s p unit plan | Survey Methodology

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Todd County Middle School Math ______________________________________________________________________ Leah Miller Grade 7 50 minutes Approx. number of students in each class: 20 Beginning date for this unit: Monday, 2/27 Ending date for this unit: 3/31 Academic Content Standards Addressed in this Unit: Analyze proportional relationships and use them to solve real-worls and mathematical problems. 1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and o
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  Todd County Middle School Math ______________________________________________________________________ Leah Miller Grade 7 50 minutes Approx. number of students in each class: 20 Beginning date for this unit: Monday, 2/27 Ending date for this unit: 3/31 Academic Content Standards Addressed in this Unit: Analyze proportional relationships and use them to solve real-worls and mathematical problems. 1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.  For example, if a person walks ½   mile in each ¼   hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour. Use random sampling to draw inferences about a population. 1. Understand 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. Understand that random sampling tends to produce representative samples and support valid inferences. 2. Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.  For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be. Draw informal comparative inferences about two populations. 3. Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.  For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. 4. Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.  For example, decide whether the words in a chapter of a seventh- grade science book are generally longer than the words in a chapter of a fourth- grade science book.   Unit Title/Theme/Focus: Samples and Populations Connection to classroom vision: Students will feel invested in math and will see that they can have an impact in their community, even as seventh graders.  Essential Questions: How can I use math to help my community? How can I tell the difference between a good survey and a bad survey? How can I create a survey to get the data I need (and ensure it’s accurate)? How can I use my results to draw conclusions about the population?  Summative Assessment (3/20–3/31): Students will create, administer, and analyze surveys, working in collaboration with local organizations so their data can be used purposefully to help their community. Students will choose to work with one of the following organizations:   White Buffalo Calf Woman Society Boys & Girls Club Sinte Gleska University Rosebud Sioux Tribe Diabetes Prevention Todd County School District Todd County Middle School Representatives from each of the organizations will come into the classroom on Tuesday, 3/21 to help students create surveys to administer to TCSD students that fit the needs of the organization. (Students will consider sampling-methods and population when administering surveys). Students will then analyze their data, and the following week, the representatives will return to help students make inferences from their data. Student products will include the survey, data analysis, and a presentation poster or PowerPoint. Students will present their projects at a family night. Titles of each lesson and lesson descriptions: Lesson One (2/28–3/3) Title: Measures of Center for Numerical Data Lesson Description: Students will learn about mean, median, mode, and range—their uses and how to calculate them. They will also learn how to calculate Mean Absolute Deviation (M.A.D.) and Interquartile Range (IQR), and their importance in describing the accuracy of the measures of center. Tasks: Calculate mean, median, mode, range, M.A.D, and IQR. Understand their importance in interpreting data. Use a box plot to represent IQR. Read data from a dot plot. Lesson Two (3/6–3/10) Title: Choosing a Sample from a Population Lesson Description: Students will realize that good survey samples are representative of an entire population. They will investigate the different types of sampling (convenience, systematic, volunteer-response, and random) and judge them on the basis of which would produce the most representative, accurate results. Students will learn about sample size and understand that the larger the sample, the more accurate the results. Tasks: Learn about samples and populations and determine which type of sampling produces the best results. Test out random sampling, plot and analyze results using a line plot and measures of center, and compare results to classmates. Create a box plot to represent data. Extrapolate data to a larger population. Compare measures of center for different sample sizes. Lesson Three (3/13–3/16) Title: Using Samples to Draw Conclusions  Lesson Description: Students will interact with different data, compare results using the “tools” learned in this unit (measures of center, box and dot plots, sample type and size), and draw conclusions from the data. Tasks: Create and compare box plots of different populations. Use mean and M.A.D to analyze dot plots to determine whether the samples differ more than what one would expect from natural variability.
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