Teacher: Shawn M



Teacher: Shawn M. Donnelly Unit: Statistics

Grade: 7th Grade Math Lesson: Sampling Validity

LESSON PLAN

PERFORMANCE INDICATOR: 7.S.9

TEACHING POINT: SWBAT analyze and determine the validity of sampling methods by predicting outcomes.

DO NOW: Chose an Acuity or NYS exam question.

CONNECTION: During an election, organizations like the Gallup Poll conduct surveys about which candidate voters are like to vote for in order to predict the outcome of the election. They contact do not contact everyone in the US, but only a small sampling of people, perhaps thousands of people. Today, we’re going to learn how to determine if a sample is valid or not.

MINI-LESSON: It is important to distinguish between a population and a sample. A population is all of the items we are interested in, and a sample is only some of the items. A sample is a subset of the population. See diagram:

Using probabilities based on the sample, predictions about the entire population can be made. However, to make an accurate prediction, the sample selected must be representative of the population. This involves randomly selecting the sample so that each member of the population has an equal chance of being selected in the sample.

To improve the accuracy of the survey, one must consider the sample chosen. The more people you survey, the more accurate the result. Also, ask people who are not biased, that is, they do not have a special interest or preference for or against something. A sample is biased if certain members are underrepresented or overrepresented relative to others in the population.

To avoid against bias in sampling, chose appropriately and consider the following about the people in your survey: Number, Age, Grade level, and Gender.

Example: Lou wants to know how many students have taken swimming lessons. Which group would be best for him to survey? 5 students at a school dance; 25 students at a school dance; 5 students on the swim team; or 25 students on the swim team.

Let’s analyze them and determine what the outcome would be for each type of sample.

5 students at a school dance seems to low – so I’ll eliminate this choice. 25 students at a school dance is greater number, so I’ll hold onto that one. If I ask 5 students on the swim team, that too is a low number, and since they are on the swim team – they most likely took swimming lessons. My enxt choice, the 25 students on the swim team, although it is larger sample, it has the same problem, namely, that most probably all of them have taken swimming lessons – so there’s a bias in that sample.

Therefore, the one that will give me a more objective view is the 25 students at a school dance. The sample is larger and offers more diversity.

ACTIVE ENGAGEMENT: Students will be directed to analyze this question.

Miranda want to know how many students have been surfing. Should she ask 10 students living by a beach, or 100 students from different schools across the state? What would be the outcome of both surveys?

The best answer is 100 across the state as the sample is larger and offers more diversity of opinion. It is more likely to provide an accurate result. If she asked only 10 living by the beach, most likely they would have been surfing.

Link: Teacher shares observations and re-teaches if necessary.

Share: Select students share what they have learned and their understanding.

INDEPENDENT PRACTICE:

Differentiated Instruction: Place on overhead or on separate task cards.

Beginners – Group A- 1, 2, 3

Intermediate - Group B - 3, 4, 5

Advanced - Group C - 5, 6, 7

1. Jamal is interested in knowing the favorite sports of students at our school. Should he survey 20 students in the lunchroom or 20 students playing soccer? What would be the outcome of both surveys?

2. Ira wants to determine the fast food restaurant preferred by the majority of twelve-year-olds in his town. He decides to question all the twelve-year-olds who leave a particular hamburger restaurant. Is this a random sample? Explain. What is the most likely outcome of Jamal’s survey? How should he change it to make it more accurate?

3. A reporter wants to know what kind of music local teenagers like best. He surveys 100 people at a symphony concert. Is this a poor sample? What would be the result if he proceeded with the survey? How can the reporter change the survey to obtain more accurate results?

4. Destiny want to know how many 7th grade students in her school buy snacks from the snack bar when they go to the movies. She decides to ask this of 15 students at her school. Name two reasons why Destiny’s sample may not give the most accurate results. Describe a sample that would be better for Destiny to ask.

5. Sophie wants to know the percentage of teenagers who like going to the dentist. Which is the best group to survey? 5 students at the library; 20 students at the library; 5 students whose mother or father is a dentist; 20 students whose mother or father is a dentist.

6. Katie and Maya want to find out what after-school activities are most popular among 7th grade students of New York State. Katie surveyed 200 7th graders from 200 7th graders from Brooklyn. Maya surveyed 5 7th graders from each of New York’s’ 62 counties. Whose survey will probably give more accurate results? Give two reasons for your answer.

7. Andre and Jared want to know how many people from New York State visited the Catskill area. Andre asked 5 people from 25 different counties across the state. Jared asked 50 students from the Catskill area. Name one reason why Andre’s sample is likely to give more accurate results than Jared’s sample. Name a different reason why Jared’s sample is not likely to give accurate results.

Teacher will conference with students according to schedule and need.

Share: Select students will share their answers, and how they determined the solution.

Journal Writing: How does a sample relate to its population? What is the advantage of taking a random sample instead of surveying the entire population?

Share: Select students share their journal writing entries.

Homework: Can be placed on task cards and assigned to differentiated groups above.

1. A student is investigating the most popular restaurant in her town. She polls 25 customers at random at a pizza parlor about their favorite eating spot every day for a week. Is this a good sample? Explain. What would be the outcome? Would you change the survey? How?

2. You survey every tenth teenager leaving a movie theater on Sunday night to find out how often teenagers in your town go to the movies. Is this a good sample? Explain. What would be the outcome? Would you change the survey? How?

3. You want to survey the students of your school about the new uniform colors. You select people to survey by placing the names of all of the students in your school into a large jar and drawing out 15 names. Is this a good sample? Explain. What would be the outcome? Would you change the survey? How?

