Rotational and Reflectional Symmetry Lab
Your Assignment: The Mayor of Ito City, Shizuoka Province, Japan is coming to Middletown, Rhode Island, U. S. A. to present a Proclamation of Friendship to the people of Middletown. During his visit the town council plans on discussing the possibility of creating a sister city relationship with Ito City. As part of the plan to impress the mayor, the town council wants to create a town crest similar to what they have in Japan. Since it is going to be on all of the manhole covers in town, it has to be in a circle. The other requirement is that it be rotationally or reflectionally symmetric, or both. Your job is to create the town crest to the satisfaction of the town council.
Part 1: Create A Rotationally Symmetric Figure
To practice your skills you first need to create a rotationally symmetric figure on the circle below. This can be a polygon or a curved figure. You should use a ruler, compass and protractor to create the image. First, locate the center of the circle and the points on the circle that represent the fractional amount of turn for your symmetric figure. Now use the compass, ruler and free-hand drawing to create each part of the symmetric figure. When your figure is completed, you should color it.
Part 2: Create A Reflectionally Symmetric Figure
To practice your skills you now need to create a reflectionally symmetric figure on the graph below. This can be a polygon or a curved figure as well. First draw your line (or lines) of reflection. Next, locate your pre-image points and then reflect them over your line(s) of reflection. Finally, complete the figure and color it.
Part 3: Create the Town Crest
You are now prepared to create the town crest. On a separate sheet of graph paper, draw a circle and create the town crest. The crest should have images that somehow have meaning to the town and should be in color. You can use your image sheet for inspiration, but you should not directly copy an image.
Part 4: Explain the Symmetry in your Work
Question #1: Explain how your work in part 1 is rotationally symmetric. Include reference to the amount of rotation needed to demonstrate this symmetry.
Question #2: Explain how your work in part 2 is reflectionally symmetric. Include reference to how you would demonstrate this symmetry.
Question #3: Explain how your work in part 3 is symmetric. Include reference to the amount of rotation needed to demonstrate this symmetry or how the reflectional symmetry is determined. Explain what the town crest represents and the symbolism used in the final product as it relates to Middletown.
Question #4: Reflect on how this lab has helped you learn about reflectional and rotational symmetry. Explain how this experience relates to the stated objectives of the Middletown High School Academic Student Learning Objectives.
The Symmetry Lesson Plan and Examples of Student Work
Below you will find the text of the lesson plan on the left and links to samples of student work for each part of the assignment on the right. Please note that part 4 was an addition that I created after I piloted the task. As such, there are no examples of this section. Also note that at the bottom of the page there is a link that provides the word document for the entire lab, including the rubric. If you enjoy my students' work, please let me know and I will share it with them. If you use my lesson plan, please let me know, so that I can share it with my principal! Just kidding! I just would like to know if it made a difference to anyone out there in cyberland. My address is: sfagan@mpsri.net Thanks!
