School Improvement in Maryland

Lesson Plan: Lesson plans were written by Maryland mathematics educators and could be used when teaching the concepts.

Goal 2 Geometry, Measurement, And Reasoning

Expectation 2.1 The student will represent and analyze two- and three-dimensional figures using tools and technology when appropriate.

Indicator 2.1.3 The student will use transformations to move figures, create designs, and/or demonstrate geometric properties.

Lesson Content

Rotational Symmetry and Rotations

Objective

The student will be able to identify the similarities and differences between the images and pre-images generated by rotations, apply rotations to determine the coordinates of vertices of figures, and apply rotations to real-world situations.

Approximate Time

45-minute lesson

Materials Needed

  • Worksheet/Answer Key: Rotational Symmetry
  • Worksheet/Answer Key: Rotations
  • protractor, ruler, patty paper, Mira™
  • Optional – Dynamic geometry software

Lesson Structure

    Essential Questions

    What are the similarities and differences between the images and pre-images generated by rotations?
     
    What is the relationship between the coordinates of the vertices of a figure and the coordinates of the vertices of the figure's image generated by rotations?
     
    How can rotations be applied to real-world situations?

    Warm-Up/Opening Activity

    Investigate rotational symmetry.
     
    Worksheet: Rotational Symmetry

    Development of Ideas

    Activity: Investigate and apply rotations using patty paper.
     
    Worksheet: Rotations

    Closure

    Summary questions
     
    Compare translations, reflections and rotations. What properties stay the same? What properties are different? Make sure to consider segment lengths, angle measures, perimeter and volume in your answer.
     
    Answer: Since translations, reflections, and rotations are isometries, all of the transformations produce congruent images, meaning the segment length, angle measure, perimeter, and volumes of pre-images and images are congruent. The orientation of the figures may be different.

Additional Resources

National Council of Teachers of Mathematics (NCTM). Navigating Through Geometry in Grades 6-8, 2002, Chapter 3 - Transformations and Symmetry, pp. 43-58.
 
National Council of Teachers of Mathematics (NCTM). Navigating Through Geometry in Grades 9-12, 2001, Chapter 1 - Transforming Our World, pp. 9-26.
 
Dixon, Juli, Movements in the Plane: Conjecturing about Properties of Transformations, NCTM Math On-Line January 2003
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