A Story of Units – Grade 4 Module 2

Sequence of SessionsOverarching Objectives of this July 2013 Network Team Institute

Participants will be able to identify the major work of each grade using the Curriculum Overview document as a resource in preparation for teaching these modules.

P-5.  Participants will draw connections between the progression documents and the careful sequence of mathematical concepts that develop within each module, thereby enabling participants to enact cross- grade coherence in their classrooms and support their colleagues to do the same.  (Specific progression document to be determined as appropriate for each grade level and module being presented.)

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 in order to fully implement the curriculum.

Participants will be prepared to implement the modules and to make appropriate instructional choices to meet the needs of their students while maintaining the balance of rigor that is built into the curriculum.   

Participants will be prepared to utilize models appropriately in promoting conceptual understanding throughout A Story of Units.

High-Level Purpose of this Session Participants will draw connections between the progression documents and the careful sequence of mathematical concepts that develop

within each module.  (Specific progression document to be determined as appropriate for each grade level and module being presented.) Standards alignment.  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. Participants will be prepared to implement the modules and to make appropriate instructional choices to meet the needs of their students

while maintaining the balance of rigor that is built into the curriculum.

Related Learning Experiences In Session 1, a curriculum overview, participants will gain an understanding of how each module contributes to the overall progression of

concepts throughout the grade-level. Session 3, Exploration of Models, will prepare participants to utilize models appropriately in promoting conceptual understanding

throughout A Story of Units. Session 4, Algorithms, will prepare participants to utilize algorithms appropriately in promoting conceptual understanding throughout

A Story of Units. Session 6, Leadership to Support A Story of Units, will help participants articulate examples of how to support implementation of the

curriculum and draw connections to the Evidence Guide for Planning and Practice in a Single Lesson.

Key Points• Each of the lesson components are necessary in order to achieve balanced, rigorous instruction and to bring the Standards to life.• Opportunities to nurture the Standards for Mathematical Practice are embedded throughout the lesson.

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?

Draw connections between Grade 4 Module 2 and the Progression documents.

Understand the instructional focus of Grade 4 Module 2. Understand and demonstrate fluency; application problems

and concept development; and problem sets, student debriefs and exit tickets and how they are to be used for differentiating instruction to meet the diverse needs of learners...

Participants will be able to describe the development of mathematical concepts that are the focus of this modules.

Participants will be able to articulate the instructional focus of Grade 4 Module 2, thereby preparing participants to teach and/or prepare their colleagues to teach these modules.

Session OverviewSection Time Overview Prepared Resources Facilitator PreparationSession Introduction 10:45-

10:50 Frame session, referencing

workshop agenda. Introduce objectives and

sequence for this session.

• Session PowerPoint• Review session notes and

PowerPoint presentation

Study of the Progression Document

10:51-11:11

Review Progression documents that describe the development of mathematical concepts that are the focus of this module.

• Relevant Progression document

• Review Progression Document

Examination of Module Overview and Assessments

11:12-Noon

Examine Module Overview. Complete and analyze module

assessments.

G4 M2 Module Overview G4 Assessments

Review G4 M2

Lesson Study 1:00-2:30 Examine Topic Openers. Detailed study of selected

lessons.

G4 selected lessons Review G4 M2

Bringing the Module to Life

2:31-3:00 Independent and small-group planning for implementation.

Whole group discussion.

Session RoadmapSection: Introduction Time: 10:45-10:49 [5 minutes]

In this section, you will…• Frame session, referencing the agenda• Introduce objectives and sequence the session

Materials used include:• Session PowerPoint

Time Slide #

Pic of Slide Script/ Activity directions GROUP

1 min 1. This Module Focus follows an opening session providing a update on the Curriculum Overview/Map of A Story of Units. At the previous NTI, sessions were dedicated to introducing the beginning module for each grade-level for Kindergarten through Grade 5. In this session, participants will explore the “next” module of their chosen grade-level, examining the mathematics of the module and analyzing the progression of concepts across the module.

2 min 2. Our objectives for this session are to explore Grade 4–Module 2 in order to:

• Draw connections between the Geometric Measurement Progression and the careful sequence of mathematical concepts that develop within each module.

• Articulate how the topics and lessons promote mastery of the focus standards and how the module

addresses the major work of the grade.• Prepare to implement the module and make

appropriate instructional choices to meet the needs of students while maintaining the balance of rigor that is built into the curriculum.

