Plan OER Structure Part 1A: Outline

College Algebra Cohort -

Let’s draft the outline of our OER below to include all the parts or chapters that we envision.

Here is a draft for the chapters:

Chapter 0: Review

  • Real Numbers
  • Algebra Essentials
  • Exponential, Radical, and Rational Expressions
  • Polynomials
  • Factoring of Polynomials

Chapter 1: Solving Equations and Inequalities

  • Solving Linear, Absolute Value, and Radical Equations Algebraically
  • Solving Quadratic Equations by factoring, using the Square Root Property, and using the Quadratic Formula
  • Complex Numbers, Quadratic Equations in the Complex Number System
  • Applications of Linear and Quadratic Equations
  • Solving Linear, Quadratic, Absolute Value, and Polynomial Inequalities Algebraically and Graphically

Chapter 2: Graphs

  • Distance and Midpoint Formulas
  • Graphs of Equations in Two Variables; Intercepts; Symmetry
  • Lines
  • Circles

Chapter 3: Functions and their graphs

  • Identifying Functions, Functional Notation, and Domains of Functions
  • Graphs of Linear, Quadratic, and Absolute Value Functions
  • Combinations and Composition of Functions
  • Definition of Inverse Functions and Finding Inverses of Functions
  • Interpreting Graphs of Functions (increasing, decreasing, max, and min)

Chapter 4: Polynomial and Rational Functions

  • Characteristics of Graphs of Polynomials and Rational Functions
  • Rational Zeros Test
  • The Fundamental Theorem of Algebra
  • Conjugate Pair and Factor Theorem

Chapter 5: Exponential and Logarithmic Functions

  • Exponential Functions and their graphs
  • Logarithmic Functions and their graphs
  • Properties of Logarithmic Functions
  • Logarithmic and Exponential Equations
  • Applications of Logarithmic and Exponential Functions

Chapter 6: Systems of Equations

  • Solving Systems in two variables Graphically
  • Solving Systems in two variables by Substitution and by Elimination
  • Applications of Systems of Equations
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I think all of these topics look good. You could make an argument to put Chapter 4 Polynomials after chapter 1, but the graphs might get pushed too far back. It could also work as it is here.

So It seems that I didn’t quite get the difference between the outline and the model. I did the model, but missed the outline. Thanks Prakash for posting.

If we are going to start with College Algebra OpenStax, then I think we should also model there chapters with some slight modifications.

Honestly, I have no desire to do a Review or Prequisite material, but won’t put up much of a fight if the teams decides to do one.

Chapter 1: Equations and Inequalities

  • 1.1 Linear Equations in One Variable
  • 1.2 Models and Applications
  • 1.3 Complex Numbers (I think should be covered before any quadratics)
  • 1.4 Quadratic Equations
  • 1.5 Other Types of Equations (Absolute Value, Radical, Rational Exponents, Quad form)
  • 1.6 Linear Inequalities and Absolute Values Inequalities
    Chapter 2: Functions
  • 2.1 Functions and Function Notation
  • 2.2 Domain and Range
  • 2.3 Rates of Change and Behavior of Graphs
  • 2.4 Composition of Functions
  • 2.5 Transformation of Functions
  • 2.6 Absolute Value Functions
  • 2.7 Inverse Functions
    Chapter 3: Linear Functions
  • 3.1 The Rectangular Coordinate Systems and Graphs
  • 3.2 Linear Functions
  • 3.3 Modeling with Linear Functions
    Chapter 4: Polynomial and Rational Functions
  • 4.1 Quadratic Functions
  • 4.2 Power Functions and Polynomial Functions
  • 4.3 Graphs of Polynomial Functions
  • 4.4 Dividing Polynomials
  • 4.5 Zeros of Polynomial Functions
  • 4.6 Rational Functions
    Chapter 5: Exponential and Logarithmic Functions
  • 5.1 Exponential Functions and Graphs
  • 5.2 Logarthimic Functions and Graphs
  • 5.3 Logathimic Properties
  • 5.4 Exponential and Logarithmic Equations
  • 5.5 Exponential and Logarithmic Models
    Chapter 6: Systems of Equations and Inequalities
  • 6.1 Systems of Linear Equations: Two Variables

This is a link to the Open Stax Table of Contents:

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Your chapter outline looks excellent to me, Ginny. I am fine going with your draft.

Both outline and model look great. We may need to make a few changes as we get into writing.
Thank you, Prakash and Ginny for your work!

