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Course Description Guide 2022-23

Math (2022-23)

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.

The math curriculum at Trinity helps all students 1) become mathematical problem solvers, 2) learn to communicate mathematically, 3) build reasoning skills, and 4) become confident in their own ability. Our course sequence begins with Algebra I. Subsequent courses include Geometry, Algebra II/Trigonometry, Pre-Calculus, Calculus, and Statistics. Beginning with Geometry, both Honors and Standard Level courses are available. Advanced Placement Statistics and Advanced Placement Calculus AB and BC are offered as well. IB Diploma candidates may enroll in IB Maths: Analysis and Approaches and for non-IB Diploma students not pursuing Calculus we offer Advanced Algebra and Statistics as an alternative sequence.

Math

List of 11 items.

  • Algebra 1 - Grades 8-9

    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 the basic building blocks of all mathematical courses. Students will learn and be assessed through the use of a variety of materials including, textbook, frequent review worksheets, and assessments. 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 subsequent math courses.

    Units of Study
    Expressions and 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 8-11

    1 Credit

    Prerequisite: Algebra 1

    Required Tools:  Scientific Calculator: TI 30 or equivalent or better

    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 learned algebraic topics to geometric problems. The course strives to integrate the use of geometry and apply it to multiple situations in a way that gives visual meaning to mathematics.

    Units of Study
    Review of Algebra
    Basic Geometric Definitions
    Logic and Reasoning
    Linear Systems
    Polygons
    Congruent Triangles
    Proportions and Similarity
    Trigonometry
    Quadrilaterals
    Circles
    Area of Polygons and Circles
    Surface Area and Volume of Solids
  • Geometry Honors - Grades 8-10

    1 Credit

    Prerequisite:  Algebra 1 and 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 them 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 9-11

    1 Credit

    Prerequisite: Teacher recommendation

    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 e-textbook, worksheets, websites, review activities,  and assessments, 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 subsequent math courses.
     
    Units of Study
    Linear Equations
    Relations and Functions
    Quadratic Function
    Polynomials and Polynomial Functions
    Inverses and Radical Function
    Exponential and Logarithmic Functions
    Rational Functions
    Trigonometric Functions
  • Algebra 2/ Trigonometry Honors - Grades 9-11

    1 Credit

    Prerequisite: B+ or higher in Honors Geometry or teacher recommendation. The ability for higher-order abstract reasoning and a commitment to learning is critical.

    Required Tools: TI-84 Plus Series calculator

    This course is designed to prepare students for Honors Precalculus. 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 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
    Linear Equations and Inequalities
    Systems of Equations
    Characteristics of Relations and Functions
    Quadratic Functions
    Properties of Exponents
    Polynomials and Higher Degree Polynomial Functions
    Inverse and Radical Functions
    Exponential and Logarithmic Functions
    Rational Functions
    Trigonometric Functions
  • Precalculus - 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 learned 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
    Trigonometric Functions
    Sequences and Series
    Probability and Counting Principles
  • IB Maths: Analysis/Precal H OR Precalculus Honors - Grades 10-12

    1 Credit

    Prerequisite: Grade of B or higher in Algebra 2/Trig Honors or approval of math teacher and department head. A 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 the previous studies 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 both study and learn independently. 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 Precalculus 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
    Sequences and Series
    Binomial Expansion
    Trigonometric Functions
    Probability
    Statistics
    Introduction to Calculus


  • Calculus - Grades 11-12

    1 Credit

    Prerequisites: Pre-Calculus and teacher recommendation

    Required Tools: TI-84 Plus Series calculator

    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. It includes a review and an extension of Precalculus skills, connecting Algebra, Trigonometry, and Geometry. 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 course includes nightly homework and weekly assessments. 

    Units of Study
    Review of Precalculus
    Limits and Their Properties
    Derivatives
    Applications of Derivatives
    Logs, Exponents, Transcendental Functions: Derivatives
    Integrals
    Logs, Exponents, Transcendental Functions: Integrals
    Differential Equations and Volume
  • Advanced Algebra and Mathematical 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
    Set Theory
    Real Number System
    Counting Methods
    Basic Probability
    Polynomials and Factoring
    Rational Expressions and Equations
    Linear Functions and Models
    Quadratic Functions and Models
  • 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
    Analyzing One Variable Statistics
    Describing the Relationships Between Two Variables
    Collecting Data
    Probability
    Random Variables
    Sampling Distributions
    One Sample Confidence Intervals
    Hypothesis Testing
    Sampling Inference Methods
    Chi-Squared Test and Regression Inference
  • AP Statistics - Grades 10-12

    1 Credit
    Prerequisites: Algebra 2 or Algebra 2 Honors with a grade of B or higher and teacher recommendation based on B or higher in current English course.

