Intervention Facilitator Guide Intervention Facilitator Guide
Topic: Evaluating Strategies with Expected Value (HS.S-MD.A.5.b)
Learning Objective
Students will evaluate and compare two or more decision-making strategies by calculating their expected values and using a structured framework to justify the "best" long-term choice.
Common Misconceptions
Thinking the Expected Value is an outcome that must happen in a single trial.
Ignoring negative signs in "loss" scenarios.
Confusing "Expected Value" with the "Most Likely" outcome.
Lesson Flow (30-40 Minutes)
5 MIN
The Hook & Concept Review
"Would you rather take $10 guaranteed, or flip a coin for $25?"
Review the formula: \(E(x) = \sum [x \cdot P(x)]\). Emphasize that EV is the average over many trials.
10 MIN
Guided Strategy Comparison
Use the "Food Truck Dilemma" scenario from the slides. Model how to fill out the side-by-side tables. Point out how "Risk" looks in the probability distribution.
15 MIN
Student "Strategy Lab"
Students work on the side-by-side comparison worksheet. Circulate and ask: "What does a negative expected value tell us about the long-term success of this plan?"
5 MIN
Decision Framework & Exit Ticket
Guide students through the reflection questions. How does the EV help us choose when outcomes are uncertain?
Intervention Support (Tier 2)
Verbal Prompts
"If we did this 1,000 times, what would the average outcome be?"
"Does the probability column add up to 1.0? If not, we missed a scenario."
Visual Aids
Use color coding: Red for losses (negative \(x\)), Green for gains (positive \(x\)).
Use the "Balance Scale" analogy for expected value.
Answer Key & Progress Tracker
The Prize Wheel Challenge
Strategy A: \( (0 \cdot 0.5) + (10 \cdot 0.3) + (50 \cdot 0.2) = 0 + 3 + 10 = \$13.00 \)
Strategy B: \( (5 \cdot 0.8) + (100 \cdot 0.2) = 4 + 20 = \$24.00 \)
Comparison: Strategy B has a significantly higher long-term payout, even though the probability of winning the "big" prize is the same.
Progress Monitoring Checklist
Skill Evidence of Mastery Data Entry Correctly assigns negative values to "costs" or "losses." Calculation Correctly multiplies \(x \cdot P(x)\) before summing. Synthesis Chooses the strategy with the higher EV and explains why. Nuance Identifies scenarios where a lower EV might be preferred (risk aversion).
Strategy Lab Slides Strategy
Showdown
Using Expected Value to Win the Long Game
The Million Dollar Choice
Option A
A 100% chance of getting $5,000 .
Safe Choice
Option B
A 10% chance of getting $60,000 (and 90% chance of $0).
The Gamble
Which is the "smarter" strategy for a business owner?
The "Average" Tool
\[E(x) = \sum [x \cdot P(x)]\]
Expected Value
Sum of
(Outcome × Prob)
It's not what happens once. It's what happens on average over time.
The Food Truck Dilemma
Where should you park your truck today?
Location 1: The Park
Weather Profit (\(x\)) Prob (\(P\)) Sunny $1,200 0.60 Rainy $200 0.40 EV $800
Location 2: Office Plaza
Workday Profit (\(x\)) Prob (\(P\)) Normal $900 0.90 Holiday -$100 0.10 EV $800
Same EV. Different Reality.
Consistency
Which strategy has a smaller "gap" between outcomes?
Risk of Ruin
Can your business survive the "negative" outcome?
"Expected value tells us the score at the end of the season. Risk tells us if we'll survive the next game."
Time for the Lab
Your Mission:
Analyze two marketing strategies.
Complete the side-by-side EV tables.
Make a data-backed recommendation.
Open your "Strategy Lab" Worksheets now
Strategy Lab Worksheet Strategy Lab Worksheet
Evaluating Strategic Outcomes
Subject: Statistics Intervention
Name:
Date:
Tool Check: The EV Formula
\(E(x) = [x_1 \cdot P(x_1)] + [x_2 \cdot P(x_2)] + \dots\)
The Prize Wheel Challenge
You are competing in a game show. You can choose to spin one of two different wheels. Your goal is to maximize your winnings over the long run.
Strategy A: "The Steady Spinner"
Outcome (\(x\)) \(P(x)\) \(x \cdot P(x)\) $0 (Lose) 0.50 ________________ $10 (Small) 0.30 ________________ $50 (Grand) 0.20 ________________ Expected Value \$ _________
Strategy B: "The High Roller"
Outcome (\(x\)) \(P(x)\) \(x \cdot P(x)\) $5 (Tiny) 0.80 ________________ $100 (Epic) 0.20 ________________ No other slots 0.00 0.00 Expected Value \$ _________
The Strategy Lab Framework
1. The Numerical Choice
Based only on the expected value, which wheel should you choose and why?
2. The Probability Analysis
Wheel A has a 50% chance of winning $0. Wheel B has a 0% chance of winning $0. How does this change how you feel about your choice?
3. Strategic Justification
If you only had one spin to pay for a $15 lunch, which wheel would you pick? Justify using the data above.
Self-Assessment Loop
I can calculate \(x \cdot P(x)\)
I can sum values for EV
I can justify a strategy
