mc-14193-39844713.us-east-1.elb.amazonaws.commc-14193-39844713.us-east-1.elb.amazonaws.com/file/... ·...

Module Focus: Grade 6 – Module 6 Sequence of Sessions

Overarching Objectives of this May 2014 Network Team Institute Participants will develop a deeper understanding of the sequence of mathematical concepts within the specified modules and will be able to articulate

how these modules contribute to the accomplishment of the major work of the grade.

Participants will be able to articulate and model the instructional approaches that support implementation of specified modules (both as classroom teachers and school leaders), including an understanding of how this instruction exemplifies the shifts called for by the CCLS.

Participants will be able to articulate connections between the content of the specified module and content of grades above and below, understanding how the mathematical concepts that develop in the modules reflect the connections outlined in the progressions documents.

Participants will be able to articulate critical aspects of instruction that prepare students to express reasoning and/or conduct modeling required on the mid-module assessment and end-of-module assessment.

High-Level Purpose of this Session● Implementation: Participants will be able to articulate and model the instructional approaches to teaching the content of the first half of the lessons.● Standards alignment and focus: Participants will be able to articulate how the topics and lessons promote mastery of the focus standards and how the

module addresses the major work of the grade.● Coherence: Participants will be able to articulate connections from the content of previous grade levels to the content of this module.

Related Learning Experiences● This session is part of a sequence of Module Focus sessions examining the Grade 6 curriculum, A Story of Ratios.

Key Points● 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). ● Students see and represent data distributions using dot plots and histograms (6.SP.B.4). ● 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. ● 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 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).

● 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).

Session Outcomes

What do we want participants to be able to do as a result of this session?

How will we know that they are able to do this?

Participants will develop a deeper understanding of the sequence of mathematical concepts within the specified modules and will be able to articulate how these modules contribute to the accomplishment of the major work of the grade.

Participants will be able to articulate and model the instructional approaches that support implementation of specified modules (both as classroom teachers and school leaders), including an understanding of how this instruction exemplifies the shifts called for by the CCLS.

Participants will be able to articulate connections between the content of the specified module and content of grades above and below, understanding how the mathematical concepts that develop in the modules reflect the connections outlined in the progressions documents.

Participants will be able to articulate critical aspects of instruction that prepare students to express reasoning and/or conduct modeling required on the mid-module assessment and end-of-module assessment.

Participants will be able to articulate the key points listed above.

Session Overview

Section Time Overview Prepared Resources Facilitator Preparation

Introduction 20 min Introduces Grade 6 Module 6• Grade 6 Module 6 PPT• Facilitator Guide

Review Grade 6 Module 6

Topic A: Understanding Distributions

60 min• Grade 6 Module 6 PPT• Facilitator Guide

Review Topic Opener A

Topic B: Summarizing a Distribution that is Approximately Symmetric Using the Mean and Mean Absolute Deviation

60 min

Explores formalizing the idea of center and spread by exploring the concept of the mean and the mean absolute deviation as one measure of spread.

• Grade 6 Module 6 PPT• Facilitator Guide

Review Topic Opener B

Mid-Module Assessment

15 minExplores and examines the Grade 6 Module 6 Mid-Module Assessment.


Review Mid-Module Assessment

Topic C: Summarizing a Distribution that is Skewed Using the Median and the Interquartile Range

60 min

Introduces the concept of the median, and then it focuses on variability and summarizing with a box plot.


Review Topic Opener C

Topic D: Summarizing and Describing Distributions

50 minExplores practicing techniques and conducting data collecting activity.


Review Topic Opener D

End-of-Module Assessment

15 minExplores and examines the End-of-Module Assessment.


Review End-of-Module Assessment

Summary and Questions

20 min Summarizes Grade 6 Module 6• Grade 6 Module 6 PPT• Facilitator Guide

Review Grade 6 Module 6 Module Overview

Session Roadmap

Section: Introduction Time: 20 minutes

In this section, you will be introduced to Grade 6 Module 6. Materials used include:• Grade 6 Module 6 PPT• Grade 6 Module 6 Facilitator Guide

• Grade 6 Module 6 Module Overview

Time Slide # Slide #/ Pic of Slide Script/ Activity directions GROUP

0 min 1. NOTE THAT THIS SESSION IS DESIGNED TO BE APPROXIMATELY 5 hours in length.Intro – 20 minutesTopic A 60 minutesTopic B 60 minutesMid module assessment 15 minutesTopic C 60 minutesTopic D 50 minutesEnd of module assessment 15 minutesSummary and Questions 20 minutes

5 min 2. Introductions and session objectives

15 min 3. We will begin by exploring the module overview to understand the purpose of this module and give you some time to look at some of the lessons in depth.Let’s get started with the module overview.