    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 the 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
    Chi-Squared Tests
    Regression Inference

IB and AP Math

List of 3 items.

  • IB Maths: Analysis and Approaches SL - Grades 11-12

    1 Credit

    Prerequisites: Students who are full IB diploma candidates and have completed a Pre-Calculus course and teacher recommendation

    Required Tools:  TI-84 Plus Series calculator

    Additional Fee: Students in this course are expected to take the IB exam.  A fee applies to all students taking this exam. 

    The IB DP Mathematics: Analysis and Approaches SL course caters to students with varied backgrounds and abilities in the IB diploma programme. It offers students opportunities to learn important concepts and techniques and to gain an understanding of a wide variety of mathematical topics, including Calculus. The focus is on developing important mathematical concepts in a comprehensible, coherent, and rigorous way, achieved by a carefully balanced approach. Students are encouraged to apply their mathematical knowledge to solve problems set in a variety of meaningful contexts. 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 IB examination. Students who select this course will not be taught the AP Calculus curriculum nor take the AP Calculus exam.

    Units of Study
    Number and Algebra (sequences and series, binomial theorem)
    Functions (linear, quadratic, exponential, logarithmic, rational, transformations)
    Geometry and Trigonometry
    Statistics
    Probability
    Calculus
  • IB Maths: Analysis and Approaches SL/AP Calculus AB - Grades 11-12

    1 Credit

    Prerequisite: Teacher recommendation based on the expectation of B or higher in Precalculus Honors or IB Maths: Analysis/Pre-Cal 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 covers 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
    Applications of Differentiation
    Integration 
    Applications of Integration
    Differential Equations
  • IB Maths: Analysis and Approaches SL/AP Calculus BC - Grades 11-12

    1 Credit

    Prerequisites: Teacher recommendation based on the expectation of B or higher in IB Maths: Analysis SL/AP Calculus AB, and a B or better in Precalculus 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: Analysis and Approaches SL and AP Calculus BC exams in the spring. Students will be exposed to previous IB and 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
    Proofs


Math Electives

List of 3 items.

  • AP Statistics - Grades 10-12

    1 Credit
    Prerequisites: Algebra 2 or Algebra 2 Honors with a grade of B or higher and teacher recommendation based on B or higher in current English course.

    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 the 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
    Chi-Squared Tests
    Regression Inference
  • 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
    Analyzing One Variable Statistics
    Describing the Relationships Between Two Variables
    Collecting Data
    Probability
    Random Variables
    Sampling Distributions
    One Sample Confidence Intervals
    Hypothesis Testing
    Sampling Inference Methods
    Chi-Squared Test and Regression Inference
  • The Art of Problem Solving - Grades 10-12

    0.5 Credit

    Prerequisites: Geometry or teacher recommendation

    Designed to introduce students to higher-level mathematics in a fun way, this course seeks to weave together many different aspects of math to create strategies to solve problems, both in and out of the classroom. The course focuses on the study of logic and of problem-solving techniques; students will also be briefly introduced to proof techniques. This course will enhance students’ abilities to problem solve in every class, math or otherwise. To be successful, students should maintain a positive attitude and an open mind.  This is not a traditional math course and students should be prepared to think outside the box, work hard, and have lots of fun!

    Units of Study
    Study of Logic
    Proof Techniques
    Problem Solving Techniques

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 Maths Analysis SL/AP Calculus AB IB Maths Analysis SL/AP Calculus BC
Pre-Calculus Honors IB Maths Analysis SL
Geometry Algebra 2/Trigonometry Pre-Calculus Calculus
Advanced Algebra
Introduction to Statistics


Math Electives

Grades 10-12 Grades 11-12
AP Statistics Introduction to Statistics
The Art of Problem Solving