# Upper School

# Mathematics

##### Math 7

This course is a first-year, Pre-Algebra-level course designed to help students begin a 2-year transition toward Algebra 1. (For more advanced students, this will be their 1 year of Pre- Algebra, and they will progress to a high school Algebra I course in 8th grade.) One of the main purposes of the Math 7 course is to assure that students have a solid foundation with all the basic topics in general math, especially ones most important for elementary algebra and geometry. The course covers the following topics: Adding, Subtracting, Multiplying & Dividing integers; Rational Numbers; Rates and Proportional Relationships; Ratios, Proportions, and Percent; Expressions and Equations; Inequalities; Modeling Geometric Figures; Circumference, Area and Volume; and an introduction to Elementary Probability and Statistics. This course follows Ohio’s standards for mathematics, and the lessons and student work are all in accordance with Common Core Math practices. 7th-grade math includes in-class assignments, independent work, homework assignments, hands-on math projects and experiences, and applications to real-world examples. Some time is spent preparing students for the standardized state test in the Spring.

Text:

Title: Go Math (Grade 7)

Authors: Burger, Dixon, Kanold, etc.

Publisher: Houghton Mifflin Harcourt

Units of Study:

• Adding, Subtracting, Multiplying & Dividing integers

• Rational Numbers

• Rates and Proportional Relationships

• Ratios, Proportions and Percent

• Expressions and Equations

• Inequalities; Modeling Geometric Figures

• Circumference, Area and Volume

• Elementary Probability and Statistics

##### 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.

Text:

Title: Algebra 1, Common Core Edition

Author: Carter, Cuevas, Day, Malloy, Casey, Holliday, Luchin

Publisher: Glenco/McGraw-Hill, Inc. 2014

Units of Study:

Unit 1 – Relations between Quantities

● Expressions, Equations, and Functions

● 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

● Quadratic Expressions and Equations

● Quadratic Functions and Equations

Unit 4 – Advanced Functions and Equations

● Radical Functions and Geometry

● Rational Functions and Equations

Unit 5 – Data Analysis

● Statistics and Probability

##### 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.

Text:

Title: Algebra 2, Common Core Edition

Author: Carter, Cuevas, Day, Malloy, Casey, Holliday

Publisher: Glenco/McGraw-Hill, Inc. 2014

Units of Study:

• Unit 1: Linear Relations and Functions

o Equations and Inequalities

o Linear Relations and Functions

o Systems of Equations and Inequalities

• Unit 2: Quadratic, Polynomial, and Radical Functions and Relations

o Quadratic Functions and Relations

o Polynomials and Polynomial Functions

o Inverses and Radical Functions and Relations

• Unit 3: Advanced Functions and Relations

o Exponential and Logarithmic Functions and Relations

o Rational Functions and Relations

o Conic Sections

• Unit 4: Discrete Mathematics

o Sequences and Series

o Statistics and Probability

• Unit 5: Trigonometry

o Trigonometric Functions

o Trigonometric Identities and Equations

##### 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.

*Text:*

Title: Algebra 2, Common Core Edition

Author: Carter, Cuevas, Day, Malory, Casy, Holiday

Publisher: Glenco/McGraw-Hill, Inc. 2014

*Units of Study:*

Unit 1: Linear Relations and Functions

- Equations and Inequalities
- Linear Relations and Functions
- Systems of Equations and Inequalities

Unit 2: Quadratic, Polynomial, and Radical Functions and Relations

- Quadratic Functions and Relations
- Polynomials and Polynomial Functions
- Inverses and Radical Functions and Relations

Unit 3: Advanced Functions and Relations

- Exponential and Logarithmic Functions and Relations
- Rational Functions and Relations
- Conic Sections

Unit 4: Discrete Mathematics

- Sequences and Series
- Statistics and Probability

Unit 5: Trigonometry

- Trigonometric Functions
- Trigonometric Identities and Equations

##### 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. A vital project assigned has students constructing 3-D Polyhedra with compass and straight-edge and using geometric software.

Text:

Title: Geometry (Glencoe)

Author: Carter, Cuevas, Day, and Malloy

Publisher: McGraw-Hill, 2012

Units of Study:

• Unit 1 Geometric Structure

o Tools of Geometry, Reasoning, and Proof, Parallel and Perpendicular Lines

• Unit 2 Congruence

o Congruent Triangles, Relationships of Triangles, Quadrilaterals

• Unit 3 Similarity

o Proportions and Similarity, Right Triangles and Trigonometry, Transformations/Symmetry

• Unit 4 Measurement

o Circles, Areas of Polygons & Circles, Surface Area/Volume, Probability & Measurement

##### Pre-Calculus

Pre-Calculus is a college-prep course designed to provide a solid background for students preparing to either take A/B or B/C Calculus. Students are exposed to a wide variety of mathematical concepts and their application in problem-solving. Concepts covered include the real number system and the basic rules of algebra, exponents, radicals, polynomials, inequalities, functions, relations and are taught and used in a variety of applications. The basics of trigonometry are presented and students gain experience solving real-world problems as they may occur in the sciences and other general studies courses. Topics in trigonometry include: the unit circle, angle measures, trigonometric functions, inverse functions, right angle problem solving, and various trigonometric formulas. Other concepts include polar coordinates, the graphing of conic sections, matrices, graphing polynomial, rational, irrational, exponential, and logarithmic functions. There is frequent use of the graphing calculator.

Text:

Precalculus / Enhanced with Graphing Utilities, 7th Edition, 2017

Author: Sullivan

Units of Study:

• Functions and Their Graphs

• Linear and Quadratic Functions

• Polynomial and Rational Functions

• Exponential and Logarithmic Functions

• Trigonometric Functions

• Analytic Trigonometry

• Applications of Trigonometric Functions

• Analytic Geometry

• Systems of Equations in 3 Variables

• Calculus Preview: Limits, Derivatives, and Integrals of Functions

##### Advanced Placement Calculus AB

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 AB Exam in the late spring. This course is authorized by the College Board Advanced Placement program.

*Text:*

Title: 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

##### 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

• Chapter 9: Testing the Difference between Two Means, Two Proportions, and Two Variances

• Chapter 10: Correlation and Regression

• Chapter 11: Other Chi-Squared Test

• Chapter 12: Analysis of Variance

• Chapter 13: Non-parametric Statistics

• Chapter 14: Sampling and Simulation

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