# Modeling: Multiplying a 2-digit number by a 1-digit number

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## Objective

SWBAT use place value to model multiplication problems to find the products.

#### Big Idea

Using area models can help you multiply and gives you a visual of the product.

## Opener

5 minutes

The students have already learned that they can use an array to help find the product to simple multiplication problems.  In today's lesson, they learn to find partial products and illustrate them with an area model to find the product of a 2-digit number by a 1-digit number.  This aligns with 4.NBT.B5 because the students are multiplying 2-digit numbers using strategies based on place value and properties of operations.

To begin the lesson, I ask the students a question.  "When might you multiply a 2-digit number by a 1-digit number?"  I let the students think about this question for a minute or two.  I encourage my students to always think before they speak.  I call on a student who does not have their hand raised.  By doing this, I want all students to be heard.  Some students think that they do not have the right answer.  We all have valuable information to lend to the conversation. He responded, "When you want to buy more than one thing."  I asked, "Does anyone want to add on to what was said?"  I call on a student with his hand raised.  He adds, "Just say if you go to the store and buy 2 new shirts.  If they cost \$10 each, then you can multiply a 2-digit number by a 1-digit number."  I let them know that they both are correct.  I let the students know that today they will learn to multiply using strategies based on place value.

## Whole Class Discussion

15 minutes

I call the students to carpet for our whole class discussion.  I like for my students to be close to me when having these discussions.  It gives us a sense of a classroom environment that works together.  The Multiplying a 2-digit by 1-digit number review power point is on the Smart board.

At the beginning of each lesson, I like to review all relevant skills that we have learned that will help with the new skill.

Review:

1.  You can use an array to help you multiply.  For example, 3 x 5 = 15.  We can show this by making an array:

xxxxx

xxxxx

xxxxx

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 2-digit number by a 1-digit number.

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?

After the review, I work a problem together with the students that shows them how to use the strategies.

Problem:

Mr. Harris has 21 students in his class.  Each student takes 4 practice tests in math.  How many practice tests will they take in all?

Our multiplication problem is 21 x 4.  In order to use place value to multiply, we use the distributive property to break apart each place.  Always begin with the ones place.  We can break apart a 2-digit by 1-digit number into 2 simpler problems.

1 x 4=4  (Both numbers are in the ones place, so their value are ones.)

20 x 4 = 80  (Notice that the 2 is in the tens place.  Therefore, we are multiplying 20, not 2.)

Add the 2 partial products, 4 + 80  = 84

We use grid paper to make an area model to check our answers (see resource).

As a class, on the Smart board we use 2 different colors to shade the appropriate areas to show the two partial products for 21 x 4 on the grid paper.

I send the students back to their desks to get ready to practice the skill in groups.

## Group or Partner Activity

20 minutes

During this group activity, the students work in pairs.  Each pair has a copy of the Group Activity Sheet Multiplying 2-digit by 1-digit. The students must work together to find the product to a 2-digit by 1-digit multiplication problem using place value (4.NBT.B5).  They must model this problem using the CentimeterGrid paper (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 must use what they have learned about Accountable Talk to communicate with their classmates.  The students communicate with each other and must agree upon the answer to the problem.  They must say things, such as, "I agree because, or I disagree because."  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 2 partial products, what must you do next?

3.  How can you represent these partial products on the grid paper?

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

As the students worked on this assignment, I walked around to monitor.  I noticed that most of the students used the distributive property correctly to break apart the 2-digit number.  They multiplied 2 simpler problems, then added the two partial products.  As you can see in the student work (Student Work - Modeling Multiplication), the students used the grid paper to model 6 x 13.  The students broke apart 13 into 10 and 3.  Their shaded areas are (6 x 10) and (6 x 3).

In the video, Multiplying 2-digit by 1-digit video, I discuss student work and the mistakes that were made by a few students.

## Closure

15 minutes

To close the lesson, I bring the class back together as a whole.  I have one or two students share their answers.  This gives those students who still do not understand another opportunity to learn it.  I like to use my document camera (Student Work - Modeling Multiplication) to show the students' 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 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.  More than one student may have had the same misconception.