Multiplying 2-Digit by 2-Digit Numbers

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SWBAT multiply using the expanded algorithm to find partial products, then add to find the product.

Big Idea

Place value can be used to multiply by finding partial products. The partial products would be added to find the product.


5 minutes

In today's lesson, the students learn to multiply a 2-digit by 2-digit number using the expanded algorithm.  This aligns with 4.NBT.B5 because the students are multiplying two two-digit numbers using strategies based on place value.

To relate this lesson to their every day lives, I ask the students a question.  "What is multiplication?"  I let the students think about the question for a few seconds.  I always encourage my students to think before they speak.  I call on a student to share his response. He responded, "Adding multiples of a number."  I was proud of this student because he is usually quiet and tries to hide.  By allowing the students to think about what the skill is about, gives them the perspective of why the lesson is important in their lives.

"Today, you learn to multiply a 2-digit number by a 2-digit number.  In previous lessons we have learned to multiply a 2-digit by 1-digit number using the expanded algorithm.  How is multiplying by a 2-digit number by 2-digit number different from a 2-digit by 1-digit number?  Let's find out." 

Whole Group Discussion

10 minutes

I call the students to the carpet as we prepare for a whole class discussion.  The power point is already up on the Smart board.  I like for my students to be near so that I can have their full attention while I'm at the Smart board.  

To begin the lesson, I let the students know that we will use the expanded algorithm to multiply a 2-digit by 2-digit number. 

 Problem:  23 x 14

Identify the ones place and the tens place to help with writing the 4 simpler problems to multiply.  To do this, I place the numbers in a box.  I write ones and tens over the correct place.







 Next, write your 4 simpler problems based upon the place value.

3 x 4 = 12

20 x 4 = 80

10 x 3 = 30

20 x 10 = 200

Add the partial products to get a product of 322.


Let's try one together.

Problem:  59 x 37

Identify the place value to help with writing the 4 simpler problems.







 Write the 4 simpler problems.

9 x 7 = 63

50 x 7 = 350

30 x 9 = 270

50 x 30 = 1,500

Add the partial products to get a product of 2,183




Group or Partner Activity

20 minutes

For this activity, I put the students in pairs.  I give each group a Group Activity Sheet Multiplying a 2-digit by 2-digit.docx. The students must work together to find the product of the 2-digit by 2-digit multiplication problem.  They must use clear definitions and terminology as they precisely discuss this problem (MP1). The students are required to multiply using the expanded algorithm based on place value (4.NBT.B5).  In this lesson, they apply skills previously learned.   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 agree upon the simpler problems in the expanded algorithm and must find the product for the problem.  This is evident in their Student Work.  This takes discussion, critiquing, and justifying of answers by both students (MP3).  As the groups discuss this task, they must be precise in their communication within their groups using the appropriate math terminology for this skill (MP6). Each pair has counters to help them with their models, thus giving them a visual of how many cupcakes will be baked (MP5). 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. 

 During the phase, I monitor and assess the students' progression of understanding through questioning.  Possible questions to help lead to the solution are as follows:

1.  What is the value of each number?

2. After you find the 4 partial products, what must you do next?

3.  How can using an area model help you understand this problem?

As I walked around to monitor and question students, I was impressed by the students conversation.  At the beginning of the school year, we implemented Accountable Talk (a trademark for the Institute for Learning).  With Accountable Talk, the students must agree or disagree in a respectful manner.  They question each other's work by asking, "Can you explain more?, How did you get that answer when the problem said...(they refer back to the text), I think, etc. From the Video, you can hear the classroom chatter and constant discussion among the students.  Before Common Core, I thought that a quiet class working out of the book was the ideal class.  Now, I am amazed at some of the conversation going on in the classroom between the students.  

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:


15 minutes

To give me a clear understanding of what each student knows, the students will do an Exit Ticket 2-Digit by 2-Digit.docx   I need to assess students independently to make sure they are all comprehending the skill.   I will put a problem on the Smart board for the students to work (see attached resource).  The students will use paper and pencil to solve the problem. 

Exit Ticket

46 x 53 =

 The exit tickets is collected to be used to determine which students I will work with in small group for remediation.  Some of the students mastered the skill, which is evident in the Student Work - Exit Ticket.

I noticed from a few of the students' work that they tried to multiply instead of add the 4 partial products.  This is the introductory lesson on multiplying a 2-digit by 2-digit using the expanded algorithm.  The students will get more practice with the skill on the next lesson.  Also, some students will be pulled in small group for intervention.