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21 st Century Lessons

This primary lesson teaches students how to distinguish between measures of center and measures of variation and how to use the interquartile range (IQR) as a measure of variation to describe data distributions.

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21 st Century Lessons

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  1. 21st Century Lessons Interquartile Range as a Measure of Variation Primary Lesson Designer: Katelyn Fournier

  2. 21st Century Lessons is funded by the American Federation of Teachers.

  3. 21st Century Lessons – Teacher Preparation Please do the following as you prepare to deliver this lesson: • Spend AT LEAST 30 minutes studying the Lesson Overview, Teacher Notes on each slide, and accompanying worksheets. • Set up your projector and test this PowerPoint file to make sure all animations, media, etc. work properly. • Feel free to customize this file to match the language and routines in your classroom. *1st Time Users of 21st Century Lesson: Click HERE for a detailed description of our project.

  4. Lesson Overview (1 of 7)

  5. Lesson Overview (2 of 7)

  6. Lesson Overview (3 of 7)

  7. Lesson Overview (4 of 7)

  8. Lesson Overview (5 of 7)

  9. Lesson Overview (6 of 7)

  10. Lesson Overview (7 of 7)

  11. Warm Up OBJECTIVE: SWBAT distinguish between measures of center and measures of variation and use interquartile range (IQR) as a measure of variation to describe data distributions. Language Objective: SWBAT write what measures of variation are, how we find them, and why we use them. Yesterday in class, you filled out an index card with real world examples of data sets with wide ranges and narrow ranges. Today as our warm up, the class will be tested on its understanding of range using the examples you created! Agenda

  12. Warm Up OBJECTIVE: SWBAT distinguish between measures of center and measures of variation and use interquartile range (IQR) as a measure of variation to describe data distributions. Language Objective: SWBAT write what measures of variation are, how we find them, and why we use them. After an example has been read aloud: • IN YOUR HEAD, determine whether the example represents a data set with a wide range or a narrow range. • When you hear a clap, move your arms to represent your answer. Arm Movements Wide range = Arms are outstretched Narrow range = Hands are close together Agenda

  13. Agenda: OBJECTIVE: SWBAT distinguish between measures of center and measures of variation and use interquartile range (IQR) as a measure of variation to describe data distributions. Language Objective: SWBAT write what measures of variation are, how we find them, and why we use them. 1) Warm Up – Review of the Range (Whole Class)5 Mins 2) Launch – Test Scores: Is the Range Useful? (Partner) 10 Mins 3) Explore – Las Vegas Weather: What Can You Expect? 20 Mins (Whole Class) 4) Summary – IQR in Simple Terms (Whole Class) 5 Mins 5) Practice – IQR Class Work (Individual) 15 Mins 6) Assessment – Exit Ticket (Individual) 5 Mins

  14. Launch – Review Turn and Talk (30 sec) number of toppings students like When we analyze data, what are we looking for? Median Center Mean Range Today! Spread (Measure of Variation) Interquartile Range Mean Absolute Deviation Shape Agenda

  15. Launch Think-Pair-Share Test Scores: Would you expect a wide or narrow range? Twenty students take a social studies test. The range of the scores is 98 points. The teacher is worried that there is such a wide range of scores. How do you think the students performed? Agenda

  16. Launch Whole Class The test scores are below. How do you think the students performed? Agenda

  17. Launch Whole Class In this example, was the range a useful measure of variation to use to determine how a class of students performed? NO!! Agenda

  18. Explore Turn and Talk Since the range is greatly influenced by outliers, we also use the interquartile range (IQR) to describe the variability of a data set. Are there any parts of the word interquartile that look familiar to you? inter quartile Between Quarters Agenda

  19. Explore Notes Quartiles: the points that divide a data set into roughly four equally-sized parts To divide the data set into fourths: 1) Find the median 64° 60° 62° 67° 59° 62° 59° 70° 66° 70° 62° 62° 67° 65° 80° 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° median Agenda 19 19

  20. Explore Whole Class Now that we have found the median (64°), how many equal parts do we have? Two roughly equal parts! What should we do next to break our data set into quartiles? Break the two parts we have in half to make four parts! Remember that quartiles are the points that divide a data set into roughly four equally-sized parts! 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° median Agenda 20 20

  21. Explore Notes Quartiles: the points that divide a data set into roughly four equally-sized parts To divide the data set into fourths: Find the median Find the lower quartile (Q1): the median of all values below the median 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° lower quartile (Q1) Agenda 21 21

  22. Explore Notes Quartiles: the points that divide a data set into roughly four equally-sized parts To divide the data set into fourths: Find the median Find the lower quartile (Q1): the median of all values below the median Find the upper quartile (Q3): the median of all values above the median 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° upper quartile (Q3) Agenda 22 22

  23. Explore Check Your Work! 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° lower quartile (Q1) upper quartile (Q3) median Agenda 23

  24. Explore Independent 1. Quartiles divide a data set into roughly four equally-sized parts. How could this be illustrated in the figure below? 2. What percentage could we write above each circle to show that each circle represents about ¼ of the data? 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° Hint Agenda Answer #1 Answer #2

  25. Explore Independent 1. Quartiles divide a data set into roughly four equally-sized parts. How could this be illustrated in the figure below? 2. What percentage could we write above each circle to show that each circle represents about ¼ of the data? 25% 25% 25% 25% 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° Q1 Q2 Q3 Q4 Next

