The Lunch Line Poll
The cafeteria wants to know what 600 students think — without asking 600 students. Teams design samples, spot the biased ones, scale a random sample up to the population, and draw three samples to see how much honest estimates wobble.
Common Core standards covered
- 7.SP.A.1Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.
- 7.SP.A.2Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.
© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
Teacher-facing overview
Big idea: Understand that random sampling supports valid inferences about a population, use sample data to estimate a population characteristic, and generate multiple samples to gauge variation in estimates.
Student target: “I can judge whether a sampling method is representative, use a random sample's statistics to estimate a population value, and use repeated samples to report how much my estimate might be off.”
Success criteria: I can explain why a sampling method is or isn't biased. · I can scale a sample percent to a population estimate. · I can compare estimates from multiple samples of the same size. · I can report an estimate as a range, not a false certainty.
Essential question
You can't ask everyone. When does a small slice of the school honestly speak for all 600 — and how sure can the slice make you?
Learning target: I can judge whether a sampling method is representative, use a random sample's statistics to estimate a population value, and use repeated samples to report how much my estimate might be off.
Success criteria
- I can explain why a sampling method is or isn't biased.
- I can scale a sample percent to a population estimate.
- I can compare estimates from multiple samples of the same size.
- I can report an estimate as a range, not a false certainty.
Why this matters
7.SP.A.1-2 is the logic of every poll, survey, and study a student will ever read: inference is legal only when selection is random, and honest estimates come with wobble attached. The multiple-samples activity is the standard's own design — variation seen, not lectured — and it plants the seed of margin of error years before the term. This is citizenship math wearing a lunch tray.
Students should already be able to
- Percent of a quantity — Unit 6.
- Proportional scaling — The Print Shop Test.
- Fraction/percent conversion.
Vocabulary to define explicitly
- Population vs sample
The whole group you care about vs the part you actually examine.
Example: All 600 students vs the 50 you poll.
Not an example: Calling the poll respondents 'the school' — the sample speaks FOR the population only if chosen well.
🔒 3 more terms with examples and non-examples — Representative sample, Biased sample, Sampling variability — are defined in the full lesson. See plans →
Where this shows up outside the classroom
Assessment plan
Formative — for feedback during the lesson
- Warm-up bias diagnosis.
- Bag-draw records during the wobble test.
- The one-number-demand debate.
Summative — the graded evidence: The exit ticket (verdict, estimate, report), scored with the four-criterion rubric.
The task students work on
Aurora Middle's 600 students may get a new lunch menu, and the cafeteria has budget to poll only 50. THE PLANS: five proposed sampling methods — first 20 in the pizza line, the whole basketball team, every 12th name from the full roster, volunteers from a poster, 50 names from a hat containing all 600. THE POLL: the chosen method returns 30 of 50 preferring pizza. THE WOBBLE TEST: two more random samples of 50 return 27 and 33. THE REPORT: the cafeteria wants one number — the class must decide what to hand over instead.
Poll worksheet — verdicts, then inference.
| Item | Data | Work | Conclusion |
|---|---|---|---|
| Plan verdicts | 5 methods | ||
| Main sample | 30 of 50 prefer pizza | ||
| Sample 2 | 27 of 50 | ||
| Sample 3 | 33 of 50 | ||
| The report | all three estimates |
Anticipated student strategies
Bias verdicts first (garbage in, garbage out), the scaling pipeline second, and the wobble last — validity, mechanics, then humility.
- Bias hunting by who-gets-missed. The student tests each plan by asking who can't end up in the sample.
The sharpest bias test — share first. A plan that can't reach part of the population can't speak for it.
🔒 2 more anticipated strategies with select-and-sequence guidance are in the full lesson. See plans →
Lesson script
The sample can only contain pizza-choosers — the method tilts the answer before a question is asked. Name the terms: population (600), sample (20), and bias (the tilt built into selection). The fix: give every student an equal shot — randomness.
Listen for: The who. A random 20 would be small but honest; a pizza-line 2,000 would still be tilted. Bias and size are different diseases.
Write the pipeline: count → percent → scale. Flag the honest asterisk: 360 is an ESTIMATE — the next ten minutes measure how soft it is.
- Random doesn't mean haphazard — it means every member gets an equal chance.
- The pipeline is proportionality: 30/50 = x/600.
Listen for: Self-selection tilts toward strong opinions — the poll measures passion, not the school. Equal CHANCE, not open door.
🔒 The remaining 4 steps — fully scripted with teacher-says lines, discourse questions, look-fors, and interventions — are in the full lesson. See plans →
Misconceptions and how to respond
- “A big sample fixes a biased method.” The pizza line at 2,000 is still the pizza line. Size shrinks wobble; only random selection removes tilt. Fix the method first.
- “Two random samples disagreeing means someone erred.” — the teacher response is in the full lesson.
- “The estimate 360 is the answer.” — the teacher response is in the full lesson.
- “Volunteers are fine since anyone COULD volunteer.” — the teacher response is in the full lesson.
🔒 Every misconception ships with a tested classroom response. See plans →
Scaffolded practice
The workbook follows gradual release rather than a page of blank prompts: 1 fully worked, 1 partially completed, then 4 independent.
- I doA random sample of 50 students (from all 600) has 30 preferring pizza. Estimate the school-wide count, showing the pipeline.
🔒 5 more prompts across all three release tiers are in the full lesson. See plans →
Worked solutions and scaffolds for every prompt are in the downloadable kit, included with membership. See plans and pricing.
Exit ticket
- Verdict and reason: polling the first 25 students off the early bus about school start times.
🔒 2 more exit-ticket questions are in the full lesson. See plans →
Worked answers, the completed answer tables, and the scoring rubric are in the downloadable kit, included with membership. See plans and pricing.
Printable handouts in the kit
All handouts are in Printable_Handouts.pdf inside the kit download.
Materials and classroom resources
Student experience
Students enter through a low-floor prompt, build or sketch a model, test a strategy, revise their thinking, collaborate, and present a final solution. The task remains accessible while allowing for sophisticated reasoning.
Detailed facilitation notes
- Step 1: Sort sampling plans into biased vs representative. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 2: Scale a random sample's percent up to the population. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 3: Draw three samples from the bag and compare estimates. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
- Step 4: Report the estimate WITH its wobble. Ask: “What do you notice?”, “What could you try next?”, and “How can you prove that?”
Differentiation and inclusion
Support: Percent-then-scale is the fixed pipeline; extend with the sample-size question (do bigger samples wobble less?).
Language support: “I started by…”, “My model shows…”, and “I know my answer is reasonable because…”.
Extension: Require a second solution, alter a condition, or have students write a challenge for another group.
Accessibility: Manipulatives, enlarged visuals, oral response choices, partner reading, and reduced-copy student pages.
Assessment plan
Formative checks: Strategy choice, accuracy, representation, collaboration, and explanation.
End evidence: One inference from a random sample, scaled to the population and reported with a range from repeated sampling.
Mastery: The student completes the task accurately and explains the strategy with limited prompting.