A Story of Units - Module Focus Grade 3 Module 2

Sequence of Sessions

Overarching 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

· 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.

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?

1. Understand the key components of Module 2 Topic C and the lessons within it

1. Understand the progressions used within Module 2

1. Understand and be able to describe how to share the information and use it 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 2 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 how they will differentiate instruction.

Session Overview

Section

Time

Overview

Prepared Resources

Facilitator Preparation

Session Introduction

10:45- 10:49

· 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

10:50-11:01

· Review module structure and consistency across the grades

· Module 2

· Review appropriate module

Examination of Module Overview and Assessments

11:01-12:00

Study and discuss

· Overviews

· Assessments

· Topic Openers

· Module 2

· Session PowerPoint

· Review appropriate module

Lesson Study

1:00-2:32

· Detailed study with discussion and practice of module components

· Review key points

· Module 2

· Session PowerPoint

Review appropriate module

Implement the Module

2:32-3:00

· Progression study and discussion

· Module 2

· Session PowerPoint

· Review appropriate module

Session Roadmap

Section: 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.

1 min

2.

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? (Call for a show of hands.) School-level leaders? Principals? District-level leaders? BOCES representatives?

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 have in common is the need to deeply understand the mathematics and the intentional instructional sequence in which the curriculum brings it 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.

1 min.

3.

Our objective for this session is to prepare to implement G3-M2, making appropriate instructional choices to meet the needs of students while maintaining the balance of rigor that is built into the curriculum.

1 min

4.

In this session, we’ll begin by spending some time with the MD and NBT progressions documents 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 series 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 Progressions documents, let’s take a quick look at the curriculum map to see how this module fits into the overall plan for Grade 3.

Section: Study of the Progression Document

Time: 10:50 – 11:01 [12 minutes]

In this section, you will…

1. Describe the structure and function of the Module Overview

1. Describe the structure and function of the Topic Opener

1. Explain how participants can use these documents as they plan their lessons and materials for class

Materials used include:

· Session PowerPoint

· Geometric Measurement Progression

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. Those who participated in the May NTI will recall that we deeply examined Grade 3 Module 1. 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? (Place Value and Problem Solving with Units of Measure)

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

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

What modules, beyond this one, might build on the concepts of this module? (G4-M1, G4-M2

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. This portion describes the mathematical concepts that will be developed, especially throughout the first half of lessons.

You’ll have about 4 minutes to read through the document independently. Then you’ll have an opportunity to discuss your thoughts with others at your table.

Allow participants 4 minutes to read independently. Then have them look at the lesson objectives for the first 11 lessons and discuss the reflection questions.

7 min.

7.

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, especially throughout the first half of lessons.

You’ll have about 4 minutes to read through the document independently. Then you’ll have an opportunity to discuss your thoughts with others at your table.

Allow participants 4 minutes to read independently. Then have them look at the lesson objectives for the first 10 lessons and discuss the reflection question.

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.

Section: Examination of Module Overview and Assessments

Time: 11:02-11:54

[52 minutes] In this section, you will…

· Independently read text from overviews, topic openers

· Complete assessments

· Group discussions about overviews, topic openers and assessments

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

9.

For those of you who may be unfamiliar with A Story of Units, I’ll take 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.

.

11 min

10.

Take 8 minutes to read the Module Overview. As you read, highlight key phrases that help build a picture of what the learning in this Module will look like. After you finish reading, gather your thoughts by jotting down 1-2 sentences that summarize the major learning of the module.

(Allow 1 minute for jotting.)

Turn and talk with others at your table. Share observations about what is new or different to you about the way these concepts are presented. (Allow 2 minutes for discussion.)

5 min.

11.

Each Overview contains multiple components that together articulate the focus of the module. These components include the following. (Quickly walk through the components using the questions below to guide you in each section.)

· Descriptive narrative (just read)

· 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

Guiding Questions:

· Which standards are the focus of this module? (3.NBT.1, 3.NBT.2, 3.MD.1, 3.MD.2)

· How is each standard addressed by the content of this module? (answer in brief discussion; participants reference lesson objective chart/overview narrative)

· Which standards are foundational to this module? (2.MD.1, 2.MD.3, 2.MD.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.2, 4, 6 and 7) While teachers will promote all practices on a regular basis as opportunities arise, the practices listed in the Overview are particularly appropriate for the lessons in this module. Activity-specific suggestions are provided in the lessons themselves.

· Read over the Terminology and Tools and Representations. How do they inform instruction for this module? (answer in brief discussion)

· What do you know about the assessment included in this module? (which standards each addresses)

8 min.

12.

Now that you know the focus of the module, let’s study how students are assessed on their mastery. Turn to the first page of the mid-module assessment.

Participants complete the assessment. Allow 4 minutes. Participants then move on to checking their work using the rubric and sample work provided. They analyze the standards alignment provided by the rubric (allow 4 minutes).

10 mins

13.

The final page of the End-of-the-Module assessment is a timed fluency task. It directly assesses student progress toward mastery of 3.OA.7, (multiplication and division facts to 10), which is the major fluency for Grade 3. The fluency in M2 continues to systematically support this goal, even though it’s not the module focus.

Since this part of the assessment is timed, we’ll complete this portion of the assessment altogether first. Flip the assessment to page 5. Pencils ready, you have 100 seconds to complete as many problems as you can. Work left to right across the page. Ready, go!

(Time participants as they take the fluency assessment.)

Stop! Now turn to the first page of the assessment and work through the remaining questions at your own pace.

Participants complete the assessment. Allow 4 minutes of independent work time. Participants then move on to checking their work using the rubric and sample work provided. They analyze the standards alignment provided by the rubric (allow 4 minutes).

5 mins

14.

Look back at the lesson objectives and compare them with the Mid- and End-of-Module assessments. Notice how the assessments reflect the objectives. Talk to your neighbor, what growth will students make in this module? Which concepts do you expect will be most challenging?

Participants keep these challenges in mind for the lesson study, using them to guide their exploration.

4 mins

15.

Now that we have a big picture understanding of the growth that students are expected to make, let’s talk about how we might create ongoing support for them based on their assessment results. Let’s look specifically at how you might use the fluency portion of the End-of-Module assessment to plan instruction.

The fluency page in the End-of-Module assessment is part of a longitudinal assessment that spans M1-M3 and assesses student mastery toward the major fluency of Grade 3 (3.OA.7). With each module the fluency page grows in complexity, making this particular example the middle of the road in difficulty. For “Question 6” on the End-of-the-Module assessment rubric, guiding questions are presented as lenses through which you might analyze the fluency.

These are the questions (click to make questions appear). Each pair at your table will take a different question. Suppose that the answer to your question is “yes” and discuss what kinds of mistakes you would expect to see. Divide and discuss at your table now (allow a maximum of 2 minutes).

8 mins

16.

Call for group attention.) With your partner, take a few minutes to browse the fluency activities in Module 2. Based on the particular need you’re working with, which activities might you use to review a concept, or build into future lessons? Why? Be prepared to share your ideas with others.

Allow 4-5 minutes for participants to identify activities. Then lead a quick discussion in which participants who “researched” each question share their ideas with the whole group. Close the discussion by reminding participants that they might use these ideas to shape the allotted day for remediation, or build them into future instruction. A similar process can be followed to analyze and use the data gathered for other concepts tested by the assessments as well.

17.

Enjoy your lunch and see you back in an hour

Section: Exploration of Selected Lessons

Time: 1:00 – 2:32

[81 minutes] In this section, you will…

· Engage in deep study of single lesson that contains all of the foundational concepts

· Study and practice fluency exercises, application problems, problem sets, debriefs and exit tickets

· Reflect on takeaways, key points and next steps

Materials used include:

· Module 1 and lesson components

Time

Slide #

Pic of Slide

Script/ Activity directions

GROUP

1 min

18

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

19

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 Topic Openers. 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. For Grade 3 Module 2, we have 5 topic openers.

Note to facilitator: quickly review the parts of a topic opener. Point out the “links from,” which is especially helpful for Special Education teachers who may have students lacking the skills for the group of lessons in any given topic. “Links From” can tell a teacher which prior modules are helpful if students need more support.

Each pair at your table will read a different Topic Opener (A, B, D, E; C is excluded for now.) We will be looking at the Topic C Opener altogether after we read the other topics. Take 3 minutes to review your Topic Opener. Be prepared to report to the group about the topic opener that you read/discussed. As you read, mark information that is key for implementation.

Allow 3 minutes for participants to read and discuss their assigned topic openers. Then have each pair report to the table on each of the topic openers sequentially, so that a clear picture of the sequence of the module unfolds.

6 min.

20.

Turn and talk with your partner about the topic opener you read. Use the questions on the slide as guiding questions to create a 1 minute summary of the topic you can share with the whole table. (2 -3 minutes)

Allow 3-4 minutes for table talk; pairs share their topic openers with others.

min.

21.

Note to facilitator: Use Topic C: Measure and Round to the Nearest Ten and Hundred, Generalizing to Round Whole Numbers Within 1000 for lesson study (L12-14).

We will read Topic C as a whole group. Use the questions on the slide as guiding questions to think about as you read.

Allow 3 minutes for participants to turn and talk about the topic opener. Then facilitate a whole-group discussion about the following questions:

· How does Topic C contribute to the overall instructional goal of the module? (It formally introduces rounding two-digit and three-digit numbers to the nearest ten and hundred. It also builds upon Grade 2 knowledge of place value. Measurement lessons are not usually directly linked to a place value module and are typically done in isolation.)

· How does Topic C bridge the concepts from the first half of the module (Topics A and B) to the second half (Topics D and E)? (Topic C bridges concrete measurements (Topics A and B) into abstract problem solving (D and E), including setting students up with a skill (rounding to estimate) for assessing the reasonableness of their calculations using measurement in Topics D and E.)

3min.

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 not familiar with A Story of Units, I’d like to point out that most lessons are comprised of four components: Fluency, Application, Concept Development, and the Student Debrief. These components work together to achieve balanced, rigorous instruction 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 in order to help students see patterns in the mathematics and think more deeply about their work.

5 min.

23.

Before we look at the lesson, let’s complete some fluency exercises to get our brains ready to round.

“Rename the tens” from Lesson 12.

T: (Write 9 tens = _____)

S: 90.

Repeat process with 10 tens, 12 tens, 27 tens, 87 tens, 84 tens, 79 tens, 113 tens

10 min.

24.

Video clip

Participants watch a segment of Lesson 9. In this segment a student creates the vertical number line using 100 milliliter increments to build 1 liter. This activity comes midway through module. It comes near the end of the measurement focus and creates a transition into the place value work that underlies the rounding and standard algorithm in the second half.

10 min.

25.

Today we will model the concept development from Lesson 12. It is the first lesson in the rounding unit where students round 2-digit measurements to the nearest 10 on the vertical number line.

Model the concept development.

3 min.

26

In the next few slides participants practice measuring and rounding various objects to simulate the “4 stations” from the Lesson 12 Problem Set.

As you take out the Lesson 12 Problem Set you will see that we have a modified version to fit our needs. Take 1 minute to read the directions for the Lesson 12 Problem Set.

Our group will move through 4 different “stations” measuring with centimeters, kilograms, milliliters, and minutes as units.

After measuring, you will apply the learning from the concept development to round each measurement to the nearest ten.

10 secs.

27.

Round the length of a pad of paper.

Actual Length: 13 cm

Rounded to the nearest ten cm: 10 cm

10 secs

28.

Round the length of a pad of paper.

Actual Length: 19 cm

Rounded to the nearest ten cm: 20 cm

10 secs

29.

Round the weight of the box.

Actual Weight: 25 kg

Rounded to the nearest ten kg: 30 kg

10 secs

30.

Round the weight of the chimp.

Actual Weight: 58 kg

Rounded to the nearest ten kg: 60 kg

10 secs

31.

Round the liquid volume in Beaker A.

Actual liquid volume: 16 mL

Rounded to the nearest ten mL: 20 mL

10 secs

32.

The liquid volume in Beaker B.

Actual liquid volume: 34 mL

Rounded to the nearest ten mL: 30 mL

10 secs

33.

Round the time of Clock A

Actual Time: 2:07

Rounded to the nearest ten minutes: 2:10

20 secs.

34.

Round the time shown on Clock B

Actual Time: 2:53

Rounded to the nearest ten minutes: 2:50

20 min.

35.

e the questions on the slide to guide your thinking as you read Lessons 13 and 14 independently. Take about 15 minutes to look those lessons over carefully and compare them.

Lead a 5 minute discussion in which participants analyze the movement of the topic. They identify concepts they expect will be most challenging and the planning they’ll need to do for successful learning outcomes.

How does each lesson add new complexity to the topic?

· In Lesson 13, the inclusion of rounding three-digit numbers to the nearest ten adds new complexity to the previous day’s learning.

· Lesson 14 concludes the module as students round three-digit and 4-digit numbers to the nearest hundred.

2 min.

36.

This is the first problem in the Lesson 17 concept development. You can see how this challenges students to transform what they have learned about rounding and apply it to make reasonable estimates. It requires students to evaluate the usefulness of rounding to the nearest ten or hundred. Understanding that rounding is not just an arbitrary procedure becomes solidified.

Students predict which way of estimating is closer by looking at the rounded numbers and thinking about how close they were to the actual numbers. In this case, students see that rounding to the nearest ten or fifty gives the most precise estimate.

2 Min.

37.

Here the students reason how in this case rounding the hundred and ten is equally precise since both numbers are very close to the hundreds unit.

2 min.

38.

This problem is from Lesson 20 where students subtract by estimating, and as you can see rounding the known part to the nearest hundred was close and easy mental math

5 min.

39.

Invite participants to propose a better method of rounding to check the reasonableness of answers. In this example, rounding one addend to the nearest hundred is a useful strategy.

5 MIN.

40.

Solution for problem on previous slide

5 MIN.

41.

In the same way that we would ask students to reflect on and discuss the lesson as it concludes, we’ll ask you to do the same for the lesson study portion of the session. Take a minute to reflect on this session. What, for you, are the most important takeaways? Jot down your thoughts. Then you will have time to share your thoughts. (Give participants 1 minute for silent, independent reflection.)

Turn and share your reflections with a partner at your table.

(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.)

What 3 things would you tell your colleague about the way Topic C concepts are presented?

· Use of the vertical number line as a tool

· Comparing the actual measurement and rounded measurement to check the reasonableness of answers helps students see the value of rounding

· The topic gets kids to understand the difference between rounding 73mL and 73 cm in the context of measurement; they can mean really different things!

2 MIN.

42.

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

· Measurement contextualizes rounding

· Place value sets the foundation for rounding

· Students use the vertical number line for rounding (because it then makes sense to round “up” and “down”)

· Students apply rounding to estimation in real-world scenarios

Section: Implement the Module

Time: 2: 32-3:00 [28 minutes]

In this section, you will…

1. Explain how participants can use these documents differentiate instruction

Materials used include:

· Session PowerPoint

· Geometric Measurement Progression

Time

Slide #

Pic of Slide

Script/ Activity directions

GROUP

1 min

43.

For the final segment of our work together, let’s consider how the specifics of implementation and differentiation will look for you. For this discussion, we’ll ask that you re-group yourselves so that you are sitting with colleagues who share similar positions.

2 min

44.

Whom it will be your primary responsibility to share learning with and support through implementation? Will it be adults at your school site? Adults within your district or BOCES group? Or will it be students? We’ll take about 15 minutes to meet in groups with others who are thinking about implementation in a similar way.

We’ll break teachers (or others interested in discussing differentiation/implementation with students) into groups by focal student population.

Determine where in the room each group will meet, possibly posting signs to help participants orient themselves. Make sure everyone is clear about which group they will join and where they will meet. Then ask participants to transition into those spaces.

15 min.

45.

Show this slide as participants discuss in groups. After about 15 minutes ask participants to transition back into their original seats.

4 MIN.

46.

Take a couple of minutes to reflect on the totality of the session using these sentence starters. Jot down your thoughts. You will have time to share your thinking.

(Give participants 2 minutes for silent, independent reflection.)

Turn and talk with a partner at your table about your reflections.

(Allow 2 minutes for participants to talk about their reflections. Have participants share out key points.)

1 MIN.

47.

These are the steps we took during this session to reach this objective. (Review the steps with participants.)

Step 1: We studied the progressions and standards to understand how they are foundational to the learning in Module 2.

Step 2: We examined the overview and assessments to become more familiar with Module 2 content and identify the planning we’ll need to do for successful learning outcomes.

Step 3: We looked at Topic C, a pivotal moment in the module, and experienced what the learning feels like. Then we took the time to think about how we might differentiate lessons in that topic to meet student needs.

Step 4: Finally, we took a step back. Each one of you thought specifically about how you might share information with the particular population you’ll be supporting with implementation.

5 MIN.

48.

Please take 5 minutes to complete the 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

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Additional Suggested Resources

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