Lesson plan

Lesson 14: Defining Rotations

teaches Alabama State Standards Geo-23.
teaches Alabama State Standards Geo-22.a.
teaches Alabama State Standards Geo-22.
teaches Alabama State Standards Geo-21.
teaches Arizona State Standards G.G-CO.A.4
teaches Common Core State Standards MP1 http://corestandards.org/Math/Practice/MP1
teaches Common Core State Standards MP5 http://corestandards.org/Math/Practice/MP5
teaches Common Core State Standards HSN-Q.A.3 http://corestandards.org/Math/Content/HSN/Q/A/3
teaches Common Core State Standards HSG-CO.A.4 http://corestandards.org/Math/Content/HSG/CO/A/4
teaches Common Core State Standards MP6 http://corestandards.org/Math/Practice/MP6
teaches Colorado State Standards HS.G-CO.A.4.
teaches Georgia State Standards MGSE9-12.G.CO.4.
teaches Kansas State Standards G.CO.1c.
teaches Kansas State Standards G.CO.1b.
teaches Kansas State Standards G.CO.1a.
teaches Kansas State Standards G.CO.1.
teaches Ohio State Standards G.CO.4.
teaches Pennsylvania State Standards CC.2.3.HS.A.1.

Lesson 14: Defining Rotations

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 Warm-up: 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 Cool-down: 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
  • Pre-printed cards, cut from copies of the blackline master
  • Protractors


  • 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. 


  • 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.HSG-CO.A.4MS.G-CO.4MO.G.CO.A.4






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