Grade 7 – Module 2 Module Focus Session

Grade 7 – Module 2 Module Focus Session
October, 2013 Common Core Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X A Story of Ratios Grade 6 – Module 6 Statistics (Lessons 1 to 18) NOTE THAT THIS SESSION IS DESIGNED TO BE APPROXIMATELY 5 hours in length. Intro – 20 minutes Topic A 60 minutes Topic B 60 minutes Mid module assessment 15 minutes Topic C 60 minutes Topic D 50 minutes End of module assessment 15 minutes Summary and Questions 20 minutes

October, 2013 Common Core Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute MATERIALS NEEDED: X Session Objectives Brief overview (big ideas) of module 6: Statistics 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) Examine sample problems in select lessons to become familiar with the progression of the statistics concepts in Grade 6. 5 minutes Introductions and session objectives

October, 2013 Common Core Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Agenda Introduction to the Module Overview of Topic A (Lessons 1 to 5) • Overview of Topic B (Lessons 6 to 11) • Mid-Module Assessment • Overview of Topic C (Lessons 12 to 16) • Overview of Topic D (Lessons 18 to 21) • End-of-Module Assessment • Final comments and questions (15 minutes) 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.

Curriculum Overview of A Story of Ratios
Grade 7 – Module 2 Module Focus Session October, 2013 Common Core Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Curriculum Overview of A Story of Ratios (3 minutes) 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.

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 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

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 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

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 5 lessons in Topic C Main focus is the median as a measure of center and IQR as a measure of variability

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 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.

Terminology Statistical Question Median Mean Dot plot Histogram Box Plot Variability Deviations from the mean Mean Absolute Deviation (MAD) Interquartile Range (IQR) Vocabulary is a big part of Grade 6 Statistics. Suggest to make a word wall with the terminology and the definitions and diagrams.

Representations (Dot Plot)
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.

Representation (Histogram)
Note: This is not a bar graph. A histogram is a graph for quantitative data and a bar graph is for displaying categorical data.

Representation (Box plot)

October, 2013 Common Core Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Agenda Introduction to the Module Overview of Topic A (Lessons 1 to 5) • Overview of Topic B (Lessons 6 to 11) • Mid-Module Assessment • Overview of Topic C (Lessons 12 to 16) • Overview of Topic D (Lessons 18 to 21) • End-of-Module Assessment • Final comments and questions (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.

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 Here are the 5 lessons Main focus on graphical display and beginning to describe a distribution (graph) estimating the center and spread

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. 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.

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). 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.

Lesson 3: Creating a Dot Plot
In Lesson 3, students construct dot plots and begin to describe data distributions. In this lesson students are asked to construct and interpret dot plots.

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

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

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.

Polya’s Problem Solving Process
1. Understand the problem Devise a plan Carry out the plan 4. Look back Many of you are familiar with George Polya’s problem solving process. This module begins with the statistical problem solving process.

Statistical Problem Solving
Pose a question that can be answered by data. Determine a plan to collect the data. Summarize the data with graphs and numerical summaries. Answer the questions posed in Step 1 using the data and summaries. 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.

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. 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.

Statistical Question? What are the favorite colors of 6th graders in my school? A statistical question should have: Stated population Measureable variable Anticipate variability 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.

Statistical Question? How old is the principal at our school? Why isn’t this a statistical question? 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?

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

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. 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.

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.

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

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. 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.

Lesson 3: Example 2 A group of 6th graders investigated the statistical question: “How many hours per week do 6th graders spend playing a sport or outdoor game?” Here are the data the students collected from a sample of 26 6th graders showing the number of hours per week spent playing a sport or a game outdoors: 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).

Frequency Table 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.

Dot Plot 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.

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 Refer to page S18 in the student lesson. Ask the participants what might be the statistical question that could be answered with this data

Ask the particpants to complete the frequency table

Building a Histogram Ask the particpants 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.

Frequency Histogram of Head Circumferences

Shape of the Distribution: Mound Shaped or Symmetric

Skewed Distribution 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.

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. 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

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. 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.

Frequency Table of Head Circumferences
This is the frequency table from Lesson 4.

Relative frequency table

Relative Frequency Histogram
Describe the center, shape and spread - this is the same as the frequency histogram from lesson 4.

Frequency Histogram of Head Circumferences

October, 2013 Common Core Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Agenda Introduction to the Module Overview of Topic A (Lessons 1 to 5) • Overview of Topic B (Lessons 6 to 11) • Mid-Module Assessment • Overview of Topic C (Lessons 12 to 16) • Overview of Topic D (Lessons 18 to 21) • End-of-Module Assessment • Final comments and questions (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

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 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

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.

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 distribution—the 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.

