· Web viewA Story of Units- Module Focus. Grade 4. Sequence of Sessions. Overarching Objectives of this May 2013 Network Team Institute. Participants will understand the focus

A Story of Units- Module Focus

Grade 4

Sequence of Sessions

Overarching Objectives of this May 2013 Network Team Institute

· Participants will understand the focus of each module presented, the instructional path, and the student outcomes; and be ready to teach and/or prepare their colleagues to teach these modules.

· Participants will examine the K–5 progressions documents and the sequence of standards foundational to developing an understanding of Number and Operations in Base Ten, thereby enabling participants to enact cross-grade coherence of NBT development in the classroom and to train their colleagues to do the same.

· Participants will understand the purpose and implementation of Fluency, Problem Sets, Student Debriefs, Exit Tickets, Application Problems and Conceptual Development within A Story of Units. They will practice these components and be prepared to use them as tools through which to meet the needs of diverse learners.

· Participants will examine formal and informal assessment within the Modules and develop an understanding of how to use the data generated to make instructional decisions.

High-Level Purpose of this Session

· Participants will know the structure of modules and lessons within The Story of Units in order to implement the modules and train other colleagues.

· Participants will understand the instructional focus of Module 1 for Grades K, 1,2,3,4, or 5, thereby preparing participants to teach and/or prepare their colleagues to teach these Modules.

· Participants will understand the function of curricular components including Fluency Practice, Application Problems, Concept Development, Worksheets, Student Debrief, and Exit Tickets for implementing each one effectively.

Related Learning Experiences

· This Module Focus Session will conclude Day 1 and will be followed on Day 2 by a session on The Progression of Visual Models and the System of Algorithms for NBT.

· There will then be a three-part series enabling participants to understand and practice the instructional routines of fluency, application problems and concept development, and problem sets, student debriefs and exit tickets. Each of these sessions will focus on how to differentiate the instructional component according the needs of diverse learners in any given classroom.

Key Points

· Modules Overviews and Topic Openers provide essential information about the instructional path of the module and are key tools in planning for successful implementation.

· Each of the lesson components are necessary in order to achieve balanced, rigorous instruction and to bring the Stards to life.

· The Exit Ticket is an essential piece of the Student Debrief and provides daily formative assessment.

· 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?

In order to be prepared to teach or train your colleagues to implement the modules, particpants will:

1. Understand the key components of Module 1 and the lessons within it

1. Explain the components for a particular grade level

1. 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.

1. Participants will identify key components of the module structure and of each lesson within The Story of Units.

1. Participants will be able to articulate the instructional focus of Module 1 for a particular grade level (GK-5), thereby preparing participants to teach and/or prepare their colleagues to teach these Modules.

1. Participants will articulate the function of curricular components including Fluency Activities, Application Problems, Concept Development, Problem Sets, Student Debrief, and Exit Tickets and how they can be used to differentiate instruction.

Session Overview

Section

Time

Overview

Prepared Resources

Facilitator Preparation

Session Introduction

1:00-1:04

· Frame session, referencing workshop agenda.

· Introduce objectives and sequence for this session.

· Session PowerPoint

· Review session notes and PowerPoint presentation

Review of Module Structure

1:04-1:08

· Review module structure and consistency across the grades

· Grade 4 Module 1


· Review appropriate module

· Review session notes and PowerPoint presentation

Examination of Module Overview, Assessments, and Topic Openers

1:08-1:44

Study and discuss

· Overviews

· Assessments

· Topic Openers

· Grade 4 Module 1

Session PowerPoint


Review session notes and PowerPoint presentation

Lesson Study

1:44-3:05

· Detailed study with discussion and practice of module compoents

· Review key points

· Grade 4 Module 1

Session PowerPoint


Review session notes and PowerPoint presentation

Coherence Across the Module

3:05-4:14

· Progresssion study and discussion

· Progression document Numbers and Operation Base 10

· Review NBT Progression document

Session Roadmap

Section: Introduction

Time: 1:00-1:04

[4 minutes] In this section, you will…

· Frame session, referencing the agenda to outline what will be covered in the session.

· Introduce objectives and sequence the session to focus participant learning.

Materials used include:


· Module

· Curriculum Map

Time

Slide #/ Pic of Slide

Script/ Activity directions

GROUP

1 min

Slide 1

NOTE THAT THIS SESSION IS DESIGNED TO BE 180 MINUTES IN LENGTH

Turnkey Materials Provided in Addition to PowerPoint:

· Grade 4—Module 1

· Video Clip: XXX (when applicable)

Additional Suggested Resources:

· A Story of Units: A Curriculum Overview for Grades P-5

· How to Implement A Story of Units

This Module Focus follows a session providing a P-12 overview of the curriculum, and a session examining the assessments of A Story of Units. In this session, participants will explore the module of their chosen grade-level, examining each of the lesson components closely as well as the progression of those components across the module. On Day 2 of this NTI, participants will further delve into various aspects of the modules with focus on implementation and differentiation.

