Module Focus: Grade 2 – Module 5 Sequence of Sessions

Overarching Objectives of this November 2013 Network Team Institute Module Focus sessions for K-5 will follow the sequence of the Concept Development component of the specified modules, using this narrative as a tool

for achieving deep understanding of mathematical concepts. Relevant examples of Fluency, Application, and Student Debrief will be highlighted in order to examine the ways in which these elements contribute to and enhance conceptual understanding.

High-Level Purpose of this Session Focus.  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. Coherence: 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.)

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 in order to fully implement the curriculum.   

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

Related Learning Experiences● This session is part of a sequence of Module Focus sessions examining the Grade 2 curriculum, A Story of Units.

Key Points• Module 5 focuses on conceptual understanding of place value as the foundation for learning the addition and subtraction algorithms.

• Students learn and are encouraged to use strategies such as compensation, arrow notation, and chip models.

• The Student Debrief is an essential element in probing, deepening, and assessing student understanding.

• All components of each lesson are valuable and contribute to the overall rigor.

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?

Focus.  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.

Coherence: 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.)

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 in order to fully implement the curriculum.   

Implementation.  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.   

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

Participants will be able to articulate the key points listed above.

Session Overview

Section Time Overview Prepared Resources Facilitator Preparation

Introduction to the Module

15 minutes

Overview of the instructional focus of Grade 2 Module 5.

Grade 2 Module 5 Grade 2 Module 5 PPT

Concept Development

4 hours, 3 minutes

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

Grade 2 Module 5 Grade 2 Module 5 PPT

Review Grade 2 Module 5 Overview, Topic Openers, and Assessments.

Module Review13 minutes

Review of the key points Grade 2 Module 5Grade 2

Module 5 PPT

Session Roadmap

Section: Introduction to the Module Time: 15 minutes

[15 minutes] In this section, you will… Provide an overview of the instructional focus of Grade 2 Module 5

Materials used include:Participant PPT and handouts

Time Slide # Slide #/ Pic of Slide Script/ Activity directions GROUP

0 1 NOTE THAT THIS SESSION IS DESIGNED TO BE 265 MINUTES IN LENGTH.Welcome! In this module focus session, we will examine Grade 2 – Module 5.

1 2 Our objectives for this session are to:• Examination of the development of mathematical

understanding across the module using a focus on Concept Development within the lessons.

• Introduction to mathematical models and instructional strategies to support implementation of A Story of Units.

1 3 We will begin by leading you through the teaching sequence, once concept at a time. Along the way, we will explore the Module Overview and the Topic Openers to understand the purpose of this module. Then we will dig into the math of the module and you will have the opportunity to prepare and demonstrate key sections of the Concept Development. We will also examine the other lesson components and how they function in collaboration with the Concept Development. Finally, we’ll take a look back at the module, reflecting on all the parts as one cohesive whole.Let’s get started by seeing where this module fits in within the Grade 2 curriculum.

0 4 The fifth module in Grade 2 is Addition and Subtraction Within 1000. The module includes 20 lessons and is allotted 24 instructional days.

3 5 Fluency using the standard algorithm is not required until Grade 4. Student work leading up to that point is rooted in experiential learning to develop an understanding of base-ten structure.Students use models and make drawings to represent numbers, their composition and decomposition, and place value.

10 6 Take 8 minutes to read the Module 5 Overview. As you read, track the information by starring key concepts, circling models and tools, and underlining important vocabulary.Pay special attention to the titles of the topics and think about their significance. Notice the organization of the lessons and how each is connected within the four overarching topics. (After 8 minutes) Talk with a neighbor about the Topic titles. What do they signal in terms of

what is most important in this module? What is the goal for our students? (The focus is on strategies, not the algorithm, and on student reasoning.)

Section: Concept Development Time: 4 hours 3 minutes

[243 minutes] In this section, you will… Examine of the development of mathematical understanding across the module using a focus on Concept Development within the lessons.

Materials used include:Participant PPT and handouts

Time Slide # Slide #/ Pic of Slide Script/ Activity directions GROU

P

0 7 Now let’s dive into Concept Development!

