# Multiplying a 3-digit number by a 1-digit number

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## Objective

SWBAT multiply a 3-digit number by a 1-digit number using strategies based on place value.

#### Big Idea

Students can multiply a 3-digit number by a 1-digit number using place value blocks as models.

## Opener

5 minutes

In the Introductory Video Multiplying 3 Digit by 1 Digit, I explain the lesson for today.

The students have already learned how to use the expanded algorithm to find simpler problems to solve a 2-digit by 1-digit multiplication problem.  In today's lesson, they learn to find partial products using place value to multiply a 3-digit number by a 1-digit number.  This gives the students a visual and helps them find the product when multiplying a 3-digit number by a 1-digit number.  This aligns with 4.NBT.B5 because the students are multiplying using strategies based on place value.

To begin the lesson, I remind the students that we have learned to multiply a 2-digit number by a 1-digit number by making an area model and using place value blocks.    I ask the students, "how did making an array help you understand the problem?"  I let the students think about the question for a few minutes, then call on a student to respond.  One student said, "I could count the pieces in the array to get my answer."   I let the students know that today they will learn to multiply a 3-digit number by a 1-digit number using strategies based on place value.

## Whole Class Discussion

15 minutes

To begin our review, I call the students to the carpet.  On the Smart board, I have the Multiplying a 3-digit by 1-digit number review slide that we will discuss as a whole class.

At the beginning of each lesson, I like to review all relevant skills that we have learned that will help with the new skill.  Since the students have already learned this information, I just want to bring it back to the forefront of their minds.

Review:

1.  You can use an array to help you multiply.  For example, 5 x 13 = 65.  We can show this by making an array:

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2.  Identity property of multiplication says that when you multiply a number by 1, the product is the other number.
3.  Commutative property of multiplication says that you can multiply factors in any order and will get the same product.
4.  Property of Zero says that when you multiply a number by zero, the product is zero.
5.  Use place value to help you multiply.  Let's review the places beginning at the right.  We have the ones, tens, hundreds, thousands, ten thousands, and hundred thousands.  Let's find out how place value can help you multiply a 3-digit number by a 1-digit number.
The properties of multiplication help the students if they multiply a number by 1 or 0.  Knowing these properties should help alleviate mistakes in their multiplication.  Also, knowing the commutative property will help the students with this lesson because if the number is written with the 1 digit number first, the students know that they can change the order of the numbers and still get the same product.

I review all of this relevant information on the Smart board with the students.  My students know that they can interact and jump in the conversation at any time.  I question my students throughout the review.  1)  How can the properties of multiplication help you to multiply other numbers?  2)  Why should we use arrays/models to help with multiplication?  I call on students who raise their hands, and at other times I call on students who do not raise their hands.  This will let all students know to listen attentively and be prepared with an answer.  From the students responses, they know that the properties of multiplication can help them multiply numbers with 1 and 0.  One student responded, "Models help us count to find the product."

After the review, we do a problem together (Practice Problem Multiplying 3-digit by 1-digit.pptx) to show the students how to use place value to write 3 simpler problems.

Problem:

My mom owns 138 flower pots.  Each flower pot has 5 flowers in it.  How many flowers does my mom own in all?

Our multiplication problem is 138 x 5=

First, we multiply the ones:  8 x 5 = 40.

Next, we multiply 5 x 30 = 150

Last, we multiply 100 x 5 = 500

Add all the partial products:  500 + 150 + 40=  690

On the Smart board, I show the Model Multiplying 3-digit by 1-digit slide that breaks down how to model with place value blocks.  After, we finish discussing this problem and the place value model, the students go back to their seats to work on the skills with their classmates.

## Group or Partner Activity

20 minutes

During this group activity, the students work in pairs.  Each pair has a copy of the Group Activity Multiplying a 3-digit by 1-digit.docx. The students must work together to find the product to a 3-digit by 1-digit multiplication problem using place value (4.NBT.B5).  The students must decontextualize the problem and represent them symbolically (MP2). They must model this problem using the place value blocks (MP5).  Before they begin the activity, each pair will be given a few minutes to think about the problem and how they will solve it (MP1).

The students are guided to the conceptual understanding through questioning by their classmates, as well as by me.  The students communicate with each other and must agree upon the answer to the problem.  Because the students must agree upon the answer, this will take discussion, critiquing, and justifying of answers by both students (MP3).  As the pairs discuss the problem, they must be precise in their communication within their groups using the appropriate math terminology for this skill (MP6).  As I walk around, I am listening for the students to use "talk" that will lead to the answer. I am holding the students accountable for their own learning.

As they work, I monitor and assess their progression of understanding through questioning.

1.  What is the value of each number?

2. After you find the 3 partial products, what must you do next?

3.  How can you represent these partial products with the place value blocks?

As I monitor to listen in on the students' conversation, I am listening for the students to justify their answers or question other students about their answer.  All of this should be done in a respectful manner.  We implemented Accountable Talk at the beginning of the year, so the students know what is expected of them.  I am listening for the students to say, "after they find the 3 partial products, they add all 3 numbers together to get the product."

From the sample of Student Work - Multiplying a 3 digit by 1 digit, you see how the students used the expanded algorithm to solve the multiplication problem.  The students accurately solved the problem by multiplying by 3 simpler problems, then adding the partial products.

Any groups that finish the assignment early, can go to the computer to practice the skill at the following site until we are ready for the whole group sharing: http://www.mathplayground.com/multiples.html

## Closure

15 minutes

To close the lesson, I bring the class back together as a whole.  We go over the answers to the problems.  I call on different pairs to share their answers.  Their classmates have the opportunity to ask any questions to get them to clarify their answer.  This gives those students who still do not understand another opportunity to learn it.  I like to use my document camera to show the Student's work during this time.  Some students do not understand what is being said, but understand clearly when the work is put up for them to see.

I was proud of the students because they caught on to multiplyig a 3-digit number by 1-digit number quickly.  They had no problem breaking apart into 3 simpler problems, but I did have to question a few students to lead them to the last step of adding the 3 partial products.  I'm quite sure that using the expanded algorithm in a previous lesson helped to make this lesson easier and helped the students get a clearer understanding place value and multiplying.

I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson.  Students need to see good work samples, as well as work that may have incorrect information.  This teaches the students what not to do in the future.