### Lesson Plan

# Branching Out With Tree Diagrams

Students will use a tree diagram to map outcomes and determine the probability of different events occurring, including mutually exclusive and complementary events.

Grades

6–8

### Quick links to lesson materials:

### Objectives

**Students will:**

- Understand how to use a tree diagram to map outcomes and determine the probability of different events occurring
- Understand mutually exclusive and complementary events

### Materials

- Shake, Rattle, and Roll Worksheet: Branching Out With Tree Diagrams printable
- Answer Key: Shake, Rattle, and Roll Worksheets printable

- Standards Chart: Shake, Rattle, and Roll printable
- Coin (for demonstration)
- Scrap paper for notes
- Introducing Shake, Rattle, and Roll: A Letter to Parents printable

- Shake, Rattle, and Roll Family Activity: Insuring for the Uncertain printable
- Shake, Rattle, and Roll Family Activity: Banking on Inflation printable
- Shake, Rattle, and Roll Family Activity: Planning for the Future printable

### Set Up

- Make a class set of the Shake, Rattle, and Roll Worksheet: Branching Out With Tree Diagrams printable.
- Print a copy of the Answer Key: Shake, Rattle, and Roll Worksheets printable for your use.
- Make class sets of the following printables, then staple together in packets to send home with students:
- Introducing Shake, Rattle, and Roll: A Letter to Parents printable

- Shake, Rattle, and Roll Family Activity: Insuring for the Uncertain printable
- Shake, Rattle, and Roll Family Activity: Banking on Inflation printable
- Shake, Rattle, and Roll Family Activity: Planning for the Future printable

- Introducing Shake, Rattle, and Roll: A Letter to Parents printable

### Lesson Directions

### Introduction to Tree Diagrams

**Step 1:** Group students into pairs. Show students the coin. Ask students to figure out what the chances are of flipping two heads in a row. Ask students to volunteer how they came up with their answers. Possible solution methods include an organized list, a table, or a tree diagram. Discuss tree diagrams. Explain that they can be used to determine the probability (or chance) of a particular scenario occurring.

### Guided Practice

**Step 2:** Ask students to complete a tree diagram to determine the probability of flipping three heads in a row (1/8 or 12.5%). Discuss answers as a class.

### Independent Practice

**Step 3**: Distribute copies of the Shake, Rattle, and Roll Worksheet: Branching Out With Tree Diagrams printable for either homework or classwork. To help students understand the data they are going to work with, discuss the Saffir-Simpson Hurricane Scale, used to categorize hurricanes according to strength. The scale is a 1–5 rating based on the hurricane's present intensity and can be used to estimate the potential property damage and flooding expected from a hurricane landfall. The scale is based on wind speed and storm surge.

**Step 4: Check for Understanding:** Review the answers with the class using the Answer Key: Shake, Rattle, and Roll Worksheets printable. Review the following as appropriate for your class:

- Demonstrate how to calculate the probability of a possible outcome using tree diagrams. This probability can be expressed as a fraction or a percentage. The determination of probability (which would be true in any tree diagram) for any given tier is to count the number of outcomes under consideration in that tier and divide it by the total number of outcomes in that tier. The results in the second tier of this activity strongly depend on the outcome of the first tier. For example, the outcome of "Tropical Depression" in the second tier is dependent on the outcome of "Tropical Storm" in the first tier.
- Explain that
*mutually exclusive*events cannot happen at the same time. For example, a Category 1 hurricane and a Category 4 hurricane are mutually exclusive.*Complementary*events are all the other outcomes that do not occur in a given scenario. For example, if an event is 'it will rain today' the complementary event will be 'it will not rain today.' If an event occurs, its complement cannot occur.

### Lesson Extensions

### Real-World Connections

Actuaries must consider all of the possible outcomes for a particular event, such as a hurricane, or the likelihood that a storm will occur and spread. They can then take these possibilities a step further and consider the effects of different scenarios on different variables, such as the type of building materials used in structures and whether they can withstand hurricanes.

For the Saffir-Simpson Hurricane Scale, visit the National Hurricane Center website.

### Home Connections

Send home the Shake, Rattle, and Roll Family Activity packets, which should include:

- Introducing Shake, Rattle, and Roll: A Letter to Parents printable

- Shake, Rattle, and Roll Family Activity: Insuring for the Uncertain printable
- Shake, Rattle, and Roll Family Activity: Banking on Inflation printable
- Shake, Rattle, and Roll Family Activity: Planning for the Future printable

### Standards

**Grade 7:**Statistics and Probability (**CCSS**7.SP.7 and 8)**Grades 6–8:**Make Sense of Problems, Model With Mathematics, Use Appropriate Tools Strategically, and Look for and Express Regularity in Repeated Reasoning (**CCSS**MP1, 4, 5, and 8);**NCTM**: Data Analysis and Probability

For more information, download the comprehensive Standards Chart: Shake, Rattle, and Roll printable.