As we move through this session, please ask questions that will help with your immediate understanding of the material. If you have questions that relate to your broader understanding of A Story of Units or how to implement the curriculum in your school or district, please write those on a sticky note along with your name and place the note on the parking lot. We will look at those questions during the lunch break and address them with the group if they are applicable to all or with you if they are specific to your situation.

1 min. 3. In order for us to better address your individual needs, it is helpful to know a little bit about you collectively. Who of you are classroom teachers? (Grade 4? Grade 5?) (Call for a show of hands.) School-level leader? Principal? District-level leader? BOCES representative? Attended Grade 4 Presentation at May NTI? NOTE TO FACILITATOR: As you poll the participants, take note of the approximate size of each group. This will make it easier for you to re-group the participants for the final portion of this presentation.Regardless of your role, what you all have in common is the need to deeply understand the mathematics of the curriculum and the intentional instructional sequence in which it is brought to life for students. Throughout this session, we ask you to be cognizant of your specific educational role and how you will be able to promote successful implementation in your classroom, school, district, and/or BOCES. Each time we pause to reflect, please do so through the lens of your own professional

responsibilities. At the close of this session, you will have the opportunity to share your thoughts, ideas, and concerns with others in a similar role.Principals in particular- You will want to make notes for yourself as a result of your observations to use in later sessions tomorrow. We will be focusing you on the areas where you will want to make notes for yourself to use later.

1 min 4. In this session, we’ll begin by spending some time with the Geometric Measurement Progression document in order to better understand the mathematical concepts that are addressed in this module. Then we will examine the Module Overview and Assessments. The major portion of our time will be dedicated to looking at a number of lessons from the module. Finally, we’ll discuss the instructional choices that you might make as you implement the module in order to best meet the needs of your students. Before we move on to the Progression document, let’s take a quick look at the curriculum map in order to see how this module fits into the overall plan for this grade.

Section: Study of the Progression Document Time: 10:50 – 11:01 [12 minutes]

In this section, you will… Examine part of the Progression document relevant to the

work of this grade and module in order to understand the development of mathematical concepts that will be addressed in the module.

Materials used include: Session PowerPoint Progression document

Time Slide #

Pic of Slide Script/ Activity directions GROUP

2 min 5. This curriculum map is found on page 3 of A Story of Units: A Curriculum Overview for Grades P-5. For those of you who participated in the May NTI, you’ll recall that we deeply examined the first module of Grade 4. In this session, we will continue that deep examination of the next module.

NOTE TO FACILITATOR: Take a moment to share briefly the following information about this module.

• What is the title of this module? (Unit Conversions: Addition and Subtraction of Length, Weight and Capacity)

• How many instructional days are allotted for this module? (7)

• What modules, prior to this one, might prepare students for success in this module? (G2 M2)

• What modules, beyond this one, might build on the concepts of this module? (G5 M1 & M4)

5 min 6. As a foundation for our study of this module, we’re going to first take some time to examine a portion of the Geometric Measurement Progression document that describes the mathematical concepts that will be developed throughout the lessons. You’ll have about 5 minutes to read through the document independently. As you read, highlight measurement concepts Grade 4 students are expected to learn. Then you’ll have an opportunity to discuss your thoughts with others at your table.As you think about what you are reading reflect on your role and what this information may mean for how you support your colleagues- consider resources such as time, money and people. For example, do I need to look at my PD schedule, do I need to shift the planning times for teachers, and do I need to order more math materials?

Allow participants 5 minutes to read independently. Then advance to the next slide for a turn and talk.

5 min. 7. • Which measurement concepts are students expected to learn in Grade 4?

Turn and talk with a partner at your table, and then you’ll have an opportunity to share your thoughts with the group.

• What appears to be missing from this progression that you would expect to find when teaching about measurement?

Turn and talk with a partner at your table, and then you’ll have an opportunity to share your thoughts with the group.

Allow 2 minutes for participants to turn and talk about their reflections. Then, facilitate a discussion.

Section: Examination of Module Overview and Assessments

Time: 11:02- [X minutes]

In this section, you will…• Examine the module overview in order to understand the

development of mathematical concepts within the module and identify new terms, tools, or representations that will support instruction

• Complete and analyze the module assessment in order to understand how student mastery of the standards addressed in this module will be measured

Materials used include:• Session PowerPoint• Grade 4 Module 2 Overview• Grade 4 End-of Module assessment and rubric• Personal white boards

Time Slide #

Pic of Slide Script/ Activity directions GROUP

1 min 8. Now that we’ve read the information provided in the Progressions documents, let’s examine how these concepts are addressed in this module.

