Lesson 27 5•2

NYS COMMON CORE MATHEMATICS CURRICULUM

Lesson 27 Objective: Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method. Related Topics: More Lesson Plans for the Common Core Math

Suggested Lesson Structure Fluency Practice  Application Problem  Concept Development  Student Debrief  Total Time

(12 minutes) (5 minutes) (33 minutes) (10 minutes) (60 minutes)

Fluency Practice (12 minutes)  Divide Decimals by Multiples of 10 5.NBT.7

(3 minutes)

 Unit Conversions 5.MD.1

(4 minutes)

 Divide Decimals by Two-Digit Numbers 5.NBT.7

(5 minutes)

Divide Decimals by Multiples of 10 (3 minutes) Materials: (S) Personal white boards Note: This drill reviews G5–M2–Lesson 24 content. Repeat the process from G5–M2–Lesson 25 using the following possible sequence: 1.2 ÷ 6, 1.2 ÷ 60, 8.4 ÷ 4, 8.4 ÷ 40, 6 ÷ 3, 6 ÷ 60, 0.32 ÷ 4, and 0.32 ÷ 40.

Unit Conversions (4 minutes) Materials: (S) Personal white boards Note: This drill reviews unit conversions and prepares students for problem solving in G5–M2–Lessons 28 and 29. T: S:

(Write 1 liter = ___ mL.) How many milliliters are in 1 liter? 1,000 milliliters.

Repeat the process for 1 ft = __ in, 1 kg = __ g, and 1 lb = __ oz.

Lesson 27: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org

Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method. 4/2/14

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Lesson 27 5•2

NYS COMMON CORE MATHEMATICS CURRICULUM

T: S:

(Write 0.732 liters = ___ mL.) On your boards, write an equation to solve, and then show how many milliliters are in 0.732 liters. (Write 0.732 × 1,000 = 732 and 0.732 liters = 732 mL.)

Repeat the process using the following possible sequence: 0.037 liters = __ mL, 0.537 kg = __ g, and 0.04 kg = __ g.

Divide Decimals by Two-Digit Numbers (5 minutes) Materials: (S) Personal white boards Note: This drill reviews G5–M2–Lesson 26 content. T: S: T:

(Write 83.03 ÷ 23.) On your boards, write a division equation to estimate the quotient. (Write 80 ÷ 20 = 4.) Use the algorithm to solve.

Repeat process using the following possible sequence: 6.76 ÷ 13, 12.43 ÷ 11, and 65.94 ÷ 21.

Application Problem (5 minutes) Michael has 567 pennies, Jorge has 464, and Jaime has 661. If the pennies are shared equally by the 3 boys and 33 of their classmates, how much money will each classmate receive? Express your final answer in dollars. Note: This problem invites different ways of working with the quantities, either as decimals or whole numbers, at different stages of the problem. Students might place the decimal point at the very end of their work or as they add from the beginning. Have them share their approach and express their dollar amounts as decimal units, too.

Concept Development (33 minutes) Problem 1 In a 77 kilometer relay race, each of 22 team members runs an equal distance. How many kilometers does each team member run? 77 ÷ 22 T: S: T:

Write a division equation to solve for the number of kilometers run by each team member. (Work.) 77 ÷ 22. (Using the standard algorithm, write 77 ÷ 22 on the board.) Let’s solve together. Tell me how you’ll estimate.

Lesson 27: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org

Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method. 4/2/14

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Lesson 27 5•2

NYS COMMON CORE MATHEMATICS CURRICULUM

S: T: S: T: S: T: S: T: S: T: S: T: S: T: S: T: S: T: S: T: S: T: S:

