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

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

3. 3 *1 st Time Users of 21 st Century Lesson: Click HERE for a detailed description of our project.HERE 21 st Century Lessons – Teacher Preparation 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. Please do the following as you prepare to deliver this lesson: Feel free to customize this file to match the language and routines in your classroom.

4. 4 Lesson 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. Student- Friendly Objective: SWBAT explain what the IQR is, why we use it, and how to find it. Lesson Description The lesson begins with students engaging in a whole-class review of range. Following the review, students participate in an activity in which they have to evaluate how a class performed on a test based on limited information (they are only given the range of the scores). The activity is designed to show students that the range may not be a useful measure of variation when a data set contains one or more outliers. During the explore time, students move from using the range as a measure of variation to using the interquartile range as a measure of variation. Much of the launch and explore time is conducted using a think-pair-share where students discuss the questions with a partner before reporting out to the class. During the practice time, students will practice finding the interquartile range of different sets of data. They will also evaluate what the IQR actually represents. During the practice time, students are expected to work individually, while also regularly checking in with a nearby partner. Following the practice, students will share their answers and strategies with the class. This share-out will serve as an additional summary of the lesson. An exit ticket will be used to assess student understanding of the concepts of both range and interquartile range. Lesson Overview (1 of 7)

5. 5 Lesson VocabularyQuartiles: the points that divide a data set into roughly four equally-sized parts Interquartile Range (IQR): the difference between the third and first quartiles in a data set. Upper quartile (Q3) – lower quartile (Q1) Materials1) Exit tickets from the previous lesson on range 2) IQR class work handout 3) Exit ticket 4) IQR homework 5) Notes for struggling students Lesson Overview (2 of 7)

6. 6 Scaffolding Scaffolding buttons throughout the lesson provide additional supports and hints to help students make important connections. Handout on how to find the IQR is provided for struggling students. Enrichment Advanced Objective: SWBAT identify real world situations where one would use the range or IQR to better inform himself/herself. Ask students to brainstorm real life applications of this concept. To support students in doing this, a copy of a newspaper or magazine may provide some ideas. Lesson Overview (3 of 7)

7. 7 Online Resources for Absent Students http://www.ixl.com/math/grade-6/interpret-charts-to-find- mean-median-mode-and-range http://www.ixl.com/math/grade-6/mean-median-mode-and- range-find-the-missing-number http://www.ixl.com/math/grade-6/calculate-mean-median- mode-and-range Lesson Overview (4 of 7) Common Core State Standard 6.SP.2: Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. 6.SP.3: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

8. 8 Lesson Overview (5 of 7) Before and After While Grade 4 provides students with some opportunities to do the pre- work necessary to understand measures of variation, measures of variation are not formally introduced until grade 6. In Grade 4, 4.MD.4 says that students "find and interpret the difference in length between the longest and shortest specimens in an insect collection," using a line plot. This provides students with limited access to the concept of range. Aside from the basic groundwork laid out in grade 4, coming into this lesson, students will have had four lessons related to statistics. The unit began with an introduction to statistical questions. From there, the mean and median were introduced as measures of center that can be used to summarize a set of data gathered in response to a statistical question. This is the second lesson in the next cluster of lessons where spread is introduced as a measure to describe the variability of a set of data gathered in response to a statistical question. By the end of the unit, students should recognize the differences between measures of center and measures of variation and also what they are useful for despite the fact that both are used to describe data sets.

9. 9 Lesson Overview (6 of 7) Before and After Continued The previous lesson in this cluster of lessons covered range as a measure of variation. This lesson will build on students’ understanding of range to explore the interquartile range as a measure of spread or variation. At the end of this lesson, students should be able to break a set of data into quartiles to find the interquartile range. They should understand why and how the interquartile range is useful, particularly when the range is not. An understanding of both range and interquartile range will lay the groundwork for future lessons on how to create and analyze box plots. This lesson is one of a group of lessons designed to show that sets of data generated by statistical questions can be analyzed by looking at the spread of the data. In Grade 6 students see that the data collected in response to a statistical question have certain attributes (center, spread, overall shape). In Grade 7, when students expand their study of statistics to work with samples, students will see that these attributes relate important information about the sample from which the data were collected.