1 min 9. For those of you who may be unfamiliar with A Story of Units, I’ll take just a moment to review the organizational structure of the modules that make up A Story of Units:

• Each grade contains 5-8 modules. Modules are comprised of topics, topics break into concepts, and concepts become lessons. Modules and topics will vary in length depending on the concepts addressed in each. In 1st through 5th grades, every lesson is designed for a 60 minute instructional period; in Kindergarten, lessons are designed for a 50 minute period; Pre-kindergarten lessons are designed for a

25 minute period. • This graphic illustrates the breakdown of the module

structure. Each component, moving from the Overview to the Lesson, provides a more specific level of information. As you plan to implement A Story of Units, each of these components will be important to your understanding of the instructional path of the module.

• The Standards, both Content and Practice, come to life through the lessons. Rigorous problems are embedded throughout the module. We will spend time in the upcoming sessions exploring this further.

9 min. 10. Each Overview contains multiple components to help educators understand more clearly the focus of the module. These components include:

• Descriptive narrative• Distribution of Instructional Minutes• Focus Grade Level Standards, Foundational Standards,

and Standards for Mathematical Practices • Overview of Module Topics and Lesson Objectives• Terminology• Suggested Tools and Representations• Scaffolds• Assessment Summary

(CLICK TO ADVANCE FIRST BULLET) Take 8 minutes to read the Module Overview independently. (CLICK TO ADVANCE SECOND BULLET) As you read, mark important information that will help build understanding of the content in preparation to implement this module. You might do so using a symbol, such as a star, or by highlighting essential portions.

8 min. 11. • How does this Module compare to your past experiences with this content?

• How does each component of the Module Overview prepare you to implement this material in your classroom?

Turn and talk with others at your table. Share your observations and ask them to do the same.

NOTE TO FACILITATOR: Allow 2 minutes for participants to turn and talk about their review of the Overview and their response to the information provided there. Then facilitate a discussion in the remaining 5 minutes using the following talking points:

• Which standards are the focus of this module? (4.MD.1, 4.MD.2)

• How is each standard addressed by the content of this module? (4.MD.1 is addressed in Topic A. 4.MD.2 is addressed in Topic A and B to apply measurement concepts)

• Which standards are foundational to this module? (2.NBT.1, 3.MD.2, 4.OA.3, 4.NBT.4) This corresponds with the information we saw in the Distribution of Instructional Minutes diagram.) These are standards with which students are expected to be familiar. This list is provided to assist teachers in helping students build on previous understandings, making logical connections across grades. In addition, and especially while the implementation of the CCLS is new, teachers should be prepared to address any gaps that may exist in these foundational understandings.

• Which Mathematical Practices are addressed in this module? (MP.1, 7, and 8) While it is certainly hoped that teachers will continue to promote all practices on a regular basis as opportunities arise, these practices listed in the Overview are particularly appropriate for

the lessons in this module. In addition to the information provided in this list, activity-specific suggestions are provided in the lessons themselves.

• How are these MPs expected to come to life in this module? (See examples from the Overview.)

• How does the Terminology provided inform instruction for this module? (It helps the teacher focus the instruction. Only metric units are taught (km, m, cm, mL, L, g, kg). Note: Mixed units are foundational for fractions and strengthen place value understanding.)

• How do these Tools and Representations support instruction in this module? (Rulers, scales, and beakers provide a visual connection to the units. Number lines and 2-column tables allow students to see the patterns of unit conversions. Tape diagrams visually support the understanding of a word problem.)

• What do you know about the assessment included in this module? (This module has only 1 assessment. It assesses both standards taught in the module and follows the instruction of Topics A and B.)

• How might you use this information in your role? (It is a quick summary of what teachers will do for the next few weeks and can be shared with parents and the community, it also summarizes what conversations should be happening in grade level meetings and what resources teachers may be requesting for their classrooms, it can be shared with other teachers in the school for the purpose of thematic unit planning.)

3 mins 12. Before we look at the module assessments, let’s complete some fluency exercises to get our brains in the measurement mode.

Complete the fluency “Meter and Centimeter Number Bonds” from Lesson 1.

T: (Project a number bond with 150 centimeters written as the whole and 1 meter as one of the parts.) How many centimeters are in 1 meter? (100 centimeters)

T: (Beneath 1 m, write 100 cm.) On your white boards, write a number bond filling in the missing part. (number bond with a whole of 150 cm and parts 1 m and 50 cm.)

