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Transform Your Geometry into a Work of Art (Grades 9-10)

Master Teacher

Larry Crosswell

Time Allotment

Two 90-minute class periods

Overview

Geometric transformations and tessellations are typically difficult concepts for many students to visualize. This lesson will use artwork to help illustrate the major ideas of transformations and tessellations.

This lesson should be taught after students have discussed the basic ideas of rotation, reflection, and translation.

Subject Matter

Mathematics

Learning Objectives

Students will be able to:

visually identify transformations including reflections, rotations, and translations

discuss how artists, particularly M.C. Escher, have used transformational geometry in their artwork

South Carolina Standards

These Standards can be found online at Office of Curriculum Standards.

III. B. 2. Translate, reflect, rotate, and dilate figures on the plane.

III. B. 3. Analyze the symmetry of objects using the language of transformations.

III. B. 4. Use transformations and their compositions to make connections between mathematics and applications including tessellations or fractals, in particular with graphing calculators and geometry software.

Media Components

Video

Three-Dimensional Symmetry looks at the symmetry that is all around us: in buildings, manufacturing, art, and nature. This 17-minute video shows how transformations create symmetries in two and three dimensions. Computer animation makes it easy to visualize relationships found in symmetrical objects. The video goes outside, too, to show symmetry in the real world. Three-Dimensional Symmetry is available from:

Key Curriculum Press
1150 65th Street
Emeryville, CA 94608
800-995-MATH
800-541-2442

Web Sites

Escher Print of "Geckos. This Web site has a picture of M.C. Escher's work "Geckos."

Escher Art Collection. On this Web site, you will find several different works of Escher. Click on any picture to get a larger image of it.

Materials

Per student:

Escher Print Worksheet
pen or pencil and paper
markers or crayons
scissors
Graphing Calculator

Prep for Teachers

Prior to teaching this lesson, bookmark the Web site used in the lesson on each computer in your classroom.

Make an overhead or project "Geckos" onto the screen in your room. The Web site for this particular Escher print is Escher Print of "Geckos.

Copy the Escher fish print (Activity Sheet 1) for each student.

When using media, provide students with a Focus for Media Interaction, a specific task to complete and/or information to identify during or after viewing of video segments, Web sites, or other multimedia elements.

Introductory Activity

Step 1: Review with your students what the different types of transformations are that will be used in this lesson. They are reflections, translations, rotations, and dilations.

Step 2: Display the "Geckos" print and ask your students to identify what types of transformational geometry they can find in the print.

Learning Activity

Step 1: Make sure that your VCR is ready to play the tape that you have cued earlier. Provide your students with a Focus for Media Interaction, asking them to look for another name for reflectional symmetry. Push PLAY on the VCR. Push PAUSE when the commentator says, "palm down in front of you, you can see they are mirror images of each other" and the screen shows the hands moving up off the screen. Check your students for comprehension. (The answer to the question is mirror reflection.)

Step 2: Make sure that your VCR is ready to play the tape that you have cued earlier. Provide your students with a Focus for Media Interaction, asking them to locate the children's playground toy that has rotational symmetry. Push PLAY on the VCR. Push PAUSE when the commentator says, "The two matching halves change places" and the screen shows the salt and pepper shakers framed. Check your students for comprehension. (The answer to the question is a merry-go-round.)

Step 3: Provide your students with a Focus for Media Interaction, asking them "In what type of career field could you use translational symmetry?" PLAY the tape. STOP the tape after the commentator says, "form this chain" and the screen shows the picture of a chain. Check for comprehension. (The answer to question is construction or architecture or another field—make sure that the students know exactly why their choice of career field would use transformational geometry.)

Step 4: Provide your students with a Focus for Media Interaction, asking them to locate an Escher drawing that has any of the following symmetries: reflection, rotation, or translation. Make sure that you have bookmarked the Escher Art Collection Web page. Allow the students 5-7 minutes to come up with their answer. Have each student print out their choice of picture and write a 1-2 paragraph explanation of the types of symmetry that are shown in their picture.

Culminating Activity

Step 1: Hand out the fish worksheet to your students. Ask them to take the fish figure on their worksheet and choose either one or two transformation types to do to the fish on their paper. Allow 25-30 minutes for the students to fill in the sheet. Encourage the students to use different colors to fill in each different fish that they draw.

Step 2: Have the students get into groups of three and share their drawings. Tell them to figure out what type of symmetries the other people used in their drawings. Have the students pick out the drawing that they like the best from their group.

Step 3: As an Assessment: Take the best drawing from each group and have the group do a presentation on it. Make sure that they include why they felt it was the best drawing and what kind of transformations were used in the drawing. Cross-Curricular Extensions

Art: Have students research the artist M.C. Escher. Have the students locate what motivated Escher to use the different types of transformational geometry in his works.

Drafting/Engineering: Have students study Frank Lloyd Wright's architecture and ask them to discover different types of transformational geometry in his work.

Science: Have the students find examples of transformational geometry in nature. If the students are advanced, have them link together transformational geometry and the Fibonacci sequence.

Community Connections

Take the students to an art museum. Have them look at the different works and try to identify how transformational geometry plays a role in the paintings.

Have an architect or contractor come to class and have a discussion about how transformational geometry is used in their line of work.

Activity Sheets:

Activity Sheet 1: Worksheet