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© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Grade 6 – Module 6 Statistics (Lessons.

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Presentation on theme: "© 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Grade 6 – Module 6 Statistics (Lessons."— Presentation transcript:

1 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Grade 6 – Module 6 Statistics (Lessons 1 to 18)

2 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Session Objectives 1.Brief overview (big ideas) of module 6: Statistics 1.Overviews of Topic A (Lessons 1 to 5), Topic B (Lessons 6 to 11), Topic C (Lessons 12 to 16), and Topic D (Lessons 18 to 21) 2.Examine sample problems in select lessons to become familiar with the progression of the statistics concepts in Grade 6.

3 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Agenda

4 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Curriculum Overview of A Story of Ratios

5 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Module Overview and Standards Topic A: Understanding Distributions (6.SP.A.1, 6.SP.A.2, 6.SP.B.4, 6.SP.B.5b) Lesson 1: Posing Statistical Questions Lesson 2: Displaying a Data Distribution Lesson 3: Creating a Dot Plot Lesson 4: Creating a Histogram Lesson 5: Describing a Distribution Displayed in a Histogram

6 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Module Overview and Standards Topic B: Summarizing a Distribution that is Approximately Symmetric Using the Mean and Mean Absolute Deviation (6.SP.A.2, 6.SP.A.3, 6.SP.B.4, 6.SP.B.5) Lesson 6: Describing the Center of a Distribution Using the Mean Lesson 7: The Mean as a Balance Point Lesson 8: Variability in a Data Distribution Lesson 9: The Mean Absolute Deviation (MAD) Lessons 10–11: Describing Distributions Using the Mean and MAD

7 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Module Overview and Standards Topic C: Summarizing a Distribution that is Skewed Using the Median and the Interquartile Range (6.SP.A.2, 6.SP.A.3, 6.SP.B.4, 6.SP.B.5) Lesson 12: Describing the Center of a Distribution Using the Median Lesson 13: Describing Variability Using the Interquartile Range (IQR) Lesson 14: Summarizing a Distribution Using a Box Plot Lesson 15: More Practice with Box Plots Lesson 16: Understanding Box Plots

8 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Module Overview and Standards Topic D: Summarizing and Describing Distributions (6.SP.B.4, 6.SP.B.5) Lesson 17: Developing a Statistical Project Lesson 18: Connecting Graphical Representations and Numerical Summaries Lesson 19: Comparing Data Distributions Lesson 20: Describing Center, Variability, and Shape of a Data Distribution from a Graphical Representation Lesson 21: Summarizing a Data Distribution by Describing Center, Variability, and Shape Lesson 22: Presenting a Summary of a Statistical Project

9 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Terminology Statistical Question Median Mean Dot plot Histogram Box Plot Variability Deviations from the mean Mean Absolute Deviation (MAD) Interquartile Range (IQR)

10 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Representations (Dot Plot)

11 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Representation (Histogram)

12 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Representation (Box plot)

13 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Agenda

14 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic A Understanding Distributions Lesson 1: Posing Statistical Questions Lesson 2: Displaying a Data Distribution Lesson 3: Creating a Dot Plot Lesson 4: Creating a Histogram Lesson 5:Describing a Distribution Displayed in a Histogram 5 Instructional Days

15 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 1: Posing Statistical Questions In Lesson 1, statistical questions are introduced in the context of a four-step process for posing and answering questions based on data. As students begin to explore data, they see the need to organize and summarize data.

16 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 2: Displaying a Data Distribution In Lesson 2, students are introduced to the idea that a data distribution can be represented graphically and that there are several different types of graphs, including dot plots and histograms, commonly used to represent a distribution of numerical data. This lesson then builds on students previous work with line plots, introducing them to dot plots (line plots, but in a data context where students are to think about the distribution of data rather than to think of individual points plotted on a number line).

17 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 3: Creating a Dot Plot In Lesson 3, students construct dot plots and begin to describe data distributions.