Repeat process with wholes of 180 cm, 120 cm, 125 cm, 105 cm, and 107 cm.

Note: Bring to life the prior conversations from the Module Overview and terminology as you demonstrate a number bond and mixed units.

2 mins 13. Here is a fluency that we created, modeling after the previous fluency, to remind you of the kilometer to meter conversion in preparation for our discussion with the mathematics of this module. Remember fluencies are a wonderful and easy tool to revise for the needs in your classroom for purposes of review.

T: (Project a number bond with 1,500 meters written as the whole and 1 kilometer as one of the parts.) How many meters are in 1 kilometer? (1,000 meters)

T: (Beneath 1 km, write 1000 m.) On your white boards, write a number bond filling in the missing part. (Write a number bond with a whole of 1,500 m and parts 1 km and 500 m.)

Repeat process with wholes of 2800 m, 5200 m, 6,635 m,

2050 m, and 4007 m.Note: Bring to life the prior conversations from the Module

Overview and terminology as you demonstrate a number bond and mixed units.

10 mins

14. Now that you know the focus of the module, let’s examine how students will be assessed on their mastery of these skills and concepts. Turn to the first page of the assessment. Consider each item and determine which standards are being addressed and how. Principals- Consider the implications of this data (quantitative and qualitative) for the professional development needs of the staff, the resources needed to support struggling students, the conversations held in the data analysis meetings. You will want to make notes on ideas you have as a result of your observations to use in later sessions tomorrow.Allow participants 10 minutes to complete this standards-alignment assessment. Then facilitate a discussion of the ways in which this assessment task measures the skills and understanding that are addressed in this module. Have participants identify the ways in which a strong understanding of the assessment prepares educators to implement the lessons in this module.

5 mins 15. Read through the top level of the rubric. Note how the rubric is structured with the levels of performance described for each assessment question. Take 2 minutes and read through the rubric.

5 mins 16. (Click to advance the bullet.) There are 3 sample student assessments. Each table has a post-it with the name Mary, Kelly, or Erin. Please read through the responses for your student and score them using the Rubric. Each question can have a value of 1, 2, 3, or 4. Use about 4 minutes.(Click to advance the bullet.) Once everyone at your table has scored the sample assessment, discuss the scores at your table. Remember to use clear evidence from the student work in conjunction with the Rubric’s Levels of Performance and the Step descriptions. Use about 3 minutes.Ask for the scores of each problem for each assessment. Talk through any large discrepancies shortly, keeping the pace of the presentation. Use about 3 minutes.(Click to advance the bullet.) Discuss how this Rubric can assist teachers in assessing student understanding.

0 mins 17. How could this rubric be used to give students feedback on complex tasks?

Section: Exploration of Selected Lessons Time: 1:00 – 2:30 [X minutes]

In this section, you will…• Examine Topic Openers in order to understand the coherence

within and between the topics that comprise the module• Engage in deep study of selected lessons that illustrate the

development of mathematical concepts across the module as well as the variety of instructional strategies that support student learning

• Reflect on takeaways, key points and next steps

Materials used include:• Grade 4 Module 2

Time Slide #

Pic of Slide Script/ Activity directions GROUP

1 min 18. When we return from lunch, we’ll start exploring the Topic Overviews and lessons. We will start with Module 2 and then explore Module 3, including the M3 Assessments. NOTE TO FACILITATOR: Make sure to review the sticky note questions during lunch and plan to address the questions with the group or individuals in the last half of the session.

8 min 19. Welcome back! Now that we are familiar with the module overview and assessments, let’s begin our examination of the topics and lessons.

5 min. 20. Within a given topic, the lessons work together to build strong understanding of a set of related concepts. (CLICK TO ADVANCE FIRST BULLET) Take 5 minutes to review both Topic Openers. Be prepared to share insights to the group about the topic openers that you read.

(CLICK TO ADVANCE SECOND BULLET) As you read, mark important information that will help educators implement these lessons. Again, you might choose to use a symbol or series of symbols, or you might simply highlight essential portions. Allow 5 minutes for participant to read and discuss the topic openers. Then have volunteers from each table report to the group on each of the topic openers sequentially, so that a clear picture of the progression of the module unfolds.NOTE TO FACILITATOR: Consider assigning topics to the tables ahead of time in order to simplify this process. You might do this just by putting a sticky note with the letter assignment on each table basket. Specify whether participants should work independently, with a partner, or as a table.

