Similarity and Scale | Prealgebra, Module 2
In this 4 week class, the second month of a prealgebra curriculum, learners will extend their explorations of geometry from rigid transformations to nonrigid transformations, and apply proportionate reasoning.
Avrila at Math With Avrila
Average rating:
4.9
Number of reviews:(11)
What's included
12 live meetings
10 in-class hoursHomework
2-4 hours per week. Learners will have homework in TeacherMade regularly, sometimes with links to GeoGebra. Tasks will include independent practice, preparation for upcoming lessons, and taking in information in written or video clip form.Assessment
Assessments will be assigned as out-of-session work using the same tools as homework.Class Experience
US Grade 6 - 8
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.) This is a full-curriculum type class, so learners will also have asynchronous assignments, including independent practice, new information in written or video clip form, and preparation assignments to start on before class. Learners will also receive access to Prodigy for optional extra practice. 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. In addition to specific skills from the previous module, learners should already be familiar with the usual previous elementary and junior high math, such as the four operations with fractions or any number of digits, basic geometry, coordinate graphing, etc. We will review briefly when using previous skills as a step, but not fully develop these skills from scratch.
Learning Goals
Learners will draw and interpret scaled figures.
Learners will apply scale in context, such as maps and floor plans.
Learners will apply transformations given as coordinate rules and describe properties of the images under these transformations as compared with the original ("preimage").
Learners will understand similarity as the relationship between figures with the same proportions but possibly different scales.
Learners will understand the relationship between congruence and similarity as in one direction a relaxation of the "same size" requirement, and in the other direction, a specification of scale factor 1.
Learners will use information about similar polygons.
Learners will explore congruency and similarity properties for triangles, using GeoGebra for counterexample hunting and transformations for proofs.
Learners will understand slope as related to the ratio of horizontal and vertical sides forming a triangle above or below a segment, including one specified by its endpoints.
Learners will understand that the slope formula encapsulates that concept of slope for calculation purposes.
Learners will use the slope formula as an unsimplified point-slope formula for linear relationships.
Syllabus
4 Units
12 Lessons
over 4 WeeksUnit 1: Using Scale
Lesson 1:
Scaled Copies and Scale Factor
50 mins online live lesson
Lesson 2:
Scaled Relationships
50 mins online live lesson
Lesson 3:
Scale Drawings
50 mins online live lesson
Unit 2: Changing Scale
Lesson 4:
Scaling Up and Down
50 mins online live lesson
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. Learners do not need an account but do provide their names to access the activity. 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.
Prodigy is a gamified math practice webapp. Using it is not required but offered.
Pre-Requisites
Transformations and Congruence module, or equivalent. Learners will also be more successful if they have generally junior high level calculation skills.
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 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.
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 Course
$57
weekly or $225 for 12 classes3x per week, 4 weeks
50 min
Completed by 1 learner
Live video meetings
Ages: 11-15
1-12 learners per class
