# Upper School Curriculum

## Mathematics

This course is a first year, Pre-Algebra-level course designed to help students begin a 2-year transition toward Algebra 1. One of the main purposes of the course is to assure that students have a solid foundation with all elementary topics in general math, especially ones most important for elementary algebra and geometry. The course covers, among other topics, Ratios and Proportions, the Real Number System, and introduction to Elementary Probability and Statistics. Incorporated within these topics are operations on integers, fractions, decimals, and percents. Close attention to the new state standards for mathematics will be paramount for the course, and all of the lessons and student work are in accord with Common Core Math practices.

*Text:*

Title: Go Math (Grade 7)

Authors: Larson, Kanold, et al.

Publisher: Houghton Mifflin Harcourt, 2014

*Units of Study:*

- Integers
- Rational Numbers
- Proportions
- Expressions and Equations
- Inequalities
- Elementary Geometry
- Data Analysis
- Probability

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 worked with in 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

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, constructing viable arguments and critique the reasoning of others, modeling with mathematics, Using appropriate tools strategically, Attending to precision, looking for and making use of structure, and looking for and expressing regularity in repeated reasoning.

*Text:*

Title: Algebra 1, Common Core Edition

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

Publisher: Glenco/McGraw-Hill, Inc. 2014

*Units of Study:*

Unit 1 – Relations between Quantities

Unit 2 – Linear Relationships

Unit 3 – Exponential and Quadratic Relationships

Unit 4 – Advanced Functions and Equations

Unit 5 – Data Analysis

*Topic List:*

- Variables
- Exponents and Powers
- Algebraic Expressions
- Integers
- Order of Operations
- Properties of Arithmetic
- Linear Equations (one Variable)
- Linear Inequalities (one Variable)
- Factoring
- Graphing/ Coordinate Plane
- Slope
- Quadratic Functions
- Radicals/Pythagorean Theorem
- Exponential Functions
- Linear Functions (two variables)
- Ratio, Proportion and Similar Figures

Algebra II is designed to continue a logical development of a second course in algebra. The primary aims are to help students understand algebra as a study of the structure of real and complex number systems, and, promote the understanding of both linear and non-linear functional forms. In addition, the course offers a deeper analysis of the relationship between equations, graphs, and tables through the modeling of real-life applications and problem-solving. Moreover, Algebra II includes a second phase of the Trigonometry that is presented in Geometry, and includes an introduction to the Unit Circle.

*Text:*

Title: Algebra 2 (Glencoe)

Author: Carter, Day, Cuevas, Malloy

Publisher: McGraw-Hill, 2014

*Units of Study:*

Unit 1 – Equations and Inequalities

Unit 2 – Linear Relations and Functions

Unit 3 – Systems of Equations and Inequalities

Unit 4 – Quadratic Functions and Relations

Unit 5 – Polynomials and Polynomial Functions

Unit 6 – Inverse and Radical Functions and Relations

Unit 7 – Exponential and Logarithmic Functions and Relations

Unit 8 – Rational Functions and Relations

This course provides students an opportunity to expand their understanding of the basic algebraic concepts of equations, inequalities and graphs. Factored polynomials and quadratic equations that lead to solutions are covered as well radicals, complex numbers, exponents, logarithms, conic sections, , and trigonometric functions. Students will explore how functions behave using calculators, computer software, online applets and programming languages. Formulas and functions will be coded onto computers using Python, a software programming language, providing students with a practical approach to logical algorithms .

** **

*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

Algebra III is designed to continue a logical development of a third course in algebra. For the 1st semester, the primary aims are to help students further develop and hone their algebra skills through review of Algebra I, Algebra II, Trigonometry, and some basic Geometry as it relates to Algebra. In the 2nd semester , the students are introduced to more complex concepts related to Advanced Algebra such as Conic Sections, Logarithms, Sequences and Series, and Inverse Trigonometric Functions.

*Textbook:*

Title: Glencoe Algebra 2

Publisher: McGraw-Hill, 2014

*Review Textbook:*

Title: Algebra 1 Concepts and Skills

Publisher: McDougal Littell, 2001

*Units of Study:*

Unit 1 – Equations and Inequalities

Unit 2 – Relations and Functions:

- Linear, Quadratic, Inverse, Radical, Exponential, Logarithmic, Rational,
- Trigonometric Linear Relations and Functions

Unit 3 – Systems of Equations and Inequalities

Unit 4 – Polynomials

Unit 5 – Conic Sections

Unit 6 – Sequence and Series

Unit 7 – Probability and Statistics

Unit 8 – Further Study in Trigonometry

Course Description:

This is a one semester course built on an approach of experiential hands-on learning through which students will be creating and displaying their original ideas. Students will gain an understanding of 21st century computer skills including an understanding of basic computer language, in-demand coding languages such as Python, project-based learning through the use of microprocessors (Arduino, Micro:bit), and creation of 3D models and animation with access to

3D printing later in the semester.

