DUE 6-13: Facilitators Guide Template - CC 6-12.docxmc-14193-39844713.us-east-1.elb.amazonaws.com/file… · Web viewModule Focus: Grade 6 – Module 2 Sequence of Sessions Overarching

Module Focus: Grade 6 – Module 2 Sequence of Sessions

Overarching Objectives of this November 2013 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 look for and uncover patterns while modeling quotients of fractions to ultimately discover the relationship between

multiplication and division.

• Students explore partitive and measurement interpretations of dividing fractions to make connections to the relationship between multiplication and division.

• Estimation and place value enable students to determine the placement of the decimal point in products and recognize that the size of a product is relative to each factor.

• Students learn to use connections between fraction multiplication and decimal multiplication.

• Students connect estimation to place value and determine that the standard division algorithm is simply a tally system arranged in place value columns

• Students make connections to division of fractions and rely on mental math strategies to implement the division algorithm when finding the quotients of decimals.

• Students explore and discover that Euclid’s Algorithm is a more efficient way to find the greatest common factor of larger numbers and see that Euclid’s Algorithm is based on long division.

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?

Understand the sequence of mathematical concepts within this module.

Articulate and model the instructional approaches that support implementation of this module (both as classroom teachers and school leaders), including an understanding of how this instruction exemplifies the shifts called for by the CCLS.

Articulate the 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.

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 the Module 4 minutes

Introduction to mathematical focus of the module and how it fits within the sequence of A Story of Ratios.

Grade 6 – Module 2 Grade 6 – Module 2 PPT

Concept Development 3 hours11 minutes

Examination of the development of mathematical understanding across the module using a focus on Concept Development within the lessons.

Grade 6 – Module 2 Grade 6 – Module 2 PPT Grade 6 – Module 2

Lesson Notes

Review Grade 6 Module 2 Overview, Topic Openers, and Assessments.

Module Review 8 minutesArticulate the key points of this session.

Session Roadmap

Section: Introduction to the Module Time: 4 minutes

[4 minutes] In this section, you will…

Introduce the mathematical focus of the module and how it fits within the sequence of A Story of Ratios.

Materials used include:

Grade 6 – Module 2 Grade 6 – Module 2 PPT

Time (mins)

Slide #

Slide #/ Pic of Slide Script/ Activity directions GROUP

1 1 Welcome! In this module focus session, we will examine Grade 6– Module 2.

1 2 Our objectives for this session are to:•Examination of the development of mathematical understanding across the module using a focus on Concept Development within the lessons.•Introduction to mathematical models and instructional strategies to support implementation of A Story of Ratios.

1 3 We will begin by exploring the module overview to understand the purpose of this module. Then we will dig in to the math of the module. We’ll lead you through the teaching sequence, one concept at a time. Along the way, we’ll also examine the other lesson components and how they function in collaboration with the concept development. Finally, we’ll take a look back at the module, reflecting on all the parts as one cohesive whole.

Let’s get started with the module overview.

1 4 The second module in Grade 6 is called Arithmetic Operations Including Division of Fractions. The module includes 19 lessons and is allotted 25 instructional days. It challenges students to build on understandings from previous modules through the introduction of division of fractions. Students clearly have experienced dividing a whole number by a fraction and a fraction by a whole number. The beginning of this module has students extending this knowledge to dividing fractions by fractions. The second topic of this module has students practicing previous algorithms of addition, subtraction, and multiplication of whole numbers and decimals, but extends to applying the division algorithm to divide decimals. Students

rely on previous number theory to connect divisibility to determine the greatest common factor and the least common multiple of numbers. Students will connect the division algorithm to the Euclidean Algorithm as a tool for efficiently determining the greatest common factor of large numbers.

Section: Concept Development Time: 3 hours 11 minutes

[3 hours 11 minutes] In this section, you will…

Examine the development of mathematical understanding across the module using a focus on Concept Development within the lessons.

