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Course Description Guide 2019-20

Math (2019-20)

The primary purpose of the Mathematics Department is to enable students to acquire the mathematical skills, understandings and attitudes that they will need to be successful in college, their careers and their daily lives. Trinity's approach is designed to help students understand the connections between mathematics and other disciplines. Trinity believes in teaching math as a way of thinking and seeing, working to develop an appreciation for logic, and for the applications of mathematics in the real world. It is Trinity's goal to have students view mathematics as achievable, fun, useful and interesting. The Mathematics Department believes that anybody can be a "math person," given the right approach to the subject.

Students are required to take Math each year. Algebra 1, Geometry, and Algebra 2 are required. Scroll down for course sequence.

Math

List of 10 items.

  • Algebra 1 - Grades 8-9

     
    1 Credit
    Prerequisite: Pre-algebra course.  A strong background with fractions, decimals, signed numbers, and the four operations of addition, subtraction, multiplication and division is essential.
    Required Tools: A four function calculator

    This course presents the basic structure and techniques of Algebra. A balance is sought between learning concepts and skills and applying them to real life problems. Graphing calculators are not allowed in this class, as students are expected to develop a strong understanding of these basic building blocks of all mathematical courses to follow Algebra. Students will learn and be assessed through the use of a variety of materials including, textbook, worksheets, an IXL account, frequent review games and activities, creative projects, quizzes, and tests. The goal for this class is to have students emerge with a confidence in the basic mathematical skills that they will continue to use throughout all other sequential math courses.

    Units of Study
    Expressions, Equations, and Functions
    Properties of Real Numbers
    Solving Linear Equations
    Graphing Linear Equations and Functions
    Writing Linear Equations
    Solving and Graphing Linear Inequalities
    Systems of Equations and Inequalities
    Exponent Rules
    Polynomials and Factoring
    Quadratic Equations
  • Geometry - Grades 8-10

    1 Credit
    Required Tools:  Scientific calculator, compass, protractor

    This course presents the basic structure of geometry. Emphasis is placed on logical thinking and developing critical thinking skills. The student gains an understanding of coordinate geometry and thus recognizes how geometry and algebra complement one another by applying previously learnt algebraic topics to geometric problems. The course strives to integrate the usefulness of geometry and apply it to multiple situations in a way that gives visual meaning to mathematics.

    Units of Study
    Linear and Quadratic Equations
    Lines
    Angles
    Congruent Triangles
    Relationships in Triangles
    Proportions and Similarity
    Right Triangles and Trigonometry
    Quadrilaterals
    Circles
    Area
    Surface Area and Volume
  • Geometry Honors - Grades 8-10

    1 Credit
    Prerequisite: Teacher recommendation. Strong analytical skills and a commitment to learning are essential.
    Required Tools: TI-84 Plus Series calculator

    This course is an honors level course that presents the basic structure of geometry. Emphasis is placed on logical thinking and developing thinking skills. The student gains an understanding of coordinate geometry and thus recognizes how geometry and algebra complement one another. The course strives to integrate its applications and apply it to situations. It is a challenging course that gives visual meaning to mathematics. The distinction between this course and standard level Geometry is the pacing and depth at which the content is covered.

    Units of Study
    Points, Lines, and Planes
    Reasoning and Proof
    Parallel and Perpendicular Lines
    Congruent Triangles
    Relationships in Triangles
    Proportions and Similarity
    Trigonometry
    Quadrilaterals
    Circles
    Area
    Surface Area
    Volume
  • Algebra 2 / Trigonometry - Grades 9-12

    1 Credit
    Required Tools: TI-84 Plus Series calculator

    This course is designed to continue and expand the concepts from Algebra 1, as well as introduce new topics in preparation for the more advanced math courses. A balance is sought between learning concepts and skills and applying them to real life problems. Varying materials, such as the textbook, worksheets, websites, review games and activities, IXL account, creative projects, quizzes and tests, will be used to reinforce, enrich, and assess student learning throughout this course. The graphing calculator will be used within this course, but will not be a substitute for paper and pencil methods; instead, it will supplement and enforce student learning and aid in the retention of concepts that are being taught. The goal for students taking Algebra 2 is to gain confidence in their ability to think logically, problem solve and understand mathematical content that they will use again in sequential math courses beyond Algebra 2.

