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# Area Models: 4 Digit by 1 Digit Multiplication

Lesson 4 of 19

## Objective: SWBAT multiply 4 digit by 1 digit using area models.

My students came in from recess and settled down quickly to work on multiplication facts on their TIMED TEST ap on iPads. When they completed one test, I asked them to list the factor pairs for 54,55,56,57,58 in their math journal.I roved around the class and checked notebooks.

When all were complete, I asked students to share the factor pairs they came up with. We worked each product. Students used their divisibility skills to decide on factor pairs. This time, it went very smoothly and students were able to easily find all the factor pairs.

Factor pairs were listed and our dialogue sounded like this:

54

1x54, 2x27, 3,? no, 4,? no 5, of course not! 6...yep. 6x9. 7? no, 8? no...and then comes the commutative pair...or turn around and we are done!

They are getting much easier! Practice makes perfect!

#### Resources

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We began this portion of the lesson by watching a.student video that was made the day before . We talked about how great it was, but that we need to include more place value language in our videos.

What are you going to do differently? I posed this first question to open up the discussion because I want my students to monitor their learning and think about how to improve and master the standards completely. One boy realized he had not lined up the numbers. Another person realized that math fact knowledge needs to be watched. Paying attention to products. One other boy decided that paying attention to details ( our class motto) was important because he wrote the wrong factor down.

This is a great way to put the responsibility of learning right into the student's lap. They know exactly what they need to do better before the next lesson. It is my hope that this is very effective in order to achieve mastery. I think it is these types of discussions that push students toward mastery of standards.

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I decided that today, students would be leveled into their respective learning groups so that they could master 4 digit times 1 digit multiplication in a way that was right for them.

I told them that I had been gradually releasing their mastery from the first day of learning about area models.

I asked them how they thought we might figure out a 4 digit problem. To my amazement, four students almost simultaneously said..draw an area model with four boxes.

I listed four random expressions on the board that were 4x1 digit. To the right of that, I listed the expectations for my high group of students ( I simply called out their names). 1. Write a story problem that involves a four digit by one digit situation equation. 2. Write an equation with a variable. 3. Solve the equation using area model. 4. Do this all on Educreations and use creativity and place value words in your work. 5. Be ready to share or use your video to help someone learn.

My middle students were to simply practice all four problems on the board. Afterward, they were to choose one problem and do an Educreations video explaining how to solve 4x1 digit problems.

My lowest group joined me on the floor. I sat and instructed them on how to solve 4x1 digit problems using a small whiteboard. Students imitated my work and then did a few problems on their own. We talked about problems by saying out loud, 3 groups of 5,432. Then we said the expanded form out loud while we listed it. I discovered that if struggling students list the expanded form using plus signs, they can easily draw the rectangle and lines like this.

My high end students did a great job with their lessons. I discovered, however, that I needed to spell out that they should use a 4 digit number with no more than one zero. My mistake.

When I approved each video, they partnered up and looked at each other's work.

While this was going on, I also had middle level students coming to me with their notebooks filled with their work from the board. I asked them to check their work with calculators. I told them if they were wrong, to start by looking at their partial product first since we had problems yesterday with basic facts. Then they should look at their addition. They began one by one to create a video about how they solved one of the problems.

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#### Assignment

*10 min*

Assignment 3 Worksheet All students were assigned the same worksheet. I did this because of the weak math facts with even the high end students. I decided it was a good thing for all levels of learners to just practice the 4x1 digit problems for tonight. Since this is really their first experiences with area models, I want to be absolutely sure everyone is mastering their work.

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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