Lesson plan - Study Island



|Math Lesson: Random Sampling |Grade Level: 7 |

|Lesson Summary: Students consider the difference between random and nonrandom samples as they conduct simple surveys with multiple samples to draw inferences about|

|a population. Advanced students research how bestseller and top ten lists are constructed. Struggling students review newspaper surveys and identify the population|

|of each. |

|Lesson Objectives: |

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|The students will know… |

|that statistics can be used to gain information about a population by examining a sample of the population. |

|generalizations about a population from a sample are valid only if the sample is representative of that population. |

|random sampling tends to produce representative samples and support valid inferences. |

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|The students will be able to… |

|use data from a random sample to draw inferences about a population with an unknown characteristic of interest. |

|generate multiple samples of the same size to gauge the variation in estimates or predictions. |

|Learning Styles Targeted: |

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|Visual |

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|Auditory |

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|Kinesthetic/Tactile |

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|Pre-Assessment: |

|Use this quick assessment to see if students understand the difference between a random survey and a non-random survey. |

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|Ask students to explain these results. Then ask which of the surveys is a random survey and which is a non-random survey. |

|In a July 2, 2010 Marist Poll, 26% of US residents did not know from which country the United States won independence. Forty percent of 18 to 29 year olds were |

|unsure or were wrong, but only 23% of people age 60 or older were unsure or did not know. |

|In a survey of high school seniors taking advanced placement in history, 100% of students answered correctly that the US won its independence from Great Britain. |

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|Note students who do distinguish between survey methodologies. |

|Whole-Class Instruction |

|Materials Needed: 200 different-colored counters |

|Procedure: |

|Presentation |

|Discuss surveys that students have taken at school or online. Make a list on the board of the different types of surveys with which students are familiar (product |

|surveys, political surveys, personality surveys). Discuss if you can trust survey results. |

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|Discuss different ways of surveying and list these on the board (internet, telephone, street polling, mail survey). Discuss the advantages and disadvantages of |

|each of these. |

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|Ask students to predict what percentage of people is allergic to peanuts. Discuss why that might be interesting to a producer of food or a drug manufacturer. Take |

|a quick poll of how many in the classroom are allergic to peanuts. Ask if the class survey results could be generalized to the world population. Why or why not? |

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|Ask how you could get a good representation of the percentage of people who are allergic to peanuts. List all student ideas, which might include survey everyone, |

|survey people at doctors' offices, and random sampling. |

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|List the characteristics of a random sample as students suggest them, including focus on a target population, ensure that everyone in the population could have an |

|equal chance of being included in the survey, and researchers have no bias in how the questions are phrased. |

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|Ask each student, without discussion, to write down on a sticky note what their favorite food for lunch is. Put all the notes in a container, mix them up and |

|select five. Use the sticky notes to create a bar graph on the board. Calculate the percentage of students that chose each food and the mode, and record these |

|results. Discuss whether this is a random, representative sample. |

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|Then add to the bar graph by recording all responses. Recalculate the percentages and the mode. Compare the whole class to the random sample. Was the sample |

|representative? Discuss ways to test if the class sample is representative of the school population. |

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|Discuss what population the random sample represents. |

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|Guided Practice |

|Prepare a bag of different-colored counters, but do not allow students to see what is in the bag. |

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|Ask students to predict how many of each color are in the bag. |

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|Divide the class into groups of five and randomly distribute 50 counters to each group. Do not attempt to even or unbalance the distribution of colors. |

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|Have students record the number of counters of each color in their group, and use the numbers to determine the ratio of the number of objects of each color to the |

|number of objects in the sample, and convert this ratio to a percent. |

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|Then have them predict the number of each color in the whole population. |

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|Combine groups of five into groups of 10, and have them compute sample ratios and percentages with the new sample size and make new predictions for the population.|

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|Combine all the counters together and list the number of each color in the entire population. Discuss predictions made from each sample size in comparison to each |

|other and to the population. |

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|Independent Practice |

|Ask students to predict how much time the average teenager spends per day watching TV and how much time the average teen spends on the computer. Explain that a |

|June 2009 Nielsen survey found that the average teenage spends 3½ hours watching TV and 1½ hours on the computer. |

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|Have students keep a daily log of the time they spend watching TV and using the computer over the course of a week. Have them compare their personal habits with |

|the survey. |

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|Then have them write survey questions and a plan to conduct a randomized survey to test the validity of the Nielsen survey. |

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|Closing Activity |

|Ask students to give examples of how it might be easy to mislead people with survey data. |

|Advanced Learner |

|Materials Needed: Internet Access |

|Procedure: |

|Have students investigate how the bestseller or top ten music lists are created and maintained. |

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|Have them present their finding to the class and explain how random sampling does or does not play a role. |

|Struggling Learner |

|Materials Needed: Newspapers |

|Procedure: |

|Work with students to look through the newspaper for survey data |

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|Identify the population of each survey and how random sampling did or did not play a role in conducting the survey. |

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|Have them present their findings to the class. |

*see supplemental resources

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