Grade 8 – Module 6 Module Focus Session

Grade 8 – Module 6 Module Focus Session
February 2014 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X A Story of Ratios Grade 8 – Module 6 Linear Functions NOTE THAT THIS SESSION IS DESIGNED TO APPROXIMATELY 200 MINUTES IN LENGTH. Approximately 90 minutes on Overview, Topic A and Topic B. Approximately 1110 minutes on Topic C and D. Note: The introduction and overview should take about 15 minutes. Welcome! In this module focus session, we will examine Grade 8 – Module 6. Introductions

February 2014 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute MATERIALS NEEDED: X Session Objectives Discuss the key ideas of what students learn in the module Linear Functions. Examine sample lessons to become familiar with the main objectives of the module Our objectives for this session are to: • discuss the connection between the 8th grade CCSSM Function Domain and the 8th grade CCSSM Statistics and Probability Domain. • work through sample lessons from each of the 4 topics

February 2014 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Agenda Introduction to the Module Concept Development Module Review (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.

Curriculum Overview of A Story of Ratios
Grade 8 – Module 6 Module Focus Session February 2014 Network Team 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 8 is called Linear Functions (click for red ring). The module had 14 lessons, a mid-module assessment and an end of module assessment. In earlier modules students have been studying the equation of a line and the definition of a function. This module extends these ideas by introducing students to bivariate data both numerical and categorical. In this module, students use their understanding of the equation of a line and functions to model the possible relationships of bivariate data by analyzing scatter plots and fitting a line to data. This module is important in setting a foundation for students’ work in algebra in Grade 9. In addition students learn how to organize and analyze bivariate categorical variables in a two-way table.

February 2014 Network Team Institute Module topics Topic A: Linear Functions 5 Lessons 8.F.B.4 and 8.F.B.5 Topic B: Bivariate Numerical Data 4 lessons 8.SP.A.1 and 8.SP.A.2 Mid-Module Assessment This and the next slide are provided for a very quick overview of the 4 topics in this module. Each topic will be discussed and a sample lesson will be examined in each of the topics. Take a moment to look at the table of contents at the beginning of the Module Overview. Notice the Module is broken into four topics which span 14 lessons. Following the Table of Contents is the narrative section. Focus and Foundational standards, as well as the standards for Mathematical Practice are listed in this overview document as well. You will want to read the entire document at your leisure, following today’s session.

February 2014 Network Team Institute Module topics Topic C: Linear and Nonlinear Models 3 Lessons 8.SP.A.1 and 8.SP.A.2 and 8.SP.A.3 Topic D: Bivariate Categorical Data 2 lessons 8.SP.A.4 End of -Module Assessment

February 2014 Network Team Institute Module’s Foundation Connection between the Function and Statistics and Probability Domains Focus Standards: Functions Domain 8.F.B.4 Rate of Change 8.F.B 5 Describe functional relationship Statistics and Probability 8.SP.A.1 Construct scatter plots 8.SP.A..2 Informally fit a line to data 8.SP.A.3 Equation of a line 8.SP.A.4 Patterns of Association Explain that the this module integrates two of the 8th grade function standard with the four 8th grade statistics and probability standards. The module begins with a focus on the 2 function standards in Topic A and then transition into the 4 Statistics standards in Topics B, C and D.

G8-M6: Vocabulary and Representations
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute G8-M6: Vocabulary and Representations Let’s start by looking at the vocabulary, tools and representations that are used in this Module. They are located near the end of the Module Overview document. Name some of the new vocabulary terms( association, two-way tables, row relative frequency, column relative frequency) What representations will be used in this Module? (tables, equations, scatter plots and two-way tables) How is this information useful? How is it useful for you in your role? (This information is useful in planning for word walls, concept-related posters, parent newsletters, interdisciplinary projects, and other ways in which math vocabulary and representations are reinforced in classrooms across the grade level, and at home. )

G8-M6: Vocabulary and Representations
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute G8-M6: Vocabulary and Representations In addition to the vocabulary and the representations, access to a graphing calculator may be helpful but this module can be completed without the graphing calculator.

February 2014 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Agenda Introduction to the Module Concept Development – Topic A Module Review Note: Topic A discussion should be approximately 30 minutes Let’s take a closer look at the development of key objectives in Topic A.

