In this unit, students work with probability and sampling. They use their understanding of basic chance experiments to quantify how likely events are to happen and develop a working understanding of probability. Then they design and use simulations to further understand probability as the frequency of the event occurring when repeating an experiment many times. Students represent sample spaces using tables, tree diagrams, and lists, and use the number of outcomes in a sample space to calculate an expected probability.

Two tree diagrams. The leftmost tree diagram has three branches for the first choice, labeled “A,” “B”, and “C.” Choices “A”, “B”, and “C” each have four branches labeled with a different number from 1 through 4. The rightmost tree diagram has four branches for the first choice, labeled 1, 2, 3, and 4. Choices 1, 2, 3, and 4 each have three branches, labeled with a different letter “A,” “B,” or “C.”

Next, students examine different ways to collect data from samples within a population to understand why random selection is useful. Then students generate samples and estimate information about the population from sample data. Finally, students compare two groups by examining the measures of center and measures of variability calculated from sample data representing each group.

Progression of Disciplinary Language

In this unit, teachers can anticipate students using language for mathematical purposes, such as describing, explaining, justifying, and comparing. Throughout the unit, students will benefit from routines designed to grow robust disciplinary language, both for their own sense-making and for building shared understanding with peers. Teachers can formatively assess how students are using language in these ways, particularly when students are using language to:

Describe

• Observations and predictions during a game (Lesson 1).
• Patterns observed in repeated experiments (Lesson 4).
• Chance experiments to model situations (Lessons 6 and 7).
• A simulation used to model a situation (Lesson 10).
• Observations about data sets (Lessons 11 and 17).

Explain

• Predictions (Lesson 2).
• How to determine which events are more likely (Lesson 3).
• Possible differences in experimental and theoretical probability (Lesson 5).
• How to use simulations to estimate probability (Lesson 7).
• How to use a simulation to answer questions about the situation (Lesson 10).

Justify

• Whether situations are surprising and possible (Lesson 4).
• Which samples are or are not representative of a larger population (Lesson 13).
• Which samples correspond with each show, which show is most appropriate for a commercial, and whether a movie is eligible for an award (Lesson 15).
• Reasoning about samples and populations (Lesson 16).
• Whether or not differences between samples are meaningful (Lesson 18, 19, and 20).

Compare

• Sample spaces and probability of outcomes for different spinners (Lesson 5).
• Methods for writing sample spaces (Lesson 8).
• Heights of two groups (Lesson 11).
• Measures of center with samples (Lesson 13).
• Sampling methods (Lesson 14).
• Populations based on samples (Lessons 18 and 20).

In addition, students are expected to critique predictions about the mean of random samples and generalize about sample spaces, predictions, sampling, and fairness. Students also have opportunities to use language to represent data from repeated experiments, represent probabilities and sample spaces, and interpret situations involving sample spaces, probability, and populations.

The table shows lessons where new terminology is first introduced in this course, including when students are expected to understand the word or phrase receptively and when students are expected to produce the word or phrase in their own speaking or writing. Terms that appear bolded are in the Glossary. Teachers should continue to support students’ use of a new term in the lessons that follow where it was first introduced.