    Units of Study
    Equations and Inequalities
    Linear Equations and Functions
    Linear Systems and Matrices
    Quadratic Functions and Factoring
    Polynomials and Polynomial Functions
    Rational Exponents and Radical Functions
    Exponential and Logarithmic Functions
    Rational Functions
    Trigonometric Ratios and Functions
  • Algebra 2/ Trigonometry Honors - Grades 9-12

    1 Credit
    Prerequisite:  B+ or higher in Honors Geometry or teacher recommendation. The ability for higher order abstract reasoning and a commitment to learning are critical.
    Required Tools: TI-84 Plus Series calculator

    This course is designed to prepare students for Honors Pre-Calculus. Content is organized around families of functions including linear, quadratic, higher degree polynomial, exponential, logarithmic, radical, rational, and trigonometric. Students will learn to work with functions in multiple ways including graphic representation, equations, verbal models, and tables. We will focus on modeling real-world situations using functions in order to solve real-world problems in every unit. Most units will require work without the use of a graphing calculator. When the student has demonstrated mastery without the calculator, calculators will be allowed on select sections. Students will be asked to use online support such as Desmos, WolframAlpha, Khan Academy, etc. to supplement the textbook.

    Students are expected to be highly motivated to learn and must be committed to staying current with daily work, both in and out of class. Students should be prepared to seek help from available resources when additional support is needed and must maintain a grade of C or higher to remain in the Honors level course.  The pace of this class is considerably faster than the standard level Algebra 2/Trigonometry course and includes a higher level of difficulty of problem-solving.

    Units of Study
    Algebraic Equations and Inequalities
    Linear Equations, Functions, and Transformations
    Systems of Equations
    Matrices
    Quadratic Functions
    Properties of Exponents
    Polynomials and Higher Degree Polynomial Functions
    Exponential and Logarithmic Functions
    Rational Functions
    Sequences and Series
    Trigonometric Functions
    Introduction to Probability and Statistics
  • Pre-Calculus - Grades 10-12

    1 Credit
    Prerequisites: Algebra 2/Trigonometry and teacher recommendation
    Required Tools: TI-84 Plus Series calculator

    This course is designed to prepare students for calculus. Precalculus relies on the foundational skills and completes the formal study of the elementary functions begun in Algebra 1 and Algebra 2. Topics previously learnt in Algebra 2 will be reviewed and expanded upon to further examine the inner-workings of the processes to prepare for more complex studies in mathematics. The information in this course will prepare students for multiple course paths, including statistics and/or calculus.  Students must be committed to daily work, both in and out of class.

    Units of Study
    Functions and Their Graphs
    Polynomial and Rational Functions
    Exponential and Logarithmic Functions
    Matrices
    Sequences and Series
    Trigonometric Functions
    Trigonometric Identities
    Laws of Sines and Cosines
    Graphs of Trigonometric Functions
    Conic Sections
    Probability and Counting Principles
    Limits
  • IB Maths: Analysis/Pre-Cal H (Grade 11) OR Pre-Calculus Honors (Grade 10)

    1 Credit
    Prerequisite: Grade of B or higher in Algebra 2/Trig Honors or approval of math teacher and department head. Good understanding of mathematical foundational skills and concepts and a strong commitment to doing nightly assignments are essential for success in this course.
    Required Tools:  TI-84 Plus Series calculator

    This course is designed to prepare students for AP or regular Calculus as well as IB Mathematics:  Analysis and Approaches SL. It is a comprehensive course that weaves together previous study of algebra, geometry, trigonometry, and functions in preparation for calculus. The course focuses on the mastery of critical skills and exposure to new skills necessary for success in subsequent math courses. The pace is rapid and students are expected to read sections of the book when they need additional explanation. Students must be committed to daily work, both in and out of class. The course will have many "no calculator" units. The distinction between this course and Standard level Pre-Calculus is the pacing and depth at which the content is covered.

    Students must maintain a grade of C or higher to remain in the Honors level course.

    Units of Study
    Functions and their Graphs
    Polynomial and Rational Functions
    Exponential and Logarithmic Functions
    Matrices
    Sequences and Series
    Binomial Expansion
    Conic Sections
    Trigonometry
    Vectors
    Probability
    Statistics
    Intro to Differential Calculus
  • Calculus - Grades 11-12

    1 Credit
    Prerequisites: Pre-Calculus and teacher recommendation
    Required Tools: TI-84 Plus Series calculator

    Students will receive a solid foundation for taking college level math. The course will progress similarly to a college level class and will explore both calculus and statistics in real life applications. The course begins with a review and an extension of pre-calculus skills, and ends with a transition into statistics. The course includes nightly homework and weekly quizzes or tests.