Materials used include: Grade 6 – Module 2 PPT Grade 6 – Module 2 Lesson Notes CCSS Progressions Document: The Number System (6-8)

Time Slide #

Slide #/ Pic of Slide Script/ Activity directions GROUP

1 5 Let’s begin with a study of the concepts of this module. We will focus on the concept development of topics A and B, then look at a few examples from the Mid-Module Assessment.

6 6 Take a look at the Progressions Document for the Number System Grades 6-8.(Click to advance slide) Take three minutes to read through the sixth grade portion and highlight areas of interest.(After 5 minutes have passed) (Click to advance slide) Take 2 minutes to discuss your findings, questions, concerns at your table.(After 2 minutes have passed) (Click to advance slide)Let’s share our findings. What is different from what has been taught before in sixth grade? What are some new terms that you notice? (3 minutes)

10 7 Take a look at the Topic Overview for Topic A.(Click to advance slide) Take two minutes to read through the topic overview for Topic A.(After 5 minutes have passed) (Click to advance slide) Take 2 minutes to discuss the overview at your table.(Click to advance slide)Let’s share our findings. What do you notice about the progression of lessons? What is different from what has been taught before in sixth grade? What are some new terms that you notice? (3 minutes)

2 8 Let’s begin with a study of the concepts of this module. We will focus on the concept development of topics A and B, then look at a few examples from the Mid-Module Assessment.(Click to advance slide) Topic A begins with a two day lesson interpreting division of a whole number by a fraction using visual models such as fraction bars, number lines and area models.(Click to advance slide) Students will continue to interpret and compute division of fractions, this time moving from dividing whole numbers by fractions to dividing fractions by fractions using models. Students are exposed to partitive division and measurement division of fraction.(Click to advance slide) In lesson five, students are creating division stories based on their choice of interpretation (measurement or partitive). They draw a model, find an answer, choose a unit, and then set up a situation. They continue to practice creating division stories in (Click to advance

slide) Lesson 6.Throughout lessons 1-6, the relationship to multiplication is hinted to during discussions and examples, however students formally understand the relationship between visual fraction models and equations in (Click to advance slide) Lesson 7.The topic concludes with (Click to advance slide) Lesson 8 where students bridge their learning from the topic to divide fractions and mixed numbers.

1 9 Let’s take a look at specific examples from the lessons in Topic A. While we are going through the examples, please note the leading questions being asked, the opportunity for discovery, as well as the direct links to the CCSS Progressions Document.

Switch to document camera and display lesson notes for Lessons 1-8.

12 10 Let’s start off looking at the Outcomes for lesson one.(Click to advance slide )Students use visual models such as fraction bars, number lines, and area models to show the quotient of whole numbers and fractions. Students use the models to show the connection between those models and the multiplication of fractions.(Click to advance slide ) Students divide a fraction by a whole number.

We are going to look at key examples and exercises from lesson 1.Switch to document camera and display lesson notes for Lessons 1.

Examination of key examples and exercises from each lesson will include opportunities for participants to engage in the lessons as students and debrief as teachers.

9 11 Let’s start off looking at the Outcomes for lesson two.(Click to advance slide ) Students use visual models such as fraction bars, number lines, and area models to show the quotient of whole numbers and fractions. Students use the models to show the connection between those models and the multiplication of fractions.(Click to advance slide )Students understand the difference between a whole number being divided by a fraction and a fraction being divided by a whole number.

We are going to look at key examples and exercises from lesson 2.Switch to document camera and display lesson notes for Lessons 2. Examination of key examples and exercises from each lesson will include opportunities for participants to engage in the lessons as students and debrief as teachers.

12 12 Let’s start off looking at the Outcomes for lesson three.(Click to advance slide ) Students use visual models such as fraction bars and area models to show the division of fractions by fractions with common denominators.(Click to advance slide )Students make connections to the multiplication of fractions. In addition, students understand that the division of fractions require students to ask, “How many groups of the divisor are in the dividend?” to get the quotient.

We are going to look at key examples and exercises from lesson 3.

Switch to document camera and display lesson notes for Lessons 3. Examination of key examples and exercises from each lesson will include opportunities for participants to engage in the lessons as students and debrief as teachers.

