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Samples & Populations 7th Grade Math Todd County Middle School Leah Miller Lesson Title: Measures of Center Objectives: Skills: Students will be able to calculate mean, median, mode, and range and describe their uses in analyzing data. Students will be able to calculate Mean Absolute Deviation (M.A.D.) and Interqua
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  Samples & Populations 7 th  Grade Math Todd County Middle School Leah Miller Lesson Title: Measures of Center   Objectives: Skills: Students will be able to calculate mean, median, mode, and range and describe their uses in analyzing data. Students will be able to calculate Mean Absolute Deviation (M.A.D.) and Interquartile Range (IQR) and describe how they show variability of data. Students will be able to visually represent data on a dot plot and a box and whisker plot. Standards: 7.SP. 1 Understand that statistics can be used to gain information about a population by examining a sample of the population. Essential for 7.SP.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. Essential for 7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. Performance-Based Assessment Strategies: Students will be assessed daily with an exit ticket or by their independent work. Exit ticket responses will determine what is reviewed and retaught the following day. Vocabulary: Mean, median, mode, range, Mean Absolute Deviation (M.A.D.), interquartile range (IQR), box and whisker plot, line plot, data, sample, outlier Considerations for Special Populations: William—opportunity to work on calculating MMMR, Touch Math packet as back up Orion—Touch Math packet. Set work to earn free time Materials and Resources Needed: Daily handouts & PPT notes, Independent Practice/Exit tickets, M&Ms, bowls, chart paper, calculators Procedures for Teaching/Learning Structure: (Engage, Explore, Explain, Elaborate, Evaluate, Closing OR I do, We do, You do) Monday Tuesday Wednesday Thursday Friday Objective SWBAT calculate mean, median, mode, and range and describe their uses. SWBAT calculate mean, median, mode, and range to answer a real-world problem. SWBAT calculate M.A.D and describe how it shows variability. SWBAT calculate M.A.D and describe how it shows variability. SWBAT calculate IQR and represent their data using a box & whisker plot Bellwork Students will fill in the guided notes for Students will practice finding the MMMR for Students will answer the question: Is this Students will practice finding the MMMR for Find the M.A.D for the data provided  mean, median, mode, and range from the PPT the data provided survey data consistent with measures of center? BIG IDEA: The measures of center should align with most of the data points to be accurate the data provided Intro to New Material  Introduce the concept of mean, median, mode, and range (MMMR). (Helpful reminders: calling someone “average” is mean, median like the middle of the road, MOde and MOst, range is distance like a shooting range). Show sample calculations for students to do under their definitions. M&Ms activity*: “What is the number of M&Ms per color in a bag?” Demonstrate how to complete the handout independently and with partners Pass out M&Ms and bowls *Special note: Make sure to tell students not to eat M&Ms before they tally their colors!! Introduce: M.A.D. BIG IDEA: M.A.D. helps us determine how spread out the data is from the mean Show how to calculate M.A.D using line plots to show two data sets with same mean. Students should see that smaller M.A.Ds indicate more consistent data Review Steps of finding M.A.D. with students *Review handout: Students should calculate mean, plot data on a line plot, and find M.A.D Introduce another way to look at data: IQR BIG IDEA: the smaller the IQR, the more consistent the data Steps to solve: 1. Find median 2. Find middle of first half 3. Find middle of second half 4. Create box and whisker plot 5. Find IQR Guided Practice Peel the Onion: #1) Students and teacher do all the steps (MMMR) together. #2) Students and teacher do MMM together, students do R independently. #3) Students and teacher do MM together, students do M&R independently #4) Students Students will work independently to calculate the mean, median, and mode for their “sample” of M&Ms Students will find a partner and combine their data, finding the mean, median, and mode Student pairs Waterfall: #1) Students and teacher calculate M.A.D together #2) Students do first step of M.A.D., students and teacher do last steps together #3) Students do steps 1&2 independently, teach and students complete together *Each time add Students whose independent work from yesterday shows they need further instruction will be pulled into a small group. The remaining students will work independently on the handout Waterfall (see Wednesday for procedure and see above for steps)   If students finish early: Play Prodigy Game Math Progress Routine: Fact fluency practice Operations with fractions Prodigy Game/Algebra practice for MM, TRS *M&Ms activity adapted from Gary Hopkins, Education World: http://www.educationworld.com/a_lesson/03/lp293-02.shtml and teacher do M together, students do MMR independently. #5) Students do all steps independently and review whole group. will find another pair and combine data… *Circulate to check students progress & understanding one step to independent practice, until student is doing the entire problem independently Independent Practice Students will work independently calculating MMMR for different sets of data. Combine whole class data; students will independently calculate the measures of center With remaining time, students will calculate M.A.D independently, with teacher circulating to provide help to those still struggling Students will work independently to calculate the M.A.D. of various data sets. Students will work independently to calculate the IQR and represent with box & whisker plots Assessment Exit ticket Use whole-class data response as exit ticket Independent work will be collected and assessed for understanding Exit ticket: “Which data set is the most consistent with the mean? How do you know?” Exit ticket: Find the IQR of the data and represent as a box & whisker plot.
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