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How Probable Is It? (Grades 4-5)

Master Teacher

Zelphine Smith

Time Allotment

Two 45-minute class periods

Overview

Probability was often referred to as a world of the unknown. Today, we see probability being used to predict the weather, improve radio communication, control traffic congestion, and evaluate flight missions for space vehicles. Florida State University Department of Statistics describes probability as the branch of mathematics, which develops models for "chance variations" and "random phenomena."

Through the activities presented in this lesson, students will become familiar with basic probability facts and have ample opportunities to apply these theories in meaningful situations. Students will examine Web sites and video clips, and participate in hands-on activities in which they can further explore probability concepts. This lesson will ideally be used as an introductory lesson to a probability unit.

Subject Matter

Math

Learning Objectives

Students will be able to:

identify and explain probability
collect and analyze data based on probability concepts
explain pertinent probability vocabulary
determine the probability of a certain event
differentiate when the probability of an event is 0 or 1

South Carolina Standards

These Standards can be found online at Office of Curriculum Standards.

4IVA1. Record the outcomes of a multiple-stage event (e.g., tossing two coins), explain the method used, and determine whether the outcomes are equally likely.

4IVB1. Using models, determine the probability of a given simple event.

5IVB2. Create a problem statement involving probability based on information from a given problem situation.

4IVC1. Give examples of events for which the probability is a fraction between 0 and 1 inclusive and explain.

5IVC1. Understand when the probability of an event is 0 or 1 and give examples in each case.

National Math Standards

(These Standards are available online at NCTM.org.)

Propose and justify conclusions and predictions that are based on data and design studies to further investigate the conclusions or predictions.

Describe events as likely or unlikely and discuss the degree of likelihood using such words as certain, equally likely, and impossible.

Predict the probability of outcomes of simple experiments and test the predictions.

Understand that a number can represent the measure of the likelihood of an event from 0 to 1.

Media Components

Video

Math Talk, Lesson 1: "Take a Chance! Exploring Probability" allows the children to explore basic probability concepts in a fun and exciting way. It incorporates fundamental concepts and illustrates them using real life experiences.

Web Sites

Weather Central: Making a Weather Forecast. This Web site allows the children to make a forecast about what to expect from the weather. It is an excellent resource to incorporate the concept of probability into weather forecasting but is not incorporated into this lesson.

Lesson on Certain and Impossible Events. This Web site allows the children to explore probability games and apply pertinent concepts. The children will experience the spinner game that is referenced in the video.

The Infamous Monty Hall Problem. This Web site allows the children to solve a problem posed on the game show hosted by Monty Hall. The children will be given a scenario and an opportunity to solve the problem.

Materials

pencil and paper
1 paper bag
20 color tiles (10 green tiles, 5 yellow tiles, 3 blue tiles, and 1 red tile)
grab bag filled with scenarios

Prep for Teachers

Prior to teaching this lesson, bookmark the Web sites used in the lesson on each computer in your classroom. Load the Shock wave plug-in onto each computer as well.

Prepare the hands-on element of the lesson by:

1. Filling a brown paper bag with 10 green tiles, 5 yellow tiles, 3 blue tiles, and 1 red tile.

2. Filling a brown paper bag with various scenarios that can be classified as possible, impossible, or likely.

When using media, provide students with a Focus for Media Interaction, a specific task to complete and/or information to identify during or after viewing of video segments, Web sites, or to the multimedia elements.

Introductory Activity

Step 1: Begin the lesson by explaining to the children that they are getting ready to play a game. Carefully explain that the game will be modeled to the whole class. Show the students the brown paper bag and explain that there are 20 tiles in the bag inclusive of the following colors: green, yellow, blue, and red. Put your hand into the bag and pull out a tile. Upon finishing, return the tile to the bag. Complete this cycle 20 times. Tell children to record and analyze the data to guess how many of each colored tile are in the brown paper bag. Upon finishing, ask the children to give their educated guesses and explain how they arrived at these answers. For example, it is expected that the color green will appear most often and the color red will appear least often. Then allow one of the students to come and pull the colored tiles out of the bag such that the class might be able to confirm or negate predictions.

Step 2: Introduce four vocabulary words to the students. One can predict the likelihood of pulling a certain tile based on probability. The previous activity was an experiment because the situation involved chance and led to a result or outcome. An outcome is the result of a single trial of an experiment. An event is one or more outcomes of an experiment. To find the probability of an event, divide the number of ways the event can occur by the total number of possible outcomes. For example, there are 10 green tiles in a bag of 20 tiles. The fraction, ½, would represent the probability of pulling out a green tile. There is a probability of ¼ for the color yellow and so on. The equivalent decimals will fall between 0 and 1. The closer the decimal is to the number 1, then the more likely the event will occur. Explain that additional experiments will yield much more accurate results.

Step 3: Explain that an event can be categorized as possible, impossible, or certain. Show the children a grab bag filled with ten scenarios. The students will pick a scenario out of the bag and decide if it is possible, impossible, or certain. For example, the scenario that states, "You will see a green lion in the street on your way home," can be categorized as impossible. Let's hope.