3 min 4. The sixth module in Grade 6 is called Statistics (click for red ring). The module had 22 lessons, a mid-module assessment and an end of module assessment.

This is really the first module focused entirely on Statistics. Grades K to 5 have very little emphasis on statistics concepts.

5. 5 lessons in Topic A

Main focus is describing a distribution using a dot plot and a histogram

Students are estimating the center and variability

6. 5 lessons in Topic B – Lessons 10 and 11 are basically the same objectives.

Main focus is the mean as the measure of center and the mean absolute deviation (MAD) as a measure of variability.

7. 5 lessons in Topic C

Main focus is the median as a measure of center and IQR as a measure of variability.

8. I refer to Topic D as Putting It all Together.

Lessons 18 to 21 give students the opportunity to put into practice the graphical and numerical summaries they learned in the first 16 lessons. These lessons also begin to present ideas from the 7th grade standards. - Mainly comparing two populations.

Lessons 17 and 22 ask the students to conduct their own data collection and present their findings.

9. Vocabulary is a big part of Grade 6 Statistics. Suggest to make a word wall with the terminology and the definitions and diagrams.

10. Note: Some textbook series place an X instead of a dot on the graph. Also some textbook series call this a line plot because it is based on a number line.

11. Note: This is not a bar graph. A histogram is a graph for quantitative data and a bar graph is for displaying categorical data.

12.

Section: Topic A: Understanding Distributions Time: 60 minutes

In this section, you will focus on graphical display and beginning to describe a distribution (graph) estimating the center and spread.

Materials used include:• Grade 6 Module 6 PPT• Grade 6 Module 6 Facilitator Guide

• Grade 6 Module 6 Topic Opener A


13. (60 minutes for Topic A)

We will begin briefly looking at the 5 lessons in Topic A. Then we will take a look in depth at Lesson 1 and 4 which both cover very new material for 6th graders.

14. Here are the 5 lessons:

Main focus on graphical display and beginning to describe a distribution (graph) estimating the center and spread.

15. Lesson 1 is on recognizing a statistical question and the types of data (quantitative and categorical). We will look at this lesson in more detail in a few minutes.

16. In this lesson, students are given dot plots and asked to interpret the plots by estimating the center and spread of the data presented in the plot.

17. In this lesson, students are asked to construct and interpret dot plots.

18. Students are asked to construct and interpret a histogram. We will look at this lesson in more detail in a little later.

19. This lesson builds on Lesson 4. It also introduces the concept of relative frequency.

20.

21. Many of you are familiar with George Polya’s problem solving process. This module begins with the statistical problem solving process.

22. Point out how similar Polya’s steps are to these 4 steps.

Suggest to post these 4 steps on the wall and refer to them throughout the module. Many of the problems will take students through this process. In Topic D students are given the opportunity to do their own data collecting experience following the 4 steps.

23. The formulation of a statistics question requires an understanding of the difference between a question that anticipates a deterministic answer (one answer) and a question that anticipates an answer based on data that vary.

24. This is an example of a statistical question.

To help students determine if a question is a statistical one-Suggest that they should be able to identify the population (who are they collecting data from), what is the variable they are measuring (collecting) and do they expect variability (different answers).

In this example: the population is 6th graders in my school. The measurable variable is favorite color, and we anticipate that students will not all say the same thing.

25. This has a deterministic (one) answer.

Ask how might they change so it is a statistical question:Possible response: How old are the teachers and administrators in our school?

26. This entire module is based on the analysis of quantitative data.

27. Categorical data is really not analyzed until Grade 8.

In Topic D when students are collecting their own data steer them toward quantitative data since that is the emphasis of this module.

28.

29. Students are given dot plots and asked to estimate the center and begin to think about the variability in the data.

30. The dot plot is similar to line plots that students made in 5th grade. Here the emphasis is on creating the correct scale for the number line and the interpretation of the graph.

31. Here is an example of a typical problem in this lesson. Notice that the problem starts with a statistical question (problem solving step 1). You may want to discuss how the data might have been collected (step 2).

32. Problem solving step 3 is the analysis step. This is where students organize the data, make graphs and calculate numerical summaries.

For this example the first step is to build a frequency table or tally chart. This makes the construction of the dot plot much easier.

33. After the dot plot is constructed it is now important to follow up with questions that lead to an answer to the statistical question.

Examples: Estimate the center, which value is the most, the least, discuss the variability and then ask students how they would answer the statistical question.

34. Refer to page S18 in the student lesson.

Ask the participants what might be the statistical question that could be answered with this data.

35. Ask the participants to complete the frequency table.

36. Ask the participants to complete the histogram.

Note: A histogram is NOT a bar graph. A bar graph is when the horizontal axis has categories not a number line.

