Dividing 3-Digit by 1-Digit Numbers

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Objective

SWBAT become familiar with the algorithm as they use models and multiplication to help them with division.

Big Idea

Multiplication and models can help students understand division.

Opener

5 minutes

In today's lesson, the students learn to use models to divide a 3-digit number by a 1-digit divisor. 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 review division with the students.  I ask, "Tell me about what you learned about division on yesterday."  I give the students a few minutes to think about the question.   I take a few student responses. One student responds, "We used place value blocks to divide numbers."  Another student responds, "We used multiplication facts to help us with the division."  A third student offered, "We learned to draw circles and put tally marks to split up the number."  I tell the students, "Today, we will continue to work on division by using place value blocks and drawing models to help divide a 3-digit number by a 1-digit divisor.  Our multiplication facts will help us.  We will write our answer using the standard algorithm"

Whole Class Discussion

10 minutes

I call the students to the carpet as we prepare for a whole class discussion.  The Dividing 3-digit by 1-digit numbers 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:

125 ÷ 3=

We can model this by using place value blocks.

Try to divide the hundreds into 3 groups.  You can not do that.  Therefore, the  1 hundred must be regrouped into 10 tens. Add 10 tens + 2 tens = 12 tens.  We can divide those 12 tens into 3 groups.  There will be 4 tens in each group.

Now, we must divide the 5 ones into 3 groups.  

There will be 1 ones in each group.  That leaves us with a remainder of 2.  

The quotient for 125 ÷ 3 = 41 r 2.

 

The standard algorithm is a way to solve division problems.

D-Divide

M-Multiply

S-Subtract

B-Bring Down (If you bring a number down, you must start the process over.)

Because  we do not have at least 3 hundreds, we must divide 3 into 12 (which is 120).  Use multiplication to help.  Multiply 3 x 4 = 12.  So, there are 4 tens in 120.  Next, subtract 12 – 12= 0.  Bring down the 5.  Now we are working with 5 ones.  Divide 3 into 5, which gives you 1.  There will be a remainder of 2, because 3 x 1 = 3 and 5 – 3=2.  

The quotient is 41 with a remainder of 2. 

Let’s try one together

Problem 2:

143 ÷ 4=

How do we know that there will be a remainder in this problem?


 

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 Dividing 3-digit by 1-digit.  The students must work together to find the quotient to the division problems.  They must draw a model to help with the division (MP4) by separating 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 use the place value blocks to help get a conceptual understanding which is evident in the Student Group Activity Image.  The algorithm may be used with the place value blocks to understand the concept of division and how it relates to the algorithm.  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.  

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 of Student Work, 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:

Because we are just beginning the division unit, there are still some students having difficulty using place value blocks to divide.  Some of them are getting confused about the regrouping using the blocks.  I must say that there has been great improvement since our first lesson with division.  I have found through the past years that division is one of the most difficult skills for fourth grade students.  We will continue to gain a conceptual understanding of division by using place value blocks, multiplication facts, and drawing models.