    Units of Study
    Review of Pre-Calculus
    Limits and Their Properties
    Derivatives
    Applications of Derivatives
    Logs, Exponents, Transcendental Functions: Derivatives
    Integrals
    Logs, Exponents, Transcendental Functions: Integrals
    Differential Equations and Volume
    Statistics
  • Mathematical Concepts and Applications - Grades 11-12

    1 Credit
    Prerequisites: Algebra 2/Trigonometry and teacher recommendation
    Required Tools:TI-84 Plus Series calculator

    This course is designed as an alternative for the student not planning to study calculus or for the student wanting foundational reinforcement before heading into a higher level math course.  Emphasis will be placed on strengthening fundamentals and applying mathematics to real-life situations involving probability and data analysis. Students learn by examples, practice sets, hands-on activities, online activities, and group work.  Keys to success in this course include: keeping an organized notebook, using good note taking skills, applying strong effort when completing assignments, and seeking help quickly when needed.

    Units of Study
    Real Number System
    Algebra Fundamentals
    Counting and Probability
    Sequences and Series
    Operations with and Factoring Polynomials
    Basic Functions and Graphs
    Scatter Plots and Linear Models
    Quadratic Functions and Models
    Systems of Equations
    Exponential and Logarithmic Functions
     
  • Introduction to Statistics - Grades 11-12

    1 Credit
    Prerequisite: Algebra 2/Trigonometry
    Required Tools: TI-84 Plus Series calculator

    Introduction to Statistics is a course designed to give students a feel for what the course of statistics is about and give them a strong foundation for any college level introductory statistics course. Most learning is done through traditional lectures with practice problem homework assignments. Hands-on activities and experiments will be done to demonstrate certain topics as time permits. Memorization of formulas and definitions is not required. Students may use notecards on tests and quizzes.  This course is excellent preparation for students with an interest in business, science, education, law, computer science, and related fields.

    Units of Study
    An Introduction to Statistics
    Describing Data Using Graphs and Tables
    Describing Data Numerically
    Describing the Relationship Between Two Variables
    Probability
    Random Variables
    Sampling Distributions
    One Sample Confidence Intervals
    Hypothesis Testing
    Two Sample Inference Methods
    Chi-Squared Tests and Regression Inference

IB and AP Math

List of 4 items.

  • IB Mathematical Studies SL - Grades 11-12

    1 Credit
    Prerequisites: Juniors or Seniors who are full IB diploma candidates and have completed an Algebra 2/Trigonometry or higher math course and teacher recommendation
    Required Tools:  TI-84 Plus or TI-85 Series calculator
    Additional Fee: Students in this course are expected to take the IB exam.  A fee applies to all students taking this exam.
    This course will be discontinued after 2019-2020.

    Mathematical Studies caters to students with varied backgrounds and abilities in the IB diploma program. It offers students opportunities to learn important concepts and techniques and to gain an understanding of a wide variety of mathematical topics. The nature of mathematical studies is such that it concentrates on mathematics that can be applied to contexts related, as far as possible, to other curriculum subjects and to common general occurrences. There is an emphasis on developing students’ mathematical reasoning, enhancing critical thinking, solving mathematical problems embedded in a wide range of contexts, and using the calculator effectively. A requirement within this course is the project: a written piece of work based on personal research involving the collection, analysis and evaluation of data. This course prepares the student for the required Standard Level IB examination in Mathematical Studies. Students most likely to select this subject are the ones whose main interests lie outside the field of mathematics.

    Units of Study
    Numbers and Algebra
    Descriptive Statistics
    Logic, sets and probability
    Statistical applications
    Geometry and trigonometry
    Mathematical models
    Introduction to Differential Calculus
  • IB Mathematics SL/AP Calculus AB - Grades 11-12

    1 Credit
    Prerequisite: Teacher recommendation based on the expectation of B+ or higher in Pre-Calculus Honors or IB Mathematics/Pre-Calculus Honors. An ability to understand abstract mathematical concepts and a strong work ethic are necessary to be a student in these courses.
    Required Tools: TI-84 Plus Series calculator
    Additional Fee: Students in this course are expected to take the AP and/or the IB exams. A fee applies to all students taking these exams.

    The course closely follows the recommendations of the Committee on Mathematics of the Advanced Placement Program (AB syllabus) as well as covering topics inherent to the IB Mathematics program. This course is designed to help students develop a conceptual understanding of college–level calculus content, as well as proficiency in the skills and practices needed for mathematical reasoning and problem solving.  Skills developed in this class are reasoning with definitions and theorems, connecting concepts, implementing algebraic/computational processes, connecting multiple representations, building notational fluency, and communicating. The pace is rapid and students are expected to read sections of the book when they need additional explanation. Students must be committed to daily work, both in and out of class. The course will have many "no calculator" units. The distinction between this course and Standard level Calculus is the pacing and depth at which the content is covered.

