Lesson objective: Make inferences based on representative samples.

Students bring prior knowledge of relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered from 6.SP.B.5d. This prior knowledge is extended to making inferences about an entire population from the measures of center and variability of a representative sample as students make inferences using proportional reasoning. A conceptual challenge students may encounter is making broad assumptions based on small statistical differences.

The concept is developed through work with a table of data, which challenges students to make future predictions using proportional reasoning.

This work helps students deepen their understanding of equivalence because maintaining equivalence through proportional reasoning allows us to generalize our understanding of a smaller representative to a much larger population.

Students engage in Mathematical Practice 6: attend to precision as they carefully compute measures of center and variability to make inferences based on a representative sample.

**Key vocabulary:**

- inference
- sample
- representative
- proportional
- population

**Special materials needed:**