## Estimation - Section 2: Core Lesson: Extending understanding through student constructed ideas

# Area Models: Extension of Understanding

Lesson 3 of 19

## Objective: SWBAT multiply three digits by one digit using an area model.

## Big Idea: This lesson is an extension of the introduction to area models. Students will use prior knowledge and logic to formulate a way to use area model to solve three digits by one digit.

Students came in today ready to create factor pairs for products 54,55,56,57 for a warm up. What patterns can we find? What divisibility rules will work? I ask these questions whenever we are solving factor pairs.

In their math notebook, they listed each of the numbers like this:

54 55 56 57

Then they began listing the factor pairs in order like this for each one.

1 x 54

2 x 27

3 x 18

4

5

6 x 9

7

8

9 x 4 stop, this is the commutative pair. Done!

When they were finished we listed each one together on the white board to check our work and to make sure we had found each factor pair. I chose 4 students to list them and then we discussed if all were listed.

#### Resources

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Yesterday, my students had learned through direct instruction how to multiply 2 digits by 1 digit using an area model. Today, I wanted to exercise their prior knowledge and get them to extend their skills to 3x1 digit through think, pair and share.

I used my Smartboard Notebook File : Area model and partial products # 2 page one to open up their minds to other possibilities. We talked through the questions and students seemed to all grasp that area model can be used for 3x1 multiplication. It was time for them to independently think and draw out a problem. So, I wrote 421 x 7 on the board and asked them to think about how they could solve it using expanded form, the area model, partial products and addition. They set to work. After about 5 minutes or so, they partnered up and shared their ideas with their partner. I roved about the classroom and could see that most of my students understood what to do and could independently show they could extend their thinking to a 3x1 digit problem on their own. The energy level and enthusisam was high. I could hear the chatter and the passing of notebooks as they worked. I could hear one person correct another student when they saw things were wrong. A few students forgot the adding of partial products.

I interviewed and listened to several of my students talk about their work. There were a few misconceptions. One boy thought he needed to estimate. Estimation. He was confused about why we needed to create an expanded form number. Other students needed help in looking at their multiplication and understanding of groupings of ten as well as not going back to repeated addition. They needed to use their basic facts and then multiply by groups of ten.Groups of 10 issues and repeated addition. Other students influenced a partner after they listened to them explaining work to me. *This is really cool to have going on in the classroom. I love partner work because of this!*I saw what you are doing and I am going to fix mine! And finally, one high end student has the concept, but I need him and most all to include place value language in all aspects of their work.Place value understanding needed.

It was time to move into creating a video tutorial to assess understanding!

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Students worked independently to create a video in the iPad app, Educreations. Their goal was to create an explanation of how and why they could use the area model to produce a product of a 3 digit times 1 digit expression.

Everyone loves this! I assigned this so that they have another way of practicing explanations. However, as I watched their videos, only one student came up with place value language in her work. In order to share Educreations with me, students have to have an account set up. I am struggling with it at this point. So, for your sample, I had a student create an explanation on my iPad. You can clearly see that the place value language is missing, even though the process is correct. The language should contain references to each place value as they multiply. For example, the student should say 2 tens times 7 ones, instead of twenty. I hope that in the next lesson, students master this understanding and practice it. We need to work on it! As we transition, this should become more fluent. Using place value language in their work helps them understand the "why" behind the process and makes the process more concretely in depth.

After everyone showed me their movies, I gave them their written assignment.

Update: Educreations has removed themselves as a free website to be able to download at this capacity since 2014.

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#### Assignment

*10 min*

Assignment 2 Area Model 2x1 & 3x1

I assigned a worksheet I designed with the area model boxes on it. I did this because I was worried that they would be all caught up in the extra process that they would forget the third box for the hundreds place and simply add up the products from the ones and tens place. I was wrong, because I clearly saw good work on their movies. This worksheet was mastered easily for most of them. This student is so proud! Proud Guy! He worked so hard and made huge progress today!

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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