Lesson plan

Lesson 8: Rotation Patterns

teaches Alabama State Standards 8-23.
teaches Alabama State Standards 8-22.
teaches Arizona State Standards 8.G.A.1
teaches Common Core State Standards MP8 http://corestandards.org/Math/Practice/MP8
teaches Common Core State Standards MP7 http://corestandards.org/Math/Practice/MP7
teaches Common Core State Standards 8.G.A.1.a http://corestandards.org/Math/Content/8/G/A/1/a
teaches Common Core State Standards 8.G.A.1.b http://corestandards.org/Math/Content/8/G/A/1/b
teaches Colorado State Standards 8.G.A.1.b.
teaches Colorado State Standards 8.G.A.1.a.
teaches Colorado State Standards 8.G.A.1.
teaches Georgia State Standards MGSE8.G.1.
teaches New York State Standards NY-8.G.1b.
teaches New York State Standards NY-8.G.1a.
teaches Pennsylvania State Standards CC.2.3.8.A.2.

Lesson 8: Rotation Patterns

In this lesson, rigid transformations are applied to line segments and triangles. For line segments, students examine the impact of a 180 degree rotation. This is important preparatory work for studying parallel lines and rigid transformations, the topic of the next lesson. For triangles students look at a variety of transformations where rotations of 90 degrees and 180 degrees are again a focus. This work and the patterns that students build will be important later when they study the Pythagorean Theorem. 

Throughout the lesson, students use the properties of rigid transformations (they do not change distances or angles) in order to make conclusions about the objects they are transforming (MP7).

Lesson overview

  • 8.1 Warm-up: Building a Quadrilateral (5 minutes)
  • 8.2 Activity: Rotating a Segment (15 minutes)
    • Includes "Are you Ready for More?" extension problem 
    • There is a digital applet in this activity.
  • 8.3 Activity: A Pattern of Four Triangles (10 minutes)
    • There is a digital applet in this activity. 
  • Lesson Synthesis
  • 8.4 Cool-down: Is it a rotation? (5 minutes)

Learning goals:

  • Draw and label rotations of 180 degrees of a line segment from centers of the midpoint, a point on the segment, and a point not on the segment.
  • Generalize (orally and in writing) the outcome when rotating a line segment 180 degrees.
  • Identify(orally and in writing) the rigid transformations that can build a diagram from one starting figure.

Learning goals (student facing):

  • Let’s rotate figures in a plane.

Learning targets (student facing):

  • I can describe how to move one part of a figure to another using a rigid transformation.

Required materials:

  • geometry toolkits


  • Access the complete Grade 8 glossary.


  • This lesson builds towards the standard:CCSS.8.G.A.1.cMS.8.G.1c






IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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