##
* *Reflection: Developing a Conceptual Understanding
Multiplying 2-digit number by 1-digit number - Section 5: Closure

Using the expanded algorithm to multiply gives students a conceptual understanding. Before Common Core, I did not like teaching the expanded algorithm because I did not use it in my personal life. I always use the standard algorithm. To be honest, I do not remember learning the expanded algorithm in school.

As teachers, sometimes we like to teach what we are comfortable with doing ourselves. After teaching the last two lessons on multiplying based on place value, I really like the expanded algorithm! All of the students were able to grasp the concept of the distributive property. A few of them still needs practice with the visual model, but they can break the problem into simpler problems, then add to get the product.

I use to dread teaching multiplying a 2-digit by 2-digit. A lot of the students could not follow the steps. I'm hopeful that since they learned multiplying a 2-digit by 1-digit using the expanded algorithm, they will be successful on the 2-digit by 2-digit with the expanded algorithm and actually understand what it means.

*Using the Expanded Algorithm*

*Developing a Conceptual Understanding: Using the Expanded Algorithm*

# Multiplying 2-digit number by 1-digit number

Lesson 9 of 23

## Objective: SWBAT multiply a 2-digit number by a 1-digit number using strategies based on place value, then justify their answers using counters.

#### Opener

*5 min*

*Rationale for teaching with a task:*

*After I have worked directly with the students on a skill, I like to use a task. A task gives the students more practice on the skill while working in differentiated groups. Allowing the students to work in groups gives the students different perspectives from their classmates. Students can learn from each other. As the students work on a task, I am the facilitator, walking around monitoring and questioning the students to lead them to the solution.*

I let the students know that today we will do a task. I remind the students of the structure and routine of a task. First, the students have private work time to think about and plan how to solve the task. Next, the students work in groups to explore the concept of the lesson. Finally, the students share/analyze/and discuss the task as a whole class. Each student has a copy of the task at their desk and counters. We have already learned how multiply a 2-digit number by a 1-digit number by using area models.

In today's lesson, the students use their understanding of the learned skilll to solve this task without direct instruction. They will be guided to the answer through questioning by me as they work in their groups. They have to find the answers by multiplying a 2-digit number by 1-digit number using strategies based on place value **(4.NBT.B5).**

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#### Task

*5 min*

Give the students about 5 minutes of independent time to read and plan to solve this Cupcake Task.docx **(MP1)**. The students should have counters at their desk. The students can use the counters at this time to plan how to solve the task** (MP5)**. The counters will help the students understand what multiplication actually means because they will have a visual of the simpler multiplication problems. After the 5 minutes of independent planning, the lesson goes to the next phase of group exploration.

Cupcake Task:

Mrs. Jones needs to make cupcakes for her daughter’s birthday party. If she bakes 24 pans of cupcakes and each pan holds 6 cupcakes, how many cupcakes will she bake?

Directions: Help Mrs. Jones figure out how many cupcakes she will bake. Use the expanded algorithm to solve your problem. Make a model of your simpler multiplication problems with the counters. Explain how using the counters to model your problem help you with finding the product.

#### Resources

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#### Group Exploration/Discovery

*20 min*

During the group exploration/discovery phase, the students work in pairs. Each group has a copy of the task. The students must work together to complete all requirements of the task. The students are required to multiply using the expanded algorithm based on place value to find out how many cupcakes Mrs. Jones will bake **(4.NBT.B5)**. The students reason abstractly and quantitatively by decontextualizing the information from the task and representing it symbolically **(MP2)**. During this phase, the students do not receive direct instruction. 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 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 this 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 task asking you to find?

2. How can the counters help you solve this problem?

3. After you find your simpler problems, what should you do next? Why?

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. In this lesson, as I listened in on one pair, I heard one studay say, "I think that the answer should be 144 because I broke the problem into 4 x 6 = 24 and 20 x 6 = 120." It is very encouraging to have students learn a skill and be able to explain their thinking.

All pairs were able to calculate the correct answer to the problem. Because we have been working with the distributive property for a whole now, and the students are quite familiar with it, I feel that this helped the students find the correct answer. Also, differentiating the students according to ability, ensured that all groups would be successful. However, I had to facilitate to make sure that all students were actively participating in the discussion and activity in order to master the skill for themselves. It is rewarding to me as a teacher because this task allowed me to assess the students understanding of the skill that has been utilized in the classroom.

