Transformations

  • Exploring Transformations

    8th grade

    Description

    Explore properties of transformations with the purpose of noticing patterns, making generalizations, and developing rules.

    Hook

    Project (or provide copies) of the Hook Overhead Sheet (PDF). To stimulate curiosity and increase student motivation, lead the class in a brief visible thinking routine called "I see, I think, I wonder". This type of experience sets the stage for inquiry-based learning. Encouraging students to be creative and thoughtful with their observations and interpretations helps promote discourse in the classroom. (More research and graphic organizers for this routine can be found online). Allow students 3-5 minutes to write their response prior to sharing in class. This can be done in a variety of ways. For example:

    • journals
    • notebooks
    • sticky notes to post on chart paper
    • etc..

    When sharing begins, encourage students to state all three of their responses at the same time, i.e. “I see… I think… I wonder…”

    Lessons

    Lesson 1 of 4

    Develop an understanding of translations in the coordinate plane and determine general rules for translations through exploration.

    Lesson 2 of 4

    Develop an understanding of reflections in the coordinate plane, and determine general rules for reflections through exploration.

    Lesson 3 of 4

    Explore rotations on a coordinate plane where (0,0) is the center; determine general rules for rotations.

    Lesson 4 of 4

    Students will develop an understanding of dilations on the coordinate plane and general rules for dilating an image through exploration.

    ARC Assessement

    Technology Resources


    Related Resources

    From Math Teaching in the Middle School, by Sharon E. Taylor and Kathleen Cage Mittag

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  • ARC Global Essential Question(s)

    What are general rules and patterns for applying each transformation to an image? Which properties of the image are preserved through each transformation?

    Keywords

    transformation, reflection, rotation, dilation, translation, slide, flip, turn, scale factor

    Vocabulary

    • coordinates
    • quadrant
    • vertex
    • x-axis
    • y-axis
    • orientation
    • congruent
    • line of reflection
    • center of rotation
    • translation
    • center of dilation
    • transformation
    • slide
    • flip
    • turn
    • extend
    • reflection
    • scale factor
    • compression
    • stretch
    • shrink

    Standards

    CCSS, Content Standards to Domain Level

    • 8.G.A.1Verify experimentally the properties of rotations, reflections, and translations:
      • Lines are taken to lines, and line segments to line segments of the same length.
      • Angles are taken to angles of the same measure.
      • Parallel lines are taken to parallel lines.
    • 8.G.A.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

    CCSS, Standards for Mathematical Practices

    • SMP 1 Make sense of problems and persevere in solving them.
    • SMP 5 Use appropriate tools strategically.
    • SMP 8 Look for and express regularity in repeated reasoning

    Contributors

    Original Sources: Adapted from an Illuminations’ lesson plan: Flip-n-Slide: Exploring Transformations through Modelings and Computer Games
    Original Author(s): Susan James
    Arc Author(s): Amber Candela, AnnMarie Varlotta
    New Editors: Katelyn Albright, Autumn Elrod, Jennifer Plumb, and AnnMarie Varlotta