Stick It in a Box: Polynomial Multiplication and Division Made Easy
In this 4-session class, learners will grasp and practice visual methods for dealing with polynomial operations and related equations and functions.
Avrila at Math With Avrila
Average rating:
4.9
Number of reviews:(11)
What's included
4 live meetings
3 hrs 20 mins in-class hoursHomework
1-2 hours per week. Learners will have practice problems in TeacherMade after each session. After session 2, practice problems will include solving quadratic equations, and after session 4, any quadratic equation may be considered. After session 3, practice problems will include long-run behavior of rational functions (i.e. limits toward infinity, an early calculus topic).Class Experience
US Grade 8 - 11
Each session will start with warm-up problems, giving learners time to settle in. After going over the warm-up problems together, as well as any questions on homework problems, we will cover the day's main topic: Session 1: Multiplying Polynomials Session 2: Factoring Polynomials Session 3: Dividing Polynomials Session 4: Completing the Square During group activities, learners will interact with the teacher and each other through verbal discussion and slides designed to be written on and organize our thinking, not just looked at. (Learners can either annotate from within Zoom, which will be reset as we move between slides but preserved in the session recording, or request the Explain Everything link, which will let them write directly on the board. Learners' contributions will be monitored for appropriateness, safety, and accuracy.) Consistent regular attendance is expected. I will not remove learners from class for missing group activity sessions, but they must take responsibility for catching up, by watching the session video and doing all work. I will be available to help if they find anything tricky. Mathematical prerequisites and target audience: Expected learners are somewhere in their high school algebra learning journey; most of the core topics are introduced mid-to-late in a typical Algebra 1 class (the exception is polynomial division, which is often omitted until Precalculus), but practiced and elaborated on throughout Algebra 2 and Precalculus, so learners later in the algebra learning process will still see new connections as well as finding ways to make their work easier. Previous familiarity with the distributive property is a must! Learners who became acquainted with the box method for multi-digit multiplication will find extending it to polynomial multiplication easier, but learners who did not can still grasp this method. Technology prerequisites: Learners must be able to follow links and switch between the Zoom meeting and a browser window, or have support for these technology tasks immediately at hand.
Learning Goals
Learners will use the box method to multiply polynomials.
Learners will use the box method and splitting the middle term compatibly with the last term to factor polynomials.
Learners will use the box method to divide polynomials.
Learners will use the box method, splitting the middle term in half, and considering the remainder to complete the square.
Learners will solve quadratic equations by factoring or completing the square.
Learners will be aware of connections between graphs of polynomials and factored and complete-square forms of the same polynomials, such as factors/roots and complete-square/transformations.
Learners will be aware of connections between the long run behavior of a rational function and its division-simplified form.
Other Details
Parental Guidance
GeoGebra Classroom is a free site running the open-source GeoGebra dynamic geometry software in such a way as to sync to the cloud and allow the teacher to view learners' work. Accounts which allow learners to sign back in with full access to previous work are offered, but not required. Learners need to give a name either when entering the class code or when setting up their accounts so that I can find their work in the teacher interface; if they wish, such as for added privacy, a nickname or pseudonym is OK.
TeacherMade is a site designed for school use which allows learners to access worksheets, tutorials, and practice problems. If they wish, such as for added privacy, learners can sign in using a nickname or pseudonym.
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.
Supply List
Scratch paper and pencils, or a whiteboard and markers. For writing in the Explain Everything meeting, as well as drawing on the TeacherMade homework pages, a touchscreen device or graphics tablet is beneficial, but learners can get by with mouse and keyboard. 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 homework 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. If you may apply to multiple colleges, consider that a digital portfolio is easier to duplicate, and can be printed if a physical copy is wanted. For this class, learners can use GeoGebra exclusively as their graphing calculator. Learners with future plans involving taking exams like the SATs should consider getting and beginning to use a calculator approved for those exams as soon as possible.
External Resources
In addition to the Outschool classroom, this class uses:
Joined May, 2021
4.9
11reviews
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
$60
for 4 classes2x per week, 2 weeks
50 min
Live video meetings
Ages: 13-18
1-12 learners per class
