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# Understanding Probability

• Subject: Data Analysis and Probability
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• Duration: One to two class periods

## Objectives

Students will:
 1 learn what probability is, 2 learn different ways to express probability numerically: as a ratio, a decimal, and a percentage, and 3 learn how to solve problems based on probability.

## Materials

The class will need the following:
 • Understanding: Probability and Odds video • Copies of Classroom Activity Sheet: Probability Problem Solving • Computers with Internet access (optional but very helpful) • Reference materials such as almanacs and encyclopedias • Copies of Take-Home Activity Sheet: Spin the Wheel!

## Procedures

 Work on the Classroom Activity Sheet as a whole-class activity. Have students write their answers as a ratio only. Then challenge students to work on the Take-Home Activity Sheet in pairs. Go over their responses in class.

## Discussion Questions

 1 Name professions that use probability. Give an example. Many scientists and social scientists use probability, including epidemiologists, psychologists, economists, and statisticians. They predict outcomes of events, such as the incidence of diseases and the strength of the stock market. 2 Imagine you are on the school debate team and the subject at hand is whether companies should drill for oil in Antarctica. What statistics would you look for if you're arguing in favor of oil exploration there? What statistics would you look for to support your argument against drilling there? What are some ways that numbers could support arguments on both sides? 3 Think about numbers you may have seen in advertisements, such as "X Juice is 90 percent real juice," or "Y cereal has 35 percent of the total vitamins needed in one day." How would you write each percentage as a ratio? 4 What does it mean when you hear the weather reporter predict a 10 percent chance of rain? Is that a high or low probability? 5 Express the probability that your mother will let you have a sleepover next weekend as a probability, assuming that the total number of outcomes is 100. What factors would increase the probability that she would say yes? (If you finish all your homework and chores, go to bed on time.) What factors would decrease the probability that she would say yes? (If you misbehave, do not finish your homework or chores, or go to bed on time.) 6 How do you think authors of The Farmer's Almanac make their predictions about weather for a year? How do you think they use probability?

## Evaluation

 Use the following three-point rubric to evaluate students' work during this lesson: Three points: demonstrates a strong understanding of probability based on their participation in class, their ability to complete the Classroom Activity Sheet, and their ability to complete the Take-Home Activity Sheet Two points: demonstrates a moderate understanding of probability based on their participation in class, their ability to complete the Classroom Activity Sheet, and their ability to complete the Take-Home Activity Sheet One point: demonstrates a weak understanding of probability based on their participation in class, their ability to complete the Classroom Activity Sheet, and their ability to complete the Take-Home Activity Sheet.

## Extensions

 Probability in Advertising Ask students to look at newspapers and magazines for examples of how numbers are used in advertisements. For example, it is not unusual to see something like "two-thirds less fat than the other leading brand" or "four out of five dentists recommend Brand T gum for their patients who chew gum." Why do advertisers use numbers like these? What information are they trying to convey? Do students think that the numbers give accurate information about a product? Why or why not? They Said What? Ask students to look at newspapers or magazines for examples of how politicians, educators, environmentalists, or others use data such as statistics and probability. Then have them analyze the use of the information. Why did the person use data? What points were effectively made? Were the data useful? Did the data strengthen the argument? Have students provide evidence to support their ideas.

 Chance and Average (Math Matters series) Grolier Education, 1999. For a brief but clear presentation of how numbers and chance work together, this volume in the Math Matters series is ideal. Important terms are underlined and included in a short glossary. Clear drawings demonstrate the concepts along with easy experiments to try. Why Do Buses Come in Threes? The Hidden Mathematics of Everyday Life Rob Eastaway and Jeremy Wyndham. John Wiley & Sons, 1998. Set up in question-and-answer format, this book offers explanations for those questions that perplex us all, starting with "Why can't I find a four-leafed clover?" The text is illustrated with line drawings, and additional problems/questions and solutions appear in shaded boxes. If you need to know "Why am I always in traffic jams?" this is your book!

## Vocabulary

 factor Definition: Something, such as a circumstance or an influence, that contributes to the production of a result. Context: Weather is an important factor to consider when planning a picnic. outcome Definition: Something that comes out of or follows from an activity or process; consequence. Context: She flipped the coin ten times, and the outcome was five heads and five tails. percent Definition: One part in one hundred. Context: He passed the test by answering 85 percent of the questions correctly. probability Definition: Fairly convincing, though not absolutely conclusive; intrinsic or extrinsic evidence of support. Context: High moisture in the air and a dropping temperature led the meteorologist to conclude a high probability of snow. random Definition: lacking or seeming to lack a regular plan, marked by an absence of bias. Context: The judges picked the winning number at random .

## Standards

 This lesson plan may be used to address the academic standards listed below. These standards are drawn from Content Knowledge: A Compendium of Standards and Benchmarks for K-12 Education: 2nd Edition and have been provided courtesy of theMid-continent Research for Education and Learningin Aurora, Colorado.   Grade level: 6-8 Subject area: Mathematics Standard: Understands and applies basic and advanced concepts of probability. Benchmarks: Understands the relationship between the numerical expression of a probability (e.g., fraction, percentage, odds) and the events that produce these numbers.

## Credit

 Marilyn Fenichel, freelance education writer and editor.