12 13 Let’s start off looking at the Outcomes for lesson four.(Click to advance slide ) Students use visual models such as fraction bars and area models to divide fractions by fractions with different denominators.(Click to advance slide ) Students make connections between visual models and multiplication of fractions.

We are going to look at key examples and exercises from lesson 4.Switch to document camera and display lesson notes for Lessons 4. Examination of key examples and exercises from each lesson will include opportunities for participants to engage in the lessons as students and debrief as teachers.

10 14 Let’s start off looking at the Outcomes for lesson five.(Click to advance slide ) Students demonstrate further understanding of division of fractions when they create their own word problems.(Click to advance slide ) Students choose a measurement division problem, draw a model, find the answer, choose a unit, and then set up a situation. Further, they discover that they must try several situations and units before finding which are realistic with given numbers.

We are going to look at key examples and exercises from lesson 5.Switch to document camera and display lesson notes for Lessons 5. Examination of key examples and exercises from each lesson will include opportunities for participants to engage in the lessons as students and debrief as teachers.

3 15 Let’s start off looking at the Outcomes for lesson six.(Click to advance slide ) Students demonstrate further understanding of division of fractions when they create their own word problems.(Click to advance slide ) Students choose a measurement division problem, draw a model, find the answer, choose a unit, and then set up a situation. Further, they discover that they must try several situations and units before finding which are realistic with given numbers.

Because this is an extension of Lesson 5, the only main difference is students are working independently to create division stories to further enhance their understanding of division of fractions. Please take 2 minutes to look over the teacher notes for this lesson and note the exercises students will be completing.

14 16 Let’s start off looking at the Outcome for lesson seven.(Click to advance slide ) Students formally connect models of fractions to multiplication through the use of multiplicative inverses as they are represented in models.

We are going to look at key examples and exercises from lesson 7.Switch to document camera and display lesson notes for Lessons 7. Examination of key examples and exercises from each lesson will include opportunities for participants to engage in the lessons as students and debrief as teachers.

3 17 Let’s start off looking at the Outcomes for lesson eight.(Click to advance slide ) Students divide fractions by mixed numbers by first converting the mixed numbers into a fraction with a value larger than one.(Click to advance slide ) Students use equations to find quotients.

This lesson is a culmination of all previous lessons, the only thing new is students will be including mixed number conversion. Please take 2 minutes to look over the teacher notes for this lesson and note the exercises students will be completing. Examination of key examples and exercises from each lesson will include opportunities for participants to engage in the lessons as students and debrief as teachers.

5 18 (Click to advance slide) What visual representations are students utilizing in Topic A?(Click to advance slide) How will these representations help students in visualizing division of fractions and making connections to multiplication?(Click to advance slide) What is the importance of student created division stories?(Click to advance slide) What are your takeaways about partitive and measurement interpretations of division?(Click to advance slide) Why is it important students know the difference between them and are able to choose the appropriate interpretation?

5 19 Take a look at the Topic Overview for Topic B.(Click to advance slide) Take two minutes to read through the topic overview for Topic B.(After 3 minutes have passed), (Click to advance slide) Take 2 minutes to discuss the overview at your table.(Click to advance slide)Let’s share our findings.

2 20 Topic B is composed of three lessons that focus on fluency with addition and subtraction algorithms,(Click to advance slide) Lesson 9 has students converting fractions to decimals in order to find sums and differences of mixed numbers(Click to advance slide) Lesson 10 has students using the distributive property to multiply multi-digit numbers with decimals,(Click to advance slide) while lesson 11 has students use fractions to show where the decimal should be placed in a product.

1 21 Let’s take a look at specific examples from the lessons in Topic B. While we are going through the examples, please note the leading questions being asked, the opportunity for discovery, as well as the direct links to the CCSS Progressions Document.

Switch to document camera and display lesson notes for Lessons 9-11.