37.

38.

39. Note the standards do not talk about when is a distribution skewed left or right. It is not important that 6th graders can distinguish the difference.

This is an example of a distribution is skewed right – this means that the unusual values (outliers) are way out to the right.

40. Student issues:Setting up and reading the intervals.

510-<530 does not include the 530 In a histogram the bars should touch and students need to know which interval a value of 530 would be in.

When there are outliers (unusual values) some students will want to create different size intervals.

41. More practice constructing and interpreting histograms. The concept of relative frequency is introduced and a relative frequency histogram.

Important point is that the shape of the histogram does not change when frequency is changed to relative frequency.

42. This is the frequency table from Lesson 4.

43.

44. Describe the center, shape and spread - this is the same as the frequency histogram from Lesson 4.

45.

Section: Topic B: Summarizing a Distribution that is Approximately Symmetric Using the Mean and Mean Absolute Deviation

Time: 60 minutes

In this section, you will focus on formalizing the idea of center and Materials used include:

spread by exploring the concept of the mean and the mean absolute deviation as one measure of spread.

• Grade 6 Module 6 PPT• Grade 6 Module 6 Facilitator Guide• Grade 6 Module 6 Topic Opener B


46. (60 minutes for Topic B)

In Topic A, students were asked to estimate the center and spread. In this Topic formalizes the idea of center and spread by exploring the concept of the mean and the mean absolute deviation as one measure of spread.

47. Lesson 6 and 7 develop the two main ways to think about what the mean of a set of data represents.

Lessons 8 and 9 develop the mean absolute deviation as one measure of spread (this is a very new concept of middle school).

Lessons 10 and 11 are giving students opportunities to use the mean and MAD to describe a distribution.

48.

49.

50.

51.

52.

53. Ask if this is a statistical question.

Yes – population is 6th graders

Measureable variable – number of pets

Expect variation

54. Represent each piece of data with a unifix cube.

55. The next 8 slides demonstrate how the evening out process would work.

56.

57.

58.

59.

60.

61.

62.

63.

64.

65. This is the formula that we are all familiar with. To find the mean find the sum of the numbers and divide by the number of values.

66.

67. Lesson 7 introduces another way to think about the mean.

68. Recommend doing this with your students.

Hard plastic rulers or half of a toilet paper tube work well. I would suggest nickels or quarters instead of pennies. They have heavier and tend to work a little better.

69. Define the vocabulary word: deviation from the mean as the distance from the mean. Positive if greater than the mean and negative if less than the mean.

The deviation can be found by subtracting the value – mean. Since integer addition and subtraction are not formally taught until 7th grade have students find the deviations by counting from zero and placing the appropriate sign.

Main point is that the mean balances the negative and positive deviations.

70. Notice that the 1 and 3 add to 4 which balances with the -4.

71. No, since the -3 and -5 does not balance with the 2.

Ask where should the mean be placed.

Answer: at 4 then deviations would be -3 and -1 and 4.

72. This lesson focuses on the concept of variability around the mean. Students are asked to compare different dot plots. They are asked to find the mean and then decide if the mean is a “typical” value.

73. The mean temperature for NY and San Fran are about the same. But the variability in NY temps is much greater than the San Fran temps.

This is also giving students the opportunity to compare distributions from two populations which is a big theme in the 7th grade statistics domain.

74. The concept of the mean absolute deviation is a new middle school topic. Lesson 9 builds on the idea of deviations from Lesson 7 and the idea of variability from Lesson 8.

75. The mean temp is 63 degrees. We want to describe the variability around the mean.

Ask the participants to first estimate how far most of the data is from the mean.

76. Steps to find the Mean Absolute Deviation is shown in the next few slides.

Step one: Find the deviations from the mean.

If the subtraction is a problem refer back to the dot plot and remind students that the deviation is the distance from the mean. Below the mean is negative and above the mean is positive. Another approach would be to allow students to use a calculator to find the deviations and verify that the sum of the deviations is zero.

77. Second step is to take the absolute value of the deviations

Note: Some students will want to skip the first step, i.e. just make all the deviations positive, but this does not help emphasize the point that the mean is the balance point.

Third step: Find the mean of the absolute deviations.

78. Notice that 7 of the 12 data values are within 3.67 degrees from the mean.

79. This is the average distance that the data values are from the mean.A large MAD means that the data is spread far from the mean.

80. These two lessons allow the students the opportunity to practice finding and interpreting the mean and MAD.

81.

82. MAD for City B is 5.3 and City C is 10.2

This means that the mean temps for city B differ from the mean of 63 by 53 degrees.

Section: Mid-Module Assessment Time: 15 minutes

In this section, you will review the Grade 6 Module 6 Mid-Module Assessment.