1 min. 21. Turn and talk with others at your table about the collection of topic openers. Share your observations and ask them to do the same. Allow 3 minutes for participants to turn and talk about the topic openers. Then facilitate a whole-group discussion about the following questions:

• How does Topic A lay the foundation for the work in Topic B? (Topic A addressed the relationship between the different units and tools for modeling conversions. Topic B applies the conversions and shares the connections they have to place value.)

• How do Topic Openers A and B allow teachers to understand the vertical alignment amongst grade levels? (Coherence Links list the connections to prior and future modules. Measurement lessons are not typically thought to link to a place value module, such as to G5-M1 and M2.)

• How are the Topic Openers useful as a planning tool for this module? (The narrative takes the information from

the overview and zooms in to summarize the topic and lay a clear outline of a set of lessons.)

2 min. 22. Now that we’ve used the Topic Openers to gain more specific understanding of this module, let’s move on to examine the lessons from the module. For those of you may not be familiar with A Story of Units, I’d like to point out that most lessons are comprised of four components: Fluency Practice, Application Problem, Concept Development, and the Student Debrief. These components work together to achieve rigor and lead toward the culminating assessment.Note that within the Concept Development students are given a time frame to work on the Problem Set. These problems are revisited during the Debrief portion in order to help students see patterns in the mathematics and think more deeply about their work

8 min. 23. We selected all the lessons in this module to demonstrate how the lessons build on each other. Lessons1-3

• Revisit the idea that this module is an opportunity to apply addition and subtraction algorithms and strategies, including tape diagrams for modeling word problems.

• Talk briefly about the terminology introduced in this module and the representations used to work with metric conversions.

• 2 column tables allow students to see side-by-side conversions for each type of measurement.

• Number lines are used to align mixed units and the smaller unit when adding and subtracting.

• Simplifying strategies are ways of solving a problem that may not require the use of an algorithm. Think of these as written representations of mental math.

• Standards alignment: Discuss how note on page 1 of lessons 1-3 does mention extending past the G4 standard of converting larger to smaller units. It will be discussed later how to revise the lessons to only match the G4 standard.

2 min. 24. Lesson 1 is the first experience students have with converting metric units. We use what they know from Grade 2 with centimeters and meters and teach the new vocabulary word, kilometer, by asking students to think about lengths of familiar objects like the width of a door, width of a staple, or the distance around a soccer field 4 times.Next students compare sizes and note the relationship between meters and kilometers using conversion equivalencies, represented in a 2-column table.(CLICK TO ADVANCE THE TABLE.) Take 1 minute to complete this table. (CLICK TO ADVANCE EACH ANSWER IN THE TABLE.) Review the answers with participants.Think about how this table reflects 4.MD.1. (It states explicitly to use a table to record measurement equivalencies.) How could you make the table more complex? (Replace a kilometer measurement with a blank, but give the meter measurement for one or more rows.) How could you provide more scaffolding? (Give an example for the first, and possibly the second, rows.)

5 min. 25. Using a number line reinforces the equivalencies between two measurement unit, for example grams and kilograms. This number line shows 10 kilograms is equivalent to 10,000 grams. A number line can be used for a counting up or counting down strategy.(CLICK TO ADVANCE THE SLIDE.) This number line shows a counting up strategy. The student starts with 2 kg 250 g or 2,250 grams.(CLICK TO ADVANCE THE SLIDE.) Mental math tells us only 750 more grams are needed to reach a nearest unit that is easier to count with, like 3 kilograms or 3,000 grams.(CLICK TO ADVANCE THE SLIDE.) Mental math again tells us only 7 kilograms or 7,000 grams are needed to reach the original amount of 10 kilograms.(CLICK TO ADVANCE THE SLIDE.) Students add the partials sums to find the difference between 10 kilograms and 2 kilograms 250 grams.

3 min. 26. Students come prepared with many strategies, which can be shared during a debrief or within the context of a problem solving lesson, like lessons 1 through 3.Here are 5 different ways we have modeled within the lessons on how students may solve addition and subtraction problems with metric units.(CLICK TO ADVANCE THE SLIDE.) Label the strategies modeled in each solution.Provide a brief discussion where participants share out the strategy modeled.(CLICK TO ADVANCE THE SLIDE.) The answer is “Algorithm using smaller units.”This may be the preferred method of students for solving. They are recently familiar with the subtraction algorithm from Module 1

7 min. 27. • Students come prepared with many strategies, which can be shared during a debrief or within the context of a problem solving lesson, like lessons 1 through 3.

