1. Range as a Measure of Variation 1

2. 2 Lesson Objective SWBAT distinguish between measures of center and measures of variation and use range as a measures of variation to describe data distributions. Student- Friendly Objective: SWBAT explain what the range is, why we use it, and how to find it. Lesson Description The lesson begins with students engaging in a whole-class review of how to find the mean. Following the review, students participate in an activity in which they have to make a decision based on limited information (they are only given the mean and median of two data sets). The activity is designed to show students that describing sets of data using only measures of center is not adequate in many instances. During the explore time, students are required to calculate the range looking at different data displays. This portion of the lesson is really the meat of the lesson. It is designed to give students experience finding the range of several data sets displayed in various graphical representations. Often students are only asked to find the range of sets of data in a list. Here they are forced to dig a little deeper. 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 are required to work backwards when they are asked to create data displays based on given characteristics. During the practice time, students are expected to work individually and have a partner check their work., Following the practice, students will complete an exit ticket which will be used to assess student understanding of the concept of range. The lesson ends with a discussion re: the usefulness of the range as a measure of variation and previews what the next lesson will cover, which is interquartile range. Lesson Overview (1 of 7)

3. 3 Lesson VocabularyRange: the difference between the least value and the greatest value in a set of data. largest value (maximum) – smallest value (minimum) Materials1) Variation class work handout 2) Index Cards (for the exit ticket) 3) Variation homework 4) Notes for struggling students Lesson Overview (2 of 7)

4. 4 Scaffolding Scaffolding buttons throughout the lesson provide additional supports and hints to help students make important connections. Handout on how to find the range 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)

5. 5 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.

6. 6 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 three 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 first 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. Spread/measures of variation have only been mentioned in passing through a brief discussion on ways to analyze data. 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.

7. 7 Lesson Overview (6 of 7) Before and After Continued This lesson will explore the range as a measure of spread or variation. Some students may have some prior knowledge about range since it is a term widely used in mathematics and life. At the end of this lesson, students should be able to describe a set of data, whether it is in the form of a list, line plot, bar graph, etc. using the range. They will use range in the next lesson as they learn about interquartile range. 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 cluster 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.

8. 8 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

9. Warm Up OBJECTIVE: SWBAT distinguish between measures of center and measures of variation and use range as a measure of variation to describe data distributions. Language Objective: SWBAT explain why the range is a useful tool for analyzing data. 9 Ten students decide to have a pizza party and each is asked to bring his or her favorite pizza. The amount paid (in dollars) for each pizza is shown in the line plot below. 1)What is the mean price paid for pizza? 2)Two more students show up for the party and they have contributed no pizza. What is the mean of the data now? Challenge: How many more students without pizza would have to show up to bring the mean price below $8.00? : ScaffoldingAgenda $12.40 $10.33 4 students

10. Warm Up OBJECTIVE: SWBAT distinguish between measures of center and measures of variation and use range as a measure of variation to describe data distributions. Language Objective: SWBAT explain why the range is a useful tool for analyzing data. 10 Ten students decide to have a pizza party and each is asked to bring his or her favorite pizza. The amount paid (in dollars) for each pizza is shown in the line plot below. 1)What is the mean price paid for pizza? 2)Two more students show up for the party and they have contributed no pizza. What is the mean of the data now? Challenge: How many more students without pizza would have to show up to bring the mean price below $8.00? : ScaffoldingAgenda $12.40 $10.33 4 students To find the mean: 1)Add up all of the values in the data set. 2)Divide the sum by how many values there are in the data set.

11. Agenda: 1)Warm Up – Review of the Mean (Individual)Warm Up – Review of the Mean (Individual) 2)Launch – Packing a Suitcase (Whole Class)Launch – Packing a Suitcase (Whole Class) 3)Explore – Finding the Range (Individual)Explore – Finding the Range (Individual) 4)Practice – Creating Data Sets (Partner)Practice – Creating Data Sets (Partner) 5)Assessment – Narrow vs. Wide Range (Individual)Assessment – Narrow vs. Wide Range (Individual) 6)Summary – When is the Range Useful? (Whole Class)Summary – When is the Range Useful? (Whole Class) 11 OBJECTIVE: SWBAT distinguish between measures of center and measures of variation and use measures of variation to describe data distributions. Language Objective: SWBAT explain why the range is a useful tool for analyzing data.

12. Launch – Review Turn and Talk (30 sec) number of toppings students like 12 When we analyze data, what are we looking for? Center Spread (Measure of Variation) Shape MedianMeanRangeInterquartile Range Mean Absolute Deviation Agenda Today!

