Simulation Guide Teacher Guide Varied Views
Teacher Facilitation Guide • Tier 2 Intervention
GRADE 7 SP.A.2
Learning Objective
Students will generate multiple samples of the same size to gauge the variation in estimates and use that variation to make more accurate predictions about a population.
Key Concept
One sample gives us a "guess." Multiple samples give us a "range." The more samples we have, the better we understand how much our predictions might vary from the actual truth.
Materials Needed
Predictor Pro Worksheets
Standard 6-sided dice (1 per student)
Colored pencils for graphing
1. The Hook: The Mystery Bag (5 mins)
Explain: "If I told you I rolled a die once and got a 6, would you believe me if I said EVERY roll will be a 6?" Prompt: Why is one sample not enough to predict the whole story?
2. Guided Simulation (15 mins)
Students roll a die 10 times (Sample 1) and record how many times they roll an even number (2, 4, 6). They repeat this for Sample 2 and Sample 3.
Scaffolding Tip: If students struggle to identify "even," provide a small reference card on the table: Even Numbers: 2, 4, 6.
3. Visualization & Comparison (10 mins)
Have students plot their 3 results on the dot plot provided on the worksheet. Discussion Questions:
Did you get the same number of evens every time?
What was your highest estimate? Your lowest?
If we rolled 100 times, would we expect exactly 50 evens? Why or why not?
4. Progress Monitoring: Inference (10 mins)
Students complete the "Inference Report" at the bottom of the worksheet. They must explain why their 3 samples were different and what that tells them about making a prediction for 1,000 rolls.
Common Misconceptions
The "Representative" Myth
Students think if they get 3 evens in one sample, the "true" population must be 30% even. Remind them that random variation happens in small samples.
The "Law of Averages" Fallacy
Students think if they rolled 0 evens in Sample 1, Sample 2 "must" be all evens to balance it out. Each sample is independent!
Predictor Pro Worksheet Predictor Pro Worksheet
Mission: Gauging Variation in Samples
NAME:
DATE:
The Mission
You are a data explorer! Your job is to roll a six-sided die to see how often an EVEN number (2, 4, or 6) appears. We will take 3 different samples to see how much our "guesses" change.
Phase 1: Roll & Record
SAMPLE 1
Roll 10 times
Total Evens:
SAMPLE 2
Roll 10 times
Total Evens:
SAMPLE 3
Roll 10 times
Total Evens:
Phase 2: Spot the Variation
Mark an X for each of your 3 results on the number line below.
0
1
2
3
4
5
6
7
8
9
10
Number of Even Rolls (out of 10)
Phase 3: The Inference Report
1. Did your three samples give you the exact same result? Why or why not?
2. If you had to predict how many evens would appear in 1,000 rolls, what number would you choose? Explain how your samples helped you decide.
The Expert Prediction
Based on all the samples from the WHOLE GROUP (not just yours), does our prediction change? Why is it better to look at many samples instead of just one?
Sample Safari Slides Sample Safari
Gauging Variation in Estimates
GRADE 7 MATH INTERVENTION
Can one piece tell the whole story?
If you see a trunk, do you know it's an elephant?
If you see one leaf, do you know the whole forest?
🐘
The Explorer's Terms
Population
The ENTIRE group we want to know about.
Example: Every student in your school.
Sample
A PART of the group we actually study.
Example: 10 students from your lunch table.
YOUR MISSION
1
Roll your die 10 times . Record how many EVENS (2, 4, 6) you get.
2
Repeat this 3 times to get 3 different samples.
3
Plot your results on the Sample Safari Dot Plot .
The Mystery of Variation
4
6
3
5
Variation means our samples are different even though we used the same die!
QUESTION: Did anyone get the exact same results for all 3 samples?
Predicting the Whole Forest
If you roll the die 1,000 times...
Which prediction is better?
Estimate from ONE sample (10 rolls)
Estimate from MULTIPLE samples (30+ rolls)
Mission Accomplished
Data Explorers know:
VARIED VIEWS • SAMPLING SECRETS
