Outschool
Open currency, time zone, and language settings
Log In

Geometry: Learning Circles

In this 9 session online course, students will learn all about circles and their properties.
Ms. Kate Mcmahon
Average rating:
4.9
Number of reviews:
(20)
Class

What's included

9 live meetings
9 in-class hours
Homework
2-4 hours per week. The homework that will be assigned will consist mainly of worksheets. Students may be given time during class to work on homework or to ask questions on homework from the previous lesson. Homework for each lesson should take up to 60 minutes to complete (about 2 hours total max per week).
Assessment
The students will be given 2 assessments during this course. These will either be quizzes or tests to gauge the students understanding. Students will be encouraged to use mistakes as learning moments to improve and as tools on the way to gain mastery of the material.

Class Experience

US Grade 9 - 11
This class will cover: 
Day 1: 
Circles Vocabulary: 
-definitions of line, ray, segment, circle, chord, diameter, radius, tangent, point of tangency, secant, semicircle, central angle, arcs (major and minor arcs)
-how these terms relate to each other
-how to identify them
Day 2:
Tangent Theorems: 
-definitions of a tangent segment, externally tangent circles, internally tangent circles, and common tangent
-Perpendicular Tangent Theorem and its converse
-tangent segments from a common external point are congruent
-how to use these theorems to solve 
Day 3:
Chord Theorems: 
-if a radius is perpendicular to a chord then it bisects that chord (converse is also true)
-the perpendicular bisector of a chord passes through the center of the circle (converse is also true)
-if two chords are equidistant to the center of a circle, then those two chords are congruent (converse is also true)
-if two chords are congruent, then their corresponding arcs are also congruent (this also applies to central angles) 
-how to use these theorems to solve
Day 4: 
Assessment of material, check on students progress to see if they not only understand the concepts but can connect the concepts to solve multi-layered problems
Day 5:
Relationships of Angles (formed inside, outside and on the circle):
-relationship from 2 intersecting chords that form an interior angle to the circle 
-definition of an inscribed angle and its relationship to its corresponding chords
-relationship from a chord and a tangent line that form an angle on the circle
-relationship from a tangent and tangent, tangent and secant, and secant and secant that all form an exterior angle to the circle
-how to use these theorems to solve
Day 6:
Segment theorems:
-Chord-Chord Power Theorem
-Tangent-Secant Segment Power Theorem
-Secant-Secant Segment Power Theorem
-how to use these theorems to solve
Day 7:
Circumference, Area, Area of a Sector, and Arc Length:
-definition of circumference, area, pi (and why we use pi for circles)
-how to determine the length of an arc on a circle
-how to determine the area of a sector of a circle
Day 8:
Review, Connection to real world concepts:
-how we use circles and these topics in real world applications
Day 9:
Final assessment of material retention 

In each class, we will start the class by answering questions from the homework from the previous lesson, then we will go over notes on the new topic, answering any questions as we work on practice problems associated with the new material. Guided notes will be provided for the lessons (outside of assessment days). Any extra time in class will be to work on the homework of that day or to answer any other questions the students may have. 
For class discussions, step by step solving of problems from notes and worksheets, and answering any questions, I will be using my personal white boards. Via Zoom, each lesson will also be using screen share to go over power-points, to show moving diagrams on my Geometer's sketchpad, and to go over answers to previous homework or quizzes.
An example of the class structure for each 60 minute meeting:
10 minutes: Welcome, Answering any questions from last lesson, going over any homework questions, encourage discussion on last covered material
40 minutes: Guided notes (with accompanying power-point) and practice problems (Students may ask questions during this time as well)
10 minutes: Answering questions from lesson, allow students to work on worksheet/homework, and discussion on topics and how they relate to every day life 
With every lesson, I allow some flexibility in the hour so that questions can be answered or topics and be revisited if needed. 

My teaching style is to connect the material to each other so that students will see how each topic relates. I encourage discussion/questions and am willing to explain the topic in different ways so the students can understand the material. I use multiple forms of media to help students who learn differently: auditory- will relate to my guided notes which allow students to listen more to my explanations of the material, visual- will relate to the many diagrams and pictures I will include in my lessons for students to understand the material, kinesthetic- will relate to me encouraging students to use whatever medium they would like to take notes and work on the material. 

Students should have pre-algebra and algebra skills for this class.
Learning Goals
Students will be able to identify parts of a circle and how they relate to each other. They will learn the different theorems about tangents and chords and be able to use those theorems to solve problems. Students will be learning about angles in, out, and on the circle. Given one of these angles with a circle, the students will be able to use properties to solve for a missing variable. Students will be learning about the relationship of different segments and their lengths with circles. Given different segments, students will be able to use these properties to solve for a missing variable. Students will be able to find the circumference and area of a circle and what that means in real world problems. Students will be able to use circumference and area to find a length or area of an arc/sector on the circle.
learning goal

Other Details

Supply List
Guided notes for each lesson will be provided as well as any homework assignments. Students are encouraged to use calculators to help them with the material (scientific calculators are ok to use as well).
External Resources
Learners will not need to use any apps or websites beyond the standard Outschool tools.
Joined June, 2020
4.9
20reviews
Profile
Teacher expertise and credentials
Georgia Teaching Certificate in Mathematics
I have my Bachelors in Secondary Mathematics Education from Kennesaw State University. I have taught in both the public and private school settings. Working with students one-on-one and in a group setting as a tutor to find what methods and strategies work best for them has been an absolute joy on top of teaching. I have worked with this topic as an instructor for over 7 years and continue to strive for the best way to make math engaging and understandable.

Reviews

Live Group Class
Share

$40

weekly or $120 for 9 classes
3x per week, 3 weeks
60 min

Completed by 3 learners
Live video meetings
Ages: 14-17
3-12 learners per class

This class is no longer offered
About
Support
SafetyPrivacyCA PrivacyLearner PrivacyManage Data PreferencesTerms
Financial Assistance
Get The App
Download on the App StoreGet it on Google Play
© 2024 Outschool