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.

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.

What do we mean by “average”?
What students say: “add em up and divide” “it’s the average” “it’s the middle number” “it’s in the center”

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 Ask if this is a statistical question. Yes – population is 6th graders Measureable variable – number of pets Expect variation

How many pets do students have? 2, 6, 2, 4, and 1
Represent each piece of data with a unifix cube.

What do you mean by “average?” The evening out or fair share value
The next 8 slides demonstrate how the evening out process would work.

Fair Share value

The results after “evening” out

Question: How many pets do students have
Question: How many pets do students have? What does “fair share” mean in words in the context of the question?

Question: How many pets do students have
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) 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.

Fair Share Value Aside: 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.

Lesson 7: The Mean as a Balance Point
The number of minutes it takes two students to get to school. Lesson 7 introduces another way to think about the mean.

If you represented the dot plot with a ruler and pennies, where would the ruler balance?
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.

What is the sum of the deviations?
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. What is the sum of the deviations?

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

Will the ruler balance at 6?
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

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. 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.

Lesson 8: Variability in a Data Distribution
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.

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. 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.

Measuring Variability
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. Mean temperature is 63 degrees

Complete the temperature deviations
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.

Mean Absolute Deviation
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 Find the mean of the absolute deviations = 3.67 This is MAD

Measuring Variability
Notice that 7 of the 12 data values are within 3.67 degrees from the mean. Mean temperature is 63 degrees

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? 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

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

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.

Lesson 10 Problem 5 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.

October, 2013 Common Core Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Agenda Introduction to the Module Overview of Topic A (Lessons 1 to 5) • Overview of Topic B (Lessons 6 to 11) • Mid-Module Assessment • Overview of Topic C (Lessons 12 to 16) • Overview of Topic D (Lessons 18 to 21) • End-of-Module Assessment • Final comments and questions 15 minutes If time is a problem this could be skipped and referred to at the end of the workshop.

Mid-Module Assessment
Have the participants look at problem 2. Discuss this problem and solutions. The mean length is 15 years MAD is 8.44 years

October, 2013 Common Core Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Agenda Introduction to the Module Overview of Topic A (Lessons 1 to 5) • Overview of Topic B (Lessons 6 to 11) • Mid-Module Assessment • Overview of Topic C (Lessons 12 to 16) • Overview of Topic D (Lessons 18 to 21) • End-of-Module Assessment • Final comments and questions 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.

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 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.

Lesson 12: Describing the Center of a Distribution Using the Median
In Lesson 12, students learn to calculate and interpret the median.

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.

Lesson 14-16 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.

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. 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

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.

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. Example to find median and quartiles

Number of french fries (n=19) in order from smallest to largest: Lower quartile Median Upper quartile The median (81) is not counted in either of the “halves” to find the quartiles

Lower quartile Median Upper quartile

Lesson 14: Summarizing a Distribution Using a Box Plot
Student Outcome Students construct a box plot from a given set of data. 5 number summary is introduced. Lessons 14 to 16 all revolve around constructing and interpreting a box plot.

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.

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. 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.

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

Interpreting Box Plots

Interpreting box plots exercise 10 (p.101)
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)

October, 2013 Common Core Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Agenda Introduction to the Module Overview of Topic A (Lessons 1 to 5) • Overview of Topic B (Lessons 6 to 11) • Mid-Module Assessment • Overview of Topic C (Lessons 12 to 16) • Overview of Topic D (Lessons 18 to 21) • End-of-Module Assessment • Final comments and questions 50 minutes for topic D

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 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

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.

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.

Example from Lesson 18 Answers: Plot 3 Plot 1 Plot 2

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

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).

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).

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.

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.

Yellow Perch

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.

October, 2013 Common Core Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Agenda Introduction to the Module Overview of Topic A (Lessons 1 to 5) • Overview of Topic B (Lessons 6 to 11) • Mid-Module Assessment • Overview of Topic C (Lessons 12 to 16) • Overview of Topic D (Lessons 18 to 21) • End-of-Module Assessment • Final comments and questions (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.

End of Module Assessment
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.

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

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

October, 2013 Common Core Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Agenda Introduction to the Module Overview of Topic A (Lessons 1 to 5) • Overview of Topic B (Lessons 6 to 11) • Mid-Module Assessment • Overview of Topic C (Lessons 12 to 16) • Overview of Topic D (Lessons 18 to 21) • End-of-Module Assessment • Final comments and questions 15 minutes for the summary

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). Summary of Topic A

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. Summary of Topic B

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). Summary of Topic C

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). Summary of Topic D

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Grade 7 – Module 2 Module Focus Session

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Grade 7 – Module 2 Module Focus Session

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