasoning, persevering, collaborating, & making connections when solving problems.

Foundations of Algebra and Geometry I (2010T)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grades: 9-12 A Level

Prerequisite: Teacher recommendation

This course will investigate and build upon the basic foundations of Algebra and Geometry in an approach that will enable students to make the connections necessary to apply their skills in a variety of application-based problems. The units of study will include patterns in data, patterns of change, linear functions, patterns in shape, and exponential functions. Important ideas are continually revisited for students to make connections and develop a lasting understanding of the mathematics they are studying. Students who are successful in this course will be expected to enroll in Algebra & Geometry I in their next course. This course will use ALEKS software to support students’ work with the course curriculum as well as their work on cumulative math review topics. ALEKS will create a learning path for students based on their performance and work in ALEKS will help to remediate or expand their knowledge of the course content. A graphing calculator (TI-83 or TI-84) is recommended because it is used extensively.

Algebra and Geometry I (2010)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grades: 9-12 A Level

Prerequisite: Teacher recommendation

This course will continue to investigate and build upon the basic foundations of Algebra and Geometry in an approach that will enable students to make the connections necessary to apply their skills in a variety of application-based problems. The units of study will include patterns in data, patterns of change, linear functions, patterns in shape, and exponential functions. Important ideas are continually revisited for students to make connections and develop a lasting understanding of the mathematics they are studying. This course will use ALEKS software to support students’ work with the course curriculum as well as their work on cumulative math review topics. ALEKS will create a learning path for students based on their performance and work in ALEKS will help to remediate or expand their knowledge of the course content. A graphing calculator (TI-83 or TI-84) is recommended because it is used extensively.

Algebra and Geometry II (2011)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grades: 9-12 A Level

Prerequisite: Past academic performance in Honors Algebra, Algebra I or Algebra & Geometry I and teacher recommendation.

This course is a continuation of the Algebra and Geometry I course. The units of study will include The Real Number System, Functions, Equations and Systems, Coordinate Methods, Regression and Correlation, Quadratic and other Non-Linear Functions and Equations, Probability and Trigonometry. This course will use ALEKS software to support students’ work with the course curriculum as well as their work on cumulative math review topics. ALEKS will create a learning path for students based on their performance and work in ALEKS will help to remediate or expand their knowledge of the course content. A graphing calculator (TI-83 or TI-84) is recommended because it is used extensively. Students who have completed Algebra and Geometry I or a full year Algebra I course must complete this course before continuing on to Advanced Math I.

Algebra and Geometry IIB (2011B)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grades: 10-12 B Level

Prerequisite: Past academic performance in Algebra or Algebra & Geometry I and teacher recommendation.

This course is a continuation of the Algebra and Geometry I course. The units of study will include The Real Number System, Functions, Equations and Systems, Coordinate Methods, Regression and Correlation, Quadratic and other Non-Linear Functions and Equations, Probability, Trigonometry. The students in this course will be a part of an Algebra and Geometry II class, however, the standards within the curriculum to be completed for mastery have been modified. This course will use ALEKS software to support students’ work with the course curriculum as well as their work on cumulative math review topics. ALEKS will create a learning path for students based on their performance and work in ALEKS will help to remediate or expand their knowledge of the course content. A graphing calculator (TI-83 or TI-84) is recommended because it is used extensively. Students who have completed Algebra and Geometry I or a full year Algebra I course must complete this course before continuing on to Adv Math IB.

Algebra and Geometry II Honors (2032)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grades: 9-12 Honors

Prerequisite: Past academic performance in Honors Algebra, Algebra I or Algebra & Geometry I and teacher recommendation. A placement test may be used.

This course will investigate and build upon topics in Advanced Algebra and Geometry. The units of study will include Functions, Equations and Systems, Coordinate Methods, Regression and Correlation, Quadratic and other Non-Linear Functions and Equations, Probability, and Trigonometry. Students who have completed Algebra and Geometry I or a full year Algebra I course must complete this course before continuing on to Advanced Math I Honors. The students in the Honors level course are expected to develop independent thinking skills as they approach new situations and investigate topics in depth. This course will use ALEKS software to support students’ work with the course curriculum as well as their work on cumulative math review topics. ALEKS will create a learning path for students based on their performance and work in ALEKS will help to remediate or expand their knowledge of the course content. A graphing calculator (TI-83 or TI-84) is recommended because it is used extensively.