18 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 4: Creating a Histogram In Lesson 4, students are introduced to histograms as another way of representing a data distribution graphically and the advantages and disadvantages of histograms relative to dot plots are discussed. * shape of a data distribution (symmetric versus skewed) * introduced to the idea that different numerical summary measures of center and variability

19 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 5: Describing a Distribution Displayed in a Histogram Lesson 5 gives students additional practice in constructing and describing histograms and introduces relative frequency histograms (histograms where relative frequency rather than frequency is used for the vertical scale).

20 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 1: Posing Statistical Questions Student Outcomes Students distinguish between statistical questions and those that are not statistical. Students formulate a statistical question and explain what data could be collected to answer the question. Students distinguish between categorical data and numerical data.

21 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Polyas Problem Solving Process 1. Understand the problem 2. Devise a plan 3. Carry out the plan 4. Look back

22 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Statistical Problem Solving 1.Pose a question that can be answered by data. 2.Determine a plan to collect the data. 3.Summarize the data with graphs and numerical summaries. 4.Answer the questions posed in Step 1 using the data and summaries.

23 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios What is a statistical question? A statistical question is one that can be answered with data and for which it is anticipated that the data (information) collected to answer the question will vary.

24 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Statistical Question? What are the favorite colors of 6 th graders in my school? A statistical question should have: Stated population Measureable variable Anticipate variability

25 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Statistical Question? How old is the principal at our school? Why isnt this a statistical question?

26 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Types of Data Quantitative variables are numerical. They represent a measurable quantity. The height of a person, the weight of German Shepherd puppies, the circumference of a ball are examples of quantitative variables.

27 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Types of Data Categorical variables take on values that are names or labels. The color of a ball (e.g., red, green, blue), the breed of a dog (e.g., collie, shepherd, terrier), or favorite pizza topping would be examples of categorical variables.

28 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 1: Problem Set Organize in small groups. Discuss and complete all the parts of problems 1 and 2 from Lesson 1 of this module. (S4) After you have completed the problems, we will discuss the answers.

29 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 2: Displaying a Data Distribution Student Outcomes Given a dot plot, students begin describing the distribution of the points on the dot plot in terms of center and variability.

30 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 3: Creating a Dot Plot Student Outcomes Students create a dot plot of a given data set. Students summarize a given data set using equal length intervals and construct a frequency table. Based on a frequency table, students describe the distribution.

31 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 3: Example 2 A group of 6 th graders investigated the statistical question: How many hours per week do 6 th graders spend playing a sport or outdoor game? Here are the data the students collected from a sample of 26 6 th graders showing the number of hours per week spent playing a sport or a game outdoors:

32 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Frequency Table

33 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Dot Plot

34 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 4: Creating a Histogram The boys and girls basketball teams at Roosevelt Middle School wanted to raise money to help buy new uniforms. They decided to sell hats with the school logo on the front to family members and other interested fans. To obtain the correct hat size, the students had to measure the head circumference (distance around the head) of the adults who wanted to order a hat. The following data represents the head circumferences, in millimeters (mm), of the adults: 513, 525, 531, 533, 535, 535, 542, 543, 546, 549, 551, 552, 552, 553, 554, 555, 560, 561, 563, 563, 563, 565, 565, 568, 568, 571,571, 574, 577, 580, 583, 583, 584, 585, 591, 595, 598, 603, 612, 618

35 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios

36 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Building a Histogram

37 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Frequency Histogram of Head Circumferences

38 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Shape of the Distribution: Mound Shaped or Symmetric

39 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Skewed Distribution

40 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Organize in small groups. Discuss and complete all the parts of problem 2 from Lesson 4 of this module. (S25) After you have completed the problems, we will discuss the answers and some areas of student concern.