13. Launch: Packing a Suitcase Whole Class 13 Humberto is going to Massachusetts for vacation. According to the weekly forecast, while he is there the median temperature will be 74° and the mean temperature will be 67°. Jim is going to California for vacation. According to the weekly forecast, while he is there the median temperature will be 66° and the mean temperature will be 64°. Agenda

14. Launch Think-Pair-Share 14 What type of clothing should Humberto and Jim pack in their suitcases? Median: 66° Mean: 64° Median: 74° Mean: 67° Agenda

15. LaunchTurn-and-talk 15 Mon.Tue.Wed.Thur.Fri.Sat.Sun. 464974 677883 Mon.Tue.Wed.Thur.Fri.Sat.Sun. 6066 67596366 Boston San Francisco Weekly Weather Forecast (in °F) After seeing the forecast, would you suggest that Humberto or Jim add or remove anything from their suitcases? Use evidence from the weather forecast to support your answer. Agenda

16. LaunchTurn-and-talk 16 Agenda The range in temperature is very different for the two cities. What does range mean?

17. LaunchVocabulary 17 What is the definition of range? The range is the difference between the least value and the greatest value in a set of data. Range = largest value (maximum) – smallest value (minimum) 15681712913 17 – 6 = 11 range Examples of data sets with a Narrow Range: Milk prices Age of 6 th graders Examples of data sets with a Wide Range: House prices Age of teachers Agenda

18. LaunchNotes 18 MondayTuesdayWedsThursFridaySatSunday 464974 677883 MondayTuesdayWedsThursFridaySatSunday 6066 67596366 Boston San Francisco Weekly Weather Forecast (Daily High Temperatures) What is the range of temperatures in Boston and San Francisco? Boston: 83 – 46 = 37° SF: 67 – 59 = 8° Agenda

19. Launch Think-Pair-Share 19 A measure of center (median and mean) uses one number to summarize or represent a set of data. What is the purpose of this measure of variation (range)? Median: 66° Mean: 64° Range: 8° Median: 74° Mean: 67° Range: 37° Agenda

20. Explore – Part 1 20 Part 1 – (5 Min) Work independently and check in with a partner to complete your class work. 1-Worksheet 2-Share Out In 5 minutes you will be asked to stop and share your answers! Click on the timer! Agenda

21. Explore – Complete Front of Worksheet 21 Part 1 – (5 Min) Agenda

22. Explore – Student Share Out 22 Part 2 – (10 Min) Students share out work. Classwork Questions Agenda

23. Explore – Sharing Question #1 23 Based on the pictures, what is the range of fruit prices? $4.99 $0.59 $3.79 $0.95 $5.29 A = $4.70 Agenda

24. 24 Based on the bar graph, approximately what was the range of precipitation in Long Beach in 2011? Explore – Sharing Question #2 A ≈ 11 inches Agenda

25. 25 Based on the line plot, what is the range of the number of children in a household? Explore – Sharing Question #3 A = 7 children Agenda

26. 26 Based on the table, what is the range of heights? What is the range of arm spans? Explore – Sharing Question #4 A = 19 inches (height) A = 19 inches (arm span) Agenda

27. 27 Based on the table, what is the range of the number of pets? Explore – Sharing Question #5 A = 21 pets Agenda

28. Practice – Create Your Own Data Sets 28 (10 Min) Students create their own data sets based on given characteristics. Practice Agenda

29. Practice – Complete Back of Worksheet 29 (10 Min) Agenda

30. Classwork Summary – Sharing Question #7 30 Agenda Write a data set of any 5 numbers that has both of the characteristics given below. range equal to 7 mean equal to 4

31. Assessment – Narrow or Wide Range? 31 Agenda On the index card in front of you, complete the following: 1.Write your name on the top (on the front) 2.On the front of the index card, write an example of a data set that would have a wide range. Explain your reasoning. 3.On the back of the index card, write an example of a data set that would have a narrow range. Explain your reasoning. 4.You have 3 minutes!

32. Summary – Usefulness of the Range 32 Students learn when the range is a useful measure of variation. Summary Agenda

33. SummaryWhole Class 33 Based on the line plot, what was the range of temperatures in Las Vegas from November 1 – 15, 2011? 80 – 59 = 21° Agenda

34. Summary Small Group 34 The range of our data is 21°. Does this measure give an accurate picture of the overall variability in the data? NO!! Agenda

35. Summary Think-Pair-Share 35 What?! My teacher told me to use the range to describe data. Now she is telling me the range is not always useful. When is it useful? Should I just flip a coin if I am not sure when to use it? Agenda

36. SummarySmall Group 36 For which sets of data would the range give a reasonable picture of overall variability? a.b. c. d. Agenda

37. SummaryWhole Class 37 Since the range is greatly influenced by outliers, we also use the interquartile range (IQR) to describe the variability of a data set. Agenda

38. Summary – Preview number of toppings students like 38 When we analyze data, what are we looking for? Center Spread (Measure of Variation) Shape MedianMeanRangeInterquartile Range Mean Absolute Deviation Agenda Tomorrow!

39. 39 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

40. 40 *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