# Upper School

# Mathematics

##### Math 7

Seventh Grade Math is a first year, Pre-Algebra level course designed to help students begin a 2-year transition to Algebra 1. One of the main purposes of this course is to assure that students have a solid foundation with all elementary topics in general math. Students will be well prepared for advancement into Algebra 1.

Units of Study (aligned to the Math Benchmarks for the State of Ohio)

- Integers
- Rational and Irrational Numbers
- Order of Operations
- Expressions and Functions
- Inequalities and equations
- Elementary Geometry, areas, volumes, angles
- Statistics and Probability
- Proportions
- Solve Real World Problems
- Analyze Sets of Data

##### Math 8

This course was introduced to CTA in 2013-14 for the purpose of more readily accommodating the new state standards. It is meant as an important second course in Pre-Algebra mathematics that will afford the students a more knowledgeable and thus smoother transition into Algebra. The topics covered, while somewhat similar to those of Math 7, indeed are explored and worked with on a broader and more in-depth level. Familiar topics such as those working within the Number System, those related to Expressions and Equations, and ones covered in basic Geometry are dealt with on a more abstract level. Alternate strategies are used to analyze topics both qualitatively and quantitatively. All of the lessons and student work are in accord with Common Core Math practices.

*Text:*

Title: Go Math (Grade 8)

Authors: Larson, Kanold, et al.

Publisher: Houghton Mifflin Harcourt, 2014

*Units of Study:*

- Real Numbers
- Exponents
- Proportional / Non-proportional Relationships
- Linear Equations
- Functions
- Systems of Equations
- Transformations with Congruence / Similarity
- Angle Relationships
- Triangles
- Pythagorean
- Volume

##### Algebra I

Course Description:

This course focuses on graphical representations and algebraic methods applied to linear and quadratic equations. Throughout the year emphasis will be placed on maintaining strong arithmetic skills while developing and maintaining fundamental algebraic skills. Emphasis will also be placed on the application and practice of the Common Core Standards: making sense of problems and persevering in solving them, reasoning abstractly and quantitatively, modeling with mathematics, using appropriate tools strategically, and looking for and making use of structure and patterns.

Units of Study:** **

Unit 1 Relations between Quantities

- Expressions, Equations, Inequalities and Functions
- Literal Equations, Dimensional Analysis, and Interpreting Graphs
- Arithmetic Sequences and Linear Equations

Unit 2 – Linear Relationships

- Linear Functions
- Equations of Linear Functions
- Linear Inequalities
- System of Linear Equations and Inequalities

Unit 3 – Exponential and Quadratic Relationships

- Exponents and Exponential Functions
- Geometric Sequences
- Quadratic Expressions and Equations
- Quadratic Functions and Equations

##### Algebra II

Course Description:

This course provides students an opportunity to expand their understanding of the basic algebraic concepts of equations, inequalities, systems of equations and inequalities, and graphs. The students will use graphing calculators to explore the behavior of polynomial, exponential, and logarithmic functions. They will learn to find the roots and zeros of functions by graphing, factoring, using the quadratic formula, and synthetic division. This course also covers radicals, complex numbers, trigonometric functions, and the unit circle. Students will explore how functions behave using calculators, online graphing calculators, and spreadsheets.

Units of Study:

Unit 1 – Polynomials, Radicals and Complex Numbers

- Exponent Rules
- Adding/Subtracting/Multiplying/Dividing Polynomials
- Remainder and Factor Theorems
- Adding/Subtracting/Multiplying/Dividing Radicals
- Imaginary and Complex Numbers

Unit 2 – Quadratic Equations

- Factoring Quadratic Equations
- Quadratics in Real Life

Unit 3 – Polynomial Functions

- Function Notation
- Composite and Inverse Functions
- Graphs of Functions and their Transformations
- Solving Polynomial Functions by Graphing and in Factored Form