Grade level-K,1, 2,3, 4,5

2 min

Slide 2

Our objectives for this session are to explore Grade X–Module 1 in order to:

· Identify key components of the module structure and of each lesson within A Story of Units.

· Articulate the instructional focus of Grade X–Module 1 lesson sequence.

· Examine lesson components including Fluency Practice, Application Problems, Concept Development with Problem Sets, and Student Debrief with Exit Tickets.

NOTE TO FACILITATOR: During this session, encourage participants to make note of any concerns they have as they prepare to implement this module. Sticky notes are provided in the table baskets and parking lots are designated on the wall for this purpose. In our sessions tomorrow, time is set aside to discuss the concerns of the group and to consider ways to overcome any anticipated obstacles.

1 min.

Slide 3

We’ll start with reviewing the module structure, then examine the Module Overview, Assessments, and Topic Openers. Next, we’ll study a lesson in great detail, uncovering the intentionality behind the instructional choices. Finally, we will take a broader look at coherence across the module.

Let’s start our review of the module structure, which is consistent across all modules of all grades in A Story of Units, by taking a quick look at the curriculum map.

Section: Review of Module Structure

Time: 1:04-1:08


1. Describe the structure and function of the Module Overview to lay the groundwork for the coherence of the curriculum.

1. Describe the structure and function of the Topic Opener as a more detailed explanation of the concept development.

1. Explain how participants can use these documents for planning their lessons and materials for class.



· A Story of Units: A Curriculum Overview for Grades P-5

Time



GROUP

2 min.

Slide 4

Move/adjust circle on slide to identify the appropriate module for this session.

Let’s start by looking at the curriculum map, found on page 3 of A Story of Units: A Curriculum Overview for Grades P-5. What information do you already know from this map? (Encourage participants to share their observations.)

NOTE TO FACILITATOR: If participants have not previously explored the Curriculum Overview and examined this map, it may be helpful to prompt them with the following questions. Make sure the following points are addressed, even if you need to state them directly.

· What is the title of this module? (Place Value, Rounding, and Algorithms for Addition and Subtraction)

· How many instructional days are allotted for this module? (25 days)

· What modules, prior to this one, might prepare students for success in this module? (G2-M2, M3, M5)

· What modules, beyond this one, might build on the concepts of this module? (G5-M1, M2)


2 min.

Slide 5

Let’s take a minute to review the organizational structure of A Story of Units:

· A Story of Units: A Curriculum Overview for Grades P-5 provides a curriculum map and grade-level overview. The curriculum map provides an at-a-glance view of the entire story, making clear the coherence of the curriculum and the role that each module plays in that progression.

· 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, but every lesson is designed for a 60 minute instructional 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

Section: Examination of Module Overview, Assessments, and Topic Openers

Time: 1:08-1:44


· Independently read text from overviews, topic openers to become familiar with the specific content of the modules.

· Complete assessments to understand the focus of the content.

· Group discussions about overviews, topic openers and assessments for common understanding with colleagues.



· Pre selected Module Overviews, Assessments and Topic Openers

Time



GROUP

1 min.

Slide 6

Now that we all understand the basic module structure, let’s examine the Module Overview, Assessments, and Topic Openers which provide detailed information for educators to understand both the content and pedagogical approaches of the lessons.


9 min.

Slide 7

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 in order to identify the content and the instructional path for teaching it.

(CLICK TO ADVANCE SECOND BULLET) As you read, mark important information that will help educators understand the content and prepare to implement this module. You might do so using a symbol, such as a star, or by highlighting essential portions.

8 min.

Slide 8

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.OA.3, 4.NBT.1, 4.NBT.2, 4.NBT.3, 4.NBT.4)

· How is each standard addressed by the content of this module? (NBT1, 2, 3 are introduced initially. NBT4 and OA3 are taught alongside each other in the 2nd half.)

· Which standards are foundational to this module? (3.OA.8, 3.NBT.1, 3.NBT.2) 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, 2, 3, 5 and 6) 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 does the Terminology provided inform instruction for this module? (Algorithm, variable, ten thousands, hundred thousands, millions)

1 million is the extent of G4 standards, but we teach ten million and hundred million and billion on the PV chart to establish the pattern of base-10.Patterns are established after an interval of 3 (thousand, million, billion).

