Eastside High School

1300 Brushy Creek Road, Phone 864-355-2800

Taylors, SC 29687 Fax 864-355-2859

Engaging Minds, Engaging Community

2018-19 Eastside High School Course Syllabus

Instructor: Mr. Smith

Course: Algebra 1 CP

Room #: 209

Phone: 864 – 355 – 2859

Email address: briansmith@greenville.k12.sc.us

Extra-Help (Days/Time): Tuesday – Thursday 8:15-8:45

Algebra 1 CP Overview

About this Course

Building on student's prior work with proportionality and linear equations in middle school, students expand their study of functions in Algebra 1. Students work closely with the expressions that define the functions, their graphs, domain, and function notation. Work with these functions is grounded in logical reasoning, where manipulations to the expressions are accomplished with intent and based on properties of arithmetic and the laws of equality. Students continue to expand and hone their abilities to model situations, including through the use of statistics, and to solve equations.

Unit 1: Representing Functional Relationships

Traditional Schedule 10-12 days

In this unit, students build on their understanding of functions and representations as they begin to explore functions represented in function notation. While students are comfortable with having the range defined as y, they now will use notation to show the range is f(x) = y. Function notation will be used to define a given relationship between two variables. Students will evaluate a function for a given input within the domain of the function. When given a real-world application, context will be used to interpret the meaning of a statement given in function notation.

Unit 2.1: Linear & Exponential Relationships - Part 1

Traditional Schedule 30-35 days

In this unit, students explore similarities and differences between the two monotonic function families of linear and exponential functions. Students will identify that while each of these functions are strictly increasing or decreasing, the rates of change define the behavior of the function. Students will begin to connect real-world scenarios to linear and exponential models and begin to differentiate between situations that result in continuous or sequential graphs. Students will understand that sequences are functions whose domains are subsets of integers representing the term numbers. Students will understand that sequences may be defined either explicitly or recursively and will write sequences in both forms. The focus in Unit 2 will be on the comparison of arithmetic and geometric sequences. Connections should made between arithmetic sequences and linear functions and between geometric sequences and exponential functions. Students will justify why a scenario is best modeled by one of the two function families

Unit 2.2: Linear & Exponential Relationships - Part 2

Traditional Schedule 10-15 days

In this part of the unit, students will distinguish the difference between correlation (or association) and causation. They will apply the modeling cycle to real-world data and situations. Students will create a scatter plot to represent and analyze bivariate quantitative data. They will describe the features of scatter plots and determine if a linear or exponential model of best fit would be appropriate. Using the correlation coefficient (for linear models), paired with an analysis of residuals, students will justify their choice and if necessary, revisit the modeling cycle with other models. Students should understand that perfect linear relationships will have a correlation coefficient of 1 or -1, and, conversely, relationships that have little to no linear correlation will have correlation coefficients close to 0. When using a linear model, students will interpret the slope and y-intercept of the equation in the context of the problem. In addition, students will be able make predictions using either linear or exponential regression models. Calculations and regressions should be performed using technology.

Unit 2.3: Linear & Exponential Relationships - Part 3

Traditional Schedule 15-20 days

In Part III of this unit, students extend understanding of linear and exponential functions to exploring systems of equations. Students will build on their work with systems of equations from Grade 8 to apply to real-world situations, and to examine simple systems of linear and exponential functions. Students will recognize through real-world application tasks that the solution, or point of intersection, will be common to the two given situations. Students will write the system of linear equations, interpret the solution, and justify solutions within the context of a real-world problem. Students will make connections between intersecting, parallel, and perpendicular lines and the meaning of the solutions they produce. They will review using algebraic strategies for solving systems.

Unit 3.1: Quadratic Functions & Modeling - Part 1

Traditional Schedule 18-25 days

In this part of the unit, students will begin to manipulate expressions to include the addition, subtraction and multiplication of linear and quadratic functions, to connect to the graphs of the new functions produced. For the purposes of Algebra I, students will focus on building quadratic functions and on recognizing the properties of quadratic functions as they emerge. As students investigate quadratic patterns, they will expand upon their skills in Unit 2 to express the patterns both recursively and explicitly. Students will begin to make connections between quadratic behavior in the real world and the features of the recursive, explicit and graphical representations of a quadratic function. By this point students should be able to distinguish among linear, exponential and quadratic functions given verbal, numeric, and/or graphical representations. Students can extend their work with modeling in Unit 1 to begin to include quadratic functions, creating equations to model a given situation and graphing these functions on coordinate axes.

