1. Comparing Numerical Data Using Box Plots 1

2. 2 Lesson Objective SWBAT compare numerical data using box plots. Lesson Description The lesson begins with a review of measures that can be used to analyze sets of data (mean, median, maximum, etc). Following the review, students are presented with the idea of using box plots to compare sets of data. During the explore time, students analyze a box plot to discover how it can be used to effectively and efficiently compare the snowfall for two ski resorts over the course of 50 years. 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 complete a worksheet that requires them to use and create box plots to compare sets of data. 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 informal summary of the lesson. After the formal summary of the lesson, an exit ticket will be used to assess student understanding of using and creating box plots to compare data. Lesson Overview (1 of 5)

3. 3 Lesson Vocabulary Box Plot: A graph that uses a rectangle to represent the middle 50% of a set of data and “whiskers” at both ends to represent the remainder of the data. Five-Number Summary: Minimum Lower Quartile (Q1) Median Upper Quartile (Q3) Maximum Materials1) Box plot class work handout 2) Exit ticket 3) Box plot homework 4) Popsicle Sticks 5) Computers (for extension problem – at teacher’s discretion) Lesson Overview (2 of 5)

4. 4 Scaffolding Scaffolding buttons throughout the lesson provide additional supports and hints to help students make important connections. Handout on how to create a box plot is provided for struggling students. Enrichment Online Resources for Absent Students Advanced Objective: SWBAT use box plots to compare two sets of real-world data. To support students in doing this, a computer or a print-out of players’ heights is necessary. See slide 26 for more information. http://www.brainingcamp.com/resources/math/box-plots/lesson.php Lesson Overview (3 of 5)

5. 5 Lesson Overview (4 of 5) Common Core State Standard Before and After 6.SP.4: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. Box plots, or box-and-whisker plots, are traditionally an eighth grade concept. As a result, students do not have a lot of prior knowledge related to them. While it is a new concept, students do come into the lesson with prior knowledge that will help them to compare two sets of data using a box plot. In the previous three lessons, students learned about the range and interquartile range. Through these lessons, students built an understanding of maximum, minimum, Q1 and Q3. Throughout the unit students have also been learning about the median. These are the five components of the five-number summary that is required to create a box plot. Furthermore, in the previous lesson, students learned how to create and analyze box plots. Going forward, students will build on their usage of graphs to compare data through the use of histograms.

6. 6 Lesson Overview (5 of 5) 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

7. Warm Up OBJECTIVE: SWBAT compare numerical data using box plots. Language Objective: SWBAT verbally analyze and compare data using content specific vocabulary. Agenda 7 If your job is to recommend a ski resort by comparing the annual snowfall of two mountains for the past 50 years, how would you compare all the data? (Hint: What are some measures we have been using to compare sets of data?) 1962 1963 1964 1965 1966 1967 … Powder Valley Mad Mountain 217 in. 132 in. 310 in. 104 in. 186 in. 287 in. … 107 in. 233 in. 207 in. 106 in. 229 in. 37 in. … Mean,Median, Minimum, Maximum, Q1, Q3

8. Agenda: 1)Warm Up – Review of Describing Data (Individual)Warm Up – Review of Describing Data (Individual) 2)Launch – Which Ski Resort Would You Recommend? (Whole Class)Launch – Which Ski Resort Would You Recommend? (Whole Class) 3)Explore – Comparing Data Using Box Plots (Whole Class)Explore – Comparing Data Using Box Plots (Whole Class) 4)Practice – Tomatoes: This Year’s or Last Year’s? (Individual)Practice – Tomatoes: This Year’s or Last Year’s? (Individual) 5)Summary – Why Use Box Plots? (Whole Class)Summary – Why Use Box Plots? (Whole Class) 6)Assessment – Exit Ticket (Individual)Assessment – Exit Ticket (Individual) 8 OBJECTIVE: SWBAT compare numerical data using box plots. Language Objective: SWBAT verbally analyze and compare data using content specific vocabulary.