Grade 3 uses variables in the equations, but do not give the term. Grade 3 uses “letter” to represent the unknown. It is introduced here in G4-M1.

Algorithm is brand new, as special strategies have been taught until now.

· How do these Tools and Representations support instruction in this module? (Place value charts and cards, number lines)

PV charts are used throughout and are needed in the Student Personal Boards across the module.

PV cards can be used when comparing numbers to help lower performing students, but are not used in any particular lesson.

Specifically mention Vertical Number Line, and it’s importance to lining up digits in order to compare.

Show example of number 536, 535, 563 vertically and horizontally on the Elmo.

· What do you know about the assessments included in this module? (answer)

The last question of each assessment, mid or end, is cumulative and is provided in a context.

Students provide direct answers as well as explanations to explain their reasoning and understanding of the subject.

Various responses (written, numerical, fill in the blank, extended response)

Include the black line master, standards, rubric, and student work.

Student responses include samples of correct answers and thoughts students may have. Credit is given for correct responses; various representations of the answers may appear.

2 min

Slide 9


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.OA.3, 4.NBT.1, 4.NBT.2, 4.NBT.3, 4.NBT.4)

· How is each standard addressed by the content of this module? (NBT1, 2, 3 are introduced initially. NBT4 and OA3 are taught alongside each other in the 2nd half.)

· Which standards are foundational to this module? (3.OA.8, 3.NBT.1, 3.NBT.2) 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, 2, 3, 5 and 6) 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 does the Terminology provided inform instruction for this module? (Algorithm, variable, ten thousands, hundred thousands, millions)

1 million is the extent of G4 standards, but we teach ten million and hundred million and billion on the PV chart to establish the pattern of base-10.Patterns are established after an interval of 3 (thousand, million, billion).

Grade 3 uses variables in the equations, but do not give the term. Grade 3 uses “letter” to represent the unknown. It is introduced here in G4-M1.

Algorithm is brand new, as special strategies have been taught until now.

· How do these Tools and Representations support instruction in this module? (Place value charts and cards, number lines)

PV charts are used throughout and are needed in the Student Personal Boards across the module.

PV cards can be used when comparing numbers to help lower performing students, but are not used in any particular lesson.

Specifically mention Vertical Number Line, and it’s importance to lining up digits in order to compare.

Show example of number 536, 535, 563 vertically and horizontally on the Elmo.

· What do you know about the assessments included in this module? (answer)

The last question of each assessment, mid or end, is cumulative and is provided in a context.

Students provide direct answers as well as explanations to explain their reasoning and understanding of the subject.

Various responses (written, numerical, fill in the blank, extended response)

Include the black line master, standards, rubric, and student work.

Student responses include samples of correct answers and thoughts students may have. Credit is given for correct responses; various representations of the answers may appear.

Slide 10

7 min.

Slide 11

Before we move on to our lesson study, let’s take a few minutes to further examine an assessment that accompanies this module. Turn to the first page of the assessment. Consider each item and determine which standards are being addressed and how.

Allow participants 5 minutes to complete this standards-alignment. 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.

NOTE TO FACILITATOR: Direct participants to examine either the Mid- or End-of-Module Assessment. Make this choice based on which lesson you have selected for the Lesson Study portion of the session (e.g., use Mid- if your lesson falls in the first half of the module).

8 min.

Slide 12

Now that we’ve spent some time becoming familiar with our Module Overview and Assessments, let’s zoom in a level and look closely at a Topic Opener. Remember, each module is divided into topics. Within a given topic, the lessons work together to build strong understanding of a set of related concepts. I’ll quickly assign one Topic to each table in our group.

(CLICK TO ADVANCE FIRST BULLET) Take 3 minutes to review your Topic Opener. Be prepared to report to the group about the topic opener that you read/discussed.

(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 3 minutes for participant to read and discuss their assigned 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.

3 min.

Slide 13

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 1 minute for participants to turn and talk about the topic openers. Then facilitate a whole-group discussion about the following questions:

· How does each topic contribute to the overall instructional goal of the module? (answer)

· How are the Topic Openers useful as a planning tool? (answer)

· What is the relationship between the Topic Opener and the other components of the module? (It repeats information from the Module Narrative, but includes further details or images to give the instructor further information for teaching this Topic.)

Section: Lesson Study

Time: 1:44-3:05


· Engage in deep study of single lesson that contains all of the foundational concepts to improve ability to implement classroom instruction.

· Study and practice fluency exercises, application problems, problem sets, debriefs and exit tickets to become familiar with each component.

· Reflect on takeaways, key points and next steps to solidify understanding and develop a plan for implementation.