Materials used include:• Grade 6 Module 6 PPT• Grade 6 Module 6 Facilitator Guide• Grade 6 Module 6 Mid-Module Assessment


15 min 83. If time is a problem this could be skipped and referred to at the end of the workshop.

84. Have the participants look at problem 2. Discuss this problem and solutions.

The mean length is 15 years

MAD is 8.44 years

Section: Topic C: Summarizing a Distribution that is Skewed Using the Median and the Interquartile Range

Time: 60 minutes

In this section, you will explore a parallel approach to the one used in Topic B. First the concept of the median is introduced, then it focuses on variability and summarize with a box plot.

Materials used include:• Grade 6 Module 6 PPT• Grade 6 Module 6 Facilitator Guide• Grade 6 Module 6 Topic Opener C


85. 60 minutes for Topic C

In Topic B the focus was on the mean and variability around the mean. Topic C focus is on the median as a measure of center and variability around the median.

86. These lessons parallel the approach used in topic B. First the concept of the median is introduced then it focuses on variability and summarize with a box plot.

87.

88.

89.

90. Student issue when finding the median. If there is an odd set of numbers the middle number is the median. If an even set of numbers then the median is the mean of the two middle numbers.

91.

92. Example to find median and quartiles.

93. The median (81) is not counted in either of the “halves” to find the quartiles.

94.

95.

96. 5 number summary is introduced.

Lessons 14 to 16 all revolve around constructing and interpreting a box plot.

97.

98. Main emphasis is on the interpretation of a box plot. Also students begin to use box plots to compare two populations – again a precursor to 7th grade.

99. These problems also give an insight into grade 7 – compare two populations.

100.

101.

102. Writing a few sentences can be very difficult for the students. Suggestions:Have the students on the 5 number summary – extremes (long whiskers), middle 50% (inside the box).

Section: Topic D: Summarizing and Describing Distributions

Time: 50 minutes

In this section, you will focus on practicing techniques learned in previous lessons and conduct data collecting activity.

Materials used include:• Grade 6 Module 6 PPT• Grade 6 Module 6 Facilitator Guide• Grade 6 Module 6 Topic Opener D


103. 50 minutes for Topic D

104. Topic D is “putting it all together.”

Lessons 18 to 21 give students the opportunity to practice the techniques they learned in Topic B and C.

Lessons 17 and 22 give students the opportunity to conduct their own data collecting activity.

105.

106.

107. Answers:Plot 3Plot 1Plot 2

108. This lesson has students compare two or more box plots. Again this is a precursor to Grade 7.

109.

110.

111.

112.

113.

114.

Section: End-of-Assessment Time: 15 minutes

In this section, you will explore the End-of Module Assessment. Materials used include:• Grade 6 Module 6 PPT• Grade 6 Module 6 Facilitator Guide

• Grade 6 Module 6 End-of-Module Assessment


115. (2 minute)

We will begin by exploring the module overview to understand the purpose of this module and give you some time to look at some of the lessons in depth.

Let’s get started with the module overview.

116. If time is a problem just refer to the assessment and suggest that the participants read through to get a sense of the overall expectations of the module.

Problem 1 displays data in a dot plot and poses questions about the data based on this plot.

117. Question 2 presents data in a histogram and box plot and students answer questions based on the data presented in these formats.

118. Question 3 presents data in a table. Students are asked to find the 5 number summary, the mean and MAD.

Section: Summary and Questions Time: 20 minutes

In this section, you will review the key topics of Grade 6 Module 6. Materials used include:• Grade 6 Module 6 PPT• Grade 6 Module 6 Facilitator Guide• Grade 6 Module 6 Overview


119. 15 minutes for the summary

120. Summary of Topic A

121. Summary of Topic B

122. Summary of Topic C

123. Summary of Topic D

124.

Use the following icons in the script to indicate different learning modes.

Video Reflect on a prompt Active learning Turn and talk

Turnkey Materials Provided

● Grade 6 Module 6 PPT● Grade 6 Module 6 Facilitator Guide● Grade 6 Module 6 Module Overview● Grade 6 Module 6 Topic Overview A● Grade 6 Module 6 Topic Overview B● Grade 6 Module 6 Topic Overview C● Grade 6 Module 6 Topic Overview D

● Grade 6 Module 6 Mid-Module Assessment● Grade 6 Module 6 End-of-Module Assessment

Additional Suggested Resources

● How to Implement A Story of Ratios● A Story of Ratios Year Long Curriculum Overview● A Story of Ratios CCLS Checklist

mc-14193-39844713.us-east-1.elb.amazonaws.commc-14193-39844713.us-east-1.elb.amazonaws.com/file/... ·...

Documents