Units of Study:

Unit 1 – Computer Language/Circuit Introduction

Unit 2 – MIT’s Scratch animator with drag and drop coding

Unit 3 – BBC Micro:Bit microprocessor coding with Python

Unit 4 – Autodesk Sketchbook graphic design program

Unit 5 – Arduino Microprocessor coding and project building

Unit 6 – Autodesk Fusion 360 3D Modeling Software

Unit 7 – Autodesk Maya 3D animation software (if time in semester)

Other Potential Project Opportunities:

- Use of Logic X and other DAWs for audio engineering
- Podcasting
- Soldering
- Website Creation
- Circuit Bending

Content Statements (ISTE Standards):

- Empowered Learner: Students leverage technology to take an active role in choosing, achieving and demonstrating competency in their learning goals, informed by the learning sciences.
- Digital Citizen: Students leverage technology to take an active role in choosing, achieving and demonstrating competency in their learning goals, informed by the learning sciences.
- Knowledge Constructor: Students critically curate a variety of resources using digital tools to construct knowledge, produce creative artifacts and make meaningful learning experiences for themselves and others.
- Innovative Designer: Students use a variety of technologies within a design process to identify and solve problems by creating new, useful or imaginative solutions.
- Computational Thinker: Students develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions.
- Creative Communicator: Students communicate clearly and express themselves

creatively for a variety of purposes using the platforms, tools, styles, formats and digital media appropriate to their goals. - Global Collaborator: Students use digital tools to broaden their perspectives and enrich their learning by collaborating with others and working effectively in teams locally and globally.

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 the 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 straightedge.

*Textbook:*

Title: Geometry (Glencoe)

Author: Carter, Cuevas, Day, and Malloy

Publisher: McGraw-Hill, 2012

*Units of Study:*

Unit 1 – Basic Tools of Geometry

Unit 2 – Reasoning and Proof

Unit 3 – Parallel and Perpendicular Lines

Unit 4 – Triangles

Unit 5 – Quadrilaterals

Unit 6 – Proportions and Similarity

Unit 7 – Right Triangle Trigonometry

Unit 8 – Transformations and Symmetry

Unit 9 – Circles

Unit 10 – Surface Area and Volume

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:*

1 Limits

2 Derivatives and Related Topics:

Definition, Properties, Graphical, Numerical, Analytic, Instant Rate of Change, Differentiability, Tangent Lines, Increasing/Decreasing Functions, Mean Value Theorem, Concavity, Inflection, Extrema, Related Rates, Velocity and Acceleration, Implicitness, Slope Fields, General Rules, Chain Rule

3 Integrals and Related Topics:

- Definition, Properties, Riemann Sums, Accumulation of a Quantity,
- Exact and Approximation Methods for Area and Volume, Fundamental
- Theorem of Calculus, Mean Value Theorem for Integrals,
- Antidifferentiation, Integration Methods, Initial Value Problems,
- Separable Differential Equations

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:*

1 Limits

2 Derivatives and Related Topics:

Definition, Properties, Graphical, Numerical, Analytic, Instant Rate of Change, Differentiability, Tangent Lines, Increasing/Decreasing Functions, Mean Value Theorem, Concavity, Inflection, Extrema, Related Rates, Velocity and Acceleration, Implicitness, Slope Fields, General Rules, Chain Rule, Analysis of Planar Curves in Parametric, Polar and Vector Forms, Euler’s Method, L’Hopital’s Rule, Derivatives of Parametric, Polar, Vector Functions

3 Integrals and Related Topics:

Definition, Properties, Riemann Sums, Accumulation of a Quantity, Exact and Approximation Methods for Area and Volume, Fundamental Theorem of Calculus, Mean Value Theorem for Integrals, Antidifferentiation, Integration Methods, Initial Value Problems, Separable and Logistic Differential Equations, Area Under Polar Curves, Arc Length, Integration by Parts and Partial Fractions, Improper Integrals, Geometric / Harmonic / Alternating Series, Tests for Convergence and Divergence of a Series, Taylor Polynomials and Series, Maclaurin Polynomials and Series, Power Series, Lagrange Error Bound.

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.

Graphic 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 calculator. In addition to the calculator, other tools to plot data will be used throughout the year including Excel.

Textbook: 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