• Here are 5 different ways we have modeled within the lessons on how students may solve addition and subtraction problems with metric units.

• Label the strategies modeled in Problem 2.• Provide a brief discussion where participants share out

the strategy modeled.• (CLICK TO ADVANCE THE SLIDE.) The answer is

“Algorithm with mixed units.”• This may also be the preferred method of students for

solving. They are recently familiar with the subtraction algorithm from Module 1.

1 min. 28. Students come prepared with many strategies, which can be shared during a debrief or within the context of a problem solving lesson, like lessons 1 through 3.Here are 5 different ways we have modeled within the lessons on how students may solve addition and subtraction problems with metric units.Label the strategies modeled in Problem 3.Provide a brief discussion where participants share out the strategy modeled.(CLICK TO ADVANCE THE SLIDE.) The answer is “Special strategy, number line.”

4 min. 29. Students come prepared with many strategies, which can be shared during a debrief or within the context of a problem solving lesson, like lessons 1 through 3.Here are 5 different ways we have modeled within the lessons on how students may solve addition and subtraction problems with metric units. Label the strategies modeled in Problem 4.Provide a brief discussion where participants share out the strategy modeled.(CLICK TO ADVANCE THE SLIDE.) The answer is “Special strategy, counting up.”

1 min. 30. Students come prepared with many strategies, which can be shared during a debrief or within the context of a problem solving lesson, like lessons 1 through 3.Here are 5 different ways we have modeled within the lessons on how students may solve addition and subtraction problems with metric units. Label the strategies modeled in Problem 5.Provide a brief discussion where participants share out the strategy modeled.(CLICK TO ADVANCE THE SLIDE.) The answer is “Special strategy, one unit at a time.”Remember students are creative in their methods for solving. Teachers will see different methods than the ones presented in the lessons. Teachers can decide what methods are best to use as direct instruction within each lesson. Perhaps one room is ready to investigate multiple means of special strategies, where another classroom is ready to explore only the algorithms in depth.

31. By the time the students get to Lesson 4 they have had some experience with the patterns in metric conversion. Lesson 4 helps the students connect these patterns to what they know about place value. The students then use their place value understanding to compare and order measurements.

32. So what do you notice about the relationship between grams and kilograms (write on whiteboards)Now let’s take that information a step farther. Write your answer as an equation. (on whiteboards)Repeat writing an equation to show the relationship between

• Kilometer and meter• Liter and milliliter • Thousand and one

33. Lesson 5 is the culminating lesson of Module 2. Completion of the lesson requires application of the concepts developed during Lessons 1-4. Lesson 5 is designed such that the Problem Set is used as part of the Concept Development. Students complete Problems 1-4 in a structured way during the Concept Development and then complete Problems 5 and 6 independently.

• Discuss structure of the lesson (RDW). (3 min.)

34. • Allow 2 minutes to draw a model of Problem 1.• Allow 1 minute for participants to share their models

with one other person. Were the models the same?• Allow 2 minutes for two participants to share their

models with the whole group. Give time for others to ask questions.

• Allow 2 minutes to solve the problem and to discuss prior knowledge needed to solve the problem. How does it build from prior lessons?

35. All four lesson components provide opportunities to nurture the Standards of Mathematical Practice and are critical in maintaining the balance of rigor. Certainly educators will need to make instructional choices when implementing these lessons, but attention to each component is key.

36. Take one minute to reflect on this session. . How do these lessons compare to your past experiences with mathematics instruction? How would you adapt/enhance your answers to the questions on the Module Overview Handout after our Lesson Study work? What are the implications for the supports and resources your colleagues will need to fully implement this curriculum with fidelity? Jot down your thoughts. Then you will have time to share your thoughts Give participants 1 minute for silent, independent reflection.(Click to advance to the next bullet.) Turn and talk with a partner at your table about your reflections.Allow 2 minutes for participants to turn and talk about their reflections. Then, facilitate a discussion that leads into the key points on the next slide.

37. Let’s review key points from our examination of these lessons

38. Module 3 is an in depth focus on multiplication and division. Although Grade 4 students are not required to use the algorithm, students are slowly introduced to the algorithm for multiplication and division. Before students learn the algorithms, models such as place value disks and the area model are used to represent the mathematics. Students build upon their Grade 3 knowledge of multiplication and division in this module, using the facts and experience with “groups of” to multiply up to 4-digit by 1 digit and 2 digit by 2-digit numbers and divide up to 4 digit by 1 digit numbers.