Students will begin to explore standard form, vertex form, and factored form to determine what key graphical information can be gathered from each form. Students will identify and interpret key features, such as intercepts, intervals where the function is increasing or decreasing, intervals where the function is positive or negative, relative maxima and minima, symmetries, and end behavior in order to sketch graphs. Additionally, they will identify any domain restrictions within the context of the problem situation. Students will graph simple cases by hand but are encouraged to use graphing technology where appropriate. Students will explore transformations of quadratic functions, examining the effects of replacing f(x) by f(x)+k, kf(x), f(kx), and f(x+k) for specific values of k, both positive and negative. Through the process of experimentation, students will be able to generate rules for transformation. Students will not only to sketch a graph of a transformed function given a symbolic representation, but also to determine the value of k given a graphical representation of a transformed function.

Unit 3.2: Quadratic Functions & Modeling - Part 2

Traditional Schedule 27-32 days

In this part of the unit, students will interpret the parts of quadratic expressions in terms of a problem situation, including terms, coefficients, and factors, leading to the investigations of the structure of equivalent expressions and student interpretations about what different forms of quadratic expressions might reveal about a problem or a graph of the function. Students will then begin to convert between forms to gather key information about the quadratic function. Students will develop a conceptual understanding of completing the square and factoring using area models, then use these techniques to find the maximum/minimum and/or zeros of the function.

Students will then determine the zeros for quadratic functions that are not factorable. Students use the method of completing the square in order to derive the quadratic formula. Then, students will explore connections between the discriminant and the number of real zeros. They are expected to solve quadratic equations by methods of taking square roots, completing the square, factoring, or the quadratic formula. Emphasis should be placed on solving the equation using the method most appropriate for the form of equation given. This understanding will then be expanded to examine a system composed of a linear function and a quadratic function. At this point, students should be exposed to the existence of the complex number system and should recognize when a quadratic function would have complex solutions. Students will not solve quadratics with complex solutions until Algebra 2.

Unit 4: Modeling with Other Functions

Traditional Schedule 15-20 days

Students will then extend their understanding of properties of exponents to explore fractional exponents. Students will make connections between fractional exponents and square root and cube root functions. Students will build fluency converting between forms and simplifying expressions with fractional exponents. Students will interpret the structure of expressions and solve problems related to unit analysis. The properties of rational and irrational numbers have been added.

As an extension of their work with various function families, students will begin to investigate the graphs of special functions, including square root, cube root, absolute value, and step functions. Students will explore graphical representations for each of these functions by hand in simple cases and by using technology in more complex cases. In all cases, students will identify key features of their graphs. Students will identify parent functions and describe or sketch the effects of simple transformations on those parent functions. Then, students will write functions to model real-world situations.

Text: Algebra 1, Holt

Materials Needed:

• Paper and Pencil daily
• Graphing calculator (optional)
• 3-ring binder with tabs
• Textbook

Grading Policy and Assessments:

Major: Summative Assessment (Tests/Projects)

60%

These categories count as 80% of your grade

Minor: Bell Ringer, T.O.D, Classwork, Homework

40%

EOC

20%

Grading Scale

A= 93-100

B= 85-92

C= 77-84

D= 70-76

F= 0-69

This course is an EOCEP Course. The S.C. State Department of Education mandates that an EOC exam counts as 20% of the yearly grade.

Attendance Policy: To receive credit for a course, students must not miss more than five (5) days for a semester course (1/2 unit course), and not miss more than ten (10) days for a yearlong course (1 unit course), as well as meet all minimum requirements for the course. Please review the Student Handbook for details.

What to do if you miss a class:

Excused Absence: If you have an excused absence, you will be allowed to make up work, tests, quizzes, and projects with no penalty, if you have an excused note. Provisions for make-up of schoolwork missed is the student’s responsibility and shall be worked out with the teacher(s) at the earliest time possible, but the time by which the work is completed and turned in should not exceed five (5) consecutive school days after you return to school.

Unexcused Absence: Teachers are not required to accept makeup work or provided testing for students with unexcused absences.

Academic and Behavioral Expectations:

An atmosphere of mutual respect between students and teachers is expected. Each teacher has the authority to enforce discipline. Student cooperation and self-discipline are expected.

Any student found guilty of academic dishonesty will be given a zero on the work. The parents will be notified by the teacher. Academic dishonesty includes “giving help” on a test or assignment as well as “receiving help.” Plagiarism is a form of academic dishonesty.

Rules and Consequences:

Rules

1. Be respectful to all around you.

2. Come to class on time and prepared.

3. No food or drink in the classroom.

4. Cell phones must be out of sight.

5. All school rules apply (agenda).

Consequences

1. Verbal Warning

2. Parent Contact

3. Discipline Referral

**Consequences may not follow this order depending on severity of situation