· Pre selected lesson

Time



GROUP

30 secs.

Slide 14

Now that we have examined the Module Overview, Assessments, and Topic Openers, let’s study a lesson and its components in detail.


6 min.

Slide 15

Now that we’ve seen both the Module Overview and Assessments as well as the Topic Openers, let’s zoom in another level and look at a specific lesson in this module.

NOTE TO FACILITATOR: Provide the context for the selected lesson. How does it fit into the overall progression of the module? Why did you select it as the focus of the Lesson Study?

· This lesson exemplifies 4.NBT.1 which is foundational for understanding the value of each digit on the place value chart.

· At the beginning of the year, teachers tend to breeze through place value lessons, either because students get bored too quickly, teachers think students understand, or teachers are not interested in teaching it. We find this lesson, and other place value lessons in the previous critical to the students’ basic and principal understandings of mathematics.

In your binders in the 3rd blue tab labeled K-5 Lesson 1, look to the 6th stapled packet to find Lesson 1 of Grade 4 Module 1. Skim through the Concept Development. Notice the use of place value disks in teaching place value, and how the lesson advances to using place value disks as representation in Problem 4. This lesson teaches ones, tens, hundreds and thousands.

Now find Lesson 2, our focus lesson for today in the right pocket of your red folder.

Take 4 minutes to read this lesson. (Allow 4 minutes for independent review of the lesson.)

You probably noticed a few structural changes that have been implemented since the last NTI:

· Each lesson objective is stated at beginning of lesson and in the Student Debrief.

· Notes are provided to describe the connection of each Fluency activity and Application Problem.

· Worksheets are now called “Problem Sets.”

· Scaffolds are structured according to the UDL framework, rather than being specific to one population of students.

Now that you’ve had a chance to briefly review the lesson in it’s entirely, let’s look at each component individually. As we do this, we will consider both the general function of the component and it’s specific function within this lesson. Throughout this session, keep in mind that each part of the lesson works together to implement the instructional shifts and achieve rigor. We’ll start with the Fluency Practice.

2 min.

Slide 14

Fluency represents a major part of the instructional vision that shapes A Story of Units. In this curriculum, fluency is a daily, substantial, and sustained activity supported by the lesson structure.

(CLICK TO ADVANCE SECOND BULLET) A Story of Units includes about 10 to 20 minutes of daily fluency work. A variety of suggestions for fluency activities are offered. They are strategically designed for the teacher to easily administer and assess. Note that the time spent each day will vary depending on the lesson and your students’ current skill level.

(CLICK TO ADVANCE THIRD BULLET) The fluency activities in A Story of Units are generally high-paced and energetic, getting students’ adrenaline flowing, and creating daily opportunities to celebrate improvement. From the beginning of the year, students see their accuracy and speed measurably increase both as individuals and as a class. Like opening a basketball practice with team drills and exercises, both personal and group improvements are exciting and prepare the players for the application in the game setting.

(CLICK TO ADVANCE FOURTH BULLET) Fluency promotes automaticity, a critical capacity that allows students to reserve their cognitive resources for higher-level thinking.

(CLICK TO ADVANCE FIFTH BULLET) By encouraging students to recognize patterns and make connections within the lessons, the fluency exercises in A Story of Units support the other two components of rigor as well as the Standards for Mathematical Practice.

2 min.

Slide 17

Fluency activities serve a variety of purposes. In general, there are three main categories of fluency work:

· Maintenance: Staying sharp on previously learned skills

· Preparation: Targeted practice for the current lesson

· Anticipation: Building foundational skills to prepare students for the in-depth work of future lessons

It is important to recognize that fluency work is always an extension of familiar content. It provides a daily opportunity for continuous improvement and individual success toward acquiring speed and accuracy

10 min.

Slide 18

Please look to the Skip Counting Fluency on the 1st page of Lesson 2. This Fluency practices counting by 3s and 4s. Our first lesson was on the multiplicative comparative. This links to this fluency. Remember fluency is meant as fast quick moving activity. Each fluency activity has a standard attached to it.

Please stand up. I will lead you through this fluency.

Find the place value template in the back of your red folder. Slide it into your sleeve the the personal board.

Now choose a leader at your table to lead the fluency for Place Value. You will have 2 minutes. Change leaders every 30 seconds so many people can lead a fluency at your table.

4 min.

Slide 17


Allow 2 minutes for participants to turn and talk about the Fluency Practice. Then facilitate a discussion that summarizes the mathematical significance of these fluencies in relation to this lesson/topic/module.

12 min.

