Module Focus: Grade 8 – Module 6 Sequence of Sessions

Overarching Objectives of this February 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 8 curriculum, A Story of Ratios.

Key Points 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

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 to Module 30 minsEstablish the instructional focus of Grade 8 Module 6.

Grade 8 Module 6 PPT Faciliatators Guide

Review Grade 8 Module 6.

Topic A Lessons 30 mins Examine the lessons of Topic A. Grade 8 Module 6 PPT Faciliatators Guide

Review Topic A.

Topic B Lessons 30 mins Examine the lessons of Topic B. Grade 8 Module 6 PPT Faciliatators Guide

Review Topic B.

Topic C Lessons 45 mins Examine the lessons of Topic C. Grade 8 Module 6 PPT Faciliatators Guide

Review Topic C.

Topic D Lessons 45 mins Examine the lessons of Topic D. Grade 8 Module 6 PPT Faciliatators Guide

Review Topic D.

Summary 20 minsReiterate key points and faciliate discussion on implementation and planning.

Session Roadmap

Section: Grade 8 Module 6 Time: 200 minutes

TimeSlide #

Slide #/ Pic of Slide Script/ Activity directions GROUP

15 min

1. Note: The introduction and overview should take about 15 minutes.

Welcome! In this module focus session, we will examine Grade 8 – Module 6.

Introductions

2. 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

2 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 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.

5. 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.

6.

7. 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.

8. 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. )

9. 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.

10. Note: Topic A discussion should be approximately 30 minutes

Let’s take a closer look at the development of key objectives in Topic A.

11. Turn to Topic Opener A in your materials. Here are the 5 lessons in topic A.

12. Here is a quick overview of each lesson in Topic A

13.

14. 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.

15. In this lesson students graph a line given an equation given in the form y = mx +bAnd they write the equation of a line given two points using the form: y – y1 = m(x –x1)

16. 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.

17. 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.

18. 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.

19. This topic begins the emphasis to the 8th grade statistics standards.

20. 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.

21.

2 min 22. 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.

23. 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.

24. 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.

25. 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.

26. 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.

27. 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.

28. 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.

29. Here is a brief overview of the lessons in topic C.

30. After reading the student outcomes – point out how the second outcome is very similar to the outcomes from Topic A.

31. 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.

32. After reading the student outcomes again point out how similar these outcomes are to those in lesson 8.

33. Give the participants about 15 minutes to complete exercise 2.

After they have completed exercise 2 use the document camera and discuss the solution.

34. 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.

35. 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.

36. Brief overview of the 2 lessons.

37.

38. 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.

39. 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.

40. Turn to page 189 in Teachers material.

Read through each problem and note the expectation for the students.

41. 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.

42. 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?

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 8 Module 6 PPT Grade 8 Module 6 Faciliator’s Guide

Additional Suggested Resources

A Story of Ratios Curriculum Overview