9. Launch Turn and Talk Agenda 9 What are some of the ways we can represent this data visually so we can compare it more easily? 1962 1963 1964 1965 1966 1967 … Powder Valley Mad Mountain 217 in. 132 in. 310 in. 104 in. 186 in. 287 in. … 107 in. 233 in. 207 in. 106 in. 229 in. 37 in. …

10. LaunchThink-Pair-Share 10 We have been using box plots to summarize sets of data. How could we show 2 sets of data on a box plot? Sketch what that might look like. 1962 1963 1964 1965 1966 1967 … Powder Valley Mad Mountain 217 in. 132 in. 310 in. 104 in. 186 in. 287 in. … 107 in. 233 in. 207 in. 106 in. 229 in. 37 in. …

11. LaunchWhole Class 11 0 50100150 200 250 300 350400 Annual Snowfall (inches) Powder Valley Mad Mountain Agenda

12. LaunchSmall Group 12 0 50100150 200 250 300 350400 Annual Snowfall (inches) Powder Valley Mad Mountain How can we use this box plot to compare the two ski resorts? (Hint: Is there a way to use the box plot to compare the values from the five number summary for each resort?) Agenda

13. ExploreWhole Class 13 From the box plot, you can easily see the median snowfall for each resort. Powder Mad Valley Mountain Median 175 inches 225 inches 0 Annual Snowfall (inches) Powder Valley Mad Mountain 50100 150200250 300350400 Agenda

14. ExploreWhole Class 14 Using the medians to compare the resorts, which resort appears to be better? Powder Mad Valley Mountain Median 175 inches 225 inches 0 Annual Snowfall (inches) Powder Valley Mad Mountain 50100150200250 300350400 Agenda

15. ExploreWhole Class 15 Using the box plot, you can identify the record high (maximum) and record low (minimum) annual snowfalls for each resort. Powder Mad Valley Mountain Median 175 inches 225 inches Record Low 75 inches 0 inches Record High 325 inches 400 inches 0 Annual Snowfall (inches) Powder Valley Mad Mountain 50100150200250 300350400 Agenda

16. ExploreWhole Class 16 Using the minimum values to compare the resorts, which resort appears to be better? Powder Mad Valley Mountain Median 175 inches 225 inches Record Low 75 inches 0 inches Record High 325 inches 400 inches 0 Annual Snowfall (inches) Powder Valley Mad Mountain 50100150200250 300350400 Agenda

17. ExploreWhole Class 17 Using the maximum values to compare the resorts, which resort appears to be better? Powder Mad Valley Mountain Median 175 inches 225 inches Record Low 75 inches 0 inches Record High 325 inches 400 inches 0 Annual Snowfall (inches) Powder Valley Mad Mountain 50100150200250 300350400 Agenda

18. ExploreThink-Pair-Share 18 What does the distance between points in the box plot tell you about how spread out the data is? The greater the distance between points in the box plot, the more spread out the annual snowfall data is. 0 50100150 200 250 300 350400 Powder Valley Mad Mountain Hint Agenda

19. ExploreThink-Pair-Share 19 What does the distance between points in the box plot tell you about how spread out the data is? The greater the distance between points in the box plot, the more spread out the annual snowfall data is. 0 50100150 200 250 300 350400 Powder Valley Mad Mountain Hint Agenda

20. ExploreWhole Class 20 Which mountain varies less in terms of the amount of snowfall from year to year? Powder Mad Valley Mountain Median 175 inches 225 inches Record Low 75 inches 0 inches Record High 325 inches 400 inches Variation small large 0 Annual Snowfall (inches) Powder Valley Mad Mountain 50100150200250 300350400 Agenda

21. ExploreWhole Class 21 Which resort has a greater chance of receiving more than 300 inches of snow? Powder Mad Valley Mountain Median 175 inches 225 inches Record Low 75 inches 0 inches Record High 325 inches 400 inches Variation small large Chance of >300 in. lesser greater 0 Annual Snowfall (inches) Powder Valley Mad Mountain 50100150200250 300350400 Agenda

22. ExploreSmall Group 22 Powder Mad Valley Mountain Median 175 inches 225 inches Record Low 75 inches 0 inches Record High 325 inches 400 inches Variation small large Chance of >300 in. lesser greater Which resort would you recommend? Agenda