10. 10 Lesson Overview (7 of 7) Topic BackgroundTurn and Talk/Think-Pair-Share: “Various researchers (e.g. Douglas Reeves, Richard Allington, Vygotsky) have linked academic success with the capacity to engage in conversation and to ask and answer questions in full sentences. One of the most powerful and easy to implement moves is called: Turn and talk, or think, pair, share, or partner talk. All of these are variations of a practice that has far reaching benefits for students. Simply defined, “turn and talk” is a teacher offered opportunity for students to turn to another student and talk something through for a very brief period of time before whole group discussion or lecture resumes.” -Lucy West & Antonia Cameron Metamorphosis Teaching Learning Communities

11. Warm Up 11 Agenda 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! 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.

12. Warm Up 12 Agenda After an example has been read aloud: 1.IN YOUR HEAD, determine whether the example represents a data set with a wide range or a narrow range. 2.When you hear a clap, move your arms to represent your answer. Wide range = Arms are outstretched Narrow range = Hands are close together 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. Arm Movements

13. Agenda: 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 13 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.

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

15. Launch Think-Pair-Share 15 Test Scores: Would you expect a wide or narrow range? Agenda 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?

16. LaunchWhole Class 16 The test scores are below. Agenda 76870 727680 82 8485 878890 9293105 How do you think the students performed?

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

18. ExploreTurn and Talk 18 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? Agenda inter quartile Between Quarters

19. ExploreNotes 19 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 19 59° 60°62° 64°65°66°67° 70° 80° 19 59° 60°62° 64° 65° 66° 67° 70° 80° Agenda median

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

21. ExploreNotes 21 59° 60°62° 64°65°66°67° 70° 80° 21 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 2. Find the lower quartile (Q1): the median of all values below the median Agenda lower quartile (Q1)

22. ExploreNotes 22 59° 60°62° 64°65°66°67° 70° 80° 22 upper quartile (Q3) 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 2. Find the lower quartile (Q1): the median of all values below the median 3.Find the upper quartile (Q3): the median of all values above the median Agenda

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

24. Explore Independent 59° 60°62° 64°65°66°67° 70° 80° Hint 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? Answer #1Answer #2 Agenda

25. Explore Independent 59° 60°62° 64°65°66°67° 70° 80° 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% Next Q1 Q2 Q3 Q4

26. ExploreTurn-and-talk 59° 60°62° 64°65°66°67° 70° 80° HintAgenda Q1 Q2 Q3 Q4 Word Bank 25%data Between¼ Now that the data has been divided into four groups, form statements about the set of data below. 25% 25% “25% of the days were between 59° and 62°” “1/4 of the days were between 67° and 80°”

27. ExploreTurn-and-talk Now that the data has been divided into four groups, form statements about the set of data below. 25% 25% Word Bank 25%data Between¼ 59° 60°62° 64°65°66°67° 70° 80° Possible sentence starters include: “25% of the days were between…” “A quarter of the days were below…” Q1 Q2 Q3 Q4 Hint “25% of the days were between 59° and 62°” “1/4 of the days were between 67° and 80°” Agenda

28. ExploreWhole Class 59° 60°62° 64°65°66°67° 70° 80° Sentence Starters Could we also form statements about the data below using 50% or ½? Hint Agenda Word Bank Greater than 50% Betweendata Less than½ “50% of the days were less than 64°” “Half of the days were between 62° and 67°”

29. ExploreWhole Class Could we also form statements about the data below using 50% or ½? Word Bank Greater than 50% Betweendata Less than½ Hint 59° 60°62° 64°65°66°67° 70° 80° Sentence Starters Possible sentence starters include: “50% of the days were between…” “Half of the days were above…” “50% of the days were less than 64°” “Half of the days were between 62° and 67°” Agenda

30. ExploreWhole Class Could we also form statements about the data below using 50% or ½? Hint 59° 60°62° 64°65°66°67° 70° 80° Sentence Starters median Word Bank Greater than 50% Betweendata Less than½ “50% of the days were less than 64°” “Half of the days were between 62° and 67°” Agenda

31. ExploreTurn and Talk 31 Now that we know what quartiles are, what is the interquartile range? HintAgenda

32. ExploreTurn and Talk 32 Now that we know what quartiles are, what is the interquartile range? HintAgenda inter quartile Between Quarters

33. ExploreVocabulary 33 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° Interquartile range 59° 60°62° 64°65°66°67° 70° 80° upper quartile (Q3)lower quartile (Q1) Agenda

34. Summary Think-Pair-Share 34 AgendaScaffolding Sentence starters could include: The interquartile range represents… The interquartile range is the spread of… How could you explain the interquartile range in sixth grade language?