Unit 4 – Systems of Equations

- Solving Linear-Linear Systems
- Solving Quadratic-Linear Systems
- Solving Systems by Graphing
- Linear Systems in Three Variables

Unit 5 – Rational, Exponential and Logarithmic Functions

- Simplifying Rational Functions
- Adding/Subtracting/Multiplying/Dividing Rational Functions
- Exponential Functions
- Logarithmic Functions, Common Log and Natural Log
- Exponential/Logarithmic Functions in Real Life

Unit 6 – Trigonometric Functions

- Six Trigonometric Ratios
- Angle Rotations and Radians
- The Unit Circle
- Trigonometric Identities

Unit 7 – Sequences and Series

- Recursive and Explicit Sequences
- Arithmetic Sequences and Series
- Geometric Sequences and Series

##### Algebra II with Trigonometry

Course Description:

This course provides students an opportunity to expand their understanding of the basic algebraic concepts of equations, inequalities, systems of equations and inequalities, and graphs. The students will use graphing calculators to explore the behavior of polynomial, exponential, and logarithmic functions. They will learn to find the roots and zeros of functions by graphing, factoring, using the quadratic formula, the rational roots theorem, and synthetic division. This course also covers radicals, complex numbers, conic sections, trigonometric functions, and the unit circle. Algebra II with Trigonometry is designed to prepare students for pre-calculus and calculus.

Units of Study:

Unit 1 – Polynomials, Radicals and Complex Numbers

- Exponent Rules
- Adding/Subtracting/Multiplying/Dividing Polynomials
- Remainder and Factor Theorems
- Adding/Subtracting/Multiplying/Dividing Radicals
- Imaginary and Complex Numbers

Unit 2 – Quadratic Equations

- Factoring Quadratic Equations
- Quadratics in Real Life

Unit 3 – Polynomial Functions

- Function Notation
- Composite and Inverse Functions
- Graphs of Functions and their Transformations
- Solving Polynomial Functions by Graphing and in Factored Form

Unit 4 – Systems of Equations

- Solving Linear-Linear Systems
- Solving Quadratic-Linear Systems
- Solving Systems by Graphing
- Linear Systems in Three Variables

Unit 5 – Rational, Exponential and Logarithmic Functions

- Simplifying Rational Functions
- Adding/Subtracting/Multiplying/Dividing Rational Functions
- Exponential Functions
- Logarithmic Functions, Common Log and Natural Log
- Exponential/Logarithmic Functions in Real Life

Unit 6 – Trigonometric Functions

- Six Trigonometric Ratios
- Angle Rotations and Radians
- The Unit Circle
- Trigonometric Identities

Unit 7 – Sequences and Series

- Recursive and Explicit Sequences
- Arithmetic Sequences and Series
- Geometric Sequences and Series

##### Geometry

Course Description:

Geometry is the investigation of shape, size, and visual patterns. The course approaches this investigation with rigorous analysis at an intermediate level while reviewing many of the concepts and mathematical techniques that students have learned from an algebra course. Basic elements of logic are introduced such as conditional statements, converses, and bi-conditionals (definitions). The students will learn much of geometry as it relates to theorems and postulates. Learning how to write formal mathematical proofs is introduced for the first time, and the writing of proofs becomes more challenging as it is stressed throughout the course. Working with quadrilaterals, triangles, and circles is of major importance, and elementary trigonometry as related to right triangles is presented and explored.

Text:

Title: Geometry (Glencoe)

Author: Carter, Cuevas, Day, and Malloy

Publisher: McGraw-Hill, 2012

Units of Study:

- Tools of Geometry
- Set Theory and Logic
- Undefined vs. Defined terms

- Beginning Proofs
- Lines and Angles
- Triangles
- Polygons
- Quadrilaterals (and other polygons)
- Proportions, Similarity, and Congruence

- Right Triangle Trigonometry
- Circles
- Measurement
- Perimeter, area, surface area, volume, etc.

