Unit Plan 26 (Grade 7 Math): Uniform and Empirical Probability Models
7th graders build and compare uniform and empirical probability models, predicting outcomes and analyzing discrepancies between theory and data. They justify model choice, discuss fairness, and explain variability using clear, data-driven reasoning.
Focus: Develop and use uniform probability models; compare with empirical results and discuss discrepancies.
Grade Level: 7
Subject Area: Mathematics (Statistics & Probability • Chance & Data)
Total Unit Duration: 5 sessions (one week), 45–60 minutes per session
I. Introduction
Students construct two kinds of probability models and learn when each is appropriate. A uniform probability model assumes equally likely outcomes (fair coin, standard die, equal spinner sectors) and supports clean, theoretical calculations. An empirical probability model is built from observed frequencies (from experiments or real data) and is used to estimate probabilities when outcomes are not guaranteed to be equal (e.g., a likely weighted spinner or an imbalanced color bag). Students test predictions, compare theory to data, and explain why discrepancies occur (sampling variability, bias, non-uniform devices).
Essential Questions
- When is it reasonable to assume outcomes are equally likely, and when should we measure instead?
- How do we build, use, and test a probability model?
- Why do experimental results differ from theoretical predictions, and what counts as a reasonable difference?
II. Objectives and Standards
Learning Objectives — Students will be able to…
- Build uniform probability models by listing sample spaces with equally likely outcomes and computing event probabilities.
- Conduct experiments and compute relative frequencies, then use them to build empirical probability models.
- Compare predictions from a model to observed results and discuss discrepancies using ideas like sample size and fairness.
- Decide which model (uniform vs empirical) is appropriate for a situation and justify the choice.
- Communicate conclusions using clear fractions/decimals/percents, appropriate vocabulary, and cautious language.
Standards Alignment — CCSS Grade 7
- 7.SP.7a: Develop a probability model by assigning equal probability to all outcomes and use the model to determine probabilities of events.
- 7.SP.7b: Develop a probability model (not necessarily uniform) by observing frequencies in data generated from a chance process; use the probabilities to predict outcomes.
- 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 build a uniform model (equally likely outcomes) and compute P(event).
- I can run trials, compute relative frequency, and build an empirical model.
- I can predict counts using a model and compare to results, explaining differences.
- I can choose the best model for a situation and tell why.
- I can write a clear conclusion in fraction/decimal/percent with cautious wording (about, likely, close to).