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## A Story of Units

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### A Story of Units

Grade 2 – Module 5

Session Objectives

- 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.

Building Towards the Algorithm: Base-Ten Structure

Conceptual understanding leading up to Module 5:

5 groups

Ten frames

Place Value disks

Make a ten strategy 8 + 6

/\

2 4

Module Overview

- Read the narrative.
- *key concepts
- models and tools
- Important vocabulary

What is the importance of place value language?

unit value tens

place value hundreds

digit

ones

Lesson Objective: Relate 10 more, 10 less, 100 more, and 100 less to addition and subtraction of 10 and 100.

Lesson 1

Lesson 1, Student Debrief

Lesson Objective: Relate 10 more, 10 less, 100 more, and 100 less to addition and subtraction of 100.

Use your number disks to show me 157 on your place value chart.

What important connection did we make today?

What are we actually doing when we talk about

10 more or 100 less than a number?

How does place value understanding lead to flexible thinking?

Lesson Objective: Add and subtract multiples of 100 including counting on to subtract.

Lesson 2

Lesson 2, Student Debrief

Lesson Objective: Add and subtract multiples of 100 including counting on to subtract.

Show 125 on your place value chart and say the number in unit form. What should you change to show 325.

Why is the arrow way a good choice when you have

a missing addend?

How is the make a ten strategy helpful when composing a new hundred?

Problem 5: 590 + 240

Lesson Objective: Add multiples of 100 and some tens within 1,000.

Lesson 3

Lesson 3, Student Debrief

Lesson Objective: Add multiples of 100 and some tens within 1,000.

Problem 5: 590 + 240

What was the most efficient way to add 280 + 640?

Did you agree or disagree with your partner?

Is there more than one way to solve?

How can we decompose numbers to make subtraction easier?

Lesson Objective: Subtract multiples of 100 and some tens within 1,000.

Lesson 4

Lesson 4, Student Debrief

Lesson Objective: Subtract multiples of 100 and some tens within 1,000.

Problem: 740 - 690

Terri solved the problem using an equal sign instead of arrows: 740 – 600 = 140 – 40 = 100 – 50 = 50.

Is her answer correct? Is her equation correct? Why can’t she use an equal sign to show the change?

How do students look for and make use of structure?

Lesson Objective: Use the associative property to make a hundred in one addend.

Lesson 5

Lesson 5, Student Debrief

Lesson Objective: Use the associative property to make a hundred in one addend.

Problem 2: Add multiples of 10 by making a hundred.

In Problem 2(b), 260 + 190, how did you use a number bond to make a new, simpler addition problem? Which number did you break apart, or decompose? Why?

What exactly is compensation?

Lesson Objective: Use the associate property to subtract from three-digit numbers and verify solutions with addition.

Lesson 6

Lesson 6, Student Debrief

Lesson Objective: Use the associative property to subtract from three-digit numbers and verify solutions with addition.

34 - 19

Explain what the compensation and number bond strategies have in common. What actions do you take to make solving easier?

How does sharing strategies improve student learning?

Lesson Objective: Share and critique strategies for varied addition and subtraction problems within 1,000.

Lesson 7

Lesson 7, Student Debrief

Lesson Objective: Share and critique strategies for varied addition and subtraction problems within 1,000.

Study the strategy your partner used. Figure out and fix any mistakes.

Compare how your strategies are the same and how they are different.

Topic B

Strategies for Composing Tens and Hundreds Within 1,000

Did we make a new ten? Did we make a new hundred?

Lesson Objective: Relate manipulative representations to the addition algorithm.

Lessons 8-9

Lessons 8-9, Student Debrief

Lesson Objective: Relate manipulative representations to the addition algorithm.

Model 303 + 37

Model 672 + 249

For Problem 1(c), how did your work with the numbers match the written addition? How did you show new groups below?

Why is it important to move from concrete to pictorial?

place value disks chip model

Lesson Objective: Use math drawings to represent additions with up to two compositions and relate drawings the the addition algorithm.

