Lesson 14: Defining Rotations
About this lesson
The purpose of this lesson is to develop a rigorous definition of rotation, building on what students know from previous courses. Students first focus on what information is important for defining a rotation and then determine properties of rotations by rotating segments to make isosceles triangles. Students attend to precision when they clarify what information they need to uniquely determine a given rotation (MP6).
Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.
Lesson overview
 14.1 Warmup: Math Talk: Comparing Angles (5 minutes)
 14.2 Activity: Info Gap: What’s the Point: Rotations (15 minutes)

14.3 Activity: Turning into Triangles (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 14.4 Cooldown: What Went Wrong? Rotation (5 minutes)
Learning goals:
 Comprehend that the term "rotation" (in written and spoken language) requires several descriptors including angle, center, and direction.
 Determine whether a figure is a rotation of another.
 Draw rotations of figures.
Learning goals (student facing):
 Let’s rotate shapes precisely.
Learning targets (student facing):
 I can describe a rotation by stating the center and angle of rotation.
 I can draw rotations.
Required materials:
 Geometry toolkits
 Preprinted cards, cut from copies of the blackline master
 Protractors
Glossary:

rotation  A rotation has a center and a directed angle. It takes a point to another point on the circle through the original point with the given center. The 2 radii to the original point and the image make the given angle.
\(P'\) is the image of \(P\) after a counterclockwise rotation of \(t^\circ\) using the point \(O\) as the center.
Quadrilateral \(ABCD\) is rotated 120 degrees counterclockwise using the point \(D\) as the center.  Access the complete Geometry Course glossary.
Standards:
 This lesson builds on the standard:CCSS.8.G.A.1MS.8.G.1MO.8.GM.A.1aMO.8.GM.A.1b
 This lesson builds towards the standard:CCSS.HSGCO.A.4MS.GCO.4MO.G.CO.A.4
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