Dividing with Remainders

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Objective

SWBAT divide whole numbers by 1-digit divisors using manipulatives.

Big Idea

Manipulatives give the students a visual of how to divide numbers by 1-digit divisiors.

Opener

5 minutes

In today's lesson, the students learn to use manipulatives to divide numbers by 1-digit divisors. They must consider the multiplication problem that supports their answer.  This aligns with 4.NBT.B6 because the students find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.

To get started, I ask the students a question.  "When might you need to divide something in the real world?"  I give the students a few minutes to think about the question.   I take a few student responses. "When you want to share something with your friends," one student answered.  "That is correct. "   I tell the students, "Today, we will use manipulatives to help divide with a 1-digit divisor.  Our multiplication facts will help us."

Whole Class 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.  

I begin by going over important vocabulary for this lesson.  The students will have to know these terms to understand the lesson.

Vocabulary:

quotient -  an answer to a division problem

divisor - a number by which another number is being divided

dividend - the amount you want to divide

remainder - the part that is left after you divide

Problem 1:

Thomas has 15 marbles.  He wants to put the same number of marbles in 4 different containers.  How many marbles will be in each container?  How many marbles will be left as a remainder?

First, I ask the students to identify what operation will be used to solve this problem.  "Division," I hear most of them yell out.  Based upon past knowledge, the clue words "same number" lets us know to divide.  Therefore, this is a division problem. The problem is 15 divided by 4. Also, the key word "left" let us know that we are going to subtract to find the remainder.  

We can use our unit blocks to make a model of the problem.  We know that there will be 4 groups.  We can take our 15 unit blocks and begin to separate them into 4 groups, 1 by 1.  Remember, that when you finish separating the unit blocks, there should be the same number of blocks in each group.  The leftover unit blocks will be your remainder.

 

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The quotient to this problem is 3 because there are 3 marbles in each group (4 x 3 = 12).  There will be 3 marbles left (15 - 12 = 3).  Therefore, the remainder is 3.  

 

Let's try another one.  

Problem 2:  37 divided by 8.

We can use our unit blocks to make a model of the problem.  We know that there will be 8 groups.  We can take our 37 unit blocks and begin to separate them into 8 groups, 1 by 1.  Remember, that when you finish separating the unit blocks, there should be the same number of blocks in each group.  The leftover unit blocks will be your remainder.

 xxxx  xxxx  xxxx  xxxx

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 The quotient to this problem is 4 because there are 4 items in each group (4 x 8 = 32).  There will be 5 marbles left (37 - 32 = 5).  Therefore, the remainder is 5.  

Group or Partner Activity

20 minutes

I give the students practice on this skill by letting them work together.  I find that collaborative learning is vital to the success of students.  Students learn from each other by justifying their answers and critiquing the reasoning of others.

For this activity, I put the students in pairs.  I give each group a group activity sheet.  The students must work together to find the quotient to the division problems.  They must use the unit blocks or an other type of manipulative (MP5) to separate the dividend into groups.  They must identify the multiplication number sentence that helps them solve this problem.  A multiplication chart is attached to assist the students.  They must communicate precisely to others within their groups. They must use clear definitions and terminology as they precisely discuss this problem.

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 must agree upon the answer to the problem.  Because the students must agree upon the answer, this will take discussion, critiquing, and justifying of answers by both students.  The students discuss the problem and agree upon the answer to the problem.  As the pairs discuss the problem, they must be precise in their communication within their groups using the appropriate math terminology for this skill.  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 dividend in this problem?

2. What multiplication problem will help find the dividend?

3.  What is the remainder?  How did you find the remainder?

As I walked around the classroom, I heard the students communicate with each other about the assignment.  I 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.  As I walk around, I hear students say things like 'there has to be the same number in each group," "we need to take one away because it's not enough to put one in each group."  

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/math/index.html

Closure

15 minutes

To close the lesson, 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 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.  During the closing of the lesson, all misconceptions that were spotted during the group activity will be addressed whole class.  

 

Misconceptions:

The biggest misconception that I saw during this lesson was that some of the students used a multiplication problem that gave a product that was larger than the dividend.  For example, with the division problem of 43 divided by 6, some students used the multiplication problem of 6 x 8 = 48.  During the closure, we discussed that fact that you cannot use a number larger than the dividend.  This is just our first week working with division.  Some of the student progress has been very inspiring.  We will continue to work on the skill.