##
* *Reflection: Checks for Understanding
Multiplying one digit by two digits using the AREA MODEL - Section 2: Concept development

As you can see in my reflection video, this lesson went much better considering this was the second time through it. I have a handful of students who are really reluctant to show the area model and want to just use the standard algorithm the way a parent has showed them. If a student can explain why the shortcut algorithm works, I let him/her use it. As of today, none of my students can do that.

Place value is such a key in understanding the algorithm that even the general public doesn't understand. The area model for multiplication is closely related to the actual computation you perform using the standard algorithm for two-digit multiplication, however without full understanding of what is happening to the digits, students then struggle with more complex problems. The area model is used to lead to the development of the standard algorithm. The algorithm becomes dependent upon each action used with the area model.

Occasionally parents will complain and remind me that the standard algorithm is generally a faster method. I agree with them and explain that unlike the area method, it does not promote understanding or encourage the development of mathematical thinking as well as supporting the important ability to estimate answers.

I mentioned in my video that I wouldn't change anything about this lesson, now that I went back and gave students more time and practice with multiplying by multiples of ten. I did mention that the only thing I wished I had more of is time. My students are getting into a really good groove of math talk, concept development and applying procedures. Our hour goes by so fast. If I could design my dream schedule, I would definitively give myself 90 minutes of math every day.

*Much better the second time*

*Checks for Understanding: Much better the second time*

# Multiplying one digit by two digits using the AREA MODEL

Lesson 7 of 22

## Objective: SWBAT find products of one digit by two digit multiplication using the area model.

#### Warm Up

*5 min*

This is a quick review from yesterday's lesson, multiplying by multiples of ten. I display these problems on the board one at a time.

60 x _____= 360

350 = 70 x _____

900= 100 x ____

80 x _____ = 640

#### Resources

*expand content*

#### Concept development

*45 min*

This lesson should look familiar to a lesson I tried last week. It became obvious during that lesson that students needed more guidance and scaffolds before they could be successful with this lesson. (In a way this is take two of a previous lesson.)

I begin this by modeling the area model for multiplication using a multiple of ten. Since my students did so well with multiplying multiples of ten in yesterday's lesson, I wanted to incorporate that and note that with an area model. I show this by writing a number sentence like 6 x 70 on the smartboard. Then I draw a long horizontal rectangle to model an area of 6 rows by 70 columns. I make explicit that in the number 70, that is **7 tens and NO ones**. I find this language crucial for students to see the relationship between what they did when multiplying by multiples of ten and then transferring that knowledge to other double digit numbers today.

Then I show an area model for a two digit by one-digit numbers sentence. I model this by decomposing a 2-digit number into tens and ones, and then model area representations and partial product arrays. So, for example, 63 x 7 can be modeled with 60 + 3 multiplied by 7 columns.

If you're not sure what the area model for multiplication is, you can watch the showme video below.

This lesson provides conceptual understanding of what occurs in a 2-digit by one-digit multiplication problem and allows students to deepen their understanding of multiplication as they build their skills in order to master CCSS 4.NBT.5. Partial product models and area models serve as transitions to understanding the standard multiplication algorithm.

After I show the area model, we do several together. Students build the area models on small graph paper. They build the rectangles, using the correct amount of squares to visually see the square units. I find this step to be necessary before using a paper and pencil model. As students use the graph paper, I discuss with them that the paper doesn't have enough rows or columns of squares to make large models. This serves as a springboard to then discuss how the model, "models" the situation and does not have to be drawn to scale.

Then I have students participate in an activity I call "Walk the Room."

Students will use clipboards as they walk around the room to solve the problems that are posted. When students did this before, they solved problems independently. I decided to have students use learning partners because I want to continue to foster their communication skills in order to develop Math Practice Standard 3. The partner work allows for opportunities to communicate with the area model and talk through problems with a peer. In the photo below, you can see a sample of a students area model.

I have many two-digit by one-digit multiplication number sentences hanging around the room for students to solve. They do not need to solve all of them, there are a lot. I tell students that I would like theme to solve between 4and 7 problems. Students can wander to a problem that is not being completed by another student. See this video for what my classroom looked like.

The area model is the easiest method for students to use. By teaching it first, I am able to build conceptual understanding for all students and provide a method that any student can use. For students that struggle with the area model, I pull them out during my re-teach time and present other alternatives, such as using base ten blocks. Students would build a number like 26 and then do that 4 times to model 4 x 26. I then make connections between the base ten block method and the area model method by rearranging the base ten blocks to show the two columns of tens together in four rows and the six columns of ones together in four rows.

*expand content*

#### Student debrief - Wrap up

*15 min*

Students spend the last 10 minutes of the lesson making a poster with their learning partner. Their poster must meet these requirements:

1. Choose a single digit by double digit multiplication problem to show on your poster. Write it BIG so people can see it from far away, but not too big. Your poster will have other items on it as well.

2. Show an AREA MODEL for your problem.

3. Using words, pictures and numbers communicate how to use an area model to find products.

Students do not have time to present their posters to the class during this time period, but as they are working on their posters, I am able to talk with partners about their posters. This is a great time to see if anyone has misconceptions that need cleared up. This is a busy and active time in my classroom. I have found that playing low classical music keeps the noise level low and students more on task. I do like reminding them about not being sheep or hogs from the partner video we've watched before.

These two students explain multiplying 46 x 9 in this video as they make their poster.

#### Resources

*expand content*

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- UNIT 1: Getting to Know You- First Days of School
- UNIT 2: Multiplication with Whole Numbers
- UNIT 3: Place Value
- UNIT 4: Understanding Division and Remainders
- UNIT 5: Operations with Fractions
- UNIT 6: Fraction Equivalents and Ordering Fractions
- UNIT 7: Division with Whole Numbers
- UNIT 8: Place value
- UNIT 9: Geometry
- UNIT 10: Measurment
- UNIT 11: Fractions and Decimals

- LESSON 1: Multiplicative Comparison Problems
- LESSON 2: Finding Factors and Prime Numbers
- LESSON 3: Multiplication arrays
- LESSON 4: Mental Math and Multiplication with Tens
- LESSON 5: One digit by two digit Multiplication
- LESSON 6: Multiplying multiples of ten - Not your Daily Grind
- LESSON 7: Multiplying one digit by two digits using the AREA MODEL
- LESSON 8: Methods of One-Digit by Two-Digit Multiplication
- LESSON 9: Compare methods of one digit by double digit multiplication
- LESSON 10: Practice Makes Perfect
- LESSON 11: Two-Digit by Two-Digit Multiplication
- LESSON 12: Looking at Different Multiplication Methods
- LESSON 13: Multplication Application with Food Service Staff
- LESSON 14: Multiplication Methods using COMPUTERS!
- LESSON 15: Multiplication and First Quarter Assessment
- LESSON 16: Using Games to practice multi-digit multiplication
- LESSON 17: Multiplication Bingo - Game Day 2
- LESSON 18: Estimate Products
- LESSON 19: Multiplication and Problem Solving to Make Bracelets Day 1
- LESSON 20: Multiplication and Problem Solving to Make Bracelets Day 2
- LESSON 21: Bracelet Wrap Up
- LESSON 22: Multiplication Card Game and Factorial Fun