Learning Activities

Step 1: Explain that the students will watch a video, "Take a Chance! Exploring Probability," about different individuals experimenting with basic probability concepts. The children are asked to revisit the previously learned concepts and apply them to this video.

Step 2: Insert the video into your VCR. START the tape at its beginning. Maria and a parrot are talking to each other on the set of Square 1 Television. The video begins by the hosts saying "Hello I'm Maria Lopez and I'm Buster the Parrot." Provide your students with a Focus for Media Interaction, asking them to explain what the caller's problem is. PAUSE the tape before it goes to the sketch. The caller will ask, "Is it about probability?" The parrot will respond "probably." (Sammie and his sister, Suzie, are playing a game called spinner. Sammie thinks that Suzie is cheating this game. There are two colors—green and yellow—on the spinner. Suzie wins if the spinner lands on green, and Sammie wins if it lands on yellow. Sammie said that Suzie won more often than he did. He suspected that something was wrong with the game but didn't know what it was.)

Step 3: Provide your students with a Focus for Media Interaction, asking them to explain the rules of the Wheel O Chance game. Is it a fair game? Why or why not? START the tape at its previous pause point. The Square 1 television sketch will take place at the fair. In the scene, you will see an older lady, young boy, and game show host. PAUSE the tape when the man says, "I just closed for lunch." The host puts an out to lunch sign on the game. (The game has a giant spinner. If the spinner lands on green, then the contestant pays a dollar. If the spinner lands on yellow, then the host pays a dollar. No, it is not a fair game because three quarters of the spinner are green and only one quarter is yellow. It is much more likely that the contestant will have to pay a dollar to the host. Remind the students of the colored tile game. The colored tile with the highest number had a greater chance of being pulled from the bag.)

Step 4: Provide your students with a Focus for Media Interaction, asking them to recall the rule of the game. Why is it less likely that Name would win the game? START the tape at its previous pause point. This segment will take place at a game show called "But Who Is Counting?" The host is having a conversation with one of the stage managers about the show. PAUSE the tape when Maria says that flipping coins is yet another game involving probability. (The rule of the game states that the person with the largest odd number wins the game. In order for Name to beat Word, she must be able to get the number nine which only occurs one out of ten chances; therefore, it is less likely for her to win the game.)

Step 5: Provide your students with a Focus for Media Interaction, asking them, "Does a pattern provide enough evidence for a certain event to happen?" START the tape at its previous pause point. This segment will be taking place at a game show about pennies. The game show host flips a penny for eight trials and wants the contestants to predict what the next result will be. STOP the tape when Buster responds that "The possibility is probable." Only Buster and Maria will be left back at the set. (Patterns can be used to formulate some mathematical opinions but are not as helpful with probability. A coin doesn't have memory; therefore, the chance of the coin landing on heads or tails is still equally likely.)

Step 6: Ask the students to log onto to The Infamous Monty Hall Problem Web site (http://www.comedia.com/hot/monty.html.) Provide your students with a Focus for Media Interaction, asking them to answer the question to the problem posed on this Web site. Upon making a decision, the students should click on the words "this link" and explore the answer based on probability.

Culminating Activity

Ask your students to log onto the following Web site, Lesson on Certain and Impossible Events. Explain that this Web site consists of several probability exercises similar to the ones demonstrated in the video. Provide your students with a Focus for Media Interaction, asking them to explore the site and answer the five questions in the Exercises.

Cross-Curricular Extensions

Language Arts: Ask students to write letters to a pen pal describing the newly learned concept of probability.

Have students survey a book and find the average length of the words in the book. The average length will dictate the book's readability.

Ask students to read a newspaper column and determine the most frequently used letters.

Social Studies: Have students research how probability is used in various countries.

Ask students to explore how traffic is controlled using probability in various cultures.

Science: Have students complete a unit on the weather and incorporate probability.

Tell students to explore how probability is used to improve radio communications.

Ask students to explore how space travel became possible due to probability.

Health: Ask students to explore how probability dictates the likelihood that a person will develop various health conditions.

Social Skills: Have students explore the probability of running into various old friends. Ask them to tell whether it is a 0 or 1 chance and why.

Have students observe a pattern of past grades and determine the likelihood that they will get a certain grade by the ending of that period.

Have students conduct a mock trial for peers. Students that have gotten discipline referrals will go before their peers and receive judgements. The students will make decisions based on the likelihood of that event happening again.

Community Connections

Take students on a field trip visit to the local State Farm Agency (or another local insurance company). Ask an agent to explain to the children how probability is used to drive the insurance business. For instance, it can help the company determine the likelihood that a customer will die in an accident. The students will research basic facts and determine how to assist the community. Ask students to write letters to family and friends explaining how various factors and decisions can cost them more money. For example, an insurance company charges a customer with traffic tickets more money because he/she is a higher risk for a traffic accident due to prior behavior.

Ask students to invent an idea for a game to submit to the state fair for next year. They must explain why this would be a good game? How was probability used to create this game? Who is more likely to win the game?