41 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 5: Describing a Distribution Displayed in a Histogram Student Outcomes Students construct a relative frequency histogram. Students recognize that the shape of a histogram does not change when relative frequency is used compared to when frequency is used to construct the histogram.

42 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Frequency Table of Head Circumferences

43 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Relative frequency table

44 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Relative Frequency Histogram

45 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Frequency Histogram of Head Circumferences

46 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Agenda

47 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic B: Summarizing a Distribution that is Approximately Symmetric Using the Mean and Mean Absolute Deviation Lesson 6: Describing the Center of a Distribution Using the Mean Lesson 7: The Mean as a Balance Point Lesson 8: Variability in a Data Distribution Lesson 9: The Mean Absolute Deviation (MAD) Lessons 10–11: Describing Distributions Using the Mean and MAD 6 Instructional days

48 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 6: Describing the Center Using the Mean In Lesson 6, students learn to calculate the mean and to understand the fair share interpretation of the mean.

49 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 7: The Mean as a Balance Point In Lesson 7, students develop an understanding of the mean as a balance point of a data distributionthe point where the sum of distances of points to the right of the mean and the sum of distances of points to the left of the mean are equal.

50 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 8: Variability in a Data Distribution Lesson 9: Mean Absolute Deviation Lessons 8 and 9 introduce the MAD as a measure of variability, and students calculate and interpret the value of the MAD.

51 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 10 and 11: Describing the Distribution using the Mean and MAD Lessons 10 and 11 give students the opportunity to use both graphical and numerical summaries to describe data distributions, to compare distributions, and to answer questions in context using information provided by a data distribution.

52 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios What do we mean by average? What students say: add em up and divide its the average its the middle number its in the center

53 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 6: Describing the Center using the Mean Question: How many pets do five randomly sampled sixth graders have? Data from five randomly chosen sixth graders: 2, 6, 2, 4, and 1

54 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios How many pets do students have? 2, 6, 2, 4, and 1

55 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios What do you mean by average? The evening out or fair share value

56 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Fair Share value

57 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Fair Share value

58 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Fair Share value

59 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Fair Share value

60 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Fair Share value

61 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Fair Share value

62 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Fair Share value

63 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios The results after evening out

64 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Question: How many pets do students have? What does fair share mean in words in the context of the question?

65 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Question: How many pets do students have? Mean is 3 – the fair share value, i.e., the number of pets that all the students would have if they all had the same number of pets is 3. (There are 15 pets to be divided evenly among 5 students. Connections to math: 15/5)

66 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Fair Share Value As ide: What if there had been 16 pets ? There would be one pet left over that needs to be divided evenly among the five children. What to do? Well, the pet would have to be chopped up into five equal pieces giving each child one piece, or more exactly 1/5 th of a piece. Hence, each child would wind up with 3 1/5 th pets. The mean would be 3 1/5 pets.

67 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 7: The Mean as a Balance Point The number of minutes it takes two students to get to school.

68 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios If you represented the dot plot with a ruler and pennies, where would the ruler balance?

69 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios What is the sum of the deviations?

70 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios

71 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Will the ruler balance at 6?

72 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 8: Variability in a Data Distribution Student Outcomes Students interpret the mean of a data set as a typical value. Students compare and contrast two small data sets that have the same mean but different amounts of variability. Students see that a data distribution is not characterized only by its center. Its spread or variability must be considered as well. Students informally evaluate how precise the mean is as an indicator of the typical value of a distribution, based on the variability exhibited in the data. Students use dot plots to order distributions according to the variability around the mean for each of the data distributions.

73 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 8: Variability in a Data Distribution

74 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 9: The Mean Absolute Deviation (MAD) Student Outcomes Students calculate the mean absolute deviation (MAD) for a given data set. Students interpret the MAD as the average distance of data values from the mean.