Slide 18

Please look to the Skip Counting Fluency on the 1st page of Lesson 2. This Fluency practices counting by 3s and 4s. Our first lesson was on the multiplicative comparative. This links to this fluency. Remember fluency is meant as fast quick moving activity. Each fluency activity has a standard attached to it.

Please stand up. I will lead you through this fluency.

Find the place value template in the back of your red folder. Slide it into your sleeve the personal board.

Now choose a leader at your table to lead the fluency for Place Value. You will have 2 minutes. Change leaders every 30 seconds so many people can lead a fluency at your table.

2 min

Slide 19


Allow 2 minutes for participants to turn and talk about the Fluency Practice. Then facilitate a discussion that summarizes the mathematical significance of these fluencies in relation to this lesson/topic/module.

2 min.

Slide 20

Now let’s examine another component of this lesson, the Application Problems. The placement of an application problem may go before or after the conceptual development. Placement before can provide important context and structure to understanding a new concept; placement after gives usefulness of a just-learned concept. Either way, students are challenged to use relevant conceptual understandings and appropriate strategies, even when not prompted to do so.

The amount of time allotted to this lesson component varies, but generally accounts for 10 to 20 minutes of the daily instruction.

The RDW process is modeled and practiced throughout the curriculum. Let’s try it now using the Application Problem from our selected lesson.

1. Read.

2. Draw and label.

1. What do I see?

2. Can I draw something?

3. What conclusions can I make from my drawings?

3. Write a number sentence. (equation)

4. Write a word sentence. (statement)

our selected lesson

Slide 21

Lead the participants through the Application. Model as you would in your classroom, describing at each point the choices you made as a “teacher” in order to guide your students through this process.

Allow time for participants to share their work with others at the table. Perhaps have some show their work to the group by using the document camera.

Consider the introduction of the Application Problem within the lesson. Having read through the lesson, what is the connection of the problem to the other lesson components? Notice that, although a note is provided, explicit instructions do not accompany the Application Problem. What specific choices would you make using this problem in your classroom?

NOTE TO FACILITATOR: Be prepared to discuss various possible instructional choices (i.e., whole group vs. small group vs. independent work) as well as the relevance of this problem in the lesson. Don’t just focus on the routine here. Mathematically, why is this problem important?

2 min.

Slide 22

Now let’s examine another component of this lesson, the Concept Development.

· The Concept Development constitutes the major portion of instruction and generally comprises at least 20 minutes of the total lesson time.

· It is the primary lesson component, in which new learning is introduced. Intentional sequencing of standards and topics within modules ensures that students have the requisite understanding to fully access new learning goals and integrate them into their developing schemas.

· Many Concept Developments articulate the standards and topics through a deliberate progression of material, from concrete to pictorial to abstract. This structure compliments and supports an increasingly complex understanding of concepts.

18 min.

Slide 23

Lead the participants through the Concept Development, including at least part of the Problem Set, describing at each point the choices you made as a “teacher” in order to guide your students through this process.

Consider the Concept Development and its accompanying Problem Set within this lesson.

· Having read through the lesson, what is the connection to the other lesson components?

Problem 1

Multiplying single units by 10 connects to Fluency

Divide by 10 extends the Fluency

Problem 2

Note this extends beyond the Grade 4 standard of working within 1 million.

Problem 3

MP 1: Make sense of problems and preserver in solving them

How does this apply here? Talk at your tables. (We move from multiplication to division.)

Problem 4

Multiple units using multiplication and division

Representation of dots and standard form on the PV chart.

· Notice that, the Concept Development elaborates on the “how-to” of delivery through models, sample vignettes, and dialogue, all meant to give teachers a snapshot of what the classroom might look and sound like at each step of the way.

· Teachers’ word choice may be different from that in the vignettes, and they should use what works from the suggested talking points, along with their knowledge of their students’ needs, as they write their own. What specific choices would you make using this Concept Development in your classroom?

Be prepared to discuss various possible instructional choices in the lesson.

5 min.

Slide 24

Lead the participants through the Concept Development, including at least part of the Problem Set, describing at each point the choices you made as a “teacher” in order to guide your students through this process.

Consider the Concept Development and its accompanying Problem Set within this lesson.

· Having read through the lesson, what is the connection to the other lesson components?

Problem 1

Multiplying single units by 10 connects to Fluency

Divide by 10 extends the Fluency

Problem 2

Note this extends beyond the Grade 4 standard of working within 1 million.

Problem 3

MP 1: Make sense of problems and preserver in solving them

How does this apply here? Talk at your tables. (We move from multiplication to division.)

Problem 4

Multiple units using multiplication and division

Representation of dots and standard form on the PV chart.