Research Methods and Algebra & Geometry II Honors (2035)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grade: 9 Honors

Prerequisite: Teacher recommendation. Must also be enrolled in Research Methods and Introductory Physics Honors or Research Methods and Biology Honors.

This course will investigate and build upon topics in Advanced Algebra and Geometry. The units of study will include Functions, Equations and Systems, Coordinate Methods, Regression and Correlation, Quadratic and other Non-Linear Functions and Equations, Probability and Trigonometry. Students who have completed Algebra and Geometry I or a full year Algebra I course must complete this course before continuing on to Advanced Math I Honors. Students in the Honors level course are expected to develop independent thinking skills as they approach new situations and investigate topics in depth. This course will also incorporate research methods in Math and Science. Students will be required to complete a yearlong research project in the field of Math and/or Science under the guidance of their teachers. Students who sign up for this course must also sign up for Research Topics & Honors Biology. This course will use ALEKS software to support students’ work with the course curriculum as well as their work on cumulative math review topics. ALEKS will create a learning path for students based on their performance and work in ALEKS will help to remediate or expand their knowledge of the course content. A graphing calculator (TI-83 or TI-84) is recommended because it is used extensively.

Advanced Math I (2014)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grades: 10-12 A Level

Prerequisite: Algebra & Geometry I and II and teacher recommendation.

This higher-level mathematics course will further the study of topics in Advanced Algebra, Geometry and Trigonometry to prepare students for the study of Pre-calculus and Calculus. The units of study will include Reasoning and Proof, Inequalities and Linear Programming, Similarity and Congruence, Polynomial and Rational Functions, Circles and Circular Functions, Modeling Sequential Change, and Inverse functions. This course will use ALEKS software to support students’ work with the course curriculum as well as their work on cumulative math review topics. ALEKS will create a learning path for students based on their performance and work in ALEKS will help to remediate or expand their knowledge of the course content. A graphing calculator (TI-83 or TI-84) is recommended because it is used extensively.

Advanced Math IB (2014B)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grades: 10-12 B Level

Prerequisite: Algebra & Geometry I and II or IIB and teacher recommendation.

This higher-level mathematics course will further the study of topics in Advanced Algebra, Geometry and Trigonometry to prepare students for the study of Pre-calculus and Calculus. The units of study will include Reasoning and Proof, Inequalities and Linear Programming, Similarity and Congruence, Polynomial and Rational Functions, Circles and Circular Functions, Modeling Sequential Change, and Inverse functions. The students in this course will be a part of an Advanced Math I class, however, the standards within the curriculum to be completed for mastery have been modified. This course will use ALEKS software to support students’ work with the course curriculum as well as their work on cumulative math review topics. ALEKS will create a learning path for students based on their performance and work in ALEKS will help to remediate or expand their knowledge of the course content. A graphing calculator (TI-83 or TI-84) is recommended because it is used extensively.

Advanced Math I Honors (2028)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grades: 10-12 Honors

Prerequisite: Past academic performance in Honors Algebra & Geometry II or Algebra & Geometry II and teacher recommendation. A placement test may be used

This higher-level mathematics course will further the study of topics in Advanced Algebra, Geometry and Trigonometry to prepare students for the study of pre-calculus and Calculus. The units of study will include Reasoning and Proof, Inequalities and Linear Programming, Similarity and Congruence, Polynomial and Rational Functions, Circles and Circular Functions, Modeling Sequential Change, and Inverse functions. Students in the Honors level course are expected to develop independent thinking skills as they approach new situations and investigate topics in depth. This course will use ALEKS software to support students’ work with the course curriculum as well as their work on cumulative math review topics. ALEKS will create a learning path for students based on their performance and work in ALEKS will help to remediate or expand their knowledge of the course content. Graphing calculator (TI-83 or TI-84) is recommended because it is used extensively.