23. ExploreThink-Pair-Share 23 How does the data gathered below relate to the pieces of a five number summary? Powder Mad Valley Mountain Median 175 inches 225 inches Record Low 75 inches 0 inches Record High 325 inches 400 inches Variation small large Chance of >300 in. lesser greater 0 Annual Snowfall (inches) Powder Valley Mad Mountain 50100150200250 300350400 Agenda

24. ExploreWhole Class 24 Original Question: If your job is to recommend a ski resort by comparing the annual snowfall between two mountains for the past 50 years, how would you compare all the data? How did we use the box plot to answer this question? 0 Annual Snowfall (inches) Powder Valley Mad Mountain 50100150200250 300350400 Agenda

25. Practice 25 Part 1 - (15 Min) Work independently and check in with a partner to complete your class work. 1-Worksheet 2-Share Out In 15 minutes you will be asked to stop and share your answers! Click on the timer! Agenda

26. Practice – Complete Worksheet (15 minutes) 26 Agenda

27. Practice – Student Share Out 27 Part 2 – (8 Min) Students share out work. Classwork Questions Agenda

28. Practice – Sharing Question #1 28 A farmer starts 9 tomato plants in a greenhouse several weeks before spring. The seedlings look a little small this year so the farmer decides to compare this year’s growth with last year’s growth. This year’s growth is measured in inches as: 128.4109.8147.91112.713.7 Last year’s growth was measured in inches as: 11.7 9 1710.513.4 15.216.8 11.5 15 Should the farmer be concerned about the tomato plants this year? Why or why not? Support your answer by creating a box plot. Agenda

29. 29 This year’s growth is measured in inches as: 128.4109.8147.91112.713.7 7.98.49.810111212.713.714 Median = 11 inchesMinimum = 7.9 inches Lower Quartile (Q1) = 9.1 inchesMaximum = 14 inches Upper Quartile (Q3) = 13.2 inches 9.1 13.2 Practice – Sharing Question #1 Agenda

30. 30 Last year’s growth was measured in inches as: 11.7 9 1710.513.4 15.216.8 11.5 15 910.511.511.713.41515.216.817 Median = 13.4 inchesMinimum = 9 inches Lower Quartile (Q1) = 11 inchesMaximum = 17 inches Upper Quartile (Q3) = 16 inches 11 16 Practice – Sharing Question #1 Agenda

31. 31 Practice – Sharing Question #1 This Year’s Growth Last Year’s Growth Agenda

32. 32 This Year Last Year Minimum 7.9 9 Q1 9.1 11 Median 1113.4 Q3 13.2 16 Maximum 14 17 The farmer should be concerned. The box plots show that this year’s seedlings are smaller than last year’s seedlings. All of the five-number summary values are less. Practice – Sharing Question #1 This Year’s Growth Last Year’s Growth Agenda

33. 33 Your job: Make a peanut butter recommendation for grocery shoppers. Suppose price is the only factor a buyer considers. Is natural peanut butter or regular peanut butter a better choice? Explain. Practice – Sharing Question #2a Grocery shoppers should purchase regular peanut butter if price is the only factor, as all of the five- number summary values are less. Agenda

34. 34 Your job: Make a peanut butter recommendation for grocery shoppers. Suppose quality is the only factor a buyer considers. Is natural peanut butter or regular peanut butter a better choice? Explain. Practice – Sharing Question #2b Grocery shoppers should purchase natural peanut butter if quality is the only factor, as all of the five- number summary values are greater. Agenda

35. Summary Think-Pair-Share 35 Methods we could have used to compare these two sets of data during our warm-up today: Mean, Median, Minimum, Maximum, Lower Quartile (Q1) and Upper Quartile (Q3) If we already have all of these strategies for comparing two sets of data, why did we learn about using box plots to compare sets of data today? 1962 1963 1964 1965 1966 1967 … Powder Valley Mad Mountain 217 in. 132 in. 310 in. 104 in. 186 in. 287 in. … 107 in. 233 in. 207 in. 106 in. 229 in. 37 in. … Agenda

36. Assessment – Exit Ticket! 36 Complete and hand in the Exit Ticket before you leave! Agenda

37. 37 *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