Lesson 14

Defining Rotations

Lesson Narrative

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.

Learning Goals

Teacher Facing

  • 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.

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.

CCSS Standards

Building On


Building Towards

Glossary Entries

  • 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.

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