##
* *Reflection: Developing a Conceptual Understanding
Division with Area Models - Section 1: Opener

Division is sometimes viewed as the scariest of the four basic operations. For me as a student I remember this being my least favorite type of problem to do in elementary school. I think one thing that the common core standards bring us is a focus on understanding the math. Gone are the days of simply memorizing an equation. Now as educators we are charged with the task of making sure students have a conceptual understanding of what is going on in the equations. I think by focusing on this conceptual understanding we can create a deeper understanding of concepts that will remain in our minds. Thinking back to even high school I can remember many test days I crammed five minutes before the test to memorize the equation needed. I’m not really sure I could recall any of those equations now. Maybe if there had been more of conceptual understanding created in my mind I would be able to recall them.

*Conceptual Understanding*

*Developing a Conceptual Understanding: Conceptual Understanding*

# Division with Area Models

Lesson 9 of 22

## Objective: Students will be able to perform simple division problems using an area model.

*50 minutes*

#### Opener

*10 min*

I see division as the last piece of the mathematical puzzle. If you think of the progression of the four basic operations it starts with addition which leads into subtraction. Then on to multiplication which involves addition. Finally, we reach division which encompasses all three of its predecessors. The hope is that by fifth grade students are secure enough in the first three to solidify their understanding of division. Because division brings the four operations full circle it is imperative that students have an understanding of this as well.

I open this lesson by asking the students a simple yet deep question.

*How are the four operations connected? If you think of each operation as a member of a family, what relationships do they have with each other?*

I allow students time to ponder these questions with their groups and bring the class back for a whole group discussion after 5-10 minutes. Student responses range from surface level connections to the deeper meanings I’m trying to elicit.

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#### Practice

*20 min*

Although division is introduced in the fourth grade standards it is important that students leave fifth grade with a definitive understanding of this fourth and final basic operation.

I begin the division review by creating area models with the students. I give each student 20 pattern blocks of random shapes. I ask students to think of them as pattern blocks and not their individual shape. Any other manipulative could be used for this activity as well.

I go through several examples with the students and focus on the process of dividing the blocks into equal groups. I create small story problems to accompany each example.

*Alright, I am starting out with twenty bunnies. Adamaris, Ana, Emonie, and Omar are each going to get the same number of bunnies. I’m going to start by making a pile for each person. One for Adamaris, one for Ana, one for Emonie, and one for Omar. Now that I have created piles I am going to go back and continue dividing the bunnies amongst these four people. (I continue giving each person one at a time.) It looks like I ran out of bunnies. Let’s make sure it is fair for everyone and they each have the same number of bunnies. Yup, each person has five bunnies and there are no bunnies left over. So 20 bunnies divided by 4 people is 5 bunnies per person. *

I have the students do a couple more examples with me and sort their blocks as I sort mine. I focus on the summary at the end which outlines the secret division sentence.

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#### Closer

*20 min*

To continue working on area models I have the students work with their partners to create their own story problems and solve them with the blocks.

*Now it’s your turn. You and your neighbor are going to take turns coming up with division story problems while each of you solves the problem with blocks. Be creative! *

I circulate the room and check for understanding of the pairs to identify any misconceptions with area model.

Video place holder students working on creating and solving.

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##### Similar Lessons

###### Show what you know + Equivalency

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- LESSON 1: Place Value Review
- LESSON 2: Ten Times
- LESSON 3: 1/10 Of...
- LESSON 4: Powers of Ten (Day 1)
- LESSON 5: Powers of Ten (Day 2)
- LESSON 6: Powers of Ten Applications
- LESSON 7: Turtlehead Multiplication
- LESSON 8: Taking it Back to the Old School
- LESSON 9: Division with Area Models
- LESSON 10: Division in Steps
- LESSON 11: Division as a Diagram
- LESSON 12: Remainder Riddles
- LESSON 13: Double Digit Division
- LESSON 14: Double Digit Division Task-2 Days
- LESSON 15: Rounding Decimals
- LESSON 16: Comparing Decimals
- LESSON 17: Adding Decimals
- LESSON 18: Subtracting Decimals
- LESSON 19: Multiplying Decimals
- LESSON 20: Decimal Operations
- LESSON 21: Operations with Decimals & Whole Numbers Review
- LESSON 22: Operations with Decimals & Whole Numbers Assessment