Introduction to Mobiles:
Math and Art in Motion
• Do Now: Show a video of Alexander Calder’s mobiles and ask students “Do you think math is involved in constructing a mobile like these? Why or why not? https://youtu.be/fI5PRaTSMUI?t=34s
• Discuss the Do Now question – allow students to share their thoughts but do not provide an answer.
• Randomly divide class into pairs.
Exploration: Is There a Mathematical Pattern in the Way Things Balance?
• Teacher demonstration: show how to set up the wooden skewer, bent paperclips, and washers as a type of mobile. Introduce the word fulcrum. Show how the distance of the weights from the fulcrum changes the balance on the mobile.
• Student challenge: find a pattern to describe specifically how the distance from the fulcrum and the mass (number of washers) affects the balance.
• Write down as many different examples of a balanced system as you can.
• All groups share their balanced equations with the class. Discus. Guide students towards discovering that when distance x mass = distance x mass the mobile is balanced. Once this equation is proposed, test it with several new combinations of distance and mass.
• Discuss “noise” in the system (i.e., not all washers are exactly the same, the mass of the wooden skewers outside of the mass is not accounted for by the equation, etc.)
• As a class, write notes about what we have discovered.
Applying the Equation
• Give students practical mobile-building advice.
o Build mobiles from the bottom, not the top.
o Show how to use center-of-balance tool.
o Demonstrate techniques for attaching parts.
• Each pair builds a two-level mobile with cardboard shapes that are pre-cut so that the shapes indicate approximate mass.
• Write equations for the mobile (one equation per level).
• Share mobiles and equations with the class. Discuss technical difficulties and any discrepancies between what the calculation predicted and what was actually required to get the mobile to balance. Brainstorm solutions and explanations. Discuss artistic possibilities for mobiles.
• Solve problems at http://solveme.edc.org/ with partners.
• Have each pair of students pick a problem to present and explain.
• Create and solve a mobile problem. Problem and solution should be on a separate page so that your classmates can solve your problem.
Video equipment to show images of Alexander Calder mobiles, computers to access SolveMe.edu, wooden skewers marked with inch markings, paperclips, washers, center-of-balance tools, pre-cut cardboard shapes, thread, glue, worksheet, scissors
Mobiles as Art:
Part II of Math and Art in Motion
• Do Now/Check Homework: Swap the mobile problem you wrote for homework with a classmate. Solve your classmate’s problem.
• After students have solved mobile problems, have each student give their answer page to the person with their question. As a class, workshop any problems where there is a discrepancy in the answers.
Creative Uses of Mobiles
• Watch Miyoki Shida Rigolo perform the Sandorn Balance Dance at https://youtu.be/-KVPA-9hofw.
• Discuss – what might the artist be expressing? What does this performance make you think or feel? How was this different or similar to the Calder mobiles we looked at in the last class?
• Sketch a plan for one or more mobiles that you would like to create. These mobiles should be artistically satisfying.
• Share and discuss plans with class.
• Create mobiles.
• Share finished mobiles with class.
• Write a reflection on your mobile. How did the mobile you built compare with the one you imagined? If you were going to build another mobile, what would you do?
Video equipment to show Miyoki Shida Rigolo’s performance, assorted mobile building materials (cardboard, glue, colored paper, thread, paperclips, wire, scissors, etc.)
Laurent Davidson – Mobile Lesson. Perf. Laurent Davidson. Youtube. Life in the Arts, 12 Nov. 2009. Web. 14 July 2015. <https://youtu.be/b5GTUM-Q2g0>.
Mobile Puzzles Build the Logic of Balancing Algebraic Equations. Perf. Jane Kang. Youtube. Heinemann Publishing, 7 Apr. 2014. Web. 14 July 2015. <https://youtu.be/aKa2QAarXgQ>.
“SolveMe Puzzles.” SolveMe Puzzles. Transition to Algebra