Research Methods and Advanced Math I Honors (2031)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grades: 10-12 Honors

Prerequisite: Past academic performance in Honors Algebra & Geometry II and teacher recommendation. Must also be enrolled in Research Topics and Honors Chemistry. A placement test may be used.

This higher-level mathematics course will further the study of topics in Advanced Algebra, Geometry and Trigonometry to prepare students for the study of PreCalculus and Calculus. The units of study will include Reasoning and Proof, Inequalities and Linear Programming, Similarity and Congruence, Polynomial and Rational Functions, Circles and Circular Functions, Modeling Sequential Change, and Inverse functions. Students in the Honors level course are expected to develop independent thinking skills as they approach new situations and investigate topics in depth. This course will also incorporate research methods in Math and Science. Students will be required to complete a yearlong research project in the field of Math and/or Science under the guidance of their teachers. Students who sign up for this course must also sign up for Research Topics & Honors Chemistry. This course will use ALEKS software to support students’ work with the course curriculum as well as their work on cumulative math review topics. ALEKS will create a learning path for students based on their performance and work in ALEKS will help to remediate or expand their knowledge of the course content. Graphing calculator (TI-83 or TI-84) is recommended because it is used extensively.

Functions & Trigonometry (2036)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grades: 11-12 A Level

Prerequisite: Past academic performance in Algebra & Geometry II and Advanced Math I or Algebra & Geometry IIB and Advanced Math IB and teacher recommendation.

This course in higher-level mathematics will continue to explore multivariable models, formalization of the concept of functions, function notation, domain and range. Students will use linear, exponential, quadratic and other polynomial functions to model situations. Trigonometric and logarithmic models will also be studied. This course will prepare students for Pre-Calculus or college level mathematics courses. Additionally, the curriculum topics will be supplemented by web-based practice of skills necessary for college placement exams.Graphing calculator (TI-83 or TI-84) is highly recommended because it is used extensively.

Research Methods & Pre-Calculus Honors (2045)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grades: 11-12 Honors

Prerequisite: Past academic performance in Honors Advanced Math I or Advanced Math I and teacher recommendation. Must also be enrolled in Research Topics and Honors Chemistry. A placement test may be used.

This Pre-Calculus course formalizes and extends important mathematical ideas drawn from the four strands of Algebra and Functions, Geometry and Trigonometry, Statistics and Probability and Discrete Mathematics. The focus will be on the Mathematics needed to be successful in college mathematics, Statistics, or Calculus courses. Topics studied will include the fundamental concepts underlying calculus and their applications including: rate of change, modeling motion, logarithmic, polynomial, and rational functions, conic sections. Emphasis will also be placed on manipulating symbolic representations of polynomial, rational, exponential, logarithmic, and trigonometric functions. Students who successfully complete this rigorous course are ready for Advanced Placement Calculus AB, Advanced Placement Calculus BC, or Advanced Placement Statistics. This course will also incorporate research methods in Math and Science. Students will be required to complete a yearlong research project in the field of Math and/or Science under the guidance of their teachers. A graphing calculator (TI-83 or TI-84) is recommended because it is used extensively.

PreCalculus (2017T)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grades: 11-12 A Level

Prerequisite: Past academic performance in Advanced Math I, Honors Advanced Math I, or Advanced Math IB & Functions & Trigonometry and teacher recommendation.

PreCalculus Honors (2018TT)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grades: 11-12 Honors

Prerequisite: Past academic performance in Algebra & Geometry II/Advanced Math I Honors, Advanced Math I Honors or Advanced Math I and teacher recommendation. A placement test may be used.

This Pre-Calculus course formalizes and extends important mathematical ideas drawn from the four strands of Algebra and Functions, Geometry and Trigonometry, Statistics and Probability and Discrete Mathematics. The focus will be on the Mathematics needed to be successful in college mathematics, Statistics, or Calculus courses. Topics studied will include the fundamental concepts underlying calculus and their applications including: rate of change, modeling motion, logarithmic, polynomial, and rational functions, conic sections. Emphasis will also be placed on manipulating symbolic representations of polynomial, rational, exponential, logarithmic, and trigonometric functions. Students who successfully complete this rigorous course are ready for Advanced Placement Calculus AB, Advanced Placement Calculus BC, or Advanced Placement Statistics. A graphing calculator (TI-83 or TI-84) is highly recommended because it is used extensively.

