Deciding Where to Start Dividing

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Objective

SWBAT use the standard algorithm to divide while using multiplication and models to illustrate the calculations.

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 by a 1-digit divisor. They must consider the multiplication problem that supports their answer.  The students learn where to start dividing because it is important for utilizing the standard algorithm.  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, "How does knowing multiplication help you solve division problems?"  I give the students a few minutes to think about the question.   I take a few student responses. One student responds, "It helps you know how many are in each group."  Another student responds, "It is the inverse because you can undo the division with the multiplication." I tell the students, "Today, we will continue to work on division by drawing models to help divide by a 1-digit divisor.  Our multiplication facts will help us.  We will record our thinking using the standard algorithm as well."


Whole Class Discussion

10 minutes

I call the students to the carpet as we prepare for a whole class discussion.  The  Decide where to start 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

I explain to the students that in this lesson, we will decide where to start dividing.  This is very important because once you decide where to start dividing, it let's you know how many digits will be in the quotient. By knowing this, this will help you self-monitor your work.

Problem:

27 divided by 2

Begin by separating the 2 tens.  If the tens can be divided evenly into 2 groups, then this is where we start.  "Can the 2 tens be separated evenly in 2 groups? Let's find out."  I draw 2 circles on the board.  I put one tens in one group, then the other tens in the second group.  "Can the 2 tens be separated evenly in 2 groups?"  The students all agree that it can.  "What multiplication sentence helps us divide the 2 tens into 2 groups?"  One student responds, "2 x 1 = 2."  I explain to the students that because the tens can be divided by 2, then this problem will have a 2-digit quotient because we still have to divide the ones.

Next, we divide the 7 ones into 2 groups.  Again, I draw 2 circles on the board to represent the 2 groups.  One by one, I divide the ones into the 2 groups.  There will be 3 ones in each group with a remainder of 1.  Again, the students identify the multiplication problem that helps to solve dividing the ones.  The multiplication sentence is 2 x 3= 6.

Lastly, I show the students the standard algorithm so that they can see the connection between the model and the algorithm.  

I send the students back to their seats to practice in groups, drawing models and using multiplication facts to solve division problems with the standard algorithm.  

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 Decide Where to Start.  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 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.  Can you divide the first number by the divisor? 

2.  How many digits will be in the quotient?

3. What multiplication problem will help find the dividend?

4.  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.  In the Video, Decide Where to Start,, you see examples of student work that illustrate modeling the division problem without place value blocks.   During the closing of the lesson, all misconceptions that were spotted during the group activity will be addressed whole class.  

 

Misconceptions:

We will continue to work on when to divide the divisor into the first number.  Some students want to take the whole number and separate it into the groups.  I want the students to conceptually understand the the first digit, whether it is tens or hundreds, can be divided first if it is the number is the same as or larger than the divisor.  For example, if the divisor is a 2 and the first digit it is 2 or higher, then the students need to separate that number first.  This goes along with deciding where to start.