Topic A: Linear Functions
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: X minutes MATERIALS NEEDED: X Topic A: Linear Functions Turn to Topic Opener A in your materials. Here are the 5 lessons in topic A.

Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute Topic A: Linear Functions In Lesson 1, students are given a verbal description of a linear relationship between two variables, and then must describe a linear model. Students graph linear functions using a table of values and by plotting points. They recognize a linear function given in terms of the slope and initial value or y-intercept. In Lesson 2, students interpret the rate of change and the y-intercept, or initial value, in the context of the problem. They interpret the sign of the rate of change as indicating that a linear function is increasing or decreasing and as indicating the steepness of a line. Here is a quick overview of each lesson in Topic A

Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute Topic A: Linear Functions In Lesson 3, students graph the line of a given linear function. They express the equation of a linear function as y=mx+b or an equivalent form when given the initial value and slope. In Lessons 4 and 5, students describe and interpret a linear function given two points or its graph.

Key Idea from Lessons 1, 2 and 3
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute Key Idea from Lessons 1, 2 and 3 Lesson 1 Modeling Linear Relationships Students determine a linear function given a verbal description of a linear relationship between two quantities. Rate of change and initial value are emphasized Lesson 2 Interpreting Rate of Change and Initial Value Students interpret the rate of change and initial value of a line in context. Given the equation of a line – interpret the slope in context Here are the key ideas presented in lessons 1,2 and 3. These lessons build on the knowledge students gained in Module 4 and 5. They are asked to write and interpret the equation of a line. Interpret the slope and the initial value.

Lesson 3: Representations of a Line
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute Lesson 3: Representations of a Line Outcomes: • Students graph a line specified by a linear function. • Students graph a line specified by an initial value and rate of change of a function and construct the linear function by interpreting the graph. • Students graph a line specified by two points of a linear relationship and provide the linear function. In this lesson students graph a line given an equation given in the form y = mx +b And they write the equation of a line given two points using the form: y – y1 = m(x –x1) Lesson 3

Lesson 4: Increasing and Decreasing Functions
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute Lesson 4: Increasing and Decreasing Functions Student Outcomes • Students describe qualitatively the functional relationship between two types of quantities by analyzing a graph. • Students sketch a graph that exhibits the qualitative features of a function based on a verbal description. Turn to lesson 4 page S19 (student version). Here are the two objectives of this lesson. We will take some time and look at this lesson more in depth.

Lesson 4 and 5: Increasing and Decreasing Functions
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute Lesson 4 and 5: Increasing and Decreasing Functions Organize in small groups. Read through Lesson 4 of this module starting on page 19 of the student edition. Answer questions 2 to 4. After you have completed the problems, we will discuss the solutions and student expectations. Give the participants about 10 minutes to work through the questions 2 to 4. Discuss the solutions and point out the emphasis on decreasing and increasing functions. Display the problem using the document camera as you discuss the solutions.

February 2014 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Agenda Introduction to the Module Concept Development – Topic B Module Review Note: Discussion of topic B should take approximately 30 minutes. Let’s take a closer look at the development of key understandings in Topic B.

Topic B: Bivariate Numerical Data
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Topic B: Bivariate Numerical Data Lesson 6 Scatter Plots Lesson 7 Patterns in Scatter Plots Lesson 8 Informally Fitting a Line Lesson 9 Determining the Equation of a Line Fit to Data This topic begins the emphasis to the 8th grade statistics standards.

Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Topic B: Bivariate Numerical Data In Lesson 6, students construct scatter plots and focus on identifying linear versus non-linear patterns. In Lesson 7 students distinguish positive linear association and negative linear association based on the scatter plot. Students describe trends in the scatter plot, along with clusters, and outliers (points that do not fit the pattern). In Lesson 8, students informally fit a straight line to data displayed in a scatter plot by judging the closeness of the data points to the line. Here is an brief overview of the 4 lessons in topic B. Notice the interrelationship between the function standards emphasized in topic A and the statistics standards.

Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Topic B: Bivariate Numerical Data In Lesson 9, students interpret and determine the equation of the line they fit to the data and use the equation to make predictions and to evaluate possible association of the variables. Based on these predictions, students address the need for a “best-fit” line, which is formally introduced in Grade 9

Big Ideas in Lessons 6 and 7
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Big Ideas in Lessons 6 and 7 Lesson 6 Scatter plots Students construct scatter plots and investigate relationships. Lesson7 Patterns in Scatter plots Students describe positive and negative trends in a scatter plot. (2 minutes) Starting with Lesson 6 we now make the transition from the Function Standards to the 8th grade statistics standards. In Grades 6 and 7 students analyzed univariate data. They focused on the center, shape and spread of distributions of one variable. They constructed graphs like: dot plots, histograms and box plots. They found means, medians, interquartile ranges and the mean absolute deviation. In Grade 8 students now begin the analysis of two variables. In lessons 6 to 12 they work with 2 quantitative variables and in lessons 13 and 14 two categorical variables.

February 2014 Network Team Institute Lesson 8 Student Outcomes • Students informally fit a straight line to data displayed in a scatter plot. • Students make predictions based on the graph of a line that has been fit to data. Lets take a closer look at Lesson 8. go to page S60 in the student version. Here are the 2 student outcomes for this lesson.

Determining the Equation of a Line Fit to Data
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute Determining the Equation of a Line Fit to Data Organize in small groups. Discuss and complete problems 1 to 6 from Lesson 8 of this module. (S60) After you have completed the problems, we will discuss the idea of development of informally fitting a line. Allow the participants about 15 minutes to complete problems 1 to 6. Use the document camera to display the answers. Discuss possible methods to draw an informal line. (Transparent ruler or piece of spaghetti to help students draw a line.) While there is not one correct way to draw an informal line some student will suggest some methods that may result in a line that isn’t the “best”. Some student pitfalls: some students will want to use the first point and last point, others may want the line go to through the origin. Others will try and have the same number of points above and below the line. While some of these methods may work for certain data sets they will not give a good fit line all the time. Encourage the students to discuss how they drew their line. Lesson 9

February 2014 Network Team Institute Exit Ticket for Lesson 8 Note: examining the exit ticket and the mid-module assessment will take approximately 15 minutes Point out that each lesson has an exit ticket. Let’s take a look at the ext ticket for lesson 8. Turn to the exit ticket in the teacher material for Lesson 8 (T103). Take a few minutes and read through problems 1 to 3. Discuss the connection to the objectives of the lesson. Remember the student outcomes for this lesson were: Students informally fit a straight line to data displayed in a scatter plot. Students make predictions based on the graph of a line that has been fit to data.

Mid- Module Assessment
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute Mid- Module Assessment Turn to the Mid-Module Assessment. This module has a mid module assessment and an end of module assessment. Take a few minutes and read through the mid-module assessment. Note the expectation for students at this point in the module.

February 2014 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Agenda Introduction to the Module Concept Development – Topic C Module Review Note: Discussion of topic C should take approximately 45 minutes. Let’s take a closer look at the development of key understandings in the final topic of the module, Topic C.

Topic C: Linear and Nonlinear Models
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute Topic C: Linear and Nonlinear Models Lesson 10: Linear Models Lesson 11: Using Linear Models in a Data Context Lesson 12: Nonlinear Models in a Data Context (Optional lesson) Here are the 3 lessons in Topic C. Lesson 10 and 11 build on lesson 8 and 9 where students drew an informal fit line. Lessons 8 to 11 form the pre-cursor to finding the line of best fit in Grade 9.

Topic C: Linear and Nonlinear Models
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute Topic C: Linear and Nonlinear Models In Lesson 10, students identify applications in which a linear function models the relationship between two numerical variables. In Lesson 11, students use a linear model to answer questions about the relationship between two numerical variables by interpreting the context of a data set. Students use graphs and the patterns of linear association to answer questions about the relationship of the data. In Lesson 12, students also examine patterns and graphs that describe nonlinear associations of data. Here is a brief overview of the lessons in topic C.

Student Outcomes in Lessons 10
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute Student Outcomes in Lessons 10 Student Outcomes • Students identify situations where it is reasonable to use a linear function to model the relationship between two numerical variables. • Students interpret slope and the initial value in a data context. After reading the student outcomes – point out how the second outcome is very similar to the outcomes from Topic A.