5 22 Let’s start off looking at the Outcomes for lesson nine.(Click to advance slide ) Students relate decimals to mixed numbers and round addends, minuends, and subtrahends to whole numbers in order to predict reasonable answers.(Click to advance slide ) Students use their knowledge of adding and subtracting multi-digit numbers to find the sums and differences of decimals.(Click to advance slide ) Students understand the importance of place value and solve problems in real-world contexts.

We are going to look at key examples and exercises from lesson 9.Switch to document camera and display lesson notes for Lessons 9.Examination of key examples and exercises from each lesson will include opportunities for participants to engage in the lessons as students and debrief as teachers.

3 23 Let’s start off looking at the Outcome for lesson ten.(Click to advance slide ) Through the use of arrays and partial products, students strategize and apply the distributive property to find the product of decimals.

We are going to look at key examples and exercises from lesson 10.Switch to document camera and display lesson notes for Lessons 10. Examination of key examples and exercises from each lesson will include opportunities for participants to engage in the lessons as students and debrief as teachers.

3 24 Let’s start off looking at the Outcomes for lesson eleven.(Click to advance slide ) Students use estimation and place value to determine the placement of the decimal point in products and to determine that the size of the product is relative to each factor.(Click to advance slide ) Students discover and use connections between fraction multiplication and decimal multiplication.(Click to advance slide ) Students recognize that the sum of the number of decimal digits in the factors yields the decimal digits in the product.

We are going to look at key examples and exercises from lesson 11.Switch to document camera and display lesson notes for Lessons 11. Examination of key examples and exercises from each lesson will include opportunities for participants to engage in the lessons as students and debrief as teachers.

3 25 (Click to advance slide) How is Lesson 9 related to Topic A?(Click to advance slide) What do you notice about the progression of the lessons from Topics A and B in terms of content building, specifically when it comes to place value?

<<Good time for a fifteen minute break>>

8 26 Let’s take a look at the mid-module assessment to further understand the topics discussed in the first part of the module. (While talking about mid-module assessment, someone should be passing out number cards)(Click to advance slide) Move to the table that is labeled with your number.(Click to advance slide) Do not look ahead to the student exemplars, and solve your assigned problem as a team while thinking like a 6th grader(Click to advance slide) You will have 7 minutes to complete the problem.

18 27 Each group will have 3 minutes to share their answers and the methods in which they chose to solve the problems.

5 28 Take a look at the Topic Overview for Topic C.(Click to advance slide) Take two minutes to read through the topic overview for Topic C.(After 3 minutes have passed) (Click to advance slide) Take 2 minutes to discuss the overview at your table.(Click to advance slide)Let’s share our findings.

3 29 Topic C is composed of four lessons that focus on division of whole numbers and division of decimals.(Click to advance slide) In lesson 12, students will estimate digits in a quotient in order to justify the reasoning in their answers.(Click to advance slide) In lesson 13, students will utilize the long division algorithm to divide multi-digit numbers. This lesson is a fluency lesson building off of prior knowledge of the division algorithm. The only thing new is the number of place values has increased from previous years. They will utilize estimation from lesson 12 to continue to justify reasoning in their work.(Click to advance slide) Students move from multi-digit whole numbers to division of decimals in lesson 14. They will convert decimals into fractions to understand and justify conversion to and dividing by a whole number.(Click to advance slide) Finally in lesson 15, students will continue division of decimals, still utilizing estimation, and supporting their work using mental math, specifically using place value and powers of ten to create whole number divisors.

1 30 Let’s take a look at specific examples from the lessons in Topic C. While we are going through the examples, please note the leading questions being asked, the opportunity for discovery, as well as the direct links to the CCSS Progressions Document.

3 31 Let’s start off looking at the Outcome for lesson twelve.(Click to advance slide ) Students connect estimation with place value in order to determine the standard algorithm for division.

We are going to look at key examples and exercises from lesson 12Switch to document camera and display lesson notes for Lessons 12. Examination of key examples and exercises from each lesson will include opportunities for participants to engage in the lessons as students and debrief as teachers.

