1080 Stomps and Angles in Circles

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Objective

SWBAT identify and apply concepts of central angles to real-world problems.

Big Idea

This lesson connects snowboarding with degrees in circles and also asks students to explore angles in circles using a hands-on folding activity.

Do Now, Snowboarding Video and Exploration

40 minutes

Students will enter class and work on a Do Now that asks them to review properties of tangent lines and also factoring a trinomial.  If students struggle with factoring trinomials, teachers may want to build in a review question in the next day’s Do Now to continue to review this pre-requisite skill.

 

To engage students in this lesson and connect their knowledge to real-world examples, teachers can start class by watching the following video of Shaun White, an Olympic snowboarder:  https://www.youtube.com/watch?v=gfTXUWlJCxk  There are questions for students to fill out on student notes, and these questions focus on students connecting the idea of rotations and degrees in a circle and semicircle. 

 

After watching the video, students will work on the Angles in Circles Exploration handout, only the first page, to explore the relationships between arcs and central angles.  I would suggest having students work in pairs on this activity and work together to complete the hands-on tasks while also answering questions.  This is an exploratory activity and does not need to be fully reviewed by the whole class. However, teachers may want to emphasize question #2 and #8 which focus on semicircles and determining that circles have 360 degrees.  Question #9 also allows teachers to transition to the idea of a central angle, the first key term which will be defined in class notes.  Please see the video narrative for a more formal explanation of this connection.  Further, these notes define important key terms in this entire unit, and students should pay close attention to definitions and use precision when utilizing these (MP 3).

Exit Ticket and Activity/Homework

15 minutes

After reviewing all examples in class notes, students can work in small groups on the practice questions attached.   I would suggest that teachers either put answers on the board or review at least 1 example from questions #1-10 and either #11 or #12.  Students can then view and analyze each other's work (MP 6).

To wrap up class, students will complete an exit ticket which asks students to find the measure of a major arc.