35. Summary Think-Pair-Share 35 How could you explain the interquartile range in sixth grade language? AgendaScaffolding 59° 60°62° 64°65°66°67° 70° 80° median Sentence starters could include: The interquartile range represents… The interquartile range is the spread of…

36. Practice – Part 1Small Group 36 Let’s go back to the test scores with a range of 98. Agenda 76870 727680 82 8485 878890 9293105 What is the interquartile range of the data?

37. Practice – Part 1Whole Class 37 1) Find the median Agenda 76870 727680 82 8485 878890 9293105 Median = 83 points

38. Practice – Part 1Whole Class 38 1)Find the median 2)Find the lower quartile (Q1): the median of all values below the median Agenda 76870 727680 82 8485 878890 9293105 Lower quartile (Q1) = 74 points

39. Practice – Part 1Whole Class 39 1)Find the median 2)Find the lower quartile (Q1): the median of all values below the median 3)Find the upper quartile (Q3): the median of all values above the median Agenda 76870 727680 82 8485 878890 9293105 Upper quartile (Q3) = 89 points

40. Practice – Part 1Whole Class 40 Interquartile Range = Agenda 76870 727680 82 8485 878890 9293105 Upper quartile (Q3) = 89 points Lower quartile (Q1) = 74 points 89 – 74 = 15 points

41. Practice – Part 1 Think-Pair-Share 41 Interquartile Range = 89 – 74 = 15 points Agenda 76870 727680 82 8485 878890 9293105 What does an interquartile range of 15 points actually mean?

42. Practice – Part 2 42 Part 2 - (10 Min) Work independently and check in with a partner to complete your class work. 1-Worksheet 2-Share Out In 10 minutes you will be asked to stop and share your answers! Click on the timer! Agenda

43. Practice – Complete Class Work 43 Part 2 – (10 Min) Agenda

44. Practice – Student Share Out 44 Part 3 – (5 Min) Students share out work. Classwork Questions Agenda

45. Practice – Sharing Question #1 45 Identify the range, median, Q1, Q3, and interquartile range (IQR). Weights of pumpkins (in lbs) 5 16 23 20 157 811 12 24 16 5 7 8 11 12 15 16 16 20 23 24 Range = 24 – 5 = 19 pounds Interquartile range = 20 – 8 = 12 pounds Agenda median Q1 Q3

46. Practice – Sharing Question #4 46 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) Median Q1 Q3 Range = 150 – 130 = 20 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. Interquartile range = 143 – 132 = 11 Agenda

47. Practice – Sharing Question #5 47 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 2667101420 7777151525 126791019 Agenda

48. Assessment - Exit Ticket Individual 48 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

49. Back to Overview 49 1 st Time Users of 21 st Century Lessons Welcome to 21 st Century Lessons! We are a non-profit organization that is funded through an AFT (American Federation of Teachers) Innovation Grant. Our mission is to increase student achievement by providing teachers with free world-class lessons that can be taught via an LCD projector and a computer. 21 st Century Lessons are extremely comprehensive; we include everything from warm–ups and assessments, to scaffolding for English language learners and special education students. The lessons are designed into coherent units that are completely aligned with the Common Core State Standards, and utilize research-based best practices to help you improve your students’ math abilities. Additionally, all of our lessons are completely modifiable so you can adapt them if you like. Description of 21 st Century Lessons: Next Slide

50. 50 1 st Time Users of 21 st Century Lessons The lesson that you are currently looking at is part of a unit that teaches the following Common Core Standards: *6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. *6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. *6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. Standards for This Unit Back to OverviewNext Slide