8 32 Let’s start off looking at the Outcome for lesson thirteen.(Click to advance slide ) Students understand that the standard algorithm of division is simply a tally system arranged in place value columns.

We are going to look at key examples and exercises from lesson 13.Switch to document camera and display lesson notes for Lessons 13. Examination of key examples and exercises from each lesson will include opportunities for participants to engage in the lessons as students and debrief as teachers.

8 33 Let’s start off looking at the Outcomes for lesson fourteen.(Click to advance slide ) Students use the algorithm to divide multi-digit numbers with and without remainders. Students compare their answer to estimates to justify reasonable quotients.(Click to advance slide ) Students understand that when they “bring down” the next digit in the algorithm, they are distributing, recording, and shifting to the next place value.

We are going to look at key examples and exercises from lesson 14.Switch to document camera and display lesson notes for Lessons 14. Examination of key examples and exercises from each lesson will include opportunities for participants to engage in the lessons as students and debrief as teachers.

3 34 Let’s start off looking at the Outcomes for lesson fifteen.(Click to advance slide ) Students use their knowledge of dividing multi-digit numbers to solve for quotients of multi-digit decimals.(Click to advance slide ) Students understand the mathematical concept of decimal placement in the divisor and the dividend and its connection to multiplying by powers of 10.

We are going to look at key examples and exercises from lesson 15Switch to document camera and display lesson notes for Lessons 15. Examination of key examples and exercises from each lesson will include opportunities for participants to engage in the lessons as students and debrief as teachers.

3 35 (Click to advance slide) Discuss the importance of estimation in this Topic.(Click to advance slide) What connections do you see between Topics A, B and C?

6 36 Take a look at the Topic Overview for Topic D.(Click to advance slide) Take two minutes to read through the topic overview for Topic D.(After 3 minutes have passed) (Click to advance slide) Take 2 minutes to discuss the overview at your table.(Click to advance slide)Let’s share our findings.

2 37 Topic D is composed of four lessons where students will be thinking logically about multiplicative arithmetic in order to connect back to the long division algorithm they worked on in Topic C.(Click to advance slide) Lesson 16 is an exploration of odd and even numbers.(Click to advance slide) In lesson 17, students will test the divisibility for the numbers 3 and 9 to finish off their study of divisibility. They will have a review of the divisibility rules from previous grades.(Click to advance slide) Students use their knowledge of divisibility rules to explore finding the least common multiple of two numbers, as well as finding the greatest common factor of two numbers. This will prepare the students for understanding (Click to advance slide) Lesson 19 where students find the greatest common factor of two numbers using the Euclidean Algorithm. Students will use their understanding of the long division algorithm to find that using the Euclidean Algorithm is sometimes a more efficient means to finding the GCF of larger numbers.

1 38 Let’s take a look at specific examples from the lessons in Topic D. While we are going through the examples, please note the leading questions being asked, the opportunity for discovery, as well as the direct links to the CCSS Progressions Document.

30 39 Look at your number card. If you are a 16, go to your designated table. If you are a 17, go to your designated table, same for 18.Your group will have 7 minutes to read through the lesson you’ve been assigned.You will discuss the representations and the flow of the lesson with your group.After discussion, your group will present the outcomes of the lesson and model one example from the lesson for the whole group.

7 40 Let’s start off looking at the Outcomes for lesson 19.(Click to advance slide ) Students explore and discover that Euclid’s Algorithm is a more efficient means to finding the greatest common factor of larger numbers and determine that Euclid’s Algorithm is based on long division.

We are going to look at key examples and exercises from lesson 19.Switch to document camera and display lesson notes for Lessons 19. Examination of key examples and exercises from each lesson will include opportunities for participants to engage in the lessons as students and debrief as teachers.

3 41 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?

Allow 2 minutes for participants to turn and talk. Bring the group to order and advance to the next slide.

5 42 Let’s review some key points of this session.

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 2 PPT

● Grade 6 Module 2 Lesson Notes

Additional Suggested Resources● A Story of Ratios Curriculum Overview

● CCSS Progressions Document: The Number System (6-8)