Thayer Problem Solving Model Example

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Honors Physics A.P. Physics Physics Olympics Problem Solving

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Honors Physics Activities A.P. Physics Activities
Step 1   Choose a General Problem
In this case, assume that there is a goldfish is a small fishbowl on the desk in front of you.  Your general task is to find the mass of the goldfish without touching or harming it.

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Step 2   Redefine the Problem
What is the mass of the goldfish in the fishbowl on the desk in the Physics room and how can it be determined without touching the fish with anything except water and without physically harming it in any way.

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Step 3   Make a List of Specifications and Constraints for this Specific Problem.  (Define Each)

                Constraint or Specification                                     Definition

               A.      Safe for the Fish                                                 No temporary or permanent physical harm.

               B.      No Contact                                                        Fish is not touched by any object except water.

               C.      Legal                                                                  Violates no state, city, or federal laws.

               D.     Moral and Ethic                                                   Consistent with out moral and ethical standards.

               E.     Time Requirements                                               Process may be completed in less than 1.5 hours.

               F.       Accuracy                                                             Measures the actual mass of the fish to + 1 gram.

              G.       Cost                                                                     Costs less than $5.

              H.       People Required                                                   Requires Less than 4 People.

              I.        Available Equipment                                              Uses Equipment Available in the Science Building.

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Step 4   Brainstorm Solutions

    "Brainstorm" a list of potential solutions for the problem.  In this part of the process, it is very important to make no judgments and do nothing to inhibit the freedom of all group members to come up with as many ideas as possible.  For this problem a list of possible solutions might include a few like this:

Option Number Potential Solution Brief Description
1 Similar Fish Buy a similar fish at the pet store.  Mass it with the laboratory balance and  and assume that its mass is close to the mass of your fish.
2 Mass by Difference Find the mass of the aquarium including all the water and the fish.  Remove the fish with a small cup of water and re-mass.  Find the new mass of the aquarium and water.  Find the mass of the fish by difference.
3 Small Container Find the mass of a small container containing some water.   Scoop the fish into this container and find the new mass.  Determine the mass of the fish by difference.
4 Mass vs. Length Collect a number of randomly sized fish from the pet store or class members home aquariums.  Find the mass of each fish with the balance and measure the length of each fish with a metric ruler.  Plot a graph of Mass vs. Length. Estimate the length of your fish, and use the graph to estimate its mass.
5 Conservation of
Momentum
Videotape a collision between the fish and an object with known mass.  Determine the velocity of each object before and after the collision and, assuming Conservation of Momentum, find the mass of the fish.
6 Quick Weigh Quickly dump the fish onto the balance pan, weigh it, and quickly dump it back into the aquarium.

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Step 5   Evaluate Potential Solutions Using a Matrix or Series of Matrices

Set up a matrix to evaluate the potential solutions versus the constraints and specifications.  As a group, you need to decide which of the constraints and specifications are the most important to you and "weight" each of these by multiplying its score by some factor.  For this problem, for example, suppose that your group decided that Fish Safety (A) and No Contact (B) were very important (x3) and that Cost (G) was moderately important (x2).

  A(x3) B(x3) C D E F G(x2) H I Total
Option 1 +++ +++ + + + - ++ + + 12
Option 2 +++ +++ + + + 0 ++ + + 13
Option 3 0 0 + + + + ++ + + 8
Option 4 +++ +++ + + 0 0 0 + - 8
Option 5 --- --- + + 0 - ++ + 0 -1
Option 6 --- --- + + + + ++ + + 2

    In some cases, you might need to do more than one matrix. You might separate your potential conclusions into a few categories, use one matrix to select the "best" category, and then use a second matrix to select one solution from this category.

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Step 6  Choose the Best Solution

Option 2, the Mass by Difference method appears to be the best.   If this were an actual Engineering Project, you might present this potential solution to your client, do a market survey, and determine the production and retail costs for the product. 

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Step 7  Reinterate

  If it doesn't work, you just start the process again.   It "cycles" back to the beginning.

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