Meanings for Division

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SWBAT use and draw models to solve division problems.

Big Idea

Drawing models can make division easier.


5 minutes

In today's lesson, the students learn the meaning of division.  This aligns with 4.NBT.B6 because the students learn division by illustrating and explaining the calculation by using equations, rectangular arrays, and/or area models.

To begin, I remind the students that they have learned that multiplication can be thought of as repeated addition.  I share with the students that today, you learn the meaning of division. Can anyone tell me about a time you had to share something with your brother or sister?  One student responds, "I had to share my candy with my little sister."  Another student responds, "I had to give my sister part of my money."

Direct Instruction

10 minutes

I call the students to the carpet to begin our whole class discussion.  I like for my students to interact with me during our whole group discussion.  I like to ask questions of them to make sure they are understanding the skill.

The Meanings of Division.pptx power point is displayed on the board.

To begin our discussion, we discuss vocabulary words that are important to this lesson.  I read the word and definition aloud.  The students repeat the word and definition after me.  I let the students know that they will have a better understanding of the vocabulary words as we go through the example in the power point.

Dividend:  The number that is being divided (total).
Divisor:  The number by which another number is being divided.
Quotient:  The answer to a division problem.
We go on to discuss the meaning of division.
 I let the students know that you can draw an array model or use two-color counters to help you divide. Let's look at this problem to find out how.
Susan has 18 books.  She wants to put the same number of books on her 3 shelves.  How many books can she put on a shelf?  Let’s find out.
We can draw a model to help us.

Susan has 3 shelves.





She has 18 books to put on each shelf.  We can draw 3 circles and divide the 18 books evenly on each shelf.

She can put 6 books on each shelf.

 Another way  to divide is by using two-color counters.

Take your counters and put them in 3 separate groups. (This is displayed in the power point on the Smart board.)
3 represents the number of shelves (divisor), so this is the number of groups in our model. 

18 represents the number of books (dividend).  This is the total that is being shared equally. The quotient will be how many books are in each group.




Group Activity

20 minutes

I put the students in pairs.  Each pair of students will get a Meanings of Division assignment sheet.  The students are to work together (Students Working) to solve the real-world problems.  The students should draw models to solve the problems. They can check their answers by making an array with the two color-counters. Here are samples of student work: Student Work and Student Work - Meaning of Division. Also, this is a video (Video -Meanings for Division) of the students working on the assignment.

I monitor the pairs as they work on the problems.  As I monitor, I ask the students questions that can help lead them to the big idea.  

Possible Questions:

What important information do you need from the word problem?

What is the total number of items that you have (dividend)?

How many groups do you have?  

What should you draw first in your model?

How can counters help you check your answer?

Early Finishers:  The students can practice the skill at the following site:



Independent Activity/Exit Ticket

10 minutes

Group work is important in the classroom, but independent work is just as important.  When students work together, they seem to really enjoy the lesson.  However, in order for me to assess mastery, I like for my students to do an independent assignment.  

The directions are displayed on the Smart board.

For this assignment, the students write a division problem.  They draw an array model to represent the division problem.  The students must tell how the model helped with solving the division problem.

After some of the students share their problems, I collect the problems to use for future planning.