8 8 For each topic, we will examine the Topic Opener first. Then you will be in the role of the students as we present the key elements of the lessons in that topic, followed by you trying out the new learning on one or two problems from the Problem Sets of selected lessons. After that, it will be your turn to play the role of the teacher, as you prepare and teach portions of lessons to the group.Allow 5 minutes to read and 3 to discuss and ask questions.

1 9 In addition to making the connection to addition and subtraction, work with 10 more and less and 100 more and less focuses students on place value, reinforcing the concept that we add and subtract like units.

10 10 As students use number disks to show 10 more or 100 less than a number, they ground their work with numbers in place value, and use place value language to express what they’re doing.

T: Show me 10 more.S: (Add a tens disk to show 1 hundred 6 tens 7 ones.)T: Use a sentence frame to describe adding 10 to 157.S: 10 more than 157 is 167. 167 is 10 more than 157.T: What did you do to change 157?S: We added 10 to the tens place.S: We added 1 ten to 5 tens and made 6 tens.T: Give me an addition sentence starting with 157.S: 157 + 10 = 167.

Talk with a neighbor: What important connection did we make today? What are we actually doing when we talk about 10 more or 100 less than a number?Apply what you learned in Lesson 1 to complete the Lesson 1 problem on the Practice Sheet.

1 11 Liping Ma, the author of Knowing and Teaching Elementary Mathematics gives the example of good math students being akin to good cab drivers -- they know many ways to reach the destination.Talk with a neighbor: How does place value understanding lead to flexible thinking, and why is flexible thinking so important? (e.g., Instead of becoming stuck using only procedural knowledge, place value understanding allows students to approach problems in a variety of ways, using varied strategies. Flexibility in thinking leads to creative problem solving.)

6 12 In this lesson, the focus is on multiples of 100. Students add and subtract disks in the hundreds place and relate that action to adding and subtracting hundreds.

T: Whisper to your partner. What did you do to change 125 to 325?S: We added 2 more hundreds.T: Give me the addition sentence starting with 125.S: 125 + 200 = 325.T: Now show me 541. (Students model.)T: Say it in unit form.S: 5 hundreds 4 tens 1 one.T: Show what happens to the number when you subtract 2 hundreds.S: (Remove 2 hundreds.)T: Say the new number in unit form.S: 3 hundreds 4 tens 1 one.T: Tell me the subtraction sentence.S: 541 – 200 = 341.

Students learn that they can record these changes using arrow notation, including counting on to subtract (541 – ___ = 341 and 341 + ___ = 541.)Talk with a neighbor: Why is the arrow way a good choice when you have a missing addend?

2 13 Talk with a neighbor: What is it about 590 + 240 that poses a challenge for some students? (90 + 40.) How can knowledge of place value and the make a ten strategy help? (It’s a general method based on place value that extends to making a hundred.)

5 14 Students are encouraged to notice and make use of the relationship of numbers.

T: (Write 590 + 240 on the board.)T: I notice something interesting about the first number. (Point to 590.) I wonder if anyone else notices the same thing.

S: It’s close to 600! It’s just 10 away from 600. I can make the next 100 to help me solve the problem.

T: Let’s try that! You write what I write. (Record arrow notation.)Talk with your neighbor: What strategy have we learned that would be an efficient way to add 590 + 240. (Arrow notation.) Is there more than one way to solve this problem?

1 15 Notice the constant focus on strategies that rely upon place value understanding. Talk with a neighbor: Use place value language to explain how the (above) strategy works.

5 16 Lesson 4 is scaffolded (450 – 200, 450 – 210, 450 – 250, 450 – 260) to lead students towards successfully solving problems such as 740 – 690 on the Problem Set independently.Let’s solve 740 - 690 together, and then discuss the debrief questions.

(The answer is correct.)(The equation is incorrect.)(740 – 600 does not equal 140 – 40, nor do either of those equal 50.)

Apply what you learned in Lesson 4 to complete the Lesson 4 problem on the Practice Sheet.

1 17 What is the recurring theme throughout all of the lessons so far? (They focus on tens and hundreds.)How will this work support later work with larger numbers and the algorithms? (These strategies are general and so will apply to larger numbers, enabling students to simplify calculations. The addition and subtraction algorithms are based on the composing and decomposing of units of 10 and 100.)