Based on the new information that there may be an OpenStax text already in Pressbooks, then I would like to modify the outline per Prakash’s original suggestion and have Chapter 0 (or 1) with Prerequisites. I don’t think we will have to make many modifications except to make sure it follows the outline that we discussed.

One thing I don’t like about the OpenStax text is Chapter2 sections 2.1 and 2.2. Section 2.1 covers Plotting points, Graphing equations by plotting points, x and y intercepts, distance and midpoint. This one its own is fine. Section 2.2 combines linear equations in one variable AND linear equations in two variables. This I would like to see separated. I would like to cover equation and inequalities in one chapter, then cover the graphing in another.
My first thought is to move the linear equations in two variable material from 2.2 to the Chapter on Linear Functions. This would avoid some of the repetition of cover lines then covering linear functions. But, I don’t know the best place to put the introductory graphing information from 2.1. I think it should be covered before tackling Functions.

Perhaps the material from Section 2.1 could be moved to the Chapter on Function and keep the label the Rectangular coordinate system and graphs.

Based off of Prakash’s original post, I am not opposed to making another Chapter Titled Graphs covering the distance and midpoint formulas, Graphing equations in two variables, intercepts. We currently don’t cover circles, and really couldn’t find any information regarding circles in OpenStax. If we want to cover circles, we may need to bring it in from another source. But this would be a really short chapter that OpenStax covers in a section.

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I wanted to make some changes to the outline per our cohort meeting 3/17/23
Add Chapter 0: Prerequisites.
Moved Rectangular coordinate system to beginning of Functions. We could add circle material in this section if desired. Added Linear Equations in Two Variables to Linear Functions chapter.

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Maybe we can move 6.1 to Chapter 3. It could build on the 3.1 that has been moved from OS 2.2) We could omit Chapter 6. For testing purposes, I don’t really like such a short chapter.

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I’m speaking from memory, so please excuse me if I missed something. I think I agree with you on moving systems of equations (6.1?) as the last section into the Linear Functions Chapter (Ch 3) We could just make it section 3.4 Systems of Equations in two variables.

Great observation Karen, move Chapter 6 to Chapter 3.

Chapter 2 has eight sections. That is long.

I have made the changes that have been discussed in this forum.
I moved OS 2.1 to the Functions Chapter.
As @csingleton noted, this is a long chapter. If you look at the section onn Absolute Value functions it is really short. Some of the same information is covered in Transformations and in the absolute value equations. This section may not be necessary since the information is basically covered in other sections.
I moved the portion of OS 2.2 dealing with linear equations in two variables to the Linear Functions Chapter into a new section titled Linear Equations in Two Variables. Since parallel and perpendicular were covered in both Linear Equations in Two Variables AND Linear Functions Sections, I removed the information from the linear functions section so as not to have duplicate information.

I moved the systems of linear Equations sections into the Linear Function Chapter after Modeling with Linear Functions. That section actually ends with an example of a system so I thought that was a good lead into Systems.

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Great points @gbradley. It sounds like it will flow well now. There are not many absolute value problems in the Transformations section, but if we keep the absolute value section, maybe it can be combined somewhere else.

I like these changes Ginny.

@gbradley, @pghimire, @karen.perilloux: I need the team’s feedback. I am working on the Chapter with Exponential and Logarithmic Functions. According to the @gbradley and @pghmire outlines in Rebus, the first section is Exponential Functions and Graphs. If I combine these two sections, then the section will be long. Here are the objectives:

  • Evaluate exponential functions
  • Use compound interest formulas.
  • Finding Equations of Exponential Functions
  • Evaluate exponential functions with base e.
  • Graph exponential functions
  • Graph exponential functions using transformations.

Do we want to keep the above objectives as is? Do we want to eliminate some of the objectives? Do want to combine objectives and eliminate some of the problems? Do we want to eliminate some of the problems? What are your thoughts?

I think the least important topic would be Finding equations of exponential functions. I teach all of the rest in my course.

I’ll be out of town for the rest of the week. Happy Easter!

@karen.perilloux: I agree that finding equations of exponential functions may be omitted.

Thank you,

Happy Easter!

Enjoy your vacation!

Sorry, I have been away. But I would like to keep the objectives as stated as I do teach finding equations of exponential functions. If you find that the section is too long, then maybe we shouldn’t combine them and leave them as is.

No sense in cutting out a section that another instructor might want to use. Maybe we shouldn’t combine them.

I agree with @karen.perilloux and @csingleton that we should not combine them if you all think it is going to be too long.