    Units of Study
    Limits
    Derivatives
    Implicit Differentiation and Related Rates
    Application of differentiation/curve sketching/optimization
    Integration and accumulation, Fundamental Theorem of Calculus
    Transcendental Functions – derivatives and integrals
    Differential equations/slope fields
    Area/volume of revolution – Application of Integration
  • IB Mathematics SL/AP Calculus BC - Grade 12

    1 Credit
    Prerequisites: Teacher recommendation based on the expectation of B or higher in IB Mathematics SL/AP Calculus AB, and a B+ or better in Pre-Calculus Honors
    Required Tools: TI-84 Plus Series calculator
    Additional Fee: Students in this course are expected to take the AP and/or the IB exams. A fee applies to all students taking these exams.

    This course is designed to prepare the student for taking the IB Mathematics SL and AP Calculus BC exams in the spring. Students will be exposed to previous IB an AP exam problems. Students who plan to take the IB Mathematics SL exam must also complete a mathematical exploration, which is a piece of written work that investigates an area of mathematics of their choice.  The pace is rapid and students are expected to read sections of the book when they need additional explanation.

    Units of Study
    Differential Calculus
    Integration
    Differential Equations
    Series Convergence
    Polar and Parametric Coordinates
    Functions, Equations and Binomial Expansion
    Circular Functions and Trigonometry
    Statistics and Probability
    Vectors
  • AP Statistics - Grades 10-12

    1 Credit
    Prerequisites: Teacher recommendation
    Required Tools: TI-84 Plus Series calculator
    Additional Fee: Students in this course are expected to take the AP exam.  A fee applies to all students taking this exam.

    This course closely follows the recommendations of the Committee on Statistics of the Advanced Placement Program. While the class is in the mathematics department, 99% of computation is done on the calculator. The class emphasizes discussion of these calculations and the meaning of the numbers. Most learning is done through traditional lectures with practice problem homework assignments. Activities and experiments are done for demonstration of concepts where appropriate and time permitting.  A successful student will have strong reading comprehension and good number sense.

    Units of Study
    Displaying Data
    Modeling Distributions
    Least Squares Regression
    Designing Studies
    Probability
    Random Variables
    Sampling Distributions
    One Sample Confidence Intervals
    One Sample Hypothesis Tests
    Comparing Two Populations or Groups
    Chi-Squared Tests
    Regression Inference and Transformations

Math Electives

List of 2 items.

  • AP Statistics - Grades 10-12

    1 Credit
    Prerequisites: Algebra 2 or Algebra 2 Honors with a grade of B or higher and English grade of B or higher
    Required Tools: TI-84 Plus Series calculator
    Additional Fee: Students in this course are expected to take the AP exam.  A fee applies to all students taking this exam.

    This course closely follows the recommendations of the Committee on Statistics of the Advanced Placement Program. While the class is in the mathematics department, 99% of computation is done on the calculator. The class emphasizes discussion of these calculations and the meaning of the numbers. Most learning is done through traditional lectures with practice problem homework assignments. Activities and experiments are done for demonstration of concepts where appropriate and time permitting.  A successful student will have strong reading comprehension and good number sense.

    Units of Study
    Displaying Data
    Modeling Distributions
    Least Squares Regression
    Designing Studies
    Probability
    Random Variables
    Sampling Distributions
    One Sample Confidence Intervals
    One Sample Hypothesis Tests
    Comparing Two Populations or Groups
    Chi-Squared Tests
    Regression Inference and Transformations
  • Introduction to Statistics - Grades 11-12

    1 Credit
    Prerequisite: Algebra 2/Trigonometry
    Required Tools: TI-84 Plus Series calculator

    Introduction to Statistics is a course designed to give students a feel for what the course of statistics is about and give them a strong foundation for any college level introductory statistics course. Most learning is done through traditional lectures with practice problem homework assignments. Hands-on activities and experiments will be done to demonstrate certain topics as time permits. Memorization of formulas and definitions is not required. Students may use notecards on tests and quizzes.  This course is excellent preparation for students with an interest in business, science, education, law, computer science, and related fields.

    Units of Study
    An Introduction to Statistics
    Describing Data Using Graphs and Tables
    Describing Data Numerically
    Describing the Relationship Between Two Variables
    Probability
    Random Variables
    Sampling Distributions
    One Sample Confidence Intervals
    Hypothesis Testing
    Two Sample Inference Methods
    Chi-Squared Tests and Regression Inference

Course Sequence

Math Core Courses

Level 1 Level 2 Level 3 Level 4 Level 5 Level 6
Algebra 1 Geometry Honors Algebra 2/Trigonometry Honors IB Maths:  AnalysisPre-Calculus Honors IB Mathematics SL/AP Calculus AB IB Mathematics SL/AP Calculus BC
Pre-Calculus Honors IB Mathematical Studies SL
Geometry Algebra 2/Trigonometry Pre-Calculus Calculus
Math Concepts
Introduction to Statistics


Math Electives

Grades 10-12 Grades 11-12
AP Statistics Introduction to Statistics