Dividing Decimals with Remainders

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SWBAT solve decimal division problems with remainders.

Big Idea

What if there's a remainder?

Do Now

10 minutes

During this unit my students have already learned an algorithm for dividing decimals. Today's Do Now problem is an assessment of their understanding of to apply it. 

Do Now

For my knitting project, I need to purchase 3.5 yards of yarn. If I spend $9.10 to purchase the yarn, how much does one yard cost?     

My students have previously used a Give, Get, How, Show Strategy to solve word problems. For this problem I will encourage students use this strategy to organize their information and solve the problem. If necessary I will help students realize that the problem is asking for the price of 1-yard and therefore they need to divide to determine a unit cost.

Once students have begin to complete the problem successfully, I will randomly select a student to show their work on the board and explain their thought process.

Mini Lesson

20 minutes

In our previous work we have developed an algorithm for dividing decimals. Since we were using long division, several students asked questions based on their prior experience with long division. In order to move their learning forward, today I will model a few problems with a remainder.

Example 1:  6.37 ÷ 0.02   What do we do with a remainder?

After performing the long division, we will have a remainder of 1. I will ask my students for some of their ideas by saying, "What should we do with the remainder?" Some students may suggest that you simply write the remainder as would in a long division problem with whole numbers (e.g., 318 remainder 1). Others may suggest that we add the remainder to the end of the quotient as a decimal (e.g., 318.1). 

Example 2: 4.56 ÷ 2.3      What happens if the decimal keeps repeating?  

Some of my students always wonder, "How can we keep dividing without changing the dividend?" I want them to realize that if we add zeros to the dividend in the decimal places at the end of the number it doesn't change the value of the number, but it does allow us to continue dividing. So, I will work through Example 2 which requires us to work with a remainder, and, to round. 

This is a good time to discuss a question like, "What does it mean to round to the nearest hundredths place? To the thousandths place?" If I ask students, some may suggest that we look at the thousandths place to determine how to round the hundredths place. But, many students do not think about this strategically when performing long division with decimals. Instead they apply the algorithm to produce a lengthy quotient (sometimes arriving at a point of frustration). If the opportunity presents itself, I will discuss this as an additional step in the algorithm: Setting the precision of the quotient.

Independent Practice

10 minutes

Students will be given a Dividing Decimals Practice Worksheet to practice their skills.  I will encourage students to compare their work and answers with their group.  As students are working, I will circulate throughout the room to answer any questions.

Lesson Review

5 minutes

My students often have difficulty with word problems and identifying key words/concepts.  To help them overcome this, at the end of today's lesson I will review key words that can help determine what type of operation a problem requires. I'll begin by writing on the board, "How do we know what operations to use when given word problems?" Then I will ask students to brainstorm a list of keywords for the four basic mathematical operations.

Students may respond with:

  • add, sum, increased by, plus, combine, gain
  • subtract, difference, minus, take away, less than, loss
  • multiply, times, of, by product, each
  • divided by, quotient, into, each, ratio