39. This curriculum map is found on page 3 of A Story of Units: A Curriculum Overview for Grades P-5. For those of you who participated in the May NTI, you’ll recall that we deeply examined the first module of Grade 4. In this session, we will continue that deep examination of the next module. NOTE TO FACILITATOR: Take a moment to share briefly the following information about this module.

• What is the title of this module? (Multi-Digit Multiplication and Division – the title has been revised to better reflect the work on the module.)

• How many instructional days are allotted for this module? (43)

• What modules, prior to this one, might prepare students for success in this module? (G3 M1, 3, and 4)

• What modules, beyond this one, might build on the concepts of this module? (G5 M1 & M2, 4 and 5)

40. Each Overview contains multiple components to help educators understand more clearly the focus of the module. These components include:

• Descriptive narrative• Distribution of Instructional Minutes• Focus Grade Level Standards, Foundational Standards,

and Standards for Mathematical Practices • Overview of Module Topics and Lesson Objectives• Terminology• Suggested Tools and Representations• Scaffolds• Assessment Summary

(CLICK TO ADVANCE FIRST BULLET) Take 8 minutes to read the Module Overview independently. (CLICK TO ADVANCE SECOND BULLET) As you read, mark important information that will help build understanding of the content in preparation to implement this module. You might do so using a symbol, such as a star, or by highlighting essential portions

41. To get a more in depth look at the module, each table has a post-it note with a letter written on it. This letter is your table’s assigned Topic to review.Using your Topic Analysis Handout, complete the focus questions for your Topic and list the standards that fit into your Topic.The first column of the handout has the focus questions. Write your responses in the 2nd column. The 3rd column provides a space to record the relevant standards.Be prepared to share your responses with the group.

42. • What context will students use to explore multiplicative comparisons? (Area and perimeter.)

• What does Topic A lay the foundation for in upcoming year? (Grade 5 scaling and Grade 6 proportional reasoning.)

• Possible answer to word problem: 32 square feet of space will be left.

43. • Why are students asked to reason between number disks and numerical work? (Allows students to see the role of place value units in multiplication and prepares them for the language of multiplying units together.)

• Topic B lays the foundation for which upcoming Module 3 Topics? (Topics C, D, and H)

Possible answer to word problem: Brianna has 180 balloons.

44. • What methods will students use to record their work in Topic C? (Distributive property, number disks, partial products, standard algorithm, area model.)

• What clarification does the footnote 1 provide for the multiplication algorithm? (The standard algorithm for multiplication is not expected to be mastered until Grade 5 – 5.NBT.5. Students are introduced, being supported by place value strategies to prepare them from Grade 5 multiplication.)

Answer to problem: 2×2 hundreds + 2×1 ten + 2×3 ones4 hundreds + 2 tens + 6 ones400 + 20 + 6 426

45. • What is the purpose of Topic D? (Students apply multiplication to solve multi-step word problems and multiplicative comparison problems.)

• What operations will students be able to use to solve the problems? (Addition, Subtraction and Multiplication.)

• Possible answer to word problem: Charlie and his parents read 7,183 pages in one month.

46. • Which foundational concepts does Topic E build upon? (Types of division – groups size unknown/partitive and size of group unknown/measurement.)

• What clarifications are provided by footnotes 2 and 3? (#2: remainders must be interpreted correctly. 7÷3 is not equal to 5÷2 since their answer is 2r1. The amount is different. #3: The division algorithm fluency is not expected until Grade 6, but is introduced alongside models to provide adequate practice.)

Answer to problem: 4 with a remainder of 2

Care must be taken with a remainder. A statement should be given as a response to show the distinction between a quotient and a remainder.*Only can the ‘r’ form of a remainder (2r1) be shown when using the algorithm.*An area model breaks down for division when there is a remainder, shown in the image above.*Use multiplication to check your work. Number bonds can aid as a model.

47. • How is Topic F connected to the work of this module? (Factors and multiples prepare students for division of larger dividends.)

• Topic F provides the foundation for which upcoming Module 3 Topic? (Topic G)

Answer to problem: True. 2 and 4 are factors of 8.Also:Numbers with 8 as a factor: 8, 16, 24, 32, 40.8÷2=4 8÷4=216÷2=8 16÷4=424÷2=12 24÷4=632÷2=16 32÷4=840÷2=20 40÷4=10

48. • Topic G builds upon the work of which Topics that came earlier in the Module? (Topic B, E and F.)

