Departments & Curriculum
Course Description Guide 2021-22

# Math (2021-22)

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

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
• #### Geometry - Grades 8-10

1 Credit
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 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
Lines
Angles
Congruent Triangles
Relationships in Triangles
Proportions and Similarity
Right Triangles and Trigonometry
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
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
Polynomials and Polynomial 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
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

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
Venn Diagrams and the Real Number System
Algebra Fundamentals
Counting and Probability
Scatter Plots and Linear Models
Basic Functions and Graphs
Systems of Equations
Sequences and Series
• #### 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
Banzai Financial Literacy

## 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 Maths: Analysis 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 Standard Level 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)
Statistics
Probability
Trigonometry
Calculus
Modelling
• #### 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 Pre-Calculus 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 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 Maths: Analysis and Approaches SL/AP Calculus BC - Grade 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 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: 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 4 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
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
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
• #### The Art of Problem Solving - Grades 10-12

.5 Credit
Prerequisites: Geometry and 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
• #### Research and Writing in Mathematics - Grades 10-12

.5 Credit
Prerequisites: Honors level in Math and English

Research and Writing in Mathematics is a semester-long course that is designed to enhance students’ proficiency in reading, research, and writing in mathematics; this will also improve their reading comprehension in scientific fields that are closely related to mathematics. Students will learn how to efficiently and quickly read mathematical and/or scientific text while gaining a deep understanding of the material. Students will go on to learn how to research in mathematics, as well as how to write a mathematical paper. The course will end with a research project of each students’ choice, which will include researching the topic, writing an exposition on the topic, and a short presentation. This course is perfect for those students who may go on to study math, science, or a related field in college. Students should be ready to work hard, learn to think in new ways, and have fun researching topics that interest them.

Units of Study
Writing in Mathematics
Research in Mathematics
Independent Research Project

## 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 Research & Writing in Mathematics

## Trinity Episcopal School

3850 Pittaway Drive | Richmond, Virginia 23235 Phone: 804.272.5864 Fax: (804) 320-1362  Email: mail@trinityes.org