Author:
William Allred, Carrie Robledo
Subject:
Mathematics
Material Type:
Activity/Lab
Level:
High School
Tags:
  • Chord
  • Circles
  • Inscribed Angles
  • Interior Angles
  • Math 3
  • Secant
  • Segment Lengths
  • Tangent
    License:
    Creative Commons Attribution Non-Commercial Share Alike
    Language:
    English

    Education Standards

    9-12 Math 3: Discovering Circles

    9-12 Math 3: Discovering Circles

    Overview

    This is a unit length multi-learning style project that teaches the theorems and properties of Circles for the NC Math 3 curriculum. It includes hands on manipulatives using Exploragons, Digital Explorations in Geogebra, and a differentiating set of homework exercises through CK12.org.

    Instructor Directions

    Engineering Design Process

     

    Project Description

    Name of ProjectDiscovering Circles
    Subject AreaMath 3
    Targeted StandardsNC.M3.G-C.2 Understand and apply theorems about circles.
    Driving Question / Problem / ActivatorWhat are the properties/theorems for a circle?
    Project SummaryThis is a unit length multi-learning style project that teaches the theorems and properties of Circles for the NC Math 3 curriculum. It includes hands on manipulatives using Exploragons, Digital Explorations in Geogebra, and a differentiating set of homework exercises through CK12.org.
    Estimated Time4 days
    Materials / Resources (including link to slideshow if available)Exploragons Set, Protractors, CK12.org accounts, ChromebooksDay 1: Circle BasicsBasic Vocabulary: radius, circumference, diameter, arc, minor arc, major arc, semicircle, degrees in a circle, supplementary angles, complementary angles, circular segment, circular sector, central angle, arc measureGo through the flashcards. (Order: 1,2,3,7,4,5,6,10,11,12,15,16,14,8,17)And Task Cards 1,2,3,4,5Students will explore the Geogebra activity https://www.geogebra.org/m/hw3TGaA3 and complete the worksheet. Include additional vocabulary from the above list in preparation for the CK-12 Assignment.Students will explore the Geogebra Circle Properties Book sections on Arcs and Chords just 10.2  https://www.geogebra.org/m/Fk8CHJCe#chapter/195851Students will complete CK12.org section practices:Parts of Circles: https://www.ck12.org/user:bwz1cnlabmnty3mub3jn/book/NMHS-Math-3-4403439/section/6.7/Arcs in Circles: https://www.ck12.org/user:bwz1cnlabmnty3mub3jn/book/NMHS-Math-3-4403439/section/6.9/Day 2: Chords, Inscribed angles, Inscribed QuadrilateralsGo through the flashcards. (Order: 9,13,18)And Task Cards 9,7 (on 9, discuss both the right angle at the top and the other inscribed angle measures in the figure)Students will explore the Geogebra Circle Properties Book sections on Arcs and Chords just 10.3,10.4,10.5  https://www.geogebra.org/m/Fk8CHJCe#chapter/195851Students will explore the Geogebra Circle Properties Book sections on Inscribed Angles https://www.geogebra.org/m/Fk8CHJCe#chapter/195853Students will complete the CK12.org section practices:Chords and Central Angles: https://www.ck12.org/user:bwz1cnlabmnty3mub3jn/book/NMHS-Math-3-4403439/section/6.10/Inscribed Angles in Circles: https://www.ck12.org/user:bwz1cnlabmnty3mub3jn/book/NMHS-Math-3-4403439/section/6.11/Inscribed Quadrilaterals in Circles: https://www.ck12.org/user:bwz1cnlabmnty3mub3jn/book/NMHS-Math-3-4403439/section/6.12/Day 3: Interior angles, Exterior Angles (two tangents problem)Go through the flashcards. (Order: 19, 20)And Task Cards 10,11 (on 10, the chords will not necessarily reach to the other side of the circle if you use the pieces described on the card. You could use longer pieces as secants and still measure the angles)Include the following problem as a task today:Students will explore the Geogebra Circle Properties Book sections on Secants, Tangents, and Angle Measures https://www.geogebra.org/m/Fk8CHJCe#chapter/195854Students will complete the CK12.org section practices:Angles on and Inside a Circle: https://www.ck12.org/user:bwz1cnlabmnty3mub3jn/book/NMHS-Math-3-4403439/section/6.13/Angles Outside a Circle: https://www.ck12.org/user:bwz1cnlabmnty3mub3jn/book/NMHS-Math-3-4403439/section/6.14/Day 4: Segment Lengths (Chords, Secants, Secant / Tangent, Tangents)Go through Task Card 8 (positioning is odd)Students will explore the Geogebra Circle Properties Book sections on Special Segments in Circles https://www.geogebra.org/m/Fk8CHJCe#chapter/195875Students will complete the CK12.org section practices:Segments from Chords: https://www.ck12.org/user:bwz1cnlabmnty3mub3jn/book/NMHS-Math-3-4403439/section/6.15/Intersecting Secant Theorems: https://www.ck12.org/user:bwz1cnlabmnty3mub3jn/book/NMHS-Math-3-4403439/section/6.16/Tangent - Secant Theorem: https://www.ck12.org/user:bwz1cnlabmnty3mub3jn/book/NMHS-Math-3-4403439/section/6.17/
    TagsMath 3, circles, inscribed angles, interior angles, segment lengths, tangent, secant, chord

    Project Outline 

    AskWhat are the properties of circles with their angles and intersecting segments?
    ImagineIf you are given a circle and only a few details, how could you find the rest of the missing parts of the circle?
    PlanBegin with a circle and the vocabulary that you have learned in previous years. Use what you learn to find the other missing dimensions of the circle.
    CreateUse the exploragon figures to explore the different theorems in circles using Task Cards
    ImprovePractice your knowledge of the theorems discussed in the Task Cards.
    Closure / Student ReflectionsGeneralize the theorems and rules we discovered in circles to fit all circles.
    Possible Modifications / ExtensionsHave the students explore using the exploragon task cards to demonstrate that the theorems work in another example other than the ones done in class.

    Evaluation (Pre/Post)  

    Insert Links to Google Forms

     

    Pretest Link: https://drive.google.com/open?id=1S11ic2mjSuzm9DpoIF86FYWbbHtn_BpC

    Post-test Link: https://drive.google.com/open?id=1fT_XY5Gmu_ETk8M3WDKQI0cxvkB69ion

    Credits or Modified From

     

     

    Additional Resources / Help for teaching this lesson

     

     

     

     

    Sample Pictures / Video

     

      
      

     

     

    Teacher Comments of what worked / did not work well

    • There are 360 degrees in a circle and 24 pegs on the Exploragons Circle; each are 15 degrees.
    • The pieces are sized according to color. The sizes are written in tiny writing on the pieces.
    • Total time should be about 4 days, Feel free to extend day 1 if necessary as day 4 has less tasks.
    • Some of the task card descriptions are odd. Try them before you use them. Pictures are included in the above document for some.

     

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