e-Learning for Educators
Course Information

Math 1: Functions

Course Description

This six week course is designed to help teachers with the functions content needed for the WV Math I curriculum. Once this course has been completed, participants will have built their content knowledge of functions, learned strategies and activities and gained additional resources to aid them in teaching the unit on functions. Participants will become more familiar with the related Functions Unit on Teach 21.

*Course registration was open to high school mathematics teachers in West Virginia. Registration for the 2012-2013 school term closed on October 1, 2102.

Course Syllabus

 Overview This six week course is designed to help teachers with the functions content needed for the WV Math I curriculum. Once this course has been completed, participants will have built their content knowledge of functions, learned strategies and activities and gained additional resources to aid them in teaching the unit on functions. Participants will become more familiar with the related Functions Unit on Teach 21.
By the end of this course, participants will:
• understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
• use function notation, evaluate functions for inputs in their domains and interpret statements that use function notation in terms of a context.
• develop a vocabulary of functions.
• investigate the learning progression for functions.
• interpret key features of graphs and tables given a function that models a relationship between two quantities.
• distinguish between situations that can be modeled with linear or exponential functions.
• find and interpret the average rate of change of a function.
• compare properties of two functions each represented in a different way (algebraically, graphically and numerically in tables).
• explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately.
• identify the effect on the graph of replacing by and for specific values of (both positive and negative); find the value given the graphs: f(x), f(x) + k, k f(x), f(kx), f(x + k).
• experiment with cases and illustrate an explanation of the effects on the graph using technology.
• interpret the parameters in a linear or exponential function in terms of a context.
• prove that linear functions grow by equal differences over equal intervals; exponential functions grow by equal factors over equal intervals.
• recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
• recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
• recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
• represent arithmetic and geometric sequences using both explicit and recursive formulas.
• use functions to find terms of sequences, and represent those terms in tables.
• explore limits of sequences by using graphs of discrete functions.
• showcase and discuss student work from selected course activities.
• create a student assessment for Math I Functions Unit.
Course Organization
This course includes several different activity components, all of which are described below. During each session, you will participate in a unique collection of these activity components, depending on the particular focus of that session.
 Read When you see this icon you will be reading relevant articles, resources, and instructional materials that will help inform your online course development process. Activities When you see this icon you will be completing activity-based curriculum and inputting various components of your course content into course project. Discuss When you see this icon you will be using the online discussion board to share ideas, resources, and thoughtful conversation with your fellow course participants and facilitator.
Prerequisites

This course is designed for High School Math 1 teachers.

High School Mathematics I Course Description (graphic)
The fundamental purpose of Mathematics I is to formalize and extend the mathematics that students learned in the middle grades. The critical areas, organized into units, deepen and extend understanding of linear relationships, in part by contrasting them with exponential phenomena, and in part by applying linear models to data that exhibit a linear trend. Mathematics 1 uses properties and theorems involving congruent figures to deepen and extend understanding of geometric knowledge from prior grades. The final unit in the course ties together the algebraic and geometric ideas studied. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

Although not a requirement, high speed Internet access definitely enhances the online experience. Participants should be proficient with using email, browsing the Internet and navigating through computer files. Access to Microsoft Office is recommended. Participants who do not have Microsoft Office should click here for some available options.
Prior to Session One course participants at to secure:
1. a WVDE WebTop account.
2. a SAS Curriculum Pathways teacher account.
3. the SAS Curriculum Pathways school account for students.
4. graphing calculators, TI-84 or TI-Inspire, for student and teacher use. Online graphing calculator information is provided within the Session One readings/resource section.
5. a scanner for scanning course assignments to be uploaded to the course drop box.

Format and Requirements
This workshop is divided into six one-week sessions which each include readings, activities, and an online discussion among workshop participants. The time necessary to complete each session is estimated to be six to seven hours.

The outline for the workshop is as follows:
 Session One Introduction to Functions Session Two Multiple Representations Session Three Building Functions from Existing Functions Session Four Building Functions in Context Session Five Using Functions to Represent Sequences Session Six Connect, Reflect and Assess
Session One: introduction to Functions
Middle school students will have studied functions mostly as input/output machines. This session reviews and extends the concept by developing an understanding of domain and range, the vocabulary of functions, and function notation. The learning progression of functions is also addressed. Course participants will investigate the function standards and explore their importance to student learning.

