Grade 7 · Mathematics · 30 minutes
Unit 3 · Sampling and probability · Lesson 1 of 2
A More Representative Lunch Survey
Evaluate a survey sample before generalizing to a whole school.
Mr. S Teaches · Original starter mini-lesson · MS7-MATH-05Learning objective
Identify sampling bias and compare estimates from two random samples.
Before you begin
- Fractions and percents
- Mean and variation
Gather your materials
- Paper and pencil
- Ruler and graph paper
Language to know
- population
- The whole group a question concerns.
- sample
- A smaller group studied for information about a population.
- bias
- A method that systematically favors some outcomes.
Understand the concept
A large sample can still be misleading if people are selected in a way related to the question. Random selection gives population members a chance to be included and tends to reduce selection bias. Random samples still vary, so one sample estimate is not an exact population fact. Repeated samples reveal that uncertainty.
Teach it step by step
- Ask whether interviewing only garden-club members fairly estimates the school’s interest in a garden lunch option.
- Define the population as all 600 students and contrast convenience selection with random names drawn from the full roster.
- Use two fictional random samples of 20: 12 prefer the option in sample A and 15 in sample B.
- Convert each proportion to a percent and a predicted count out of 600.
- Discuss why neither predicted count proves the actual number and why similar methods can give different estimates.
Make the thinking visible
Worked example or model response
Sample A estimates 12/20 = 60%, or 360 of 600 students. Sample B estimates 15/20 = 75%, or 450 students. A 90-student difference can arise from sampling variation; it does not by itself show that preferences changed.
Guided practice
Compare a voluntary online poll with drawing 30 names randomly from the roster. For samples with 18/30 and 21/30 in favor, calculate two estimated percents.
Independent practice
1. Why might surveying only bus riders misrepresent all students’ transportation preferences? 2. A random sample has 16 of 40 students preferring an early lunch. Estimate the count in a 500-student school and state a limitation.
Quick assessment
Would asking twice as many garden-club members automatically fix the original selection problem?
Answer key & assessment criteria
Answers and teaching guidance
- Guided: The roster draw has a better chance of representing all students; voluntary participation can bias results. Estimates are 60% and 70%.
- Independent 1: Non-riders are excluded and may have different preferences. 2: 40%, or an estimate of 200 students; the sample estimate can differ from the population value.
- Quick check: No. Increasing a biased sample does not remove systematic exclusion.
Look for: Look for an explanation of the choices, not only a final answer. Require units and a check against the context.
Make it work for your learner
More support
Use colored counters to represent subgroups and physically draw a sample without looking.
Extension challenge
Simulate five equal-size random samples and compare the spread of their estimates.
Selected contributions · Official sources
Standards connections
Contributes to Common Core standard
7.SP.A.1Common Core · Grade 7
Evaluate whether a sample can represent its population.
Read the official standard ↗This lesson contributes selected skills; it does not fully address the standard.
Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.
Contributes to Common Core standard
7.SP.A.2Common Core · Grade 7
Compare estimates from multiple samples and discuss variation.
Read the official standard ↗This lesson contributes selected skills; it does not fully address the standard.
Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.