Advanced Quantitative Reasoning (2037T)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grade: 12 A-level

Prerequisite: Advanced Math I and PreCalculus or Advanced Math I and Functions & Trigonometry and teacher recommendation.

This course offers a problem-based curriculum using a range of applied contexts while helping students develop college and career readiness skills such as collaborating, conducting research, and making presentations. We will build on, reinforce, and extend what students have learned in previous math courses, as well as cover a range of new mathematics topics, including probability, data science and statistical studies, finance, functions, and numerical analysis. Additionally, the curriculum topics will be supplemented by web-based practice of skills necessary for college placement exams. The TI83 or TI84 graphing calculator is highly recommended.

Advanced Quantitative Reasoning Honors (2038T)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grade: 12 Honors

Prerequisite: PreCalculus or Pre-Calculus Honors and teacher recommendation.

This course offers a project-based curriculum using a range of applied contexts while helping students develop college and career readiness skills such as collaborating, conducting research, and making presentations. This course is for advanced seniors who are interested in exploring how to analyze, think critically about and reason with data. There are a lot of careers that students will study in college that require them to manage and make interpretations about data. This course will support students to make models, interpretations and predictions for problems that are relevant in a wide variety of applications. Additionally, the curriculum topics will be supplemented by web-based practice of skills necessary for college placement exams. The TI83 or TI84 graphing calculator is highly recommended.

Calculus Honors (2021)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grade: 12 Honors

Prerequisite: Past academic performance in PreCalculus or PreCalculus Honors and teacher recommendation. A placement test may be used.

A firm foundation in calculus is necessary for pursuing careers in science, mathematics, business, and some social sciences. This course is designed for advanced seniors who want to continue their studies along the Calculus pathway, but are not interested in taking an Advanced Placement Exam. The student must have a strong background in trigonometry, coordinates, graphs, lines, functions, and algebraic manipulations. Topics include: functions and limits, differentiation, applications of differentiation, integration, applications of the definite integral, logarithmic and exponential functions, inverse and hyperbolic functions, and techniques of integration. Graphing calculator (TI-83 or TI-84) is highly recommended because it is used extensively. Summer work to review prerequisite material may be assigned (recommended but not required).

Advanced Placement Statistics (2023)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grade: 11-12 Advanced Placement

Prerequisite: Past academic performance in Advanced Math I Honors, PreCalculus Honors or PreCalculus, strong teacher recommendation, successful completion of summer work.

This course will investigate the major concepts and tools for collecting, analyzing, and drawing conclusions from data. The four major conceptual themes are: 1) Exploring Data: Interpreting and analyzing graphical displays and descriptive statistics, 2) Sampling & Experimentation: Planning and conducting observational studies and experiments, 3) Probability and Simulation: Exploring random phenomena, and 4) Statistical Inference: Estimating population parameters and testing hypotheses. Summer work and an end-of-year project are required. Students are expected to take the AP exam in the spring. The focus throughout the year will be on preparation for the AP exam, with the goal of completing the curriculum with the rigor of a college level course. The TI-83/84 graphing calculator will be used extensively.

Advanced Placement Calculus AB (2022)

Meets Expectations for Student Learning: 1,2,3,4,7,8

Elective Full Year Grade: 12 Advanced Placement

Prerequisite: Past academic performance in PreCalculus Honors, strong teacher recommendation, and successful completion of summer work. A placement test may be used.

A firm foundation in calculus is necessary for pursuing careers in science, mathematics, business, and some social sciences. AP Calculus should provide the building materials for success on the advanced placement exam, thus enabling those students who successfully complete this course to begin their college careers on firm footing. In order to have a successful year students must understand that calculus will involve a great deal of their time and energy during the year and in preparation for the AP exam. Topics to be studied include polynomial, trigonometric, logarithmic, and exponential functions and their graphs; limits; differentiation; integration; applications of each of these; definite integrals; and techniques of integration. A TI83 or TI84 graphing calculator is required. Summer reading and/or a special project may be required. Students are expected to take the Advanced Placement Exam in May.

