Function Fundamentals and Linear Functions | Precalculus, Part 2
This 4-week online course continues a full year Precalculus class.
Avrila at Math With Avrila
Average rating:
4.9
Number of reviews:(13)
What's included
8 live meetings
6 hrs 40 mins in-class hoursHomework
2-4 hours per week. Learners will have practice problems to work in Rover for each lesson. Other assignments, quizzes, and tests will be in TeacherMade. Occasionally, such as in advance to clear group time for interactive tasks or when lecture topics take longer than anticipated, learners will be assigned video tutorials to watch outside class time.Assessment
Learners will receive numerical grades for practice and for each major assignment in a written report at the end of the class, and a current draft of their grades so far upon request during the class.Grading
includedClass Experience
US Grade 10 - 12
The general key topics for the second month will be functions and linear functions, with an emphasis on linear modeling. For details of what will be addressed within these areas, see the learning goals list. We will use the OpenStax Algebra and Trigonometry curriculum from Rice University as an outline and reference; while this is not a test prep class, I am mindful of the fact that learners may have passing credit-bearing exams like CLEP Precalculus as a goal, and the scope and rigor will be consistent. (The next month's unit will be available for enrollment as students near completion of this course.) Week-by-week we will follow approximately this schedule, adjusting as needed based on learners' interests and needs: Week 1: Lessons 3.1-3.3 -- Function Basics and Rates of Change Week 2: Lessons 3.4-3.6 -- Combining and Changing Functions and Absolute Value Week 3: Lessons 3.7-4.2 -- Working Backwards and Linear Functions Week 4: Lesson 4.3 and additional related topics from statistics -- Linear Regression Class sessions will generally include: * A warmup problem set using related previous skills * An outline of the session's objectives, together with an opportunity to ask questions either about recent homework or to clarify concepts mentioned in the objectives * Presentation of concepts and problems using slides in a Miro whiteboard; learners will be able to use a provided link to write on the slides for purposes like solving an equation or marking important information for setting up a word problem Between class sessions, learners will be given other information in written, graphical, and video form, as needed based on the topic (for example, a problem-solving process would usually be given in video rather than written form, to allow for proper notation and verbal step-by-step explanation), in the class discussion area. This is intended as a continuation of my Precalculus Part 1 class. Learners who have taken other classes giving a similar functional level of proficiency with its objectives are welcome to join and I'm happy to provide practice problems so learners can test themselves.
Learning Goals
Learners will interpret, use, and translate between multiple representations of relations (equation, table, graph, or mapping).
Learners will understand domain and range.
Learners will understand piecewise functions, including absolute value functions.
Learners will know and apply the criteria for which relations are functions (unique output for input, including the visual "vertical line test").
Learners will know and apply the criteria for which functions are one-to-one (unique input for output, including the visual "horizontal line test").
Learners will evaluate functions.
Learners will find average rate of change for a function across a subdomain interval.
Learners will identify subdomain intervals where a function is increasing, decreasing, or constant.
Learners will understand and identify local and absolute extrema and connect local extrema with increasing/decreasing subdomains.
Learners will perform algebraic operations on functions, including composition.
Learners will understand and perform transformation of functions, including shifts, reflections, and stretches, both vertically and horizontally.
Learners will identify functions as even, odd, neither, or both.
Learners will understand and verify inverse functions based on composition of functions.
Learners will understand that functions are fully invertible if and only if they are one-to-one i.e. pass the horizontal line test.
Learners will invert functions algebraically, graphically, and using tables.
Learners will understand linear functions as functions with a constant rate of change.
Learners will understand, find, and interpret slopes, intercepts (x or y), and other points of linear functions.
Learners will find equations for linear functions based on slope and y-intercept, point and slope, two points, or situational information equivalent to any of these.
Learners will find equations for parallel or perpendicular lines.
Learners will translate between graphs and equations for vertical or horizontal lines.
Learners will use exact calculation where applicable, visual estimation with a scatterplot, or technology to fit linear models to problem solving situations. Where technology is used, learners will understand r as a "grade" of the model.
Learners will understand the difference between interpolation and extrapolation and some potential pitfalls of extrapolation.
Learners will use various forms of the slope formula.
Other Details
Parental Guidance
Explain Everything is a shared whiteboard, similar to Google Jamboard but more flexible. Learners do not need an account and can access the board to write on it through a link. Learners who do not specifically want to write on the board don’t need to access Explain Everything at all – I will share the screen in Zoom and they can watch.
Rover is an automatic-scored practice site based on the OpenStax precalculus-level textbooks. Learners will need to set up accounts; costs will be covered as part of their tuition for the class.
GeoGebra is a free, open-source math calculator, graphing calculator, and dynamic geometry site. Learners do not need an account to use it.
Google Sheets is a free cloud-based spreadsheet site, part of the Google Suite. I will provide links to blank sheets or sheets with preloaded data, with editing permissions, so learners do not need their own accounts and I can help them with troubleshooting.
Supply List
Scratch paper and pencils, or a whiteboard and markers. Learners who are preparing for college admissions are advised to keep a portfolio (digital or on paper) of major assignments and 2-3 different types of problems, fully worked, per routine practice assignment; the materials of the student's choice should be available for this from the beginning of class. Examples include a Google Drive or Dropbox folder, LibreOffice software (Writer and Math), a binder and hole-punched printer paper or a hole puncher, etc. Consider that if you are applying to multiple colleges, a digital portfolio is easier to duplicate, and can be printed out if a physical copy is wanted. For this class, learners can use GeoGebra exclusively as their graphing calculator, but students whose intent is to take a credit-bearing exam should begin practicing with a calculator approved for that exam as soon as possible.
External Resources
In addition to the Outschool classroom, this class uses:
Sources
OpenStax Precalculus
OpenStax Algebra and Trigonometry
OpenStax Statistics
Joined May, 2021
4.9
13reviews
Teacher expertise and credentials
Master's Degree in Mathematics from Western Governors University
I have a master's degree in math education for grades 5-12, as well as further graduate coursework in mathematics, and teach developmental, dual credit, and regular math classes for my local junior college.Reviews
Live Group Class
$38
weekly2x per week, 4 weeks
50 min
Completed by 1 learner
Live video meetings
Ages: 15-18
1-12 learners per class
