## Activity Sections

### Introduction

Students test the hypothesis that a 100-year flood happens once every hundred years, learning how the probability of a flood does not mean that floods happen at regular intervals.

### Credits

Activity developed by Lisa Gardiner for the UCAR Center for Science Education based on an activity on the back of the USGS Watersheds Poster

### Grade Level

Middle and high school

### Time Required

One class period

### Student Learning Objectives

- Students learn how the probability of a flood relates to the occurrence of a flood.
- Students learn how to test and falsify a hypothesis.

### Learning Goal

Students collect, analyze and interpret data on the probability of a flood to understanding the potential for future catastrophic events.

### Lesson Format

Hands-on inquiry experiment

### Standards Addressed

#### Next Generation Science Standards

- MS-ESS3.B: Natural Hazards
- Science and Engineering Practices: Constructing Explanations and Designing Solutions
- Crosscutting Concepts: Cause and Effect

**Common Core Standards**

- CCSS.Math.Content.7.SP.C.5 Understand the probability of a chance event
- CCSS.Math.Content.HSS-MD.B.6 Use probabilities to make fair decisions
- CCSS.Math.Content.HSS-MD.B.7 Analyze decisions and strategies using probability concepts

### Materials

For each pair of students:

- One paper bag
- 100 small pieces of paper of the same shape and size - one of which is labeled with the word “FLOOD!”
- Paper and pencils for data collection (or a computer and spreadsheet)

**Introduction:**

- Assign students one of the following sources to learn the meaning of the term 100-year flood:

- Ask students: what are the chances of a 100-year flood in any given year? (Answer: 1%)
- Tell students that this is the same chance of pulling the one piece of paper that says “FLOOD!” out of the bag when there are a total of 100 pieces of paper.
- Modification: You may wish to build student understanding of probability more gradually. For example, if half the objects were of one color and half the other color, then there would be a 50% chance that you would pull a given color out of the bag.

**To do this activity as guided inquiry:**

- Tell students that to approximate the changes of a 100-year flood they will fill their bag with 99 pieces of paper of one color and one piece of a different color. The differently color paper represents a flood.
- Tell students that, in this experiment, they will test the hypothesis that in the 100-year floodplain, a flood happens once in every hundred years.
- One student pulls a piece of paper from the bag while another student record its color. They need to do this 100 times to test their hypothesis. You may want to have students do this several hundred times to see how many floods occur or just do it until they get a flood.
- After students have collected their data, make a chart on the board (or in a spreadsheet projected onto a screen) where student pairs can record their results

**To do this activity as full inquiry:**

- Tell students to develop an experiment using the bag and paper pieces that will allow them to test the hypothesis that a 100 year flood happens once every hundred years.
- Ask students to write a paragraph that describes their methods. Remind students that they will need to replace the paper they have selected back into the bag before the next trial to keep the odds the same for all trials.
- After you check their work, allow them to perform their experiment, report results, and draw conclusions.

**Discussion:**

Whether doing this activity in a guided inquiry format or as full inquiry, have student pairs report their results to the rest of the class. Discuss why different groups got different answers. Ask them how many times a flood happens in 100 years. Ask them whether the data supports the hypothesis that a 100-year flood happens once every hundred years. (The data should falsify the hypothesis.)

**Background**

In the United States, maps of floodplains often indicate the 100-year floodplain. This is used by the insurance industry to assess risk and by city planners to determine where building should and should not be located.

A 100-year flood is often mistakenly thought to be a flood that happens once every 100 years. In this activity, students explore that this is not the case. A 100-year flood is a flood that has a probability of 1 in 100 (1%) of occurring in any given year. With a 1% probability each year, it is possible for floods to happen two years in a row.