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Background
Nonverbal Communication
Say Whaaat?
Creative Writing
Trends and Patterns
Problem Solving
Creative Thinking
Say It – Do It (Scientific Writing)
Three Dimensional TANGOES *
Negotiation (Basic)
Supply and Demand
Monopoly
Teamwork
PDCA Cycle
Beyond Disabilities
Group Decision Making Dynamics



Problem Solving

Summary/Suggested Uses
This exercise is an excellent way to assess the general level of creativity and problem-solving ability of a group. Use it as an introduction to the scientific method or as a warm-up on exam day. Allow 30 minutes if you have time or reduce the number of trials for something quicker.

Objectives
Participation in this exercise will enable students to
  1. Identify at least 3 ways to construct a square using the TANGOES * shapes.
  2. Explain the statement, "there’s always more than 1 way to solve a problem"
  3. Practice visualizing spatial relationships
Materials
  1. One set of TANGOES * pieces per student
  2. Blank paper and pencil for each student
Directions
  1. Explain that throughout history many scientific discoveries have been made while man was trying to solve a problem. Sometimes the discovery related directly to the problem and sometimes a solution for a totally different problem was discovered. Today’s challenge is to see how many ways a square can be made using a given set of shapes.
  2. Have students take out paper and pencil and issue a set of TANGOES * pieces to each student.
  3. Allow time for students to try to make a square shape with TANGOES * silently. Each time they construct a square, they should draw the configuration of pieces on their paper. With less advanced students, you may want to review the definition of a square.
  4. After about 5 minutes, divide students into groups of three and have them compare solutions.
  5. On board, tally the number of solutions found by each group or by the class as a whole. Get agreement that each solution meets the criteria of being a square.
  6. Keeping students in their triads, have them devise more solutions using all 21 TANGOES * pieces. As before, students should draw each configuration on a sheet of paper. It may be helpful to label each one with a number, indicating the total number of pieces used.
  7. Call time. Have each group present their solutions to the class. Tally the number of different solutions found. Discuss each solution, getting consensus that it meets the criteria of being a square and noting similarities or differences to solutions proposed earlier. If desired, define synergy and discuss how having more brains involved and more pieces to use helped create more solutions. How might this apply to scientific discoveries and research programs today?
Debrief and Transition
As you can see, there are many combinations of shapes that make a square and many ways to solve this problem. This is true for almost any problem – there are usually multiple solutions.

Solving problems sometimes requires thinking creatively, trying different options, and looking at the pieces or parts of a problem differently. This is sometimes called stepping "out of the box." It means not being so locked in to our previously established beliefs that we cannot see anything different.

What examples of scientists can you think of that demonstrate stepping out of their box? (Galileo, Columbus, Oppenheimer, others) What problems did their discoveries help to solve? Take input) What are some problems scientists are working on today? (Take input- medical research, alternative energy sources, the age of the universe, etc.) How did thinking differently about your problem help you find new solutions? (Take input)

Note that in this class, students may frequently need to step out of their box in order to understand the material. Assure them that with practice they can learn to do this.

Transition to regular lesson plan by relating this discovery process to your other material.