- Transformations

##### Advanced Placement Pre-Calculus

Course Description:

Precalculus is the branch of mathematics which studies a variety of functions and their properties. AP Precalculus is specifically designed to teach students the material taught in the first semester of a college precalculus course. The goal of the class is to appropriately prepare students for higher level college math, including calculus. Students will be taking the coordinating exam in early May, the results of which can determine the amount of college credit they earn.

Texts:

This class has been approved by College Board and will be following the Course and Exam Description as put forth by them, and can be found here: AP Precalculus CED

Additionally, the course will be guided by AP Daily lessons and precalculus.flippedmath.com materials for notes.

**Units of Study:**

**Unit 1**

- Polynomial Functions
- Rational Functions

**Unit 2**

- Exponential Functions
- Logarithmic Functions

**Unit 3**

- Trigonometric Func.
- Polar Functions

**Unit 4** (Not on AP Exam)

- Parametric Functions
- Vectors & Matrices

##### Advanced Placement Calculus AB

Course Description:

Calculus is the branch of mathematics that explores change, limits, and analysis of functions via integration and series. Calculus AB is specifically designed to teach students the material taught in a first semester college calculus course. The goal of the class is to appropriately prepare students to enter college calculus with a strong foundation of the material. Students will be taking the coordinating exam in early May, the results of which can determine the amount of college credit they earn.

Texts:

This class has been approved by College Board and will be following the Course and Exam Description as put forth by them, and can be found here: AP Calculus CED

Additionally, the course will be guided by AP Daily lessons and calculus.flippedmath.com materials for notes.

Units of Study:

**Semester 1:**

- Limits & Continuity
- Basic Differentiation
- Complex Differentiation
- Contextual Applications of Differentiation

**Semester 2:**

- Analytical Applications of Differentiation
- Integration and Accumulation of Change
- Differential Equations
- Applications of Integration

##### Advanced Placement Calculus BC

Course Description:

This is a rigorous course in introductory single variable calculus, divided into roughly one semester of differential calculus and one semester of integral calculus. Students learn standard techniques and apply skills to solving real-world problems in mathematics, physics, engineering, business, and economics. The course is taught with the expectation of students succeeding on the national AP Calculus BC Exam in the late spring. This course is authorized by the College Board Advanced Placement program.

*Text*:

Calculus (AP Edition/4th Edition)

Authors: Finney, Demana, Waits, and Kennedy

Publisher: Prentice-Hall, 2012

*Units of Study:*

- Unit 1: Limits and Continuity
- Unit 2: Differentiation: Definition and Fundamental Properties
- Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
- Unit 4: Contextual Applications of Differentiation
- Unit 5: Analytical Applications of Differentiation
- Unit 6: Integration and Accumulation of Change
- Unit 7: Differential Equations
- Unit 8: Applications of Integration
- Unit 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions
- Unit 10: Infinite Sequences and Series

##### Statistics

Course Description:

Statistics, offered to 12th graders, fulfills a math requirement for the State of Ohio. The course is very language-based. Students who have historically not enjoyed math often like Statistics. Students will read and analyze current articles and advertisements in order to learn how statistics are used and misused in the media. The goal is for students to question how the data were collected, how the information could be biased, and the validity of the conclusions being made from the information available.

Graphing calculators will be an integral part of the learning process. As we move through the different aspects of statistics, students will become more adept in the use of their calculators. In addition to the calculator, other tools to plot data will be used throughout the year including Excel.

Text:

Elementary Statistics: A Step-by-Step Approach by Alan G. Bluman. 9th edition published by McGraw Hill in 2014

Units of Study:

• Chapter 1: The Nature of Probability and Statistics

• Chapter 2: Frequency Distribution and Graphs

• Chapter 3: Data Description

• Chapter 4: Probability and Counting Rules

• Chapter 5: Discrete Probability Distributions

• Chapter 6: The Normal Distribution

• Chapter 7: Confidence Intervals and Sample Size

• Chapter 8: Hypothesis Testing

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