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.funbrain.com/cgi-bin/ttt.cgi?A1=s&A2=13&A3=0

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#### Share/Discuss/Analyze

*15 min*

During this phase of the lesson, student solution paths are shared. While the students were working in groups and I was walking around monitoring and questioning, I identified solution paths to be shared as a whole class for this phase.

I call groups to the front to share their solutions. This part of the lesson is lead by the teacher through asking assessing questions. The students may also have questions that they would like to ask. The students are required to use Accountable Talk and show respect to their classmates as they present their solutions. I use a document camera to display the student work on the Smart board for all students to see.

During this phase, I like to organize the sharing of the solution paths in a strategic manner. I begin with a group that did an excellent job at breaking about the problem into 2 simpler problems. I have the students discuss how they know that their 2 simpler problems are correct. I am listening for the students to reference place value in their answer. From there, I have another group explain how to find the product after you have broken the problem into simpler problems. I have already determined while they were working in groups that these two students knew to add the two simpler problems to get the product. Last, I have a pair of students explain how using counters can help them with this skill. While these two students were working in pairs, they were able to explain that the counters can show the total number of cupcakes. As one of them said, "All you have to do is add them up."

I feel that this is a well rounded lesson on how to multiply a 2-digit number by a 1-digit number using the expanded algorithm based on place value because the students are responsible for their own learning. I feel that this lesson was a success because the students showed me that they could multiply a 2-digit number by a 1-digit number using the distributive property. The students were given the tools and resources needed, and they accomplished their goal of solving the task.

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#### Closure

*10 min*

After the share/discuss/analyze phase of the lesson, close the lesson out by having the students do an Exit Ticket Multiplying a 2-digit by 1 digit number.docx. This will enable me to see how well the students understood how to multiply a 2-digit number by a 1-digit number using place value.

The students will receive an exit ticket to complete their answers. I will collect these exit tickets to evaluate the students' understanding. Those students who need remediation will work with me in small group the next day.

A sample of a student's exit ticket (Student Work - Multiplying a 2-digit by 1-digit) is attached.

Results of Exit Ticket:

All of the students, except for 2, could use the distributive property correctly. These 2 students are my lower level students. Even though they were able to write it in their groups, when it came to doing it independently, they got confused about how to break apart the 2-digit number. They knew to break apart the 15, but they broke it about into 1 and 5, not 10 and 5. These students could show me 3 sets of 15 counters to get the correct product of 45. However, they could not write it with the distributive property. This is okay because the important thing is that they can come up with the product.

I will work with these 2 students in small group on how to use the distributive property because it is necessary because of how our students are tested on our state test.

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- UNIT 1: Fractions
- UNIT 2: Skills Review
- UNIT 3: Algebra
- UNIT 4: Geometry
- UNIT 5: Patterns & Expressions
- UNIT 6: Problem-Solving Strategies
- UNIT 7: Decimals
- UNIT 8: Measurement and Data
- UNIT 9: Multiplication and Division Meanings
- UNIT 10: Place Value
- UNIT 11: Adding and Subtracting Whole Numbers
- UNIT 12: Multiplying and Dividing

- LESSON 1: Multiplying by Multiples of 10 and 100
- LESSON 2: Using Rounding to Estimate
- LESSON 3: Is Your Answer Reasonable?
- LESSON 4: Using Clues to Multiply or Divide
- LESSON 5: Using Mental Math to Multiply 2-Digit Numbers (Are You My Match?)
- LESSON 6: Multiplying 2-Digit Numbers by Multiples of Ten
- LESSON 7: Multiplying Greater Numbers
- LESSON 8: Modeling: Multiplying a 2-digit number by a 1-digit number
- LESSON 9: Multiplying 2-digit number by 1-digit number
- LESSON 10: Multiplying a 3-digit number by a 1-digit number
- LESSON 11: Estimating Products
- LESSON 12: Multiplying 2-Digit by 2-Digit Numbers
- LESSON 13: Multiplication: Arrays and an Expanded Algorithm
- LESSON 14: Multiplication Unit Assessment
- LESSON 15: Using Mental Math to Divide
- LESSON 16: Estimating Quotients
- LESSON 17: Dividing with Remainders
- LESSON 18: Dividing 2-Digit by 1-Digit Numbers
- LESSON 19: Dividing 3-Digit by 1-Digit Numbers
- LESSON 20: Deciding Where to Start Dividing
- LESSON 21: How Much Will They Get?
- LESSON 22: Factors
- LESSON 23: Prime and Composite Numbers