51. 51 1 st Time Users of 21 st Century Lessons *6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots. MA.4.a. Read and interpret circle graphs. *6.SP.5 Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Standards for This Unit Back to OverviewNext Slide

52. 52 1 st Time Users of 21 st Century Lessons In order to properly use 21 st Century Lessons you will need to possess or arrange the following things: Required: PowerPoint for P.C. (any version should work) Note: Certain capabilities in the PowerPoint Lessons are not compatible with PowerPoint for Mac, leading to some loss of functionality for Mac PowerPoint users. An LCD projector Pre-arranged student groups of 2 – (Many lessons utilize student pairings. Pairs should be seated close by and be ready to work together at a moment’s notice. Scissors – at least 1 for every pair Requirements to teach 21 st Century Lessons: Back to OverviewNext Slide

53. 53 1 st Time Users of 21 st Century Lessons Computer speakers that can amplify sound throughout the entire class “Calling Sticks” – a class set of popsicle sticks with a student’s name on each one A remote control or wireless presenter tool– to be able to advance the PowerPoint slides from anywhere in your classroom Personalize PowerPoints by substituting any names and pictures of children we included in the PowerPoint with names and pictures of your own students. Since many lessons utilize short, partner-processing activities, you will want a pre- established technique for efficiently getting your students’ attention. (“hands- up”, Count from “5” to “0” etc.) Project onto a whiteboard so you or your students can solve problems by hand. (Lessons often have a digital option for showing how to solve a problem, but you may feel it is more effective to show the work by hand on a whiteboard.) Internet connectivity – without the internet you may not have full functionality for some lessons. Strongly Suggested to teach 21 st Century Lessons: Back to OverviewNext Slide

54. 54 1 st Time Users of 21 st Century Lessons We suggest spending 30-45 minutes reviewing a lesson before teaching it. In order to review the lesson run the PowerPoint in “Slideshow “- Presenters View and advance to the “Lesson Overview” slide. By clicking on the various tabs this slide will provide you with a lot of valuable information. It is not necessary to read through each tab in order to teach the lesson, but we encourage you to figure out which tabs are most useful for you. Note: All of our lessons are designed to be taught during a 45-55 minute class. If your class is shorter than this you will have to decide which sections to condense/remove. If your class is longer we suggest incorporating some of the “challenge” questions if available. Lesson Preparation (Slide 1 of 2) Back to OverviewNext Slide

55. 55 1 st Time Users of 21 st Century Lessons After reviewing the overview slide, click your way through the PowerPoint. As you go, make sure to read the presenter note section beneath each slide. The note section is divided into two sections: “In-Class Notes” and “Preparation Notes.” The In-Class Notes are designed to be concise, bulleted information that you can use “on the fly” as you teach the lesson. Included in In-Class Notes are: a) a suggested time frame for the lesson, so you can determine whether you want to speed up, slow down, or skip an activity, b) key questions and points that you may want to bring up with your students to get at the heart of the content, and c) answers to any questions being presented on the slide. The Preparation Notes use a narrative form to explain how we envision the activity shown on the slide to be delivered as well as the rationale for the activity and any insight that we may have. Lesson Preparation (Slide 2 of 2) Back to OverviewNext Slide

56. 56 1 st Time Users of 21 st Century Lessons There are several features which have been incorporated into our PowerPoint lessons to help make lessons run more smoothly as well as to give you access to additional resources during the lesson should you want them. These features include: Agenda Shortcuts – On the agenda slide, click on any section title and you will advance to that section. Click the agenda button on any slide to return to the agenda. Action Buttons – On certain slides words will appear on the chalk or erasers at the bottom of the chalkboard. These action buttons give you access to optional resources while you teach. The most common action buttons are: Scaffolding – gives on-screen hints or help for that slide Answers – reveals answers to questions on that slide Challenge – brings up a challenge questions for students Agenda – will return you to the agenda at the beginning of the lesson Features built into each PowerPoint lesson Back to OverviewNext Slide

57. The goal of 21 st 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. 21 st Century Lessons The goal… 57

58. 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 21 st Century Lessons Brian Connor – Technology Coordinator 21 st Century Lessons The people… 58