60 ones ÷ 20 = 3 ones. What is 3 ones times 22? NOTES ON 66 ones. MULTIPLE MEANS OF How many ones remain? ACTION AND 11 ones. EXPRESSION: Decompose 11 ones. How many tenths is that? Students should continue to be 110 tenths. encouraged to interpret remainders and decimal portions of quotients. Tell your neighbor how you’ll show the zero tenths in Challenge students with the following the whole. questions: I’ll write a decimal point and a zero in the tenths place  How many kilometers would need to next to the 7 ones in 77. be added to the race for each runner Now divide 110 tenths by 22. Tell me how you’ll to run a 4 kilometer distance? A 4.5 estimate. kilometer? A 5 kilometer? 100 tenths 20 = 5 tenths.  Change the context of the problem so that the interpretation of the What is 5 tenths 22? remainder must change. 110 tenths.  77 students need to board buses. How many tenths remain? The buses have 22 seats. How many buses are needed? Zero tenths.  22 students will share 77 What is our quotient? t-shirts. How many students 3.5. could receive more than 1 shirt? So how many kilometers will each team member run during the race? Each team member will run 3 and 5 tenths kilometers. Is your answer reasonable? What is 5 tenths kilometer as meters? 500 meters! What fraction of a kilometer is 500 meters? Half!  So each runner ran 3 and a half kilometers.  3.5 kilometers is the same as 3 kilometers and 500 meters or 3 and a half kilometers.

Problem 2 A vial contains 14.7 mL of serum that is then split equally into 21 tiny containers. How much serum is in each new container? 14.7

21 T: S:

Work with a partner to write a division equation that matches this story problem. (Work.) 14.7 21.

Lesson 27: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org

Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method. 4/2/14

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Lesson 27 5•2

NYS COMMON CORE MATHEMATICS CURRICULUM

T:

(Using the standard algorithm, write 14.7 21 on the board.) Before dividing, let’s reason about what our quotient might be. Will there be more than 1 mL in each container or less NOTES ON than 1 mL? Justify your thinking. MULTIPLE MEANS OF S: It will have to be less than 1 mL because there are more ACTION AND containers than mL of serum.  To have 1 mL in each EXPRESSION: container, there would have to be 21 mL of serum. We only Many lessons, including this one, have about 15. require students to understand and use precise vocabulary. You can help T: Great reasoning. Now tell me how you will estimate students gain familiarity with new 14.7 ÷ 21 numerically. words by displaying them on posters. S: 140 tenths 20 = 7 tenths. There are several ways to make T: Work with a partner to solve. posters more effective: T: What is the quotient?  Be judicious when deciding how many posters to display. If there are S: 0.7. too many, students tend not to see T: Is our actual quotient reasonable? Does the placement of them. the decimal make sense?  Place the posters in odd places, such S: Yes, it’s the exact same as the estimated quotient.  We as on the floor in the doorway or in said we should have less than 1 mL, and we did. If the the washroom. This may capture decimal was behind the 7 it wouldn’t make sense because attention. that would be 7 mL in each container.  It couldn’t have  Try to use pictures or graphics been 7 hundredths. If the divisor had been 2, then the instead of wordy definitions. answer would be 7. We had 21, which is about 10 times as  When a student is struggling for a large, so we had to divide by 10 which is 7 tenths not 7 precise word, point to a poster. This hundredths. shows students that posters can be support materials. T: Did you check your work? S: Yes. T: Answer the question using a complete sentence. S: Zero and 7 tenths milliliters of serum is in each tiny container. The same context may be repeated for the following: 22.47 ÷ 21. This problem requires the recording of a zero in the quotient. Problem 3 The surface area of a rectangular piece of construction paper is 140.25 square inches. If the paper’s length is 17 inches, what is the width? 140.25 T: S:

17 What equation would you use to solve this problem? (Work.) 140.25 17.

Lesson 27: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org

Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method. 4/2/14

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Lesson 27 5•2

NYS COMMON CORE MATHEMATICS CURRICULUM

T:

S: T: T: S: T: S:

(Using the standard algorithm, write 140.25 17 on the board.) Before dividing, let’s reason about what our quotient might be. Tell me how you’ll estimate 140.25 17. 140 ones 20 = 7 ones. Work independently to solve this problem. Share your work with a neighbor after each step in the division process. What is the quotient? 8.25. Answer the question using a complete sentence. The other side of the paper was 8 and 25 hundredths inches long.

Problem Set (10 minutes) Students should do their personal best to complete the Problem Set within the allotted 10 minutes. For some classes, it may be appropriate to modify the assignment by specifying which problems they work on first. Some problems do not specify a method for solving. Students solve these problems using the RDW approach used for Application Problems.