  26. Explore Turn-and-talk Now that the data has been divided into four groups, form statements about the set of data below. Word Bank 25% data Between ¼ 25% 25% 25% 25% 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° Q1 Q2 Q3 Q4 “25% of the days were between 59° and 62°” “1/4 of the days were between 67° and 80°” Hint Agenda

  27. Explore Whole Class Could we also form statements about the data below using 50% or ½? Word Bank Greater than 50% Between data Less than ½ 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° “50% of the days were less than 64°” “Half of the days were between 62° and 67°” Sentence Starters Agenda Hint

  28. Explore Turn and Talk Now that we know what quartiles are, what is the interquartile range? Hint Agenda

  29. Explore Vocabulary What is the interquartile range? The interquartile range is the difference between the upper and lower quartiles in a data set. Interquartile Range = upper quartile (Q3) – lower quartile (Q1) 67° – 62° = 5° 59° 59° 60° 62° 62° 62° 62° 64° 65° 66° 67° 67° 70° 70° 80° lower quartile (Q1) upper quartile (Q3) Interquartile range Agenda

  30. Summary Think-Pair-Share How could you explain the interquartile range in sixth grade language? Sentence starters could include: The interquartile range represents… The interquartile range is the spread of… Scaffolding Agenda

  31. Practice – Part 1 Small Group Let’s go back to the test scores with a range of 98. What is the interquartile range of the data? Agenda

  32. Practice – Part 1 Whole Class 1) Find the median Median =83 points Agenda

  33. Practice – Part 1 Whole Class • Find the median • Find the lower quartile (Q1): the median of all values below the median Lower quartile (Q1) = 74 points Agenda

  34. Practice – Part 1 Whole Class • Find the median • Find the lower quartile (Q1): the median of all values below the median • Find the upper quartile (Q3): the median of all values above the median Upper quartile (Q3) = 89 points Agenda

  35. Practice – Part 1 Whole Class Interquartile Range = 89 – 74 = 15 points Lower quartile (Q1) = 74 points Upper quartile (Q3) = 89 points Agenda

  36. Practice – Part 1 Think-Pair-Share Interquartile Range = 89 – 74 = 15 points What does an interquartile range of 15 points actually mean? Agenda

  37. Practice – Part 2 Part 2 - (10 Min) Work independently and check in with a partner to complete your class work. 1-Worksheet 2-Share Out Click on the timer! In 10 minutes you will be asked to stop and share your answers! Agenda

  38. Practice – Complete Class Work Part 2 – (10 Min) Agenda

  39. Practice – Student Share Out Part 3 – (5 Min) Students share out work. Classwork Questions Agenda

  40. Practice – Sharing Question #1 Identify the range, median, Q1, Q3, and interquartile range (IQR). Weights of pumpkins (in lbs) 5 16 23 20 15 7 8 11 12 24 16 Range = 24 – 5 = 19 pounds Interquartile range = 20 – 8 = 12 pounds 5 7 8 11 12 15 16 16 20 23 24 Q1 median Q3 Agenda

  41. Practice – Sharing Question #4 Ms. Wheeler asked each student in her class to write their age in months on a sticky note. The 27 students in the class brought their sticky note to the front of the room and posted them in order on the white board. The data set is listed below in order from least to greatest. What are some observations that can be made from the data display? (Hint: Think about measures of variation) Q1 Median Range = 150 – 130 = 20 Interquartile range = 143 – 132 = 11 Q3 • ¼ of the students in the class are between 130 and 132 months old. • 25% of the students in the class are 143 months old or older. • ½ of the class is between 132 and 143 months old. Agenda

  42. Practice – Sharing Question #5 Write a data set of any 7 numbers that has all of the characteristics given below. • range equal to 18 • interquartile range equal to 8 • median equal to 7 2 6 6 7 10 14 20 7 7 7 7 15 15 25 1 2 6 7 9 10 19 Agenda

  43. Assessment - Exit Ticket Individual I am a bit confused! Today we talked about measures of center, measures of variation, range, quartiles, and interquartile range. These words still look like jibberish to me! Can you give me an overview of: • what measures of variation are • how to find measures of variation • why measures of variation are used Please include range, quartiles, and interquartile range in your explanation. Agenda

  44. 21st Century Lessons The goal… The goal of 21st Century Lessons is simple: We want to assist teachers, particularly in urban and turnaround schools, by bringing together teams of exemplary educators to develop units of high-quality, model lessons. These lessons are intended to: • Support an increase in student achievement; • Engage teachers and students; • Align to the National Common Core Standards and the Massachusetts curriculum frameworks; • Embed best teaching practices, such as differentiated instruction; • Incorporate high-quality multi-media and design (e.g., PowerPoint); • Be delivered by exemplary teachers for videotaping to be used for professional development and other teacher training activities; • Be available, along with videos and supporting materials, to teachers free of charge via the Internet. • Serve as the basis of high-quality, teacher-led professional development, including mentoring between experienced and novice teachers.

  45. 21st Century Lessons The people… Directors: Kathy Aldred - Co-Chair of the Boston Teachers Union Professional Issues Committee Ted Chambers - Co-director of 21st Century Lessons Tracy Young - Staffing Director of 21st Century Lessons Leslie Ryan Miller - Director of the Boston Public Schools Office of Teacher Development and Advancement Emily Berman- Curriculum Director (Social Studies) of 21st Century Lessons Carla Zils – Curriculum Director (Math) of 21st Century Lessons Brian Connor – Technology Coordinator

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