75 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Measuring Variability Mean temperature is 63 degrees

76 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Complete the temperature deviations

77 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Mean Absolute Deviation Find the mean of the absolute deviations = 3.67 This is MAD

78 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Measuring Variability Mean temperature is 63 degrees

79 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Mean Absolute Deviation What does a MAD of 3.67 represent in context? If MAD is large what would that indicate about the variability of the data?

80 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 10 and 11: Describing Distributions Using the Mean and MAD Student Outcomes Students calculate the mean and MAD for a data distribution. Students use the mean and MAD to describe a data distribution in terms of center and variability.

81 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 10: Problem Set Organize in small groups. Discuss and complete all the parts of problems 5 and 6 from Lesson 10 of this module. (S69) After you have completed the problems, we will discuss the answers.

82 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 10 Problem 5

83 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Agenda

84 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Mid-Module Assessment

85 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Agenda

86 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic C: Summarizing a Distribution that is Skewed Using the Median and the Interquartile Range Lesson 12: Describing the Center of a Distribution Using the Median Lesson 13: Describing Variability Using the Interquartile Range (IQR) Lesson 14: Summarizing a Distribution Using a Box Plot Lesson 15: More Practice with Box Plots Lesson 16: Understanding Box Plots 5 Instructional Days

87 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 12: Describing the Center of a Distribution Using the Median In Lesson 12, students learn to calculate and interpret the median.

88 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 13: Describing Variability Using the Interquartile Range (IQR) Quartiles are introduced in Lesson 13, and the quartiles are then used to calculate the IQR. Students also learn to interpret the IQR as a measure of variability in a data distribution.

89 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson Summarizing a Distribution Using a Box Plot Lessons 14–15 introduce box plots. Box plot is a graph of five key summary statistics of a data set (the minimum, lower quartile, median, upper quartile, and the maximum). Lesson 16 has students use box plots to compare groups, setting the stage for future work on comparing groups in Grade 7.

90 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 12: Describing the Center of a Distribution Using the Median Student Outcomes Given a data set, students calculate the median of the data. Students estimate the percent of values above and below the median value.

91 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 13: Describing Variability Using the Interquartile Range (IQR) Student Outcomes Given a set of data, students describe how the data might have been collected. Students describe the unit of measurement for observations in a data set. Students calculate the median of the data. Students describe the variability in the data by calculating the interquartile range.

92 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Finding the Median and Quartiles The owner of the chain decided to check the number of french fries at another restaurant in the chain. Here is the data for Restaurant B: 82, 83, 83, 79, 85, 82, 78, 76, 76, 75, 78, 74, 70, 60, 82, 82, 83, 83, 83.

93 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Finding the Median and Quartiles Number of french fries (n=19) in order from smallest to largest: Lower quartile MedianUpper quartile

94 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Finding the Median and Quartiles n= 18: Lower quartile MedianUpper quartile

95 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Finding the Median and Quartiles n= 16: Lower quartile MedianUpper quartile

96 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 14: Summarizing a Distribution Using a Box Plot Student Outcome Students construct a box plot from a given set of data.

97 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 15: More Practice with Box Plots Student Outcomes Given a box plot, students summarize the data by the 5-number summary (Min, Q1, Median, Q3, Max.) Students describe a set of data using the 5- number summary and the interquartile range. Students construct a box plot from a 5-number summary.

98 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 16: Understanding Box Plots Student Outcomes Students summarize a data set using box plots, the median, and the interquartile range. Students use box plots to compare two data distributions.

99 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 15: Problem Set Organize in small groups. Discuss and complete all the parts of exercises 6 to 10 from Lesson 15 of this module. (S100) After you have completed the problems, we will discuss the answers.