Advanced Placement Calculus BC (2025)

Meets Expectations for Student Learning: 1,2,3,4,7,8

Elective Full Year Grade: 12 Advanced Placement

Prerequisite: Past academic performance in PreCalculus Honors, strong teacher recommendation, and successful completion of summer work. A placement test may be used.

A firm foundation in calculus is necessary for pursuing careers in science, mathematics, business, and some social sciences. AP Calculus BC should provide the building materials for success on the advanced placement exam, thus enabling those students who successfully complete this course to begin their college careers on firm footing. In order to have a successful year, students must understand that calculus will involve a great deal of their time and energy during the year and in preparation for the AP exam. Topics to be studied include polynomial, trigonometric, logarithmic, and exponential functions and their graphs; polar and parametric curves; limits; differentiation; integration; applications of each of these; definite integrals; basic and advanced techniques of integration; series. Summer reading and/or a special project may be required. Students are expected to take the Advanced Placement Exam in May. A graphing calculator (TI-83 or TI-84) is highly recommended because it is used extensively.

Mathematical Modeling Honors (2039)

Meets Expectations for Student Learning: 1,2,3,4,5,6,7

Elective Full Year Grade: 12 Honors

Prerequisite: Completed or currently taking an AP Calculus course.

This course will introduce topics typically studied in undergraduate mathematics courses, such as Advanced Problem Solving, Number Theory and Linear Algebra. The course will be centered around problem-based learning where students will collaborate about and investigate topics through open-ended problem solving and computer simulations (using a software program such as Mathematica). Students will develop and use mathematical models to approach real-world problems across discipline areas. This course is meant for students who enjoy solving challenging mathematical problems and who are interested in learning strategies and background information for solving these problems. This course is for seniors who are currently enrolled in an AP Calculus course or for students who have already completed an AP Calculus course.

Math Internship (2026)

Meets Expectations for Student Learning: 1,2,3,4,7,8

Elective Semester Grades: 10-12 A Level

Prerequisite: Past academic performance in Advanced Math I, Advanced Math I Honors, PreCalculus or PreCalculus Honors and strong teacher recommendation.

Students will be assigned by the department director to work in an underclassmen class as an assistant to the teacher in that class. Interns will assist in their assigned class by helping students as needed with their questions on class work. The teacher may ask interns to facilitate work with small groups of students or create study guides and review materials with or for students. The intern may also assist students with the creation and organization of their notebooks and mathematics toolkits. Students who participate in this program will meet with their cooperating teacher and will complete monthly feedback forms. The grade for this class will be a pass/fail grade determined by attendance and the feedback forms completed by both the teacher and student.

Essential Math 9/10 (9902)

Meets Expectations for Student Learning: 1,2,3,4,6,7

Prerequisite: Permission of Instructor

This course, which features smaller class sizes and more individualized learning experiences, is designed to improve the student's critical thinking and reasoning skills to master a variety of concepts and independent life skills related to practical math applications. Students will demonstrate acquisition of skills by applying their knowledge to varied practical math and consumer math concepts including rational numbers, percents, decimals, and word problems. Important ideas are regularly reviewed and include Patterns of Change, Linear Models, Patterns in Data and Geometry.

Essential Math 11/12 (9902)

Meets Expectations for Student Learning: 1,2,3,4,6,7

Prerequisite: Permission of Instructor

This course, which features smaller class sizes and more individualized learning experiences, is designed to improve the student's critical thinking and reasoning skills to master a variety of concepts and independent life skills related to practical math applications. Students will apply their knowledge to varied practical math and consumer math concepts including whole numbers, percents, decimals, and word problems. Students will be introduced and exposed to areas that include banking, budgeting, money application and salary, job exploration, career development, job attainment, basic skills needed on the job, and skills related to self-development and other necessary life skills.