GROUP A

1. Jamal is interested in knowing the favorite sports of students at our school. Should he survey 20 students in the lunchroom or 20 students playing soccer? What would be the outcome of both surveys?

2. Jamal wants to determine the fast food restaurant preferred by the majority of twelve-year-olds in his town. He decides to question all the twelve-year-olds who leave a particular hamburger restaurant. Is this a random sample? Explain. What is the most likely outcome of Jamal’s survey? How should he change it to make it more accurate?

3. A reporter wants to know what kind of music local teenagers like best. He surveys 100 people at a symphony concert. Is this a poor sample? What would be the result if he proceeded with the survey? How can the reporter change the survey to obtain more accurate results?

GROUP B

1. A reporter wants to know what kind of music local teenagers like best. He surveys 100 people at a symphony concert. Is this a poor sample? What would be the result if he proceeded with the survey? How can the reporter change the survey to obtain more accurate results?

2. Destiny want to know how many 7th grade students in her school buy snacks from the snack bar when they go to the movies. She decides to ask this of 15 students at her school. Name two reasons why Destiny’s sample may not give the most accurate results. Describe a sample that would be better for Destiny to ask.

3. Sophie wants to know the percentage of teenagers who like going to the dentist. Which is the best group to survey? 5 students at the library; 20 students at the library; 5 students whose mother or father is a dentist; 20 students whose mother or father is a dentist.

GROUP C

1. Sophie wants to know the percentage of teenagers who like going to the dentist. Which is the best group to survey? 5 students at the library; 20 students at the library; 5 students whose mother or father is a dentist; 20 students whose mother or father is a dentist.

2. Katie and Maya want to find out what after-school activities are most popular among 7th grade students of New York State. Katie surveyed 200 7th graders from 200 7th graders from Brooklyn. Maya surveyed 5 7th graders from each of New York’s’ 62 counties. Whose survey will probably give more accurate results? Give two reasons for your answer.

3. Andre and Jared want to know how many people from New York State visited the Catskill area. Andre asked 5 people from 25 different counties across the state. Jared asked 50 students from the Catskill area. Name one reason why Andre’s sample is likely to give more accurate results than Jared’s sample. Name a different reason why Jared’s sample is not likely to give accurate results.

Mini-Lesson Example

Lou wants to know how many students have taken swimming lessons. Which group would be best for him to survey?

A) 5 students at a school dance B) 25 students at a school dance

C) 5 students on the swim team D) 25 students on the swim team

Active Engagement

Miranda want to know how many students have been surfing. Should she ask 10 students living by a beach, or 100 students from different schools across the state? What would be the outcome of both surveys?

Journal Writing

How does a sample relate to its population? What is the advantage of taking a random sample instead of surveying the entire population?

Homework

1. A student is investigating the most popular restaurant in her town. She polls 25 customers at random at a pizza parlor about their favorite eating spot every day for a week. Is this a good sample? Explain. What would be the outcome? Would you change the survey? How?

2. You survey every tenth teenager leaving a movie theater on Sunday night to find out how often teenagers in your town go to the movies. Is this a good sample? Explain. What would be the outcome? Would you change the survey? How?

3. You want to survey the students of your school about the new uniform colors. You select people to survey by placing the names of all of the students in your school into a large jar and drawing out 15 names. Is this a good sample? Explain. What would be the outcome? Would you change the survey? How?

A population is all of the items we are interested in.

A sample is only some of the items. A sample is a subset of the population.

To improve the accuracy of the survey, one must consider the sample chosen.

• The more people you survey, the more accurate the result.

• Ask people who are not biased, that is, they do not have a special interest or preference for or against something.

• A sample is biased if certain members are underrepresented or overrepresented relative to others in the population.

• The sample must be representative of the population.

✓ This involves randomly selecting the sample so that each member of the population has an equal chance of being selected in the sample.

Independent Practice

1. Jamal is interested in knowing the favorite sports of students at our school. Should he survey 20 students in the lunchroom or 20 students playing soccer? What would be the outcome of both surveys?

2. Ira wants to determine the fast food restaurant preferred by the majority of twelve-year-olds in his town. He decides to question all the twelve-year-olds who leave a particular hamburger restaurant. Is this a random sample? Explain. What is the most likely outcome of Jamal’s survey? How should he change it to make it more accurate?

3. A reporter wants to know what kind of music local teenagers like best. He surveys 100 people at a symphony concert. Is this a poor sample? What would be the result if he proceeded with the survey? How can the reporter change the survey to obtain more accurate results?

4. Destiny want to know how many 7th grade students in her school buy snacks from the snack bar when they go to the movies. She decides to ask this of 15 students at her school. Name two reasons why Destiny’s sample may not give the most accurate results. Describe a sample that would be better for Destiny to ask.

5. Sophie wants to know the percentage of teenagers who like going to the dentist. Which is the best group to survey? 5 students at the library; 20 students at the library; 5 students whose mother or father is a dentist; 20 students whose mother or father is a dentist.

6. Katie and Maya want to find out what after-school activities are most popular among 7th grade students of New York State. Katie surveyed 200 7th graders from 200 7th graders from Brooklyn. Maya surveyed 5 7th graders from each of New York’s’ 62 counties. Whose survey will probably give more accurate results? Give two reasons for your answer.

7. Andre and Jared want to know how many people from New York State visited the Catskill area. Andre asked 5 people from 25 different counties across the state. Jared asked 50 students from the Catskill area. Name one reason why Andre’s sample is likely to give more accurate results than Jared’s sample. Name a different reason why Jared’s sample is not likely to give accurate results.

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Population

Sample

POPULATION

SAMPLE

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