February 2014 Network Team Institute Lesson 10: Linear Models Organize in small groups. Discuss and complete problems 1 and 2 (S81)and problem 11 (S86) from Lesson 10 of this module. After you have completed the problems, we will discuss the answers Give the participants about 5 minutes for problems 1 and 2 and another 10 minutes for problem 11. After they have finished discuss the solutions to problems 1 and 2 using the document camera. After discussing problems 1 and 2, use the document camera and discuss problem 11. Point out the connection to the functions standards from Topic A. Lesson 10

Lesson 11: Using Linear Models in a Data Context
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute Lesson 11: Using Linear Models in a Data Context Student Outcomes • Students recognize and justify that a linear model can be used to fit data. • Students interpret the slope of a linear model to answer questions or to solve a problem. After reading the student outcomes again point out how similar these outcomes are to those in lesson 8. Lesson 11

Determining the Equation of a Line Fit to Data
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute Determining the Equation of a Line Fit to Data Organize in small groups. Discuss and complete exercise 2 from Lesson 11 (S91)of this module. After you have completed the problems, we will go through the solutions. Give the participants about 15 minutes to complete exercise 2. After they have completed exercise 2 use the document camera and discuss the solution. Lesson 11

February 2014 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Agenda Introduction to the Module Concept Development – Topic D Module Review Note: discussion of Topic D should take about 45 minutes Let’s take a closer look at the development of key understandings in the final topic of the module, Topic C.

Topic D: Bivariate Categorical Data
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute Topic D: Bivariate Categorical Data Lesson 13: Summarizing Bivariate Categorical Data in a Two-Way Table Lesson 14: Association between Categorical Variables Topic D changes the focus from analyzing numerical variables to summarizing bivariate categorical variables. Topic D is new material for the students. This topic prepares the students for further analysis of bivariate categorical data in 9th grade. Remember that a categorical variable take a value that is one of several possible categories. As naturally measured, categorical variables have no numerical meaning. Examples: Hair color, gender, field of study, college attended, political affiliation, status of disease infection.

Topic D: Bivariate Categorical Data
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute Topic D: Bivariate Categorical Data In Lesson 13, students organize bivariate categorical data into a two-way table. They calculate row and column relative frequencies and interpret them in the context of a problem. In Lesson 14, students informally decide if there is an association between two categorical variables by examining the differences of row or column relative frequencies. They interpret association between two categorical variables as meaning that knowing the value of one of the variables provides information about the likelihood of the different possible values of the other variable. Brief overview of the 2 lessons.

Lesson 13: Summarizing Bivariate Categorical Data in a Two-Way Table
Student Outcomes • Students organize bivariate categorical data into a two-way table. • Students calculate row and column relative frequencies and interpret them in context. Lesson 13

Summarizing Bivariate Categorical Data in a Two-Way Table
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute Summarizing Bivariate Categorical Data in a Two-Way Table Organize in small groups. Discuss and complete exercises 11 to 22 from Lesson 13 of this module. (S106) After you have completed the problems, we will discuss the set up of the two-way table and the vocabulary. Give the participants about 20 minutes to discuss and work through exercises 11 to 22. After they have completed the exercises use the document camera and work through the problems. Lesson 11

February 2014 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 0 minutes MATERIALS NEEDED: X Agenda Introduction to the Module Concept Development Module Review The module review and time for questions should be about 20 minutes. As we begin to finish our session we want to take a few minutes and look through the end of module assessment.

End of Module Assessment
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute End of Module Assessment Turn to page 189 in Teachers material. Read through each problem and note the expectation for the students.

Module Summary: Key Ideas
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute Module Summary: Key Ideas Grade 8 Module 6 is a key. More use of functions and preparation for Grade 9 Algebra and Functions Conceptual Categories. Big theme is ASSOCIATION Key ideas: •Patterns in Scatter plots (Association between two numerical variables) • Equation of a line • Fitting a line to data • Analyzing categorical data from two-way frequency tables. • Association between two categorical variables Here are the key ideas of the module. Recall that the main focus of Topic A was the 2 function standards. As we moved into Topic B the focus began to shift to the Statistics Standards.

Final Comments and/or Questions
Grade 8 – Module 6 Module Focus Session February 2014 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: X Final Comments and/or Questions Take two minutes to turn and talk with others at your table. During this session, what information was particularly helpful and/or insightful? What new questions do you have?

Grade 8 – Module 6 Module Focus Session

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Grade 8 – Module 6 Module Focus Session

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