Skip to Main Content

Share Suggestion

Symmetry and Transformations of Polygons

Unit Plan

Symmetry and Transformations of Polygons

Objectives

In this unit, students will extend their understanding of the properties of two-dimensional shapes as they build on their earlier work with symmetry and congruence to encompass transformations, including those that produce line and rotational symmetry. Students will investigate and develop an understanding of transformations, including reflections, rotations, and translations. Studying transformation geometry will allow students to develop an understanding of how the orientation of a shape changes as it moves in space. Students will:

  • compare two-dimensional figures to determine which have reflective or rotational symmetry.

  • identify and describe symmetry within a figure or pattern.

  • identify and describe transformations, including translations, reflections, and rotations.

  • use polygons and other figures to demonstrate transformations.

  • design and analyze simple tilings using geometric figures and the rules of transformations.

  • use the concepts of symmetry to create and justify all possible tetromino figures.

  • create tessellating patterns using transformations including reflections, rotations, and translations.

Essential Questions

  • What strategies can we use to verify symmetry and congruency?

Related Unit and Lesson Plans

Related Materials & Resources

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

Formative Assessment

  • View

    Multiple Choice Items:

    1. Which of the following figures has no line symmetry?


    A
    01a.PNG


    B

    01b.PNG


    C


    01c.PNG


    D


    01d.PNG




    1. How many lines of symmetry does the figure below have?



    02a.PNG


    A 0
    B 1
    C 3
    D 5



    1. Which figure below has a line of symmetry marked that is not correct?

    03a.PNG



    4. Which figure below has 90° rotation (turn) symmetry?

    04a.PNG






    5. Select the figure below that has both reflection (flip) symmetry and rotational (turn) symmetry.

    05a.PNG



    6. What types of transformations are taking place in the figure below?

    06a.PNG


    A Rotation (turn)
    B Translation (slide)
    C Rotation and reflection (turn and flip)
    D Reflection, rotation, and translation (flip, turn, and slide)

    7. Select the figure which shows the use of translations (slides).

    07a.PNG




    8. Use the figure below to answer the question.

    08a.PNG


    Which transformation is shown?
    A reflection
    B reflection and translation
    C rotation
    D translation

    9. Which game board below (ignore game pieces) is not using translation (slide) as the main design element?

    09a.PNG



    Multiple-Choice Answer Key

    1. D

    2. D

    3. B

    4. A

    5. C

    6. D

    7. B

    8. D

    9. A


    Short Answer Items:

    10. Draw the reflection (flip) of the figure below over the center vertical line.


    10a.PNG

    11. Define how a translation (slide) changes a figure. Use an example to help explain.

    ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
























































































    12. Rotate (turn) the figure below 90° about the origin.
    12a.PNG


    Short-Answer Scoring Rubrics:

    10.



    10key.PNG






    11. A translation is when a figure stays the same shape and size and faces the same direction, but it slides up, down, left, or right on the paper. Examples will vary. This example shows a translation of up one and right 7 spaces.


    11key.PNG


    12.

    12key.PNG

    Use the following rubric for short answers 10–12.

    Points

    Description



    2
    • Written explanation and/or drawing is complete and detailed.
    • Demonstrates thorough understanding of the concept.
    • Answer is correct (and in proper form when applicable).



    1
    • Written explanation and/or drawing is correct but brief or simplistic.
    • Demonstrates partial understanding of the concept.
    • Answer is partially correct, a minor error in process is evident, or answer may not be in proper form.



    0
    • Written explanation and/or drawing is incorrect or missing.
    • Demonstrates no understanding of the concept.
    • Answer is incorrect, incomplete, or missing.
    Performance Assessment:


    CLASSROOM QUILT SQUARES


    paquilt1.PNG
    Each student will create a quilt square. The individual quilt squares of all of the students in the class will be combined to create a symmetry display.

    Directions to Student

    “Design a quilt square using symmetry and transformations. Use dot or grid paper that is 8 x 8 inches. Begin by drawing both a vertical and horizontal line through the center of your square and two diagonal lines through the center. Your design should be started in one quadrant (corner section) of the grid. You may choose to use pattern blocks or to create your own figures. You may also choose to use translations (slides), reflections (flips), and rotations (turns) within the first quadrant design or wait until the next step. Continue your quilt square by using translations, reflections, and rotations to fill the remaining sections of the quilt square with the same design as in the first section. You should use each of the three types of symmetry somewhere in your quilt square. Each shape used in your design should be shown four times, once in each of the four quadrants. Use color to decorate the quilt square and emphasize the elements within the design.

    Prepare a brief summary of your design describing the symmetry and transformations used. Describe them in detail including the color of each part. This description will be included in a class book about the quilt square display. Write neatly and be prepared to read your description to the class to introduce your design to the class.”


    Sample starting square:
    pastartingsquare.PNG

    Performance Assessment Scoring Rubric:

    Points


    Description

    4
    • Completed a detailed design within four quadrants of the quilt square.
    • The design in any quadrant is repeated accurately in each of the other quadrants using the concepts of symmetry and transformation.
    • Quilt square design incorporates reflection, translation, and rotation, each multiple times.
    • Demonstrates advanced understanding of the mathematical ideas and processes related to transformation and symmetry.
    • Written summary of design is neat, thorough, and detailed.
    • Worked beyond the problem requirements, possibly by using extra steps of rotation and/or incorporating technology or exceptional amount of detail in design.

    3
    • Completed a design within four quadrants of the quilt square.
    • The design in each quadrant is repeated in each of the other quadrants using the concepts of symmetry and transformation with very few errors (1 or 2).
    • Quilt square design incorporates reflection, translation, and rotation at least once each.
    • Demonstrates solid understanding of the mathematical ideas and processes related to transformation and symmetry.
    • Written report is neat and thorough.
    • Meets all of the problem requirements.

    2
    • Completed a design within the quilt square but divided it into something other than quadrants.
    • The design in any section is repeated in each of the other sections using the concepts of symmetry and transformation with but with 3 or more errors.
    • Quilt square design incorporates 2 of 3 elements, reflection, translation, or rotation, at least once.
    • Demonstrates some understanding of the mathematical ideas and processes related to transformation and symmetry.
    • Written report is too brief, lacking detail on several components of symmetry.
    • Partially meets the problem requirements.


    1
    • Completed a design within the quilt square, but it is not divided into quadrants or sections of any recognizable size.
    • Major errors in redrawn sections of the design and/or missing parts in the repetitions.
    • Quilt square design incorporates 1 of 3 elements, reflection, translation, or rotation, at least once.
    • Demonstrates substantial lack of understanding of portions of the problem related to transformation and symmetry.
    • Written report is significantly incomplete or has inaccuracies throughout.
    • Does not meet several of the problem requirements.

    0
    • Incomplete design within the quilt square, with or without divisions.
    • Major portions of the repeated design sections missing or not drawn with symmetry to match other design parts.
    • Quilt square design incorporates none of the elements; reflection, translation, or rotation, or incorporates 1 partially.
    • Demonstrates a complete lack of understanding of the problem.
    • Written report is missing.
    • Does not meet any of the problem requirements.

DRAFT 10/19/2010
Loading
Please wait...