OVERVIEW: During previous lessons on patterns and sequences, symmetry, asymmetry, and symmetry breaking have been taught. Here is a great cooperative learning lesson which links the art and beauty of oriental carpets to math class.
OBJECTIVES:
1. Students will work cooperatively to create on graph paper an oriental carpet.
2. Students will be able to show their understanding of symmetry, asymmetry, and symmetry breaking.
RESOURCES/MATERIALS:
1. Large graph paper
2. Colored pencils/magic markers
3. Ruler
4. Compass
5. Samples of carpets
6. Photos of carpets
7.Symmetry and Pattern: The Art of Oriental Carpets
PROCEDURE:
1. Group Size: 3-4 students per group depending on class size.
2. Assignment to Group: Teacher assigned, heterogenous groups.
3. Room Arrangement: Tables(desks) spread around room to ensure a good working environment.
4. Assigning Roles: Students will be randomly assigned roles of:
A. FACILITATOR- the student who leads the group and makes sure that the group stays on task.
B. ENCOURAGER- the student who watches to make sure that everyone is participating and invites everyone to join in. They also offer positive reinforcement.
C. CHECKER- the student who checks to make sure that all group members understand the ideas of symmetry, asymmetry, and symmetry breaking.
D. If necessary, the fourth member can act as material provider.
ACTIVITY:
1. TASK: Using the field of patterns taken from Symmetry and Pattern: The Art of Oriental Carpets, students will choose from 17 systems displayed and from them design their own graph paper oriental carpet.
2. POSITIVE INTERDEPENDENCE: The task will be done cooperatively. This means:
1. One carpet will be created by the whole group.
2. Each group member should have a clear understanding of symmetry, asymmetry, and symmetry breaking.
3. Each group member should be able to explain the strategies required for the making of the carpet.
3. INDIVIDUAL ACCOUNTABILITY: Each group member is responsible for understanding the basic concepts of symmetry. On an assigned date students should expect a quiz involving taking the letters of the alphabet and identifying them as symmetrical or asymmetrical.
4.CRITERIA FOR SUCCESS:
A= completed full project and clearly displayed the patterns involved from the lessons.
B= did not complete the full project, but showed strong evidence of understanding the patterns.
C= did not complete the project and showed confusion or lack of understanding the patterns.
D= did not complete the project and showed little evidence of any understanding of patterns.
F= made no attempt at the project.
5.MONITORING AND PROCESSING: The teacher must walk around room and monitor groups. Occasionally, ask a student in a group to explain what is going on ans keep an eye out for those who might be off task. It is very important to keep yourself outside the group. Turn student questions back to the group. Only intervene if it is absolutely necessary and always try to have the group solve the problem.
At the end of the lesson groups will take turns displaying carpets and giving positive feedback. They will join in a class discussion about how they felt working together.
6.TYING IT ALL TOGETHER:
1. Have students take a walk around the neighborhood and observe automobile hubcaps. How many different kinds of symmetry can be found?
2. Have students bring in junk mail from home to gather company logos. Then have them analyze the symmetries. Most companies use symmetry in their logos and very few use asymmetry or symmetry breaking. (Apple is one of the few who use asymmetry).