Dividing a Decimal by a Whole Number

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Objective

SWBAT divide a whole number by a decimal.

Big Idea

Decimals can be divided by whole numbers, and the quotient can be validated by using multiplication.

Whole Class Discussion

15 minutes

Today's lesson is dividing a decimal by a whole number.  In yesterday's lesson we learned to multiply a decimal by a whole number.  To review what we learned about division earlier in the school year, we review the vocabulary.  On the Smart board, the vocabulary is displayed.

 Vocabulary – Review

•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

 To practice the skill, the students are at their desks with a piece of paper and pencil.  The students have also been given a manipulative kit.  I instruct the students to take out the money (bills and coins) from the manipulative kit.  On the Smart board, I display the following problem: 28.4 divided by 4.  I ask the students to tell me the word name for this number.  Student response:  twenty-eight and four tenths.  I ask, "If this is money, how much would it be?"  Student response:  twenty-eight dollars and forty cents.  (There were 2 or 3 students that said twenty-eight dollars and four cents.)  I review with the students that the tenths place is like dimes.  

I instruct the students to take out $28.40 from their kits.  Some of the students started taking out 5 dollar bills.  I stopped the class because the students were not thinking about place value as they took out the money.  Therefore, I asked, "What place is the 2 in?"  Student response:  tens.  "What money can we use to represent the tens place?"  Student response:  ten dollar bills.  "How many ten dollar bills will we need to represent the 20?"  Student response:  2.  "What place is the 8 in?"  Student response:  ones.  "What money should we use to represent the 8?"  Student response:  one dollar bills.  "What place is the 4 in?"  Student response:  tenths.  I remind the students that we know that the tenths place can be modeled with dimes.  I tell the students to take out 4 dimes for the tenths place.  

As we divide with the money, the students solve the problem on paper using the standard algorithm for division.  I remind the students that division means that we are putting them in equal groups.  I ask, "How many groups are we trying to divide 28.4 into?"  Student response: 4.  I let the students know that they are correct because 4 is our divisor.  First, I ask the students to divide their 2 tens into 4 groups.  I ask, "Can you do it?"  The students pick up the tens to begin dividing, and soon realize that they cannot share them equally into 4 groups.  I explain to the students that if we can not divide the tens equally, then we need to regroup.  We need to turn the tens in for something else.  I ask, "What do I turn the tens in for?"  Some students responded fives, others responded ones.  I reminded the students that we were using money to represent place value.  Therefore, we would trade the tens in for ones.  The students counted out 20 ones and added them to the 8 ones for a total of 28 ones.  I explain to the students that we just modeled what it means to regroup by exchanging money of one value for money of another value.   

I asked the students to separate the 28 ones into the 4 groups.  The students put 7 ones into each group.  In the standard algorithm on their papers, the students wrote a 7 in the quotient.  Last, the students divided the 4 dimes into groups.  The students put 1 dime in each group.  On their papers, the students wrote a 1 in the quotient.  I tell the students that we always line the decimal in the quotient with the decimal in the dividend.  The answer to the problem is 7.1.  I remind the students that multiplication helps us with division.  I told the students that they should always check their answers by using multiplication.  I remind them that we have just learned to multiply a decimal by a whole number. The students multiply 7.1 x 4 = 28.4.  

 

Skill Building/Exploration

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 (MP3).

For this activity, I put the students in pairs.  I give each group a Divide a Decimal by a Whole Number.docx activity sheet, Multiplication Chart.pdf, and money.  The students must work together to solve the division problems by using money.  The students must check their answers by using multiplication.  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 (MP3).  From the Video - Dividing Decimals, you can hear 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 your divisor divide into the number?  If not, what should you do?

2.  What multiplication sentence can help you with the problem?

3.  Where should you put the decimal?

4.  Does your answer check correctly?

As I walk around the classroom, I hear the students communicate with each other about the assignment.  From the video, you can 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.  

 

Closure

15 minutes

To close the lesson, I bring the students back together as a whole class.  I feel that it is very important to let the students share their answers as a whole class.  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, Student Work - Dividing Decimals and Student Work - Dividing a decimal by a whole number, 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 activity will be addressed whole class. 

I collect all papers from the students.  All struggling students identified as I monitored during their independent activity will receive further instruction in small group.

Misconception(s):

I noticed that a few students were making mistakes on placing the decimal in the answer.  Some students had the correct numbers at the top, but the decimal in the wrong place.  We referred back to the money to help correct this mistake.  The students had to tell me the amount of money in each group, then see if it matched their answers.