Actuarial Modeling Techniques

Overview

In this 4th lesson of the unit, students compare modeling strategies using expected value to make a decision. They practice building a simple model from probabilities and interpreting which option is better under reasonable assumptions.

Learning intentions

Students will be able to:

• Explain what expected value means in a real-world risk decision.
• Compute expected values for at least two policy options using given probabilities.
• Compare strategies and justify which choice is better based on expected value.
• Check whether their conclusions make sense in context (reasonable magnitudes, not just calculations).

Success criteria

• I can compute an expected value from a probability table or scenario.
• I can compare two strategies (e.g., deductibles) using expected value.
• I can clearly state my conclusion in context, including assumptions.
• I can verify my calculations and determine if the result is reasonable.

Curriculum links

• Statistics and Probability: evaluate and compare strategies using expected values (high-deductible vs. low-deductible insurance idea).
• Mathematical Practice: make sense of problems, plan a pathway, and monitor progress (MP1).
• Mathematical Practice: use precise language and communicate clearly with correct units/labels (MP6).
• Mathematical Practice: apply math to everyday decision-making contexts (MP4).

Lesson structure (30 minutes)

1. 0–3 min · Quick recap (Decision models). Teacher briefly reviews expected value as “average payoff if repeated many times,” and posts the day’s target: compare strategies. Students write one sentence: “Expected value helps me decide by…”

2. 3–8 min · Mini-example walkthrough (guided). Teacher presents a simple scenario (small class discussion example): “If a $50 claim happens with probability 0.2, otherwise no claim” and shows how to compute expected cost or payoff. Students compute the expected value on their own paper, then check with a partner.

3. 8–18 min · Modeling task: policy comparison. Teacher distributes two-option problem cards (insurance-style context): each option includes premium, deductibles, and two claim levels (minor vs. major) with given probabilities. Students:

• Identify outcomes and assign each probability.
• Compute expected cost for Option A and Option B (including how deductibles change what the insurer pays, or what the customer pays).
• Record an “assumptions” line (e.g., probabilities are reasonable, claims are independent enough for this simplified model).
• Choose the better strategy using expected value and write a one-paragraph justification.

4. 18–25 min · Compare strategies (teacher-led discussion). Teacher facilitates a structured comparison:

• “What quantity are we averaging—cost or payout?”
• “Which term changes when the deductible changes?”
• “Do both options use the same probability structure?” Students do a quick gallery-style share in pairs, then volunteer one key reasoning step that led to their comparison.

5. 25–28 min · Sanity check (reasonableness). Teacher asks: “If the expected value for Option A is lower, does it match the story of the problem? Could there be a sign error?” Students complete a two-question check:

• Is the expected value closer to the more likely outcome?
• Is the magnitude plausible given premiums and deductibles?

6. 28–30 min · Exit ticket (individual). Teacher gives a short exit ticket with a smaller two-outcome comparison (two options with different probabilities or costs). Students compute both expected values and state which option is better in one sentence.

Resources

• Actuarial modeling problem cards (2-option policy comparison; minor/major claim probabilities; premiums; deductibles)
• Student work sheets with space for outcome table, expected value calculations, and justification paragraph
• Exit ticket slips (individual, short expected value comparison)
• Calculators (optional; encourage showing computations clearly)
• Projector/board with expected value template and sentence frames
• Highlighters or colored pencils for labeling outcomes and probabilities

Assessment

• Formative during work time: teacher listens for correct outcome identification and correct probability use.
• Formative checks at mid-lesson: students’ mini-example expected value and partner verification.
• Exit ticket: correctness of expected value calculations for two options plus a context-based justification statement.

Differentiation

• Support: Provide a partially completed outcome/probability table and sentence starters:
• “The outcomes are…”
• “Expected value is…”
• “I choose because…”
• Support for computation: Offer a step-by-step expected value chart (Outcome → Probability → Cost → Probability × Cost).
• Extension (for early finishers): Ask them to compute expected value using a different reasonable rounding (e.g., probabilities rounded to two decimals) and discuss whether the decision changes.
• EAL/SEN: Allow verbal explanation with sentence frames and reduce copying by giving printed tables; focus assessment on expected value setup and conclusion clarity.