Process
Assignment 1
Before you can create a tessellation or a Kaleidoscope you need to understand the mechanics and the vocabulary of transformational geometry. To accomplish this task you will need to start a new section in your geometry notebook where you will define all the terms and record all the assignments involved in transformations. First let’s start with an introductory investigation. On the following link read through the introductory information on Transformational Geometry then perform the all the different Sketchpad Transformations. Finish by exploring the tessellations pages.
Now that you have introduced yourself to transformational geometry create a vocabulary section in your notebook for the following:
Transformation Glide reflection
Image Composition of isometries
Rigid transformation or isometry Point Symmetry
Translation Translational Symmetry Glide-reflectional Symmetry Glide reflection Monohedral tiling
Edge-to-edge tessellation Regular tessellation
Semiregular tessellation Demiregular tessellation
Dual of polygon tessellation
You may use the link above, chapter 8 of Discovering Geometry, a good mathematics dictionary, or web sources you may find. The following links may also be helpful in accomplishing this task.
Make sure to try the dynamic illustrations of transformation in this link:
If you find a web resource that seems applicable see me so we can evaluate the site and add it to our resources.
Now that you have a basic understanding of transformations complete exercise 8.1 from Discovering Geometry for more experience working with transformations.
I will provide you with due dates for each of the assignments at the start of your quest. I will check each piece and provide feedback at each due date.
Assignment 2
Now that you have a background in Transformations it is time to start looking at tessellations and kaleidoscopes. First explore the link below to see how a tessellation moves.
The next link will explain some basics of tessellations and explain what shapes tessellate.
As you see, many different shapes tessellate, the next link will show you how artist Hans Kuiper uses different shapes to create his art. Explore several of his pieces. Which one is your favorite?
Now it is time for you to get some hands on practice. Open sketchpad and the following links to create your own tessellation by translation and rotation. When you finish each piece make sure to fit it to page and print your results. Make notes on any difficulties you had and what you found easy. Add both pieces and narratives to your notebook.
This exercise will introduce you to the transformations needed for Kaleidoscopes. When you complete this exercise save it to the technology resource folder. Again please write a narrative about your successes and frustrations with this exercise.
If you have time and would like to try the ever popular Ferris wheel construction ask me for the instruction as the links I found do not work.
I will provide you with due dates for each of the assignments at the start of your quest. I will check each piece and provide feedback at each due date.
Assignment 3
You have now had experience with tessellations and kaleidoscopes and should have a feel for which you would prefer to make.
If you choose to make a tessellation you can either make one by hand using the instructions in Discovering Geometry chapter 8 or on Sketchpad using the instructions on the links in assignment 2. If you choose to use Sketchpad we can use the poster size printer to print the final draft.
If you choose to make a Kaleidoscope, I have included links with instructions or you can use the instructions in chapter 8 of Discovering Geometry. If you need some specialized materials let me know and I will try to find it for you.
Constructed Response
This assignment is something of a departure from what you have been doing. For one thing, it lays a heavy emphasis on applying geometry to create art. Write a constructed response that convinces the reader of the connection between geometry and art (adapted from Discovering Geometry by Michael Serra). Use Inspiration to organize and outline your response and attach it to your final product.
I will provide you with due dates for each of the assignments at the start of your quest. I will check each piece and provide feedback at each due date.
Assignment 4: The Conclusion
You will now work in an assigned group of four to explain and showcase the process and products you have created over the course of this Quest. You and your group will explain what you learned about transformational geometry and how you created you work of art.
You will need to include:
The basics of transformational geometry
Basic instructions on how you each created your artwork
You may choose to showcase your work in a PowerPoint, Video, Web page, Podcast or any other approved technology showcase.
Each member should be assigned pieces of the basics to do and each member needs to explain their piece and as a group put it all together in an interesting presentation using technology. For more information on requirements please see the final project rubric.
I will provide you with due dates for each of the assignments at the start of your quest. I will check each piece and provide feedback at each due date.
I see a certain order in the universe and math is one way of making it visible.
*May Sarton