Student Debrief (10 minutes) Lesson Objective: Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method. The Student Debrief is intended to invite reflection and active processing of the total lesson experience. Invite students to review their solutions for the Problem Set. They should check work by comparing answers with a partner before going over answers as a class. Look for misconceptions or misunderstandings that can be addressed in the Debrief. Guide students in a conversation to debrief the Problem Set and process the lesson. You may choose to use any combination of the questions below to lead the discussion. 



When dividing a decimal by a two-digit divisor, when is it useful to think of decimals in various units? (During estimation, it can be easier to think of a whole number as an equivalent amount of smaller units.) Discuss the multi-step problems in the Problem Set. Ask students to explain how they knew their placement of the decimal point was reasonable, how they knew their quotient was reasonable, and how to interpret the decimal portion of the quotient.

Lesson 27: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org

Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method. 4/2/14

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

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Lesson 27 5•2

NYS COMMON CORE MATHEMATICS CURRICULUM





The quotients for Problem 1(e) and (f) are the same. Divide them again and express the remainders as whole numbers. What do you notice? Are the division equations equal to each other? Why or why not? We expressed our remainders today using decimals. Does it always make sense to do this? Give an example of a situation where a whole number remainder makes more sense? Do you notice a pattern to these examples?

Exit Ticket (3 minutes) After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help you assess the students’ understanding of the concepts that were presented in the lesson today and plan more effectively for future lessons. You may read the questions aloud to the students.

Lesson 27: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org

Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method. 4/2/14

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NYS COMMON CORE MATHEMATICS CURRICULUM

Name

Lesson 27 Problem Set 5•2

Date

1. Divide. Check your work with multiplication. a. 5.6 ÷ 16

d. 36 ÷ 24

g. 5.4 ÷ 15

b. 21 ÷ 14

e. 81 ÷ 54

h. 16.12 ÷ 52

c. 24 ÷ 48

f.

i.

15.6 ÷ 15

2.8 ÷ 16

2. 30.48 kg of beef was placed into 24 packages of equal weight. What is the weight of one package of beef?

Lesson 27: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org

Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method. 4/2/14

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NYS COMMON CORE MATHEMATICS CURRICULUM

Lesson 27 Problem Set 5•2

3. What is the length of a rectangle whose width is 17 inches and whose area is 582.25 in2?

4. A soccer coach spent $162 dollars on 24 pairs of socks for his players. How much did five pairs of socks cost?

5. A craft club makes 95 identical paperweights to sell. They collect $230.85 from selling all the paperweights. If the profit the club collects on each paperweight is two times as much as the cost to make each one, what does it cost the club to make each paperweight?

Lesson 27: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org

Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method. 4/2/14

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

2.G.46

NYS COMMON CORE MATHEMATICS CURRICULUM

Name

Lesson 27 Exit Ticket 5•2

Date

1. Divide a. 28 ÷ 32

b. 1,201.68 ÷ 24

Lesson 27: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org

Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method. 4/2/14

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2.G.47

NYS COMMON CORE MATHEMATICS CURRICULUM

Name

Lesson 27 Homework 5•2

Date

1. Divide and check. a. 7 ÷ 28

c. 6.5 ÷ 13

e. 561.68 ÷ 28

b. 51 ÷ 25

d. 132.16 ÷ 16

f.

604.8 ÷ 36

2. In a science class, students water a plant with the same amount of water each day for 28 consecutive days. If the students use a total of 23.8 liters of water over the 28 days, how many liters of water did they use each day? How many milliliters did they use each day?

Lesson 27: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org

Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method. 4/2/14

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NYS COMMON CORE MATHEMATICS CURRICULUM

Lesson 27 Homework 5•2

3. A seamstress has a piece of cloth that is 3 yards long. She cuts it into shorter lengths of 16 inches each. How many of the shorter pieces can she cut?

4. Jenny filled 12 pitchers with an equal amount of lemonade in each. The total amount of lemonade in the 12 pitchers was 41.4 liters. How much lemonade would be in 7 pitchers?

Lesson 27: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org

Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about the placement of the decimal point, and making connections to a written method. 4/2/14

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

2.G.49