100 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Interpreting Box Plots

101 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Interpreting Box Plots

102 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Interpreting box plots exercise 10 (p.101)

103 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Agenda

104 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic D: Summarizing and Describing Distributions Lesson 17:Developing a Statistical Project Lesson 18: Connecting Graphical Representations and Numerical Summaries Lesson 19:Comparing Data Distributions Lesson 20:Describing Center, Variability, and Shape of a Data Distribution from a Graphical Representation Lesson 21:Summarizing a Data Distribution by Describing Center, Variability, and Shape Lesson 22:Presenting a Summary of a Statistical Project 6 Instructional Days

105 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic D: Summarizing and Describing Distributions In Topic D, students integrate what they have learned about graphical and numerical data summaries in the previous topics. They match dot plots and histograms to numerical measures of center and variability. Students estimate means and medians from graphical representations of data distributions. They also estimate mean absolute deviation (MAD) and interquartile range (IQR) from graphical representations based on an understanding of data distributions in terms of shape, center, and variability.

106 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 18:Connecting Graphical Representations and Numerical Summaries Student Outcomes Students match the graphical representations and numerical summaries of a distribution. Matches involve dot plots, histograms, and summary statistics.

107 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Example from Lesson 18

108 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 19:Comparing Data Distributions Student Outcomes Given box plots of at least two data sets, students will comment on similarities and differences in the distributions.

109 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 20:Describing Center, Variability, and Shape of a Data Distribution from a Graphical Representation Student Outcomes Given a frequency histogram, students are able to describe the data collected, including the number of responses, an estimate of the mean or median, and an estimate of the interquartile range (IQR) or the mean absolute deviation (MAD).

110 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 21: Summarizing a Data Distribution by Describing Center, Variability, and Shape Student Outcomes Given a data set, students are able to describe the data collected, including the number of responses, mean or median, and the MAD or the interquartile range (IQR).

111 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 20: Problem Set Organize in small groups. Discuss and complete all the parts of problems 1 to 11 from Lesson 20 of this module. (S134) After you have completed the problems, we will discuss the answers.

112 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Ex 1: The Great Lakes Yellow Perch Scientists collected data from many samples of yellow perch because they were concerned about the survival of the yellow perch. What data do you think researchers might want to collect about the perch? Scientists captured yellow perch from a lake in this region. They recorded data on each fish, and then returned each fish to the lake. Consider the following histogram of data on the length (in centimeters) for a sample of yellow perch.

113 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Yellow Perch

114 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 17 and 22:Developing a Statistical Project Two of the lessons in this topic (Lessons 17 and 22) allow students to experience the four-step process described at the beginning of this module through completion of a project. In this project, students experience the four-step investigative process by (1) formulating a statistical question, (2) designing and implementing a plan to collect data, (3) summarizing collected data graphically and numerically, and (4) using the data to answer the question posed.

115 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Agenda

116 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios End of Module Assessment

117 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios End of Module Assessment

118 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios End of Module Assessment

119 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Agenda

120 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Summary of the 4 Topics In Topic A, students begin to think and reason statistically, first by recognizing a statistical question as one that can be answered by collecting data (6.SP.A.1). Students learn that the data collected to answer a statistical question has a distribution that is often summarized in terms of center, variability, and shape (6.SP.A.2). Beginning in Topic A, and throughout the module, students see and represent data distributions using dot plots and histograms (6.SP.B.4).

121 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Summary of the 4 Topics In Topic B, students study mean as a measure of center and mean absolute deviation as a measure of variability. Students learn that these measures are preferred when the shape of the distribution is roughly symmetric.

122 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Summary of the 4 topics in Topic C, students study median as a measure of center and interquartile range as a measure of variability. Students learn that these measures are preferred when the shape of the distribution is skewed. Students develop in Topic B, and reinforce in Topic C, the idea that a measure of center provides a summary of all its values in a single number, while a measure of variation describes how values vary, also with a single number (6.SP.A.3).

123 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Summary of the 4 topics In Topic D, students synthesize what they have learned as they connect the graphical, verbal, and numerical summaries to each other within situational contexts, culminating with a major project (6.SP.B.4, 6.SP.B.5).

124 © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Questions and/or Comments


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