5 18 Students decompose one addend to make a ten or a hundred with the other addend.

T: (Write 190 + 120 on the board.)T: Is one of these numbers close to the next hundred?S: Yes!T: Which one?S: 190!T: Which hundred is it close to?S: 200!T: How many more do we need to make 200?S: 10 more!T: Where can we get 10 more?S: From 120!

Apply what you learned in Lesson 5 to complete the Lesson 5 problem on the Practice Sheet. Then take a moment to discuss the debrief questions with a neighbor.

3 19 Talk with a neighbor: Explain your understanding of compensation. (Invite participants to share their understanding. )Students worked with compensation in Module 4, and the concept is presented in the two fluency activities that precede this lesson. (Use linking cubes to model how 8 – 5 = 9 – 6.) In this lesson, the ease of subtracting a multiple of 100 is highlighted again. Students add or subtract a multiple of 10 to both the minuend and subtrahend to make an equivalent problem that involves no renaming.

10 20 Talk with a neighbor: What do you notice about one of the numbers that can help us simplify this problem? (19 is close to 20.)Watch how we can draw a tape diagram to show how to simplify this problem.Talk with a neighbor: Use place value language to explain how this strategy works.Apply what you learned in Lesson 6 to complete the Lesson 6 problem on the Practice Sheet.

1 21 A hallmark of A Story of Units is the value this curriculum places on student reasoning, in keeping with the Standards for Mathematical Practice.

Those standards include problem solving, reasoning and proof, communication, representation, and connections (from the Common Core State Standards for Mathematics, p.6).

7 22 Solve this problem using a strategy of your choice. Then share your strategy with a neighbor.Discuss Student C and Student D’s work. Are they both correct? (No.) What error did Student C make? (He added 20 to 380 but took 20 from 864, thereby changing the difference.)

6 23 As you read Topic B, think about the ways in which Topic A prepared students for this next step in the progression of learning.Allow 4 minutes to read and 2 minutes to discuss and ask questions.

2 24 Talk with a neighbor: Why is it important to relate manipulatives to the algorithm? (Physically representing numbers with place value disks strengthens students’ place value understanding and helps them systematically model the standard addition algorithm, including the composition of a ten or a hundred. As they move the manipulatives, students use place value language to express the action as they physically make a ten with 10 ones and exchange them for 1 ten. They record each change in the written method, step by step. This all helps students develop conceptual understanding for how and why the algorithm works.)

6 25 Why are the problems written horizontally? (Writing problems vertically signals the use of the algorithm. Writing them horizontally triggers the search for number relationships that lend themselves to other strategies.) Let’s solve these problems by modeling them with place value disks. As we make a change to our model, we record it on the algorithm.Now, use place value language to explain to a neighbor how your work with the numbers matches the written addition.

1 26 The use of concrete objects allows students to manipulate numbers in ways that deepen their understanding. Pictorial representations are a move towards abstract thinking, and they are more practical than concrete models because they can be done most anywhere and can represent very large numbers.

7 27 Now, instead of actual disks, we will draw a chip model of the addition. We will record each step of the process on the algorithm. As we do so, use place value language to explain each step to a partner.Apply what you learned in Lessons 10 and 11 to complete the Lesson 11 problem on the Practice Sheet.

30 seconds

28 Encourage students to explore multiple ways of solving problems, and to critique strategies for efficiency.

6 29 Talk with a neighbor: What are some strategies you could use to solve this problem?Try to solve the problem 2 different ways. Which was easiest?Allow 2 minutes for sharing and solving, and another minute to share a few strategies with the whole group.Apply what you learned in Lesson 12 to complete the Lesson 12 problem on the Practice Sheet.

6 30 In Topic C, students ask the questions, Do I have enough ones to subtract? and Do I have enough tens to subtract? as now the focus shifts to decomposition and subtraction.Allow 4 minutes to read and 2 minutes to discuss and ask questions.

1 31 The magnifying glass is a visual cue serving several purposes:• It reminds students to set the problem up for subtraction. • It reminds them that the minuend is the whole from which they are

taking a part. • It short-circuits the habit of seeing numbers as columns of isolated,

unrelated digits.• It prevents the common error of switching the top and bottom digits

when the digit on top is too small.