· Notice that, the Concept Development elaborates on the “how-to” of delivery through models, sample vignettes, and dialogue, all meant to give teachers a snapshot of what the classroom might look and sound like at each step of the way.

· Teachers’ word choice may be different from that in the vignettes, and they should use what works from the suggested talking points, along with their knowledge of their students’ needs, as they write their own. What specific choices would you make using this Concept Development in your classroom?

Be prepared to discuss various possible instructional choices in the lesson.

8 min.

Slide 25

Complete the Problem Set. As you do so, take note of the sequence. What do you notice?

· Move from 2, 3, to 4

· Move from ten, hundreds, to thousands, to ten thousands

· What is the value of Questions 4 and 5? Why should teachers choose to complete these problems over completing every problem in number 1 or 2?

NOTE TO FACILITATOR: Be prepared to discuss the progression of mathematical ideas from simple to complex throughout the Concept Development and, specifically, in the Problem Set.

2 min.

Slide 26

Like the other lesson components, the Student Debrief section includes sample dialogue or suggested lists of questions to invite the reflection and active processing of the totality of the lesson experience. The purpose of these talking points is to guide teachers’ planning for eliciting the level of student thinking necessary to achieve this. Rather than ask all of the questions provided, teachers should use those that resonate most as they consider what will best support students in reaching self-articulation of the focus from the lesson’s multiple perspectives.

Rather than stating the objective of the lesson at its beginning, we wait until the dynamic action of the lesson has taken place. Students then reflect back on it to analyze the learning that occurred, articulate the focus of the lesson, and make connections between parts of the lesson, concepts, strategies, and tools on their own. We recognize or introduce key vocabulary by helping students appropriately name the learning they describe.

Sharing and analyzing high quality work gives teachers the opportunity to model and then demand authentic student work and dialogue. Conversation constitutes a primary medium through which learning occurs in the Student Debrief. Teachers can prepare students by establishing routines for talking early in the year. For example, “pair-sharing” is an invaluable structure to build for this and other components of the lesson. During the debrief, teachers should circulate as students share, noting which partnerships are bearing fruit, and which need support. They might join struggling communicators for a moment to give them sentence stems. Regardless of the scaffolding techniques that a teacher decides to use, all students should emerge clear enough on the lesson’s focus to either give a good example or make a statement about it.

“Exit Tickets” close the Student Debrief component of each lesson. These short, formative assessments are meant to provide quick glimpses of the day’s major learning for students and teachers. Through this routine, students grow accustomed to showing accountability for each day’s learning and produce valuable data for the teacher that becomes an indispensable planning tool.

Slide 27

Lead the participants through the Student Debrief, describing at each point the choices you made as a “teacher” in order to guide your students through this process. Administer the Exit Ticket. “Assign” homework to be done after school.

Point 1: Extend past 1 million, to create patterns

Point 3: Shifting, movement of decimal. Talk amongst table. Discuss as a whole.

Point 6: Talk amongst the table

Point 7: Talk amongst your table

Point 8: 6 tens times 10, what are we multiplying? Talk to your table.

Point 11: Multiply by 10, change the digits or units? Make examples at your table.

NOTE TO FACILITATOR: Be prepared to discuss various possible instructional choices in the Debrief.

Complete Exit ticket if time allows.

Slide 28

Lead the participants through the Student Debrief, describing at each point the choices you made as a “teacher” in order to guide your students through this process. Administer the Exit Ticket. “Assign” homework to be done after school.

Point 1: Extend past 1 million, to create patterns

Point 3: Shifting, movement of decimal. Talk amongst table. Discuss as a whole.

Point 6: Talk amongst the table

Point 7: Talk amongst your table

Point 8: 6 tens times 10, what are we multiplying? Talk to your table.

Point 11: Multiply by 10, change the digits or units? Make examples at your table.

NOTE TO FACILITATOR: Be prepared to discuss various possible instructional choices in the Debrief.

Complete Exit ticket if time allows.

4 min.

Slide 29

What do you notice looking at the Distribution of Instructional Minutes for the lessons in this module?

All four lesson components provide opportunities to nurture the Standards of Mathematical Practice.

4 min.

Slide 30

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.

1 min.

Slide 31

Let’s review the key points so far which were stated at the start of this session in the objectives :

· Modules Overviews and Topic Openers provide essential information about the instructional path of the module and are key tools in planning for successful implementation.

· Each of the lesson components are necessary in order to achieve balanced, rigorous instruction and to bring the Standards to life.

· The Exit Ticket is an essential piece of the Student Debrief and provides daily formative assessment.

· Opportunities to nurture the Standards for Mathematical Practice are embedded throughout the lesson.

