MATHART

Connecting Geometry and Art

A WebQuest for High School Students

Introduction | Task | Process | References |Evaluation Conclusion

Introduction

Scenario:  I must go out of town for the last two weeks of the semester.  You are going to be the teacher!  Research, design and then teach a lesson to help review for the semester exam.  Think about what you've learned about basic geometric figures, congruence, similarity, polygons, and transformations.  It's time to get creative with math - integrate it with art. Make your lesson fun, relevant and/or unusual. Devise a lesson for your classmates to create works of art.  You will be making new connections between math and art utilizing a hands-on approach. Choose one of the following topics:  cartography, technical drawing, tessellations, fractals, tangrams, the golden rectangle, wycinanki, or origami.  Let's get started.

The Task

Your task is to design and present a lesson that integrates art and geometry.  Research material from a variety of online web resources. Utilize these as a starting point to expand on previously learned geometric concepts.  Include the historical background and significance of the art form.  Plan for a hands on, creative art project that demonstrates the art form.  Instruct the class to complete the project.  Your presentation must include:

•  Research on the history of this topic:  What mathematician and/or artist has used this type of mathematics and in what way?
•  A summary of how this topic relates to the units studied this semester:   What mathematical skills do you need to understand the art?
• Prepare a 5 –10 minute presentation about the method you chose. Teach the class some of the basics of what you have learned and design a quick problem for a volunteer to practice (Don’t pick a goof ball). DO NOT READ BORING PARAGRAPHS TO THE CLASS! Discuss it like you know what you are talking about! Use several visual aids to help the class understand the topic.

The Process
1. Examine one of the following topics: the golden rectangle, fractals, tangrams, technical drawing, cartography, or wycinanki (Polish paper cutting). Visit the various links and see what items might interest you.   Place your top three topic choices on a piece of paper in numerical order.  2. When you get into your groups, share ideas and brainstorm and see who would be the best person to perform each task. 3. With your team members, look at the websites for your topic and think about the questions from your role's perspective.
4.  Many of the websites will have lessons and instructions pertaining to your subject.  As a group discuss what kind of art lesson you could create.  Design the art lesson.  5. Remember the overriding goal is to relate geometric principles to your art project using proper vocabulary terms related to math. The project is based on a core understanding of the geometry involved. You may want to consult your textbook or some of the other geometry books in class to help in making the connections.
6. Look at the Design Principles for help in creating your art lesson for the class. 7. Design a presentation for the class to teach the art lesson.   Make sure the lesson includes all the items described in the task.  Each member of your team should have a speaking and/or teaching part in the presentation. 8. With your group decide how to present the material required in the task. You may use presentation software such as PowerPoint. It may be done in the classroom using the tv-computer monitor.  Include examples of artists' works in your presentation.  You may teach the entire class or you may use a volunteer (no goofballs) for your art lesson. 9. Hand in a portfolio of your team's work.  It should include the following: Summary of the historical background including citations for your references  Summary of how what you previously studied in class relates to your topic Summary of the connection between math and art Completed lesson plan  Evaluation rubric for lesson plan Reflection paper summarizing your experience - see the conclusion
References for Math Art
Select your topic and then click to explore and learn! Feel free to use other sites and/or library reference materials for your project.  Just be sure to include proper citations in your research.
Fractals
Introduction to fractal - read this first
History of Mandelbrot
Lots of information about fractal
Fractals and mathematics
What does broccoli have to do with fractals?
Understand the mathematics of fractals
Great pictures of fractals
Computer assisted fractals
Paper folding fractals
Tangrams
Easy tangrams
Play with tangrams now!
Tangram puzzles and solutions
History of tangrams
More difficult tangram puzzles
Mathematical properties
How do they fit together?
Directions for constructing tangrams
Pythagorean tangram
An interesting tangram problem
Online puzzle
Technical Drawing
Perspective in drawing
How to draw 3-D geometric shapes
History of use of depth in art
Geometry of 3-D drawing
Perspective and links to examples in art
Mathematics of perspective
Renaissance art and mathematical perspective
History of perspective
Nice lessons on all types of perspective
Unusual applications of perspective by Ecsher
Cartography
Mathematics of map coloring
Topology
History of mapmaking
Mapmaking and mathematics
Algorithms and Ice Cream for All
The Four Color Problem and Origami
Some unsolved problems
History of the 4 color problem
Cartography for kids
Wycinanki
Introduction to Polish paper cutting
Website of  wycinanki
Background of papercutting
History of paper cutting
Start from a snowflake
Computer assisted wycinanki
Pictures of wycinanki
Example of wycinanki lesson

	Evaluation
Web Quest Evaluation Rubric
Conclusion
What have you learned about "teaching" after completing this project?  Was it easier or more difficult than you expected?  Did completing this project give you a better understanding of the material we have studied this semester?  What topics were especially interesting?  What topics would you like to explore further?  Write a reflection paper commenting on the above topics.  Include it in the team's portfolio.
Based on a template from The WebQuest Page.