# Lesson 4

Tables of Relative Frequencies

### Lesson Narrative

The mathematical purpose of this lesson is to make connections between two-way tables and relative frequency tables and to use the tables to determine probabilities for some events. The work of this lesson connects to previous work because students used sample spaces to calculate probabilities of compound events. The work of this lesson connects to upcoming work because students will use tables and Venn diagrams to determine probabilities for some events. When students use two-way tables to estimate probabilities they are seeing and making use of structure (MP7).

### Learning Goals

Teacher Facing

• Interpret (orally and in writing) a two-way table that represents a sample space.
• Use information in a two-way table to calculate relative frequencies and to estimate probabilities.

### Student Facing

• Let’s use tables to organize probabilities.

### Required Preparation

One standard number cube is needed for each student.

### Student Facing

• I can use information in a two-way table to find relative frequencies and to estimate probability.

Building On

Building Towards

### Glossary Entries

• chance experiment

A chance experiment is something you can do over and over again, and you don’t know what will happen each time.

For example, each time you spin the spinner, it could land on red, yellow, blue, or green.

• event

An event is a set of one or more outcomes in a chance experiment. For example, if we roll a number cube, there are six possible outcomes.

Examples of events are “rolling a number less than 3,” “rolling an even number,” or “rolling a 5.”

• outcome

An outcome of a chance experiment is one of the things that can happen when you do the experiment. For example, the possible outcomes of tossing a coin are heads and tails.

• probability

The probability of a chance event is a number from 0 to 1 that expresses the likelihood of the event occurring, with 0 meaning it will never occur and 1 meaning it will always occur.

• sample space

The sample space is the list of every possible outcome for a chance experiment.

For example, the sample space for tossing two coins is: