A Story of Units Module Focus TIME ALLOTTED FOR THIS SLIDE:

A Story of Units Module Focus TIME ALLOTTED FOR THIS SLIDE:
July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute THE TIMES FOR ALL SLIDES NEED TO TOTAL 195 MINUTES MATERIALS NEEDED: X A Story of Units Module Focus NOTE THAT THIS SESSION IS DESIGNED TO BE 195 MINUTES IN LENGTH Turnkey Materials Provided in Addition to PowerPoint: Grade 4—Module 2 Grade 4 – Module 2 Student Sample Assessment Responses Grade 4 – Module 3 Overview Grade 4 – Module 2 Solutions Strategies Handout Grade 4 – Module 3 Topic Analysis Handout Geometric Measurement Progression document Personal White Boards Additional Suggested Resources: Number and Operations in Base 10 Progression document Operations and Algebraic Thinking Progression document A Story of Units: A Curriculum Overview for Grades P-5 How to Implement A Story of Units 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.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 2 minutes MATERIALS NEEDED: Geometric Measurement Progression Session Objectives Draw connections between the progression documents 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. 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.

Participant Poll Classroom teacher School leader Principal
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute MATERIALS NEEDED: X Participant Poll Classroom teacher School leader Principal District leader BOCES representative Attended Grade 4 Presentation at the May NTI 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.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute MATERIALS NEEDED: Geometric Measurement Progression Document AGENDA Study of the Progression Document Examination of Module Overview and Assessments Exploration of Selected Lessons Bringing the Module to Life 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.

TIME ALLOTTED FOR THIS SLIDE: 2 minutes MATERIALS NEEDED:
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 2 minutes MATERIALS NEEDED: Curriculum Map 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 and Problem Solving with Metric Measurement) 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)

Progression Study Read the Geometric Measurement Progression page 20.
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 10 minutes MATERIALS NEEDED: Geometric Measurement Progression Document Progression Study Read the Geometric Measurement Progression page 20. Highlight the information relevant to the content of this module. Which measurement concepts are students expected to learn in Grade 4? 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, 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.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: Geometric Measurement Progression Document Progression Study Which measurement concepts are students expected to learn in Grade 4? What appears to be missing from this Progression that you would expect to find when teaching about measurement? 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.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute MATERIALS NEEDED: Module Overview and Assessments AGENDA Study of the Progression Document Examination of Module Overview and Assessments Exploration of Selected Lessons Bringing the Module to Life Now that we’ve read the information provided in the Progressions documents, let’s examine how these concepts are addressed in this module.

Review of Module Structure
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute MATERIALS NEEDED: X Review of Module Structure Module Overview Topic L1 L2 L3 L4 L5 L6 L7 L8 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.

Module Overview Read the descriptive narrative.
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 9 minutes MATERIALS NEEDED: Grade 4 Module Overview Module Overview Read the descriptive narrative. Make note of important information that will help educators understand the content and prepare to implement this module. 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.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 8 minutes MATERIALS NEEDED: Module Overview Module Overview 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 about your observations. 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.)

Module Mathematics in Practice
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: Personal White Boards Module Mathematics in Practice 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. (Write a 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.

Module Mathematics in Practice
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 2 minutes MATERIALS NEEDED: Personal White Boards Module Mathematics in Practice 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. 500 m

Module Assessments Complete the End of Module Assessment.
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 10 minutes MATERIALS NEEDED: Module Assessment and Module Standards Module Assessments Complete the End of Module Assessment. Label each problem with the standard it assesses. 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.

Module Assessments: Rubrics
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: End of Module Assessment Rubric Module Assessments: Rubrics 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.

Module Assessments: Scoring Sample Student Work
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 10 minutes MATERIALS NEEDED: End of Module Assessment Rubric Module Assessments: Scoring Sample Student Work Score the assessment assigned to your table using the Rubric. Discuss the scores at your table. How can the Levels of Performance and the Step descriptions assist a teacher in assessing student understanding? (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.) The discuss how this Rubric can assist teachers in assessing student understanding.

Module Assessments: Reflection
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: X Module Assessments: Reflection How could this rubric be used? How could this rubric be used to give students feedback on complex tasks?

Module Focus July 2013 Network Team Institute Lunch Break When we return from lunch, we’ll start exploring the Topic Overviews and lessons. We will start with Module 2 and than 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.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute MATERIALS NEEDED: X AGENDA Study of the Progression Document Examination of Module Overview and Assessments Exploration of Selected Lessons Bringing the Module to Life Welcome back! Now that we are familiar with the module overview and assessments, let’s begin our examination of the topics and lessons.

Topic Openers Read the descriptive narrative.
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 6 minutes MATERIALS NEEDED: Grade 4 Module 2 Topic Openers A and B Topic Openers Read the descriptive narrative. Make note of important information that will help educators implement these lessons. 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.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: X Topic Openers How does Topic A lay the foundation for the work in Topic B? How do Topic Openers A and B allow teachers to understand the vertical alignment amongst grade levels? How are the Topic Openers useful as a planning tool for this model? 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.)

Lesson Study Fluency Practice Application Problems Concept Development
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute MATERIALS NEEDED: X Lesson Study Fluency Practice Application Problems Concept Development Student Debrief 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.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: X Lesson 1-3 Unit conversions with metric measurements of length, weight, and capacity. Application of Module 1: addition and subtraction; algorithms and strategies New Terms: kilometer, milliliter, mass, mixed units 2-column table used to show conversions Number line used as a strategy for counting up or down. Simplifying strategies are encouraged. Standards alignment 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.

Lesson 1 2- column tables Distance km m 1 2 3 7 10
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 4 minutes MATERIALS NEEDED: X Lesson 1 2- column tables Distance km m 1 2 3 7 10 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.)

10 kg – 2 kg 250g Lesson 2 Number Lines TIME ALLOTTED FOR THIS SLIDE:
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 2 minutes MATERIALS NEEDED: Lesson 2 10 kg – 2 kg 250g Number Lines 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.

Lesson 3 Label the strategy modeled in each solution. Problem 1:
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 2 minutes MATERIALS NEEDED: Handout: 5 solutions to solving a metric subtraction problem. Lesson 3 Label the strategy modeled in each solution. Problem 1: Algorithm with mixed units Algorithm using smaller units Special Strategy, one unit at a time Special Strategy, number line Special Strategy, counting up 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.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 2 minutes MATERIALS NEEDED: Handout: 5 solutions to solving a metric subtraction problem. Lesson 3 Label the strategy modeled in each solution. Problem 2: Algorithm with mixed units Algorithm using smaller units Special Strategy, one unit at a time Special Strategy, number line Special Strategy, counting up 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.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 2 minutes MATERIALS NEEDED: Handout: 5 solutions to solving a metric subtraction problem. Lesson 3 Label the strategy modeled in each solution. Problem 3: Algorithm with mixed units Algorithm using smaller units Special Strategy, one unit at a time Special Strategy, number line Special Strategy, counting up 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.”

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 2 minutes MATERIALS NEEDED: Handout: 5 solutions to solving a metric subtraction problem. Lesson 3 Label the strategy modeled in each solution. Problem 4: Algorithm with mixed units Algorithm using smaller units Special Strategy, one unit at a time Special Strategy, number line Special Strategy, counting up 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.”

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 2 minutes MATERIALS NEEDED: Handout: 5 solutions to solving a metric subtraction problem. Lesson 3 Label the strategy modeled in each solution. Problem 5: Algorithm with mixed units Algorithm using smaller units Special Strategy, one unit at a time Special Strategy, number line Special Strategy, counting up 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.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute MATERIALS NEEDED: Lesson 4 Lesson 4: Know and relate metric units to place value units in order to express measurements in different units. Connect metric units to place value units. Compare and order measurements 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.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 4 minutes MATERIALS NEEDED: Lesson 4 Personal white boards Lesson 4 What do you notice about the relationship between grams and kilogram? 1 kilogram = 1,000 grams Write your answer as an equation. 1 kg = 1,000 x 1g 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

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: Lesson 5 Lesson 5: Use addition and subtraction to solve multi-step word problems involving distance, liquid volume, and mass. Apply what students learned in Lessons 1-4 Structured to use the Problem Set within the Concept Development Utilize the RDW strategy Lesson 5 is the culminating lesson of Module 2. Completion of the lesson requires application of the concepts developed during Lessons 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.)

Lesson 5: Problem Set- Problem 1
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 7 minutes MATERIALS NEEDED: Lesson 5 Lesson 5: Problem Set- Problem 1 The potatoes Beth bought weighed 3 kilograms 420 grams. Her onions weighed 1050 g less than the potatoes. How much did the potatoes and onions weigh altogether? 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?

Balanced, Rigorous Instruction
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute MATERIALS NEEDED: X Balanced, Rigorous Instruction 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.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 4 minutes MATERIALS NEEDED: X Biggest Takeaways How do these lessons compare to your past experiences with mathematics instruction? Turn and talk with a partner at your table about your reflections. 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.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute MATERIALS NEEDED: X Key Points Measurement provides a context to apply addition and subtraction skills and strategies. Measurement provides a context to strengthen place value patterns and number theory. Students are encouraged to track their thinking through written work (simplifying strategies vs. mental math). Let’s review key points from our examination of these lessons:

Module 3 Multi-Digit Multiplication and Division
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minutes MATERIALS NEEDED: X Module 3 Multi-Digit Multiplication and Division 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.

TIME ALLOTTED FOR THIS SLIDE: 1 minutes MATERIALS NEEDED:
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minutes MATERIALS NEEDED: Curriculum Map 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)

Module 3 Overview Read the Module Overview independently.
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 8 minutes MATERIALS NEEDED: G4 M3 Module Overview Module 3 Overview Read the Module Overview independently. Mark important information that will help the implementation of this module. 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.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: G4 M3 Module Overview Module 3 Topic Analysis Handout Module 3 Overview Re-read the Overview to find your table’s assigned Topic Using the Topic Analysis Handout, complete the focus question for your Topic and list the standards. Column 1 - Focus questions Column 2 - Answers Column 3 - Standards addressed 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.

Module 3 Topic A Multiplicative Comparison Word Problems
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: G4 M3 Module Overview Module 3 Topic Analysis Handout Module 3 Topic A Multiplicative Comparison Word Problems What context will students use to explore multiplicative comparisons? What does Topic A lay the foundation for in upcoming year? 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. The width of David’s tent is 5 feet. The length is twice the width. David’s rectangular air mattress measures 3 feet by 6 feet. If David puts the air mattress in the tent, how many square feel of floor space will be available for the rest of this things?

Module 3 Topic B Multiplication by 10, 100, and 1000
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: G4 M3 Module Overview Module 3 Topic Analysis Handout Module 3 Topic B Multiplication by 10, 100, and 1000 Why are students asked to reason between number disks and numerical work? Topic B lays the foundation for which upcoming Module 3 Topics? 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. Brianna bought 3 packs of balloons for a party. Each pack had 60 balloons. How many balloons does Brianna have?

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: G4 M3 Module Overview Module 3 Topic Analysis Handout Module 3 Topic C Multiplication of Up to Four-Digit by Single-Digit Numbers What methods will students use to record their work in Topic C? What clarification does the footnote 1 provide for the multiplication algorithm? 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 ones 4 hundreds + 2 tens + 6 ones 426

Module 3 Topic D Two-Step Multiplication Word Problems
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: G4 M3 Module Overview Module 3 Topic Analysis Handout Module 3 Topic D Two-Step Multiplication Word Problems What is the purpose of Topic D? What operations will students be able to use to solve the problems? 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. In one month, Charlie read 814 pages. In the same month his mom read 4 times as many pages as Charlie, and that was 143 pages more than Charlie’s dad read. What was the total number of pages read by Charlie and his parents?

Solve using an array and an area model.
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: G4 M3 Module Overview Module 3 Topic Analysis Handout Module 3 Topic E Division of Tens and Ones with Successive Remainders Which foundational concepts does Topic E build upon? What clarifications are provided by footnotes 2 and 3? 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. 22 ÷ 5 Solve using an array and an area model.

Is the following statement true?
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: G4 M3 Module Overview Module 3 Topic Analysis Handout Module 3 Topic F Reasoning with Divisibility How is Topic F connected to the work of this module? Topic F provides the foundation for which upcoming Module 3 Topic? 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=2 16÷2=8 16÷4=4 24÷2=12 24÷4=6 32÷2=16 32÷4=8 40÷2=20 40÷4=10 Is the following statement true? Any number that has 2 as a factor and 4 as a factor also has 8 as a factor. Prove your answer.

Module 3 Topic G Division of Thousands, Hundreds, Tens and Ones
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: G4 M3 Module Overview Module 3 Topic Analysis Handout Module 3 Topic G Division of Thousands, Hundreds, Tens and Ones Topic G builds upon the work of which Topics that came earlier in the Module? What is the purpose of using number disks in this Topic? 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 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. Use number disks to model this problem: Zach filled 581 one-liter bottles of apple cider. He distributed the bottles to 4 stores. How many liter bottles will each store receive? Will there be any bottles left over? If so, how many?

Use the area model to solve
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 3 minutes MATERIALS NEEDED: G4 M3 Module Overview Module 3 Topic Analysis Handout Module 3 Topic H Multiplication of Two-Digit by Two-Digit Numbers Why is the work of Topic H placed last in this Module? What should students understand about partial products written vertically? 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 Use the area model to solve 23 × 15.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 1 minute MATERIALS NEEDED: AGENDA Study of the Progression Document Examination of Module Overview and Assessments Exploration of Selected Lessons Bringing the Module to Life 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.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: Another Look Given your role, consider the next steps you would need to take to move forward with this work. Jot down a mini action plan of 3-5 steps. 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.

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 13 minutes MATERIALS NEEDED: Chart paper Markers Tape? Action Plans Meet with a group of 4-6 people who have a similar role. Create a combined action plan. 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.

Biggest Takeaways / Next Steps
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 4 minutes MATERIALS NEEDED: X Biggest Takeaways / Next Steps I now know… I need to figure out… The first thing I’ll do is… Turn and talk with a partner at your table. Take one minute to reflect on this session using these sentence starters. 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.)

Key Points These lessons are carefully designed.
Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 2 minutes MATERIALS NEEDED: X Key Points These lessons are carefully designed. Teaching these lessons requires thought and preparation. Preparing teachers to use these lessons also requires thought and preparation. Collaboration and communication are key! Let’s summarize the key points that you have identified as a group during this session:

Module Focus July 2013 Network Team Institute TIME ALLOTTED FOR THIS SLIDE: 5 minutes MATERIALS NEEDED: X Pulse Check Please go to fill out the online plus-delta for the P-5 Math session. Thank You! EngageNY.org

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