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# Dividing Signed Decimals

Lesson 20 of 27

## Objective: SWBAT divide signed decimals using a procedure

## Big Idea: Students verify that the signs of decimal quotients follow the same pattern as integer quotients. Students practice dividing signed decimals including the context of rates and equations.

*50 minutes*

#### Introduction

*10 min*

I open with the essential question: Do the signs of decimal quotients follow the same rules as integer quotients? I'll then ask students to take a minute to fill in the sign of quotients for a dividend and quotient with the same sign and with a different sign.

Next, I want to remind students that the rules for signs are not arbitrary or magical; they are based on mathematical properties. I say remind because this work was done with integer quotients. Students take a two multiplication facts and write related division facts. Of course, we have already explored the signs of products. The resulting division facts confirm that division of decimals is just like the division of integers in terms of the resulting sign. This exercise speaks to **MP3**, as students take some of the math they already know and related it to a new task.

Now that we have confirmed the signs of quotients, I want to go to a more fundamental check. The remainder of the lesson focuses on fluency of decimal long division. Therefore, I present students with 8 various division problems and ask them to set up the long division problem without actually solving for the quotient. I want to make sure students know how to handle decimals in both the divisor and the dividend.

#### Resources

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#### Guided Practice

*15 min*

Students will now solve 6 problems with my guidance and the help of their partners. Some students may be more successful with long division if they are given graph or grid paper. In this case, they must be instructed to write only 1 digit per square. This grid paper makes it much easier for students to correctly place and align values. So many of the mistakes in long division come simply from misaligned work!

Throughout this section (and in the later sections) I have tried to include problems that are not overly tedious. I believe only 1 of the problems requires students to complete values beyond the thousandths place. There is also one answer that has a repeating decimal value.

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Now students work along. The first 6 problems mirror the guided practice problems. The last 4 problems are rate problems. Students are asked to find the unit rate. Two of these four problems use very friendly numbers just to remind students that unit rates can be found through division. I include these problems as a subtle way to review and perhaps extend some of their unit rate work from a previous grade, while getting them prepared for the next unit on ratios and proportional reasoning.

The extension consists of several one-step rational number multiplication equations. Consequently students now get to practice solving equations using division. This too is a way to prepare the students for a later unit on expressions and equations while practice rational number division.

Note: I have not given a lot of room to show work in the resource. I may have my students do the work on whiteboards or notebook paper.

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#### Exit Ticket

*5 min*

The exit ticket has 4 problems that (again) are similar to problems students have just finished completing. I may consider given two points per problem: 1 for the correct sign for the quotient; 1 for the correct value. This way I assess that students understand that when dividing values with the same sign the quotient is positive, otherwise the quotient is negative. Yet I also just assess their ability to do long division calculations.

#### Resources

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- LESSON 1: Fractions as Quotients - Using Long Division to Convert a Fraction to a Decimal
- LESSON 2: Finding the Distance Between Integers On a Number Line
- LESSON 3: Where Do We Go From Here? Adding Integers on the Number Line
- LESSON 4: What is the Sign of the Sum?
- LESSON 5: Algorithms for Adding Integers
- LESSON 6: How Addition and Subtraction are Related (Part 1 of 3)
- LESSON 7: Subtracting for More or Less. Subtracting Integers on a Number Line
- LESSON 8: How Addition and Subtraction are Related (Part 2 of 3)
- LESSON 9: How Addition and Subtraction are Related (Part 3 of 3)
- LESSON 10: Algorithms for Subtracting Integers
- LESSON 11: Assessment - Fluency and Concepts of Integer Sums and Differences
- LESSON 12: Integer Product Signs - Using Counters to Discover Signs of Products
- LESSON 13: Integer Quotients
- LESSON 14: Expand Expressions Using the Distributive Property
- LESSON 15: Integers Assessment
- LESSON 16: Finding the Distance Between Signed Decimals on a Number Line
- LESSON 17: Adding and Subtracting Positive and Negative Decimals on a Numberline
- LESSON 18: Adding and Subtracting Signed Decimals Using a Procedure
- LESSON 19: Multiplying Signed Decimals
- LESSON 20: Dividing Signed Decimals
- LESSON 21: Finding the Distance Between Signed Fractions on a Number Line
- LESSON 22: Adding and Subtracting Positive and Negative Fractions on a Numberline
- LESSON 23: Adding and Subtracting Positive and Negative Fractions Using Counters
- LESSON 24: Adding and Subtracting Signed Fractions Using a Procedure
- LESSON 25: Multiplying Signed Fractions
- LESSON 26: Dividing Signed Fractions
- LESSON 27: Rational Numbers Operations - Final Unit Assessment