Rating the Difficulty of Context Rich Problems

Use the strategy below to decide whether you think each given context-rich problem is a good individual problem, group practice problem, or group test problem. Explain your reasoning for each decision.

1. Read the context rich problem statement. Draw the diagrams and determine the equations needed to solve the problem.

2. Reject if:

• the problem can be solved in one step,
  
• the problem involves long, tedious mathematics, but little physics; or
  
• the problem can only be solved easily using a "trick" or shortcut that only experts would be likely to know. (In other words, the problem should be a straight-forward application of fundamental principles.)

3. Check* for the eleven characteristics that make a problem more difficult:

1. unfamiliar context
2. hard to learn physics (e.g., circular motion, rolling friction, waves, Gauss's Law)
3. more than one approach is needed to solve the problem (e.g., force or kinematics)
4. more than two subparts are needed to solve the problem (e.g., two separate force diagrams then onto kinematics)
5. the target variable is not specified (i.e., more than one correct way to solve the problem)
6. more information is given than needed to solve the problem
7. needed information is missing
8. assumptions (idealizations) must be made to solve the problem
9. the solution involves vector components
10. finding the target variable requires trigonometric identities
11. the solution requires simultaneous equations or calculus (i.e., non-constant variables)

    4. Decide if the problem would be a good (easy, medium, difficult) individual problem, group practice problem (20 - 25 minutes), or group test problem (45 - 50 minutes).
    

    1. "Easy" individual problems usually have 0 - 1 of the chararacteristics that make a problem difficult. "Medium" difficulty individual problems have 1 - 3 of the difficulty characteristics, and "difficult" individual problems have 3 - 4 of these characteristics (excluding 1).
       
    2. Group practice problems should be somewhat shorter and mathematically easier than group test problems. That is, they usually have 2 - 4 difficulty characteristics, including some of the characteristics 2 - 7).
       
    3. Group test problems can be more complex mathematically, and they usually have 3 - 5 of the difficulty characteristics.

    * As you become more sophisticated, you can give these difficulty characteristics weightings of 0, 1 and 2 instead of simple checks. For example, a problem that requires both the conservation of energy and momentum (weighting of 1) is easier than a problem that requires both circular motion and energy concepts (weighting of 2).

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