##
* *Reflection: Developing a Conceptual Understanding
Introduction to Area Models - Section 3: Assignment: Practice in class

Results: In this group, it was consistent. They have mastered the concept and process. Now I need to get them to discuss it. Several students still don't understand the function of place value yet when it came to dealing with a zero. Zeros seem to be a difficult situation and so I will now focus on working with them to get them to understand that the zero has value as a place holder and keeps us understanding that each place value is 10 times the next to help reinforce the standard.

*Samples of Work*

*Developing a Conceptual Understanding: Samples of Work*

# Introduction to Area Models

Lesson 2 of 19

## Objective: SWBAT use an area model to solve a simple two digit by one digit multiplication problem.

## Big Idea: Using an area model, students learn to separate two digit numbers into expanded form and then multiply using a partial product first, and then add to get the final product.

*40 minutes*

Mastery of factor pairs to 100 is to be mastered by 5th grade. So, each day, I choose 3 products between 50-100 to have students use to create factor pairs.

We started with 51 & 52 to warm up. We had in the past listed our factor pairs to 50 by using factor pair cards in the lesson x50.

They listed their factor pairs like this:

50

1 x 50

2 x 25

3 ( no)

4 ( no)

5 x 10

6 ( no)

7 ( no)

8 (no)

9 (no)

10 x 5 ( This is the commutative pair and so all factor pairs are listed.)

And so, students use this systematically to help them be sure that all factor pairs are listed.

#### Resources

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#### Understanding Area Models

*10 min*

After we got done with our factor pair warm up, I gathered my students on the floor with their iPad and math journal to take notes as I presented their first exposure to area model/partial product concepts of multiplication. This method of learning to multiply multi-digit numbers deepens student understanding of the role of place value in a standard algorithm, later on. It lays the foundation needed to solve multi-digit number algorithms.

I had prepared this Multiplication, Place Value and Area Models Notebook file so that we had a solid guide for an area model. I opened up the lesson asking them if they had ever heard the word "area model" or used one. None of my students had, but two of them recalled it being on their pretest.

I asked a student to read the first standard listed on my board which refers to mastering multiplication using an area model to show place value understanding. *I always ask students to read the standard or goal we are learning for the day to connect CCSS to their learning immediately. It helps them get used to the idea that they are expected to master their work. It sets the tone for diligence and goal setting.*

The first slide on the notebook file covers a little review on arrays and leads to understanding that arrays won't work very well with larger numbers. I shared with the class, (with the student's permission), the clip of a classmate using array strategies to solve larger multiplication values. It opened up a **great **conversation about how it was so hard to do this and be accurate at the same time. It helped students talk about how there must be a better way to solve multiplication problems involving 2 or more digits. I flipped to the second page on the notebook file and we began solving and understanding area models and partial products.

To solve as partial products, we created the box first and then broke apart the numbers into expanded form. Each number is multiplied by the one digit factor. Students worked these problems in their notebooks as we solved them together on the Smart Board.

After we solved about 3 more problems, I sorted out who understood and who needed help. I was ready to assign homework practice and allowed time in class to do it. That way, I could monitor their mastery and progress. I worked with individuals who were stuck in the process.

They worked till the end of class. This skill takes some adjustment and time, but really solidifies a foundation that helps in the future teaching of algorithms.

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Houghton Mifflin " Math Expressions" pages 226-227

I assigned pages 226 8-15 and 227 1-6 ( one step word problems). I had copied off notes ahead of time for some of my students directly from the Notebook lesson so that they could refer to them while I taught. It was my hope that they would all use their notes while they worked on their assignment. No deal. I had to remind them. They just aren't used to it yet! This skill of using notes is foreign to them and it tells me that I need to work on teaching them how.

We worked for about 20 minutes until I saw that everyone could master at least 3 problems. I turned them loose on the story problems with no instruction except to tell them to use their KWS ( What do I know?, What do they want to know?, and How do I solve it?) strategy. I am just looking for the solution today. Tomorrow I plan to have them write equations using variables. They are so anxious to solve first, I just decided that for today, mastering area model, recognizing that these problems were multiplication of money and labeling them correctly was enough. I am hoping to see some variables from my higher level students.

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- UNIT 1: Place Value and Multi-Digit Addition & Subtraction
- UNIT 2: Metric Measurement
- UNIT 3: Graphing and Data
- UNIT 4: Concepts of Multiplication
- UNIT 5: Geometry
- UNIT 6: Fractions 1: Understanding Equivalence in Fractions and Decimals
- UNIT 7: Fractions 2: Addition and Subtraction Concepts/ Mini unit
- UNIT 8: Fractions 3 Mini Unit: Multiplying Fractions by Whole Numbers
- UNIT 9: Division Unit
- UNIT 10: Addition and Subtraction: Algorithms to One Million
- UNIT 11: Place Value
- UNIT 12: Addition and Subtraction Word Problems
- UNIT 13: Multiplication Unit

- LESSON 1: Pretesting The Multiplication Unit
- LESSON 2: Introduction to Area Models
- LESSON 3: Area Models: Extension of Understanding
- LESSON 4: Area Models: 4 Digit by 1 Digit Multiplication
- LESSON 5: Getting Ready to Quiz: The Greatest Product Game
- LESSON 6: Quiz 1 in Multiplication: Area Model fluency 1x2,1x3 & 1x4 digits
- LESSON 7: Estimation of Products Using 1 Digit up to 4 Digit Equations.
- LESSON 8: Multistep Word Problems, Algebraic Concepts & Equations: Strategy Toward Mastery!
- LESSON 9: Quiz 2 : Multiplication Word Multi-Step Problems: 1x2,1x3,1x4 digit and estimation
- LESSON 10: An 1870's Classrom Meets Common Core: Drilling Math Facts & a Game of What's Wrong with This Answer?
- LESSON 11: Double Digit Multiplication and the Area Model
- LESSON 12: Powers of Ten: Review and Practice and Writing Clear Explanations
- LESSON 13: Multi-step word problems: Review and Support to Mastery
- LESSON 14: Quiz 3: Double Digit Multiplication, Estimation and Solving Word Problems
- LESSON 15: Estimating Double Digit by Double Digit Multiplication
- LESSON 16: Reviewing for Multiplication Assessment: A student jigsaw presentation.
- LESSON 17: RTI: Making Solving One Step Word Problems a Piece of Cake!
- LESSON 18: Estimation Scenarios: Writing Estimation story problems.
- LESSON 19: Assessing Multiplication