Actuarial Science Intro

Overview

Today students are introduced to actuarial science as a way to use data and math to make fair, informed decisions in real-world insurance contexts. The lesson builds the habit of identifying key quantities, modeling relationships, and explaining results clearly.

Learning intentions

Students will be able to:

• Identify the problem context and name important quantities in an insurance/decision scenario.
• Create and interpret a simple representation (table/diagram) of “chance of event” and “cost/impact.”
• Discuss how expected value compares choices using reasonable probability assumptions.
• Explain whether a conclusion makes sense in the real situation.

Success criteria

• I can list the relevant quantities (event, probability/chance, cost, decision option).
• I can build a simple table or diagram showing how outcomes affect expected value.
• I can compare two strategies/policies using expected value.
• I can communicate my reasoning using clear units, labels, and precise math language.

Curriculum links

• Mathematical Practice: Apply mathematics to solve problems in everyday life using diagrams, tables, graphs, and formulas; interpret results in context and revise if needed (MP4).
• Mathematical Practice: Understand the problem, plan a solution pathway, and check whether answers make sense (MP1).
• Mathematical Practice: Communicate reasoning precisely using symbols, definitions, and appropriate units/labels (MP6).
• Statistics and Probability (Grades 9–12): Evaluate and compare strategies using expected values (e.g., comparing insurance policies with different deductibles and accident chances).

Lesson structure (30 minutes)

1. 0–4 min · Hook with scenario. Teacher reads a short insurance story: two car insurance plans for the same driver, different deductibles and different chances of paying a small vs. large expense. Students turn-and-talk: “What decision is being made, and what information would we need to decide fairly?”

2. 4–10 min · Direct teach: actuarial thinking. Teacher explains that actuaries use probability and expected value to compare choices; they map relationships between events and costs. Emphasize the idea of assumptions (reasonable chances) and interpreting results. Students follow along, adding two columns to their notes: “What can happen?” and “What does it cost?”

3. 10–18 min · Guided practice: build a simple model. Teacher presents two simplified options on the board:

• Plan A: Lower deductible, so costs are usually smaller when there is a claim.
• Plan B: Higher deductible, so fewer/smaller payments on minor events but bigger payments if a major event happens. Teacher provides example chances (for this class): “minor claim” happens with some reasonable probability, “major claim” with another smaller probability, and “no claim” otherwise. Students in pairs complete a three-row table: Outcome | Chance | Cost to policyholder, then calculate each plan’s expected value using the table.

4. 18–24 min · Compare strategies (expected value). Teacher prompts: “Which plan is better for this driver based on expected value, and why?” Clarify that expected value is an average cost/impact over many possible outcomes, not a prediction of one single year. Students write a short comparison statement: “Based on expected value, Plan __ has lower expected cost because…”

5. 24–28 min · Reasonableness check + communicate precisely. Teacher models MP1 and MP6 by asking: “Do the chances add up to 1? Are costs labeled with units? Does the comparison match the story?” Students do a quick check on their own work and revise one part if something is missing (a label, a calculation step, or a sentence explanation).

6. 28–30 min · Exit ticket. Students answer one prompt: “List two quantities you used to compare the plans, and explain in one sentence how expected value helped you decide.”

Resources

• Projected scenario text (or printed handout) describing Plan A and Plan B with labeled outcomes and sample probabilities
• Student note-catchers with a three-row table template (Outcome / Chance / Cost)
• Calculator access (optional; can be done by hand with provided numbers)
• Markers/chalk and board for teacher model
• Exit ticket slips or a digital form

Assessment

• Formative check during pair work: teacher circulates to confirm students’ tables include labeled outcomes, chance, and cost.
• Formative check during whole-class discussion: teacher listens for correct comparison language tied to expected value (not just “my favorite plan”).
• Exit ticket: evaluates whether students can name quantities and explain how expected value supported the decision.

Differentiation

• Support: Provide sentence starters for the comparison statement (e.g., “Expected value compares… by averaging outcome costs weighted by chance.”) and a partially filled table for students who need it.
• Support: Offer a labeled example of how “chance” and “cost” should appear in the table with units.
• Extension: Ask advanced students to test a “what-if” assumption: “If the chance of a major claim were slightly higher, which plan would change first and why?”
• EAL/SEN: Use visual icons for outcomes (minor/major/no claim) and allow verbal explanation first, then sentence completion; keep vocabulary consistent (event, probability/chance, cost, expected value, compare).