Lesson Plan

Degrees of Confidence, Expected Value and Expected Utility

Grade Level: 6-12

Length: 45-60 minutes

DE Domain: TP

  • Adding degrees of confidence to predictions and estimations.
  • Using calculations of Expected Value and Expected Utility to make decisions.

Students will learn to apply degrees of confidence to predictions and use expected value/utility calculations in decision-making. Through interactive exercises and real-world scenarios, they will develop skills in assigning probability estimates and evaluating outcomes quantitatively to make more informed choices.

TP.2- Strategically apply appropriate numeracy and probability techniques.

TP.5- Use probabilistic thinking to weigh decision options and their possible outcomes.

Lesson:

Engage (5 minutes):

  • Display a blank number line for the whole group to see.
  • Ask students a series of questions to help them identify and fill in the most common values that likely feel somewhat intuitive to them (possibly 0%, 25%, 50%, 75%, and 100%).
  • Suggested Prompts and Language:
    • How likely is it for a purple furry fish to come walking through our classroom door? There is a 0% likelihood this will happen. [add 0 to the number line] We can say with total certainty this will not happen.
    • How likely is it that you will see someone you know before the end of the day? Since you are at school, there is a 100% likelihood this will happen. [add 100 to the number line]. We can say with total certainty that this will happen.
    • If I flip this coin, how likely is it that it will land on tails? In a fair coin flip, there is a 50% likelihood this will happen. [add 50 to the number line] One way to think about this is if there are two worlds, in one world the coin will land on tails and in the other it won’t.

Add any additional prompts you want for the remaining percentages

Apply (40 minutes):

Watch (5 Minutes)

Degree of Confidence

Activity (15 Minutes)

  • Distribute confidence scale cards to each student (e.g., 0%, 20%, 40%, 60%, 80%, 100%).
  • Read out a series of statements related to various topics (e.g., weather predictions, historical events, personal preferences).
  • After each statement, give students a moment to privately choose a confidence level and hold up the corresponding card without revealing their choice.
  • Facilitate a class discussion about the choices students made on the confidence scale for different statements.
  • Explore the reasons behind their confidence levels and any challenges they encountered while assigning certainty to certain situations.
  • Instruct each student to write down a statement on a sticky note.
  • Ask them to place their statement on the confidence scale and briefly explain their reasoning for their chosen confidence level.

Watch (10 Minutes)

Expected Utility and Expected Value

Activity (10 Minutes)

Expected Value and Expected Utility

Reflect (5 minutes):

Journal Entry

  • How do we use probabilistic thinking to make predictions about future outcomes in real-world contexts, and how do uncertainties impact these predictions?

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