Section: Coherence Across the Module

Time:3:05-4:15


· Review and discuss progression documents to identify the sequence of instruction.

· Review the remaining lessons in the module to determine how the sample lesson fits in the lesson sequence.

· Analyze the problem sets and their role in assessment to determine the intentional sequence of concept development.



· NBT Progression document with preselected portions

· Module X

Time



GROUP

1 min.

Slide 32

That concludes our Lesson Study. When we return from the break, we’ll take a look at coherence across the module.


10 min.

Slide 33

To continue our study of Module 1, we’re going to first take some time to examine a portion of the Progression document that serves as the foundation for this module. You’ll have about 10 minutes to read through the document independently or with a partner. As you read, highlight the information that is relevant to the content of this module.

Allow participants 10 minutes to read independently. Encourage them to highlight and make notes.

NOTE TO FACILITATOR: Your group will be provided with the Progression that best aligns with the content and focus standards of this module. Determine which passage of the given Progression is most relevant for your lesson study (may include multiple grades).

5 min.

Slide 34

How does this module implement the expectations described in the Progression that we just read? What particular portions of the module are evidence for this? Turn and talk with a partner at your table, and then you’ll have an opportunity to share your thoughts.

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

15 min.

Slide 35

Earlier, we examined a single lesson in great detail and recognized the coherence within the lesson. Now that you’ve had an opportunity to see the development of the mathematical concepts outlined in the Progression document, let’s take some time to return to Module 1 for a broader view of coherence across the lessons.

We’ve provided a sample of lessons that illustrate the development of Module 1. With your partners or table groups, analyze the progression of each of the lesson components using the guiding questions provided here. Be prepared to share your observations with the group.

Allow 15 minutes for participants to complete this analysis. Then advance to the next slide.

NOTE TO FACILITATORS: The “sample of lessons provided” will be distributed as handout during your session. You have some latitude in selecting these. For example, you could choose a single topic or several non-consecutive lessons depending on what you feel gives the best representation of the development of mathematical concepts over time. Including the lesson examined in the Lesson Study, aim for 5 or 6 total.

5 min.

Slide 36

Facilitate a discussion. Be sure to include answers to the provided questions, specifically addressing the progression of mathematics in Module 1.

· What does the sequence of Fluency Practices accomplish as a whole?

· L9: Multiply, round; L10: Round, multiply; L11: Round, multiply, add units; L12: Round, Mental math sums; L13: Sums, Differences

· How does the sequence of Application Problems connect to topic/module?

· Reviews previous lesson content, some bridge

· Highlight Lesson 11

· How does the sequence of Concept Development and Student Debrief build toward mastery of the topic/module?

· Rounding proves your understanding of place value knowledge

· Rounding allows students to estimate answers to addition and subtraction

· All use and support place value knowledge, building upon each other, level of complexity builds on each lesson

7 min.

Slide 37

Now we’re going to examine the careful sequencing within each problem set. Then, as a group, we’ll consider the ways in which this sequencing can also be seen through the progression of the module. With your table, analyze the selected Problem Set.

NOTE TO FACILITATOR: Assigned different Problem Sets to each table so that all Problem Sets from your selected lessons are addressed within the group.

Allow 7 minutes for discussion by the table groups, then advance to the next slide.

8 min.

Slide 38

Facilitate a discussion by inviting the tables to share out in sequential order beginning with the first lesson in the set and progressing to the final lesson in the set.

NOTE TO FACILITATOR: Be prepared to lead an insightful discussion about each of the Problem Sets individually as well as collectively.

Sequence simple to complex

Number relationships

Purposeful number choice

Familiar context for word problems

Careful use of vocabulary

Use of RDW in word problems

Use of zero, not separating the use of zero to a particular lesson

Careful scaffolding of questioning

Formats of problem sets align with assessments

4 min.

Slide 39

Take one minute to reflect on this session. What, in your opinion, 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.)

1 min.

Slide 40

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

NOTE TO FACILITATOR: As you prepare the previous slides examining the Progression document and coherence within the module, articulate the key points from your study of Module 1 on this slide.

Make 10, break 10

Make a 10, break a 10 (K-1)

Bundle a 10, unbundle a 10 (1-5)

Change a 10 ones for 1 ten, change 1 ten for 10 ones (2-5)

Rename 10 ones as a ten, rename 1 ten as 10 ones (2-5)

Regroup 10 ones as a ten, rename 1 ten as 10 ones (2-5)

Compose a larger unit from a smaller unit, decompose a larger unit into smaller units (4-5)

5 min.

Slide 41

As we end this session, take a moment to reflect on the objectives of this session, either privately or with your colleagues and answer these questions about your next steps:

· How can you transfer what you know about the structure of a module and its key components to next steps in the planning process?

· What is your plan for sharing this module with the administrators/teachers at your school(s)/districts(s)?

· What is your plan for redelivery 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

· PowerPOints

· Handouts

Additional Suggested Resources

· How to Implement A Story of Units

© 2012 Common Core, Inc. All rights reserved. commoncore.org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units

Module Overview •  Focus Standards

•  FoundaBonal Standards

•  MathemaBcal PracBces

•  Terminology

•  Tools and RepresentaBons

9

©2012CommonCore,Inc.Allrightsreserved.commoncore.org

NYSCOMMONCOREMATHEMATICSCURRICULUM

AStoryofUnits

ModuleOverview

• FocusStandards

• FoundaonalStandards

• MathemacalPracces

• Terminology

• ToolsandRepresentaons

9



Standards for Mathema>cal Prac>ce

10

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quanCtaCvely. 3. Construct viable arguments and criCque others’. 4. Model with mathemaCcs. 5. Use appropriate tools strategically. 6. AKend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.



AStoryofUnits

StandardsforMathemacalPracce

10

1.Makesenseofproblemsandpersevereinsolvingthem.

2.Reasonabstractlyandquantavely.

3.Constructviableargumentsandcriqueothers’.

4.Modelwithmathemacs.

5.Useappropriatetoolsstrategically.

6.Aendtoprecision.

7.Lookforandmakeuseofstructure.

8.Lookforandexpressregularityinrepeatedreasoning.



Lesson Study: Fluency PracBce

18



AStoryofUnits

LessonStudy:FluencyPracce

18



Lesson Study: Fluency PracBce

•  In what skills should students be fluent in order to achieve success in this module?

•  At your table, examine the Fluency PracDces in this lesson, considering their specific funcDon within the lesson.

19



AStoryofUnits

LessonStudy:FluencyPracce

• Inwhatskillsshouldstudentsbefluentinorder

toachievesuccessinthismodule?

• Atyourtable,examinetheFluency

Praccesinthislesson,considering

theirspecificfunconwithinthelesson.

19



Lesson Study: ApplicaBon Problems

21

Amy is baking muffins. Each baking try can hold 6 muffins.

a)  If Amy bakes 4 trays of muffins, how many muffins will she have all together?

b)  The corner bakery has made 10 Gmes as many muffins as Amy baked. How many muffins did the bakery produce?

Bonus: If the corner bakery packages the muffins in boxes of 100, how many boxes of 100 could they make?



AStoryofUnits

LessonStudy:ApplicaonProblems

21

Amyisbakingmuffins.Eachbakingtrycanhold6muffins.

a) IfAmybakes4traysofmuffins,howmanymuffinswill

shehavealltogether?

b) Thecornerbakeryhasmade10mesasmanymuffins

asAmybaked.Howmanymuffinsdidthebakery

produce?

Bonus:Ifthecornerbakerypackagesthemuffinsinboxes

of100,howmanyboxesof100couldtheymake?



Lesson Study: Concept Development

23



AStoryofUnits

LessonStudy:ConceptDevelopment

23




24



AStoryofUnits


24




•  Complete the problem set. •  What do you no?ce about the

sequence of problems?

25



AStoryofUnits


• Completetheproblemset.

• Whatdoyounoceaboutthe

sequenceofproblems?

25



Lesson Study: Student Debrief

27



AStoryofUnits

LessonStudy:StudentDebrief

27



Lesson Study: Student Debrief

28



AStoryofUnits

LessonStudy:StudentDebrief

28



Key Points

40

•  The base-‐10 system allows for consistency across all units. •  Consistency applies to rounding, as the methods used in Grade 3 rounding are applied to Grade 4 rounding of larger units.

•  “10 Dmes as much” builds on the understanding of bundling groups of 10.

•  “Bundling” and “unbundling” from Grade 2 progresses to the addiDon and subtracDon algorithms.



AStoryofUnits

KeyPoints

40

• Thebase-10systemallowsforconsistencyacrossallunits.

• Consistencyappliestorounding,asthemethodsusedinGrade3roundingareappliedto

Grade4roundingoflargerunits.

• “10mesasmuch”buildsontheunderstandingofbundlinggroupsof10.

• “Bundling”and“unbundling”fromGrade2progressestotheaddionand

subtraconalgorithms.

Documents

· Web viewA Story of Units- Module Focus. Grade 4. Sequence of Sessions. Overarching Objectives of this May 2013 Network Team Institute. Participants will understand the focus