Lesson Title: Angle Relationships in a Circle (Central Angle Thm)
Course: Geometry (G..C.2)
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Lesson Objective(s): What mathematical skill(s) and understanding(s) will be developed?
G.C.2: Identify and describe relationships among inscribed angles, radii, and chords.
Lesson Launch Notes: Exactly how will you use the first five
minutes of the lesson?
Draw a circle on the board containing a radius, diameter,
and chord. Use capital letters to identify endpoints. Have
students use your drawing to name and define a:
1. radius
2. diameter
3. chord
Lesson Closure Notes: Exactly what summary
activity, questions, and discussion will close the
lesson and provide a foreshadowing of tomorrow?
List the questions.
How do we find the central angle, given the
inscribed angle?
How do we find the inscribed angle, given the
central angle?
Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations,
problems, questions, or tasks will students be working on during the lesson?
1. Lesson Launch – This will determine students’ prior knowledge regarding parts of a circle.
(UDL I:3) Have students share their responses.
2. Introduction of Task – Explain to students that they will be investigating angle relationships
formed by radii, diameters, and chords. They will be constructing circles and using their
protractors to measure angles. (If necessary, review how to use a protractor.)
3. As a whole class, instruct students on what constitutes a central angle and an inscribed angle. Have
students construct a circle and draw and label a central angle, with an inscribed angle intercepting
the same arc.
4. In small groups, have each student construct three different circles with a compass. Each circle
should have a central angle and inscribed angle (using a ruler). Each student should use the
protractor to measure the central and inscribed angles in each circle. Have students discuss their
results with their group to see if they can come up with a conjecture regarding the relationship
between the angle measures. (UDL I:2)(UDL II:5)
5. As an alternative for students that have difficulty using the compass and protractor, students can use
Geometer’s Sketchpad for their constructions and measurements. (UDL I:1, 2, 3)(UDL II:4, 5)
6. As students are working, you may want to have the following website
http://www.mathopenref.com/arccentralangletheorem.html available for students struggling with
the construction or measurement. (UDL III:8)
7. Bring the class back together. Have groups share what they learned through their investigation.
Students should be able to informally state the Central Angle Theorem. Provide the formal
definition.
8. Ask students to conjecture what would be the measure of a central angle if the inscribed angle was
a right angle. Allow time for students to use their construction and measurement tools to check out
their conjecture. Then share as a class. (UDL III:8)
March 14, 2012
Lesson Title: Angle Relationships in a Circle (Central Angle Thm)
Course: Geometry (G..C.2)
Date: _____________ Teacher(s): ____________________
Start/end times: _________________________
Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I
measure student mastery? That is, deliberate consideration of what performances will convince you (and any outside
observer) that your students have developed a deepened (and conceptual) understanding.
Students will be able to explain the central angle theorem.
Students will be able to calculate the measure of an inscribed angle, given a central angle.
Students will be able to calculate the measure of a central angle, given the inscribed angle.
Notes and Nuances: Vocabulary, connections, common mistakes, typical misconceptions, etc.
Central angle, inscribed angle
Students might double an angle when they are supposed to divide it by two.
Students may make arithmetic mistakes.
Resources: What materials or resources are essential for
Homework: Exactly what follow-up homework
students to successfully complete the lesson tasks or activities?
tasks, problems, and/or exercises will be assigned
upon the completion of the lesson?
Protractor
Provide a worksheet of circles with either the
Ruler
inscribed angle or central angle measure provided.
Compass
Make sure to include some inscribed right angles.
Computers with internet access
Geometers Sketchpad
http://www.mathopenref.com/arccentralangletheorem.html
Lesson Reflections: What questions, connected to the lesson objectives and evidence of success, will you use to
reflect on the effectiveness of this lesson?
Were students able to do the constructions and draw conjectures on their own?
How can this be connected to measures of intercepted arcs?
March 14, 2012