Unit Plan 23 (Grade 7 Math): Sampling & Representative Data

Focus: Understand random sampling, generate samples, and use sample statistics to draw informal inferences about populations.

Grade Level: 7

Subject Area: Mathematics (Statistics & Probability • Data, Sampling, Inference)

Total Unit Duration: 5 sessions (one week), 45–60 minutes per session

I. Introduction

Students learn how to select random samples, why randomness matters for representativeness, and how to use sample statistics (proportions/means) to make informal inferences about populations. They compare random vs biased methods, generate multiple samples to see sampling variability, and describe results with estimates and plausible ranges rather than exact certainties.

Essential Questions

• What makes a sample representative, and how does randomness reduce bias?
• How can we use a sample proportion or mean to say something reasonable about a population?
• Why do different random samples from the same population give different results, and how can we describe that variability?

II. Objectives and Standards

Learning Objectives — Students will be able to…

1. Describe and perform random sampling (simple random; stratified overview) and identify biased methods (convenience, voluntary response).
2. Generate multiple random samples from a known “population” and compute sample proportions/means.
3. Use patterns in the distribution of sample statistics (center/spread) to make informal inferences about the population.
4. Explain why larger, random samples generally give more stable estimates than small or biased samples.
5. Communicate conclusions with clear language that reflects uncertainty (for example, “about,” “likely between,” “reasonable range”).

Standards Alignment — CCSS Grade 7

• 7.SP.1: Understand that statistics can be used to gain information about a population by examining a sample; generalizations are valid only if the sample is representative; random sampling tends to produce representative samples and support valid inferences.
• 7.SP.2: Use data from a random sample to draw informal comparative inferences about two populations; generate multiple samples (or use simulated samples) of the same size to gauge variation in estimates.
• Mathematical Practices emphasized: MP.1 (make sense), MP.3 (justify), MP.4 (model), MP.5 (use tools), MP.6 (precision).

Success Criteria — Student Language

• I can explain what makes a sample random vs biased.
• I can take a random sample and find a sample proportion or mean.
• I can compare multiple samples and describe the variability I see.
• I can make a reasonable claim about the population and say how confident I am in everyday language.
• I can compare two populations using sample data and state a clear, context-based conclusion.