Intervention Playbook Teacher Guide Intervention Playbook
Lesson: Evaluating Strategies via Expected Value (HS.S-MD.A.5.b)
Teacher Guide
Instructional Objective
Students will be able to evaluate and compare two competing strategies by calculating the expected value of each and providing a data-driven justification for their choice.
Tier 2 Scaffolding
Graphic organizers for calculations
Sentence stems for justification
Visual probability distributions
Lesson Flow (45 Minutes)
1. The Hook: High Stakes Decisions (5 min)
Introduction
Use the Strategy Showdown Slides to present a "Go for it" vs. "Punt" scenario in football. Ask students to vote based on intuition first.
"In sports and business, we don't just guess. We use the 'Long-Run Average'—the Expected Value—to see which choice wins over time."
2. Guided Practice: The Business Move (15 min)
I Do / We Do
Model the formula: \[E(X) = \sum [x \cdot P(x)]\]
Show how to multiply the "Outcome" by the "Probability."
Highlight that $P(x)$ must sum to 1.
Scaffold: Use physical "Value Tiles" or a digital table to show the weighting of each outcome.
3. Collaborative Comparison (15 min)
You Do (Together)
Students work in pairs on the Value Verdict Worksheet . They must compare two athletes' scouting reports.
Key Scaffolding Question:
"Player A has a higher potential score, but Player B is more consistent. How does the expected value help us decide who to sign?"
Value Verdict Answer Key
Scenario 1: Sports Scouting
Player A: $(10 \cdot 0.2) + (20 \cdot 0.5) + (30 \cdot 0.3) = 2 + 10 + 9 = \mathbf{21}$ pts
Player B: $(15 \cdot 0.4) + (22 \cdot 0.4) + (28 \cdot 0.2) = 6 + 8.8 + 5.6 = \mathbf{20.4}$ pts
Verdict: Player A has a higher EV (21 vs 20.4).
Scenario 2: Marketing
Campaign X: $(-1000 \cdot 0.3) + (5000 \cdot 0.7) = -300 + 3500 = \mathbf{\$3,200}$
Campaign Y: $(1000 \cdot 0.6) + (3000 \cdot 0.4) = 600 + 1200 = \mathbf{\$1,800}$
Verdict: Campaign X is riskier but has higher EV.
Common Misconceptions
"Highest single value wins": Students often ignore probability and pick the highest possible score. Remind them: "It only happens 20% of the time!"Probability sum: Ensure they check that $P(x)$ totals 100% or 1.0. Strategy Showdown Slides Strategy Showdown
Winning with Expected Value
Sports
Business
The Big Game Decision
Option A: Play It Safe
A low-risk play that gets you 3 points 90% of the time.
90% SURE
Option B: Go Big
A high-risk play for 7 points, but only works 40% of the time.
40% CHANCE
Which one wins over a whole season?
What is Expected Value?
It is the Long-Run Average of a decision.
If you made the same choice 1,000 times, what would your average score or profit be?
"Data beats intuition every time."
The Power Tool
Expected Value Formula
\[E(X) = \sum [x \cdot P(x)]\]
\(x\)
The Outcome
\(P(x)\)
The Probability
Scouting Strategy
Who should we start? Let's check the numbers.
Outcome (Points) Probability Calculation 10 pts 0.20 \(10 \cdot 0.2 = 2.0\) 20 pts 0.50 \(20 \cdot 0.5 = 10.0\) 30 pts 0.30 \(30 \cdot 0.3 = 9.0\) Total Expected Value 21.0 pts
Marketing ROI
A new ad campaign costs $1,000 today.
Possible Results:
Fail: -$1,000 30%
Success: +$5,000 70%
Your Turn!
Calculate the Expected Value:
\[ (-1000 \cdot 0.3) + (5000 \cdot 0.7) \]
EV = ?
Value Verdict
"Expected value is the math, but strategy is the move."
Discuss with your team:
Why would a manager choose a lower EV if they are afraid of losing money?
Is the highest EV always the "best" choice?
Value Verdict Worksheet Value Verdict Worksheet
Strategy & Expected Value Intervention
Name
Date
The Strategy Formula
\[E(X) = \sum [x \cdot P(x)]\]
x = The Outcome (Value)
P(x) = The Probability (Chance)
\(\sum\) = Sum (Add them all up!)
Scenario 1: Scouting the Star
You are the coach. You need to pick a player for the final quarter. Player A is high-risk but high-reward. Player B is consistent. Calculate the Expected Value (EV) for both.
Player A (Aggressive)
Outcome Prob. Product 10 pts 0.20 2.00 20 pts 0.50 _______ 30 pts 0.30 _______ Total EV _______
Player B (Reliable)
Outcome Prob. Product 15 pts 0.40 6.00 22 pts 0.40 _______ 28 pts 0.20 _______ Total EV _______
Scenario 2: The Marketing Gamble
Your startup has $1,000. You must choose between two marketing campaigns. Campaign X has a higher possible payout but a risk of loss. Campaign Y is a guaranteed "slow and steady" win.
Calculate Campaign X:
Outcome 1
Loss of $1,000 (30%)
Outcome 2
Profit of $5,000 (70%)
( -1000 • 0.30 ) + ( 5000 • 0.70 ) = $ __________
Calculate Campaign Y:
Outcome 1
Profit of $1,000 (60%)
Outcome 2
Profit of $3,000 (40%)
( 1000 • 0.60 ) + ( 3000 • 0.40 ) = $ __________
Collaborative Verdict
Compare Scenario 2. Which campaign would you recommend to the CEO and why?
Verdict:
Reason 1:
Reason 2:
"Based on the data, Campaign ____ is the better long-term choice because its Expected Value is $__________ higher than the alternative."
Decision Check Exit Ticket Decision Check
Exit Ticket
Student Name
Strategy Score (EV)
The Final Call
A tech company is deciding between two software updates. Which update has the higher Expected Value of users gained?
Update A: Stability
1,000 Users (0.80)
5,000 Users (0.20)
Show Calculation:
EV = _________
Update B: New Feature
500 Users (0.40)
4,000 Users (0.60)
Show Calculation:
EV = _________
Final Verdict
Which strategy should the company choose?
Update A
Update B
Justify your answer using the data:
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