Facilitator Briefing Teacher Guide Facilitator Briefing
Lesson: Model Match Intervention
Tier 2 Small Group Statistics & Probability
Learning Objective
Students will evaluate whether a specified model is consistent with observed results by using technology-based simulations to generate sampling distributions and identifying "unusual" outcomes.
Standard Alignment
CO HS.S-IC.A.2: Decide if a specified model is consistent with results from a given data-generating process.
Common Hurdles
• Single-Trial Bias: Students often think one lucky result proves a model is wrong.
• Definition of "Unusual": Struggling to distinguish between "unlikely" and "impossible."
• Tool Literacy: Difficulty translating a physical problem into parameters for a simulator.
Lesson Roadmap
01
The Hook: The Suspect Spinner (10 min)
Use the Model Lab Slides to present the "Suspect Spinner" scenario. Engage students in a "gut-check" prediction. Is the spinner fair if we get 8/10 Reds? What about 6/10?
02
Guided Probe: Manual Logic (15 min)
Work through the Probability Probe Worksheet . Focus on physical simulation (flipping a coin) to ground the abstract concept of "long-run behavior" before moving to digital tools.
03
Digital Lab: Simulation Safari (20 min)
Using a site like Rossman/Chance or StatKey , students complete the Simulation Safari Log .
04
Closing: Progress Check (10 min)
Administer the Data Check Progress Monitor . Use the data to determine if students need more practice with tail probabilities or if they are ready for formal Hypothesis Testing intro.
Intervention Strategies
Visual Scaffolding
Use high-contrast dot plots. Ask: "Where would our observed result sit on this mountain of data?"
Verbal Framing
Instead of "Consistent," use "Does this result look normal or weird based on what we expected?"
Modeling
Think-aloud while entering parameters into the simulation: "I'm setting probability to 0.5 because the model claims it is fair."
Model Lab Slides Statistical Lab 02
MODEL
MATCH
Deciding if observed data fits the theoretical model.
The Core Question
"Is what we saw consistent with what we expected?"
Option A: Consistent
The difference is small. It happened by random chance . The model is likely true.
Option B: Inconsistent
The difference is huge! It is unlikely to happen by chance. The model is suspect.
Case Study
ID: SPN-101
The Model
A spinner is claimed to be 50% Blue and 50% Red.
Observed Data
We spin it 10 times. We get 8 Reds and 2 Blues.
Is the claim consistent?
"Could a fair spinner really do this?"
The "What If?" Machine
We use a Simulation to see what "Fair" looks like over many trials.
1
Assume the Model is True (p=0.5)
2
Run 1,000 samples
3
Count the "8 or more" Reds
Results (n=1,000)
5 Reds: 255 times
6 Reds: 202 times
7 Reds: 118 times
8 Reds: 45 times
9+ Reds: 12 times
Total Extreme Results: 57 / 1,000
Making the Call
"Our result (8+ Reds) happened 5.7% of the time."
5.7%
Threshold
If probability is under 5% , the model is likely WRONG.
Our Verdict
5.7% is over 5% . The model is Consistent.
Probability Probe Worksheet Probability Probe
Investigation Log #01
Name:
Date:
Research Goal: Use a physical simulation to decide if a coin is fair.
1 The Claim
Model Claim
50% HEADS
You flip a coin 10 times and observe 8 Heads.
"I don't think this coin is fair," your friend says. "It gave way too many heads!"
Is 8/10 Heads enough evidence to call the coin "unfair"?
Yes, it's unfair.
No, it's just luck.
2 Physical Simulation (Small Group Lab)
Let's test the "Fair Model." Grab a coin and flip it 10 times. Record how many Heads you get. We will do this 10 times total to see what "Fair" actually looks like.
Trial 1
# of Heads
Trial 2
Trial 3
Trial 4
Trial 5
Trial 6
Trial 7
Trial 8
Trial 9
Trial 10
Analyze Your Results:
1. Out of your 10 trials, how many times did you get exactly 5 heads?
2. Out of your 10 trials, how many times did you get 8 or more heads?
3 The Verdict
Based on your small experiment, does getting 8/10 heads seem like something that "just happens" to a fair coin sometimes, or is it extremely rare?
Note: In statistics, we usually need thousands of trials to be sure. Next, we use the computer!
Simulation Safari Log Simulation Safari Log
Researcher:
Lab Station:
Digital Tool Required
01. Machine Setup
Open your simulation tool and enter the following settings:
Probability (p) 0.50
Sample Size (n) 20
Number of Samples 1,000
02. The Observed Result
Suppose you toss a real coin 20 times and get 15 Heads.
Research Question
Is getting 15/20 Heads consistent with a fair coin (p=0.50)?
03. Recording Digital Results
Run the 1,000 samples and look at the resulting distribution.
A. Visual Check
Where is the center of the distribution?
B. Tail Count
How many samples resulted in 15 or more heads?
Calculate the Proportion
# from (B)
1,000
=
(p-value)
04. The Final Verdict
Does the model (p=0.50) fit the results (15/20)?
YES, it is CONSISTENT.
The result happened 5% of the time or more. It was probably just luck.
NO, it is NOT CONSISTENT.
The result happened less than 5% of the time. This coin might be biased!
Data Check Progress Monitor Data Check
Exit Ticket • Model Match Intervention
Student:
Date:
The Mission
A nutritionist claims that exactly 25% of students eat breakfast every day.
OBSERVED
You survey 40 students. Only 4 students (10%) say they eat breakfast.
1
A simulation assumes the 25% claim is true. Out of 1,000 trials, the computer found that getting 4 or fewer breakfast-eaters happened only 12 times.
Calculate the probability (p-value) for this result:
0. _ _ _
(12 ÷ 1,000)
2
Is the "25% model" consistent with your survey results?
CONSISTENT
The result happened by luck.
NOT CONSISTENT
The result is too rare.
3
Justify your answer.
Compare your probability to the 5% (0.05) threshold.
Student Self-Reflection
How confident do you feel explaining "consistency"?
🙁
😐
🙂