• What is the purpose of using number disks in this Topic? (Visually supportive for decomposition alongside the algorithm.)

Answer to problem: Each store will receive 145 liter bottles. One bottle will be left over

Tape diagrams model word problems. Division tape diagrams with remainders will need to be redrawn. For this problem, students initially draw 1 bar representing 581 bottles, and divide the bar into 4 parts. But 581 does not divide equally into 4 parts, so we must create a 5th part to the bar. We erase our old lines, and draw new ones after the algorithm or model shows us the remainder. The remainder in the tape diagram is shaded and labeled below, as shown in the model above.

49. • Why is the work of Topic H placed last in this Module? (Most abstract and students have had more time to solidify their understanding of area models. Also, placing 2-by-2 digit multiplication before 1-digit divisors does not allow students to connect 1 digit multipliers and their models.)

• What should students understand about partial products written vertically? (They connect explicitly to the distributive property. Partial products can be 4 or 2 numbers.)

• Answer to problem: 345

Shading the lower half of the area model provides a visual support for seeing the new addition to the area model for multiplication. Solving 5 times 23 was address in Topic C. The new complexity is 10 times 23, which is represented in the shaded portion of the area model. Using the distributive property, students can find the answer using the area model, as well as multiplying with partial products or the standard algorithm

Section: Bringing the Module to Life Time: 3:30-4:00[65 minutes] In this section, you will…

• Review and discuss progression documents Materials used include:

• Session PowerPoint

• Review the remaining lessons in the module• Analyze the problem sets and their role in assessment

•

Time Slide #

Pic of Slide Script/ Activity directions GROUP

1 min 50. Now that we’ve examined all aspects of the module, let’s consider concerns regarding implementation and differentiation. For this discussion, we ask that you re-group yourselves so that you are sitting with colleagues who share similar roles.

NOTE TO FACILITATOR: Assist the participants in regrouping within the room by professional role.

5 min 51. Give participants 4 minutes to create a mini-action plan independently. Participants might come up with any of the following:

• Teacher- time to read through the modules, discuss the lessons with a co-teacher, solve the problems, find/order materials, highlight key questions

• School Leader- identify areas that may need the most support, consider how to bridge the gaps in student understanding, identify what teachers need to know to effectively implement the modules, find/order materials

• Principal- provide time for teachers to plan, facilitate discussions around modules to encourage team problem solving, consider how the module impacts the way teachers demonstrate lesson planning, consider how this impacts what will been seen during an observation, organize/support the process of

gathering/ordering materials• District Leader – provide funding and resources

necessary for staff development, curricular materials, and assessment. Consider implications of new curriculum and new tests and prepare stakeholders for change.

BOCES Representative – Identify economies of scale for staff training. Consider implications of new curriculum and new tests and prepare stakeholders for change.

20 min.

52. Collaborating with individuals who share your role and responsibilities is critical. For this discussion, we will ask that you re-group yourselves so that you are sitting with colleagues who share similar roles. There are signs around the room that will help you find other participants who share your role. Before we move, let’s take a moment to discuss the work you will do in your role group.

When I give you the signal, you will move to the appropriate area of the room based on your role. Find a group of 4-6 people with a similar role. Take 5 minutes to collaboratively create an action plan and record it on chart paper. Make sure you list your role somewhere on the chart paper. Are

there any questions? Go!

After groups have had 5 minutes to work, bring the group together to do a gallery walk of the action plans.

After 4 minutes of a gallery walk, invite participants to share their observations with the whole group, taking note of any steps that are not on their chart but would be important ways to move forward. Invite them to look for ways to collaborate with members of other role groups.

1 min 53. Take one minute to reflect on this session. What, for you, is the biggest takeaway? Jot down your thoughts. Then you will have time to share your thoughts.(Give participants 1 minute for silent, independent reflection.)(CLICK TO ADVANCE ANIMATION ON SLIDE.)Turn and talk with a partner at your table about your reflections.(Allow 2 minutes for participants to turn and talk about their reflections. Then, facilitate a discussion that leads into the key points on the next slide.)

2 mins. 54. Let’s summarize the key points that you have identified as a group during this session:

5 mins. 55. Plus / Delta

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

Additional Suggested Resources