Decision Coach Guide Decision Coach Guide
Intervention Focus: Probability & Strategy (HS.S-MD.B.7)
Duration 45-60m
Learning Objectives
Analyze real-world decisions using conditional probability .
Construct and interpret tree diagrams for medical testing scenarios.
Distinguish between False Positives and False Negatives .
Use the "Population of 1,000" method to simplify abstract percentages.
Tier 2 Scaffolding Strategies
Concrete to Abstract: Start with physical "counts" of people rather than decimals (e.g., "10 out of 1,000" vs "0.01").
Color Coding: Use consistent colors for "Has Disease" (Red) and "Does Not Have Disease" (Blue) across all visuals.
Verbal Cues: Consistently use "Given that..." to highlight the denominator in conditional probability.
Lesson Flow & Facilitation
10m
The Goalie Gamble (Warm-up)
Slide 2 in Presentation
Present the scenario: Down by 1 goal with 1 minute left. Why pull the goalie? Focus on the "risk vs. reward" logic. Ask: "What are the only two ways we can tie this game?"
Key Misconception: Students often think "But we might get scored on!" Validate this, then point out that losing by 1 or losing by 2 are both just "losses." The goal is the tie.
20m
The Medical Testing "I Do / We Do"
Slides 3-6 & Decision Map Worksheet
Walk through the "Rare Disease" scenario. CRITICAL: Use the 1,000-person population method. It makes the false positive rate much more intuitive.
Step 1: Total Population (1,000)
Step 2: Reality (10 have it, 990 don't)
Step 3: Test Results (Who gets a "Positive"?)
15m
Strategy Lab (Independent/Collaborative Practice)
Strategy Lab Worksheet
Students apply the same logic to a "Product Testing" scenario. This mirrors the medical test but in a manufacturing context (Defective vs. Non-defective parts).
Progress Monitoring & Success Criteria
Emerging
Student can fill in the branches of a tree diagram with numbers provided but struggles to calculate the final conditional probability.
Proficient
Student calculates the probability of a false positive and explains why a positive test doesn't always mean "disease."
Exceeding
Student can suggest how to change the test (e.g., re-testing) to improve decision accuracy.
Decision Lab Slides Decision Lab
PROBABILITY & STRATEGY
Strategic Logic
Medical Analysis
The Goalie Gamble
The Scenario:
Your team is down by 1 goal . There is 1 minute left in the game.
The Big Decision:
Keep your goalie (Safe defense)
Pull the goalie (Extra attacker!)
Probability shows pulling the goalie doubles your chances of tying...
But why?
The Medical Paradox
A test for a rare disease is 99% accurate. You take the test and it comes back Positive.
Your Instinct Says:
"I definitely have the disease."
Probability Says: "Not so fast!"
Mapping 1,000 People
Total Population 1,000
Has Disease 10
No Disease 990
Result Count
True Positives: 10
False Positives: 10
Total Positives: 20
Out of 20 positives, only 10 actually have it? That's only 50%!
Know the Errors
False Positive
The test says YES, but the reality is NO.
"The fire alarm went off, but there was no smoke."
False Negative
The test says NO, but the reality is YES.
"The thief walked right past the silent security alarm."
Why Strategy Matters
In business, sports, and medicine, we can't just look at the Accuracy.
We have to look at the consequences of being wrong.
The Strategic Question:
"Is a False Positive better or worse than a False Negative?"
Cancer Screening Security Scans
Decision Map Worksheet Decision Map
Medical Strategy Lab
Student:
Date:
The Rare Disease Challenge
Imagine a city with 1,000 residents. A rare condition affects exactly 1% of the population. Doctors use a diagnostic test that is 90% accurate (this means it correctly identifies 90% of sick people, but it also gives a "False Positive" result to 10% of healthy people).
Step 1: Complete the Population Tree
1,000
Total People
Sick (1%)
Healthy (99%)
Test Pos.
Test Neg.
Test Pos.
Test Neg.
Step 2: Transfer to the Decision Matrix
Reality → Actually Sick Actually Healthy TOTALS Test Positive (+) Test Negative (-) TOTALS 1,000
Step 3: The Moment of Truth
If a person gets a Positive Test, what is the probability they actually have the disease?
Probability =
True Positives
/
Total Positive Results
=
Reflection Question:
In a cancer screening, why is it usually better to have a False Positive than a False Negative ?
Strategy Lab Worksheet Strategy Lab
Advanced Decision Matrix
Mission: Analyze & Conquer
Code: S-MD.B.7
PART 1
The Defect Detector
"You are the manager of a smartphone factory. Out of 500 phones made, only 5 are defective . Your testing robot is 98% accurate ."
Data Entry:
Total Phones: 500
Actually Defective: 5
Actually Perfect:
Calculate the False Positives:
(Take 2% of the "Perfect" phones — these are the ones the robot wrongly flags as broken.)
0.02 ×
=
Decision Check:
If the robot flags a phone as "Defective," is it more likely that the phone is actually broken, or that the robot made a mistake? (Explain your reasoning)
PART 2
The Goalie Pull
In hockey, pulling the goalie gives you an extra attacker, but leaves your net empty. Research shows:
With Goalie: 10% chance to score.
Pulled Goalie: 25% chance to score.
1. The Math of Desperation:
If you pull the goalie, you are 15% more likely to tie the game. Why do many coaches wait until the very last 30 seconds to do it?
Critical Analysis:
Strategy isn't just about the best outcome. It's about minimizing the worst outcome. If you are trailing by 1, does it matter if you lose by 1 goal or 5 goals?
Yes, it matters.
No, a loss is a loss.
How does your answer change your willingness to take a risk?
Probability Pulse Check Probability Pulse Check
Exit Ticket • Strategic Decisions
Strategist Name
Success Rating (1-5)
1
Match the scenario to the correct error type:
"The security alarm goes off, but there is no intruder."
"A person has a virus, but the test result is negative."
False Positive
False Negative
2
Consider these test results for 100 people:
True Positives
5
False Positives
10
=
Total Positives
15
If you get a positive test, what is the probability you are actually sick?
out of
3
Strategic Question:
Why might a company choose to use a test that has a high "False Positive" rate rather than one with a high "False Negative" rate?
Decision Lab Assessment Protocol
