## Instructor Directions

## Project Description | |

Name of Project | Discovering Circles |

Subject Area | Math 3 |

Targeted Standards | NC.M3.G-C.2 Understand and apply theorems about circles. |

Driving Question / Problem / Activator | What are the properties/theorems for a circle? |

Project Summary | 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. |

Estimated Time | 4 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/ |

Tags | Math 3, circles, inscribed angles, interior angles, segment lengths, tangent, secant, chord |

## Project Outline | |

Ask | What are the properties of circles with their angles and intersecting segments? |

Imagine | If you are given a circle and only a few details, how could you find the rest of the missing parts of the circle? |

Plan | Begin 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. |

Create | Use the exploragon figures to explore the different theorems in circles using Task Cards |

Improve | Practice your knowledge of the theorems discussed in the Task Cards. |

Closure / Student Reflections | Generalize the theorems and rules we discovered in circles to fit all circles. |

Possible Modifications / Extensions | Have 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

**Geogebra Circle Properties Book:****https://www.geogebra.org/m/Fk8CHJCe****CK12.org Math 3 Book:****https://www.ck12.org/user%3Abwz1cnlabmnty3mub3jn/book/NMHS-Math-3-4403439/****Math 3 Digital Notebook for additional notes:****https://drive.google.com/open?id=0BxClYaZamogrd3dvdGUyeUptOGM**

## 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.