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

Line Symmetry and Reflections

Objective

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

Approximate Time

45-minute lesson

Materials Needed

Lesson Structure

    Essential Questions

    What are the similarities and differences between the images and pre-images generated by reflections?
     
    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 reflections?
     
    How can reflections be applied to real-world situations?

    Warm-Up/Opening Activity

    Investigate reflectional symmetry.
     
    Worksheet: Line Symmetry

    Development of Ideas

    Activity:
     
    Investigate and apply reflections using a Mira™ and patty paper.
     
    Worksheet: Reflections
     
    Optional Activity
     
    Investigate and draw reflections on a coordinate plane.
     
    Worksheet (Cabri): Reflections on a Coordinate Plane

    Closure

    Summary questions
     
    Compare translations and reflections. What is the same? What is different?
     
    Answer: The size and the shape of the pre-image and image are the same (because they are isometries) but the orientation is different in reflections compared to translations (pre-image and image have the same orientation).
     
    Janet constructed the perpendicular from each of the vertices of a triangle to a line. How will this help her to find the image of the triangle reflected over the line?
     
    Answer: Since Janet has constructed the perpendicular to a line from each vertex, she can use each constructed line to help create a reflection. Janet can measure the distance from each vertex to the line, copy that distance to the other side of the line and mark a new vertex. This new vertex will be the reflection of the original vertex. Repeating this for each vertex and connecting the vertices, Janet will complete a reflection of the original triangle.

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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