Lessons 10-11

Lessons 10-11, Student Debrief

Lesson Objective: Use math drawings to represent additions with up to two compositions and relate drawings to the addition algorithm.

Draw a chip model to solve 545 + 278

What important math vocabulary have we used recently to talk about making a new unit? (Compose, bundle, rename, change)

The value of flexible thinking.

Lesson Objective: Choose and explain solution strategies and record with a written addition method.

Lesson 12

Lesson 12, Student Debrief

Lesson Objective: Choose and explain solution strategies and record with a written addition method.

Share with your partner: Which strategy was most efficient for Tracy to use? Why? Do you agree or disagree with your partner?

Topic C

Strategies for Decomposing Tens and Hundreds Within 1,000

Do we have enough ones to subtract?

Do we have enough tens to subtract?

What is the purpose of the magnifying glass?

Lesson Objective: Relate manipulative representations to the subtraction algorithm, and use addition to explain why the subtraction method works.

Lesson 13

Lesson 13, Student Debrief

Lesson Objective: Relate manipulative representations to the subtraction algorithm, and use addition to explain why the subtraction method works.

How can you use addition to explain why the subtraction works? Use part-whole language to explain your thinking.

How can we use addition to explain why a subtraction method works?

Lesson Objective: Use math drawings to represent subtraction with up to two decompositions, relate drawings to the algorithm, and use addition to explain why the subtraction method works.

Lessons 14-15

Lessons 14-15, Student Debrief

Lesson Objective: Use math drawings to represent subtraction with up to two decompositions, relate drawings to the algorithm, and use addition to explain why the subtraction method works.

584 – 147

How can you prove that this statement is true:

If 584 – 147 = 437, then 147 + 437 = 584.

What is the most efficient way to subtract from a multiple of 100?

Lesson Objective: Subtract from multiples of 100 and from numbers with zero in the tens place.

Lessons 16-17

Lessons 16-17, Student Debrief

Lesson Objective: Subtract from multiples of 100 and from numbers with zero in the tens place.

800 – 463

Think like a detective: When you are subtracting three-digit numbers, when do you choose to unbundle a hundred? When do you choose to solve mentally? What clues in the numbers help you to choose a solution strategy?

Is there one right strategy?

Lesson Objective: Apply and explain alternate methods for subtracting from multiples of 100 and from numbers with zero in the tens place.

Lesson 18

Lesson 18, Student Debrief

- Lesson Objective: Apply and explain alternate methods for subtracting from multiples of 100 and from numbers with zero in the tens place.
- Use compensation to solve 300 - 159
- Add to solve 400 – 278
- Solve 605 – 498 using the algorithm and a chip model
- Choose your favorite strategy to solve 500 – 195
- Choose one of these strategies to explain to a partner.

Topic D

Student Explanations for Choice of Solution Methods

Which solution strategies are fastest and easiest for you?

Lesson Objective: Choose and explain solution strategies and record with a written addition or subtraction method.

Lessons 19-20

Lessons 19-20, Student Debrief

Lesson Objective: Choose and explain solution strategies and record with a written addition or subtraction method.

Look at Problem 1(c). Compare your strategy to your partner’s. Which one was more efficient? Defend your reasoning.

Lesson Preparation and Demonstration

- At your table, prepare to demonstrate the main section of the Concept Development.
- Think about:
- What is the most important understanding I need my students to take from this lesson?
- What is the key learning component in the lesson that supports students learning this concept.

Fluency

- Fluency is fun and engaging!
- It can be used to:
- maintain previously learned content.
- prepare for the upcoming lesson.
- anticipate content knowledge students will need in the future.

Application Problems

Lesson 10, Application Problem

2.OA.1: Use addition and subtraction within 100 to solve

one- and two-step word problems.

Biggest Takeaway

- Turn and Talk:
- What insights do you have about the trajectory of learning, both leading up to and throughout Module 5?
- What can you share with others about the importance of place value language, flexible thinking, the use of structure, and strategies such as make a ten?
- What is the value of a conceptual vs. procedural
- approach to learning the addition and subtraction
- algorithms?

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.

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