Session Two: Multiple Representations
Multiple representations aids student understanding of functions. Participants will focus on identifying the key features of functions given a table, a graph or an equation and decide which representation is best to use to solve a problem.

Session Three: Building Functions from Existing Functions
Participants will investigate through different resources the effect of changing the parameters of given functions. They will also explain the effects on the graph of a function using technology.

Session Four: Building Functions from Context
This session will focus on interpreting the parameters in linear and exponential functions. Participants will distinguish between situations the can be modeled with and solved by using linear and exponential functions.

Session Five: Using Functions to Represent Sequences
Participants will investigate the different types of sequences and represent them in the form of a table, a graph and an equation. They will use function notation with subscripts to represent arithmetic and geometric sequences, both explicitly and recursively. Participants will deepen their understanding of sequences by exploring the limits of sequences using the graphs of discrete functions.

Session Six: Connect, Reflect and Assess
Participants will complete the portfolio requirements by completing all session reflections and including the student work samples. Participants will also develop a Math 1 Functions comprehensive student assessment/solution key with work.

Assessment

Workshop participants will complete an orientation and then six weekly workshop sessions that include readings, activities, and online discussions. There will be a pre-workshop survey and a post-workshop survey. In addition, participants will incrementally develop a Math I portfolio components throughout the duration of the course. The time for completing each session is estimated to be six to seven hours weekly.

Math 1 Portfolio:
Course participants will choose three activities to use in their classroom from those suggested throughout this Math I Functions course. The activities must be from three different sessions throughout Math I Functions. Portfolio items are to be selected from the following course activities:

Session One-Activity 3:
Teach 21 Math 1 NxG Unit 2: Linear and Exponential Relationships
Lesson 2
Function Notation Activity

Teach 21 Math 1 NxG Unit 2: Linear and Exponential Relationships
Lesson 8
Function Card Game

Session Three-Activity 1:
Teach 21 Math 1 NxG Unit 2: Linear and Exponential Relationships
Lesson 11
Transforming Equations Activity

Session Four-Activity 1:
Filling Containers

Session Five-Activity 1:
SAS Curriculum Pathways Quick Launch #101

Session Five-Activity 3:
Teach 21 Math 1 Nxg Unit 2: Linear and Exponential Relationships
Lesson 14
Attachment 1A (including all pages of 1B and 1C which are within Attachement 1C)

Complete the following for each activity to be submitted to your portfolio:

• Submit two samples of your students’ work that show different levels of understanding.
• Explain why you selected each sample of student work and describe the level of understanding demonstrated by each student.
• Discuss how this particular lesson or activity has helped develop your students’ understanding of the mathematics involved.

A total of six student samples are to be included in your portfolio for Math I Functions.

Culminating Assessment:
Course participants will create a Math 1 Functions culminating assessment for students along with a solution key, complete with all work. This assessment may be used with Math I students to evaluate their conceptual understanding of the Next Generation CSO’s that were targeted in this course. Categories and indicators from the Student Assessment Rubric are to be used to guide the development of the Math 1 Functions culminating assessment for students.

Self-Assessment of the Culminating Assessment for Students:
Course participants will complete a self-assessment of their Math 1 Functions student assessment using the Student Assessment Rubric.

Discussion Participation
Participants will be evaluated on the frequency and quality of their participation in the discussion forum. Participants are required to post a minimum of one substantial original posting each session reflecting on the question for that session. They are to read all original postings made by the other workshop participants and reply thoughtfully to at least two of them per session. Participants’ original postings will be evaluated on their relevance, demonstrated understanding of workshop concepts, examples cited, and overall quality. Postings that respond to other participants will be evaluated on relevance, degree to which they extend the discussion, and tone.

Certificate of Completion
Upon successful completion of this course, Math 1 Functions, and the successful panel portfolio review participants will receive a Certificate of Completion documenting successful completion of the course requirements.

Participants in this course are eligible to receive non-degree graduate credits from either West Virginia University, Marshall University or Concord University. Credits will be awarded at the end of the semester in which the course occurs. Additional information is available on the course News/Welcome Page.

Content and Technology Standards

This workshop, Math 1 Functions, will help participants meet the ISTE Educational Technology Standards and Performance Indicators for All Teachers (http://edtechleaders.org/documents/NETSAdminTeachers.pdf), especially Standards II, III, IV, and V. For more information about Technology Integration visit: http://www.iste.org

In addition, participants will identify specific WV Content Standards and Objectives (http://wvde.state.wv.us/csos/) as they engage in course content.