6 32 Students return to place value disks to model decompositions while simultaneously recording these changes in the algorithm.We will record each step of the process on the algorithm. As we do so, use place value language to explain each step to a partner.

2 33 Students demonstrate an understanding of the relationship between addition and subtraction as they use number bonds, related facts, and part-whole thinking to explain why the subtraction method works.Talk with a neighbor: How does a number bond represent addition and subtraction?

5 34 Draw a model of the subtraction and solve, recording changes in the algorithm. Then draw a model of the corresponding addition. Can you use the drawing to show the whole as well as the parts?Apply what you learned in Lessons 14-15 to complete the Lessons 14-15 problem on the Practice Sheet.

1 35 Return to concrete models when you anticipate a concept that students will struggle with. Some students will be able to grasp the concept of renaming 1 hundred as 9 tens 10 ones, using just their chip models, while others may need the physical proof of what is happening as they rename. These latter students may also need the intermediate step of renaming 1 hundred as 10 tens before renaming a ten as 10 ones.

7 36 Talk with a neighbor: What do you notice about these numbers? Solve using a favorite strategy and share that strategy.Now let’s solve it using a chip model. First we’ll solve it with 2-step renaming of a hundred, then we’ll solve by renaming in one step. Apply what you learned in Lessons 16-17 to complete the Lessons 16-17 problem on the Practice Sheet.

2 37 By this point, students have multiple means of solving problems at their disposal. It’s a good math habit for them to think about the numbers and how they relate to each other before deciding on a strategy.Sometimes students are given free choice in how they solve a problem. In this lesson, they are asked to solve problems using a given strategy. Explanation is a key component of this lesson and in general. Whatever method students use, they should be able to explain it.

7 38 Allow 4 minutes for participants to complete these problems and explain one of the methods to a partner.Apply what you learned in Lesson 18 to complete the Lesson 18 problem on the Practice Sheet.

3 39 In this final topic, students choose which strategy is most efficient for given problems. Students defend their choices using place value language and their understanding of the properties of operations.Take 2 minutes to read Topic D and 1 minute to discuss.

30 seconds

40 In Lessons 19 and 20, students apply their learning to answer the question: Which strategy is best for this problem? They analyze chosen methods and decide which is the most efficient for the given problem type.

8 41 For this last lesson, complete the Lessons 19-20 problem on the Practice Sheet. Find someone who solved in a different way than yours, and discuss which strategy is more efficient.

60 42 Tables will have approximately 15 minutes to review a particular lesson’s concept development, and then prepare to demonstrate the key components through presenting the lesson to the group.Topic A: Lessons 1, 2, 3, 4, 5, 6, 7Topic B: Lessons 8-9, 10-11, 12Topic C: Lessons 13, 14-15, 16-17, 18Topic D: Lessons 19-20Allow 15 minutes for preparation, and approximately 3 minutes per group presentation.

20 43 Fluency is a crucial component of the Concept Development. It presents the opportunity to maintain, prepare, or anticipate content, plus it’s fun and engaging!Let’s examine the fluency component to see how it supports the work of Module 5. Each table will then have the opportunity to practice and demonstrate a fluency activity for the group.

20 44 Throughout Module 5, students maintain addition and subtraction fluency within 100 as they use these skills during their daily application work to solve one- and two-step word problems of all types (2.NBT.5, 2.OA.1). We will examine these problem types, with a focus on tape diagrams.

Section: Module Review Time:

[13 minutes] In this section, you will…Reflect on the key points of the module overall

Materials used include:PPT and participant materials

Time Slide # Slide #/ Pic of Slide Script/ Activity directions GROUP

0 45 Now that you’ve had the chance to see and practice the concepts, skills, and models of Module 5, let’s take a moment to reflect back on the module overall.

5 46 Take two minutes to turn and talk with others at your table. During this session, what information was particularly helpful and/or insightful? What new questions do you have?Allow 5 minutes for participants to turn and talk.

8 47 Take 3 minutes to review key points, then close the session with an opportunity for participants to ask any further questions.

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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