Engage NY Module 1 LESSON 15 Objective: Divide decimals using place value understanding, including remainders in the smallest unit.

SPRINT – MULTIPLY BY EXONENTS This Sprint will help students build automaticity in multiplying decimals by 𝟏𝟎 𝟏 , 𝟏𝟎 𝟐 , 𝟏𝟎 𝟑 , and 𝟏𝟎 𝟒 .

FIND THE QUOTIENT 0.48 ÷ 2 = _____. 48 hundredths ÷ 2 = ____ hundredths = _____ tenths ____hundredths = _____ 48 hundredths ÷ 2 = 24 hundredths = 2 tenths 4 hundredths = 0.24 Now solve using the standard algorithm. 0.2 4 2 0. 4 8 -0 0 4 -0 4 08 -08

FIND THE QUOTIENT 0.42÷ 3 = _____. 42 hundredths ÷ 3 = ____ hundredths = _____ tenths ____hundredths = _____ 42 hundredths ÷ 3 = 14 hundredths = 1 tenth 4 hundredths = 0.14 Now solve using the standard algorithm. 0.1 4 3 0. 4 2 -0 0 4 -0 3 12 -12

FIND THE QUOTIENT 3.52÷ 2 = _____. 3 and 52 hundredths ÷ 3 = _____ 3.52 ÷ 2 = 1.76 Now solve using the standard algorithm. 1.7 6 2 3. 5 2 -2 1 5 -1 4 12 -12

FIND THE QUOTIENT 9.6÷ 8 = _____. 96 tenths ÷ 8 = _____ 9.6 ÷ 8 = 1.2 Now solve using the standard algorithm. 1. 2 8 9. 6 -8 1 6 -1 6

APPLICATION PROBLEM Jose bought a bag of 6 oranges for $2.82. He also bought 5 pineapples. He gave the cashier $20 and received $1.43 change. What did each pineapple cost? $20 $20 - $1.43 - $2.82 = $15.75 8.00 1.20 +0.20 $9.40 $2.82 ? $1.43 Jose’s $ The only place that makes sense is between the 9 and the 4 because he will pay between (4 x $2) and (4 x $3). oranges pineapples change $15.75 $15.75 ÷ 5 = 15 ones ÷ 5 + 75 hundredths ÷ 5 =3 ones + 15 hundredths =$3.15 Each pineapple costs $3.15. ? pineapples

Concept Development - Problem 1 Solve 1.7 ÷ 2 using disks on your place value chart. 2 1 . 7 -0 1 7 Ones Tenths Show 1.7 on your place value chart with your disks. Let’s begin with our largest units. Can 1 one be divided into 2 groups? How many tenths are in each group? We need to keep sharing. How can we share this single one disk? 17 tenths divided by 2. How many tenths can we put in each group? 8 tenths Cross them off as you divide them into our 2 equal groups. How many tenths did we share in all? 16 tenths.

Concept Development - Problem 1 Solve 1.7 ÷ 2 using disks on your place value chart. Ones Tenths Hundredths 0 8 2 1 . 7 -0 1 7 -1 6 1 Explain to your partner why we are subtracting the 16 tenths. How many tenths are left? Is there a way for us to keep sharing? You unbundle the one tenth into 10 hundredths. Have you changed the value of what we needed to share? Explain. No, it’s the same amount to share, but we are using smaller units. The value is the same as 1 tenth is the same as 10 hundredths. I can show this by placing a zero in the hundredths place. Now we have 10 hundredths, can we divide this between our 2 groups? How many hundredths are in each group?

Concept Development - Problem 1 Solve 1.7 ÷ 2 using disks on your place value chart. Ones Tenths Hundredths 0 . 8 5 2 1 . 7 0 -0 1 7 -1 6 1 0 - 1 0 Let’s record 5 hundredths in the quotient. How many hundredths did we share in all? How many hundredths are left? Do we have any other units left to share? Tell me the quotient in unit form and in standard form. 0 ones 8 tenths 5 hundredths; 85 hundredths; 0.85 How is today’s problem different than yesterday’s problem? (Show 6.72 ÷ 3 in the standard algorithm, then compare the problems.)

Concept Development - Problem 2 Show 2.6 ÷ 4 on your place value mat and work the problem using the standard algorithm. Ones Tenths Hundredths

Concept Development - Problem 3 17 ÷ 4 = _____ Look at this problem; what do you notice? Turn and share with your partner. In fourth grade we recorded the remainder as r1. What we have we done today that lets us keep sharing the remainder? We can trade it for tenths or hundredths and keep dividing in between our groups. Now solve this problem using the place value chart with your partner. Partner A will draw the number disks and Partner B will solve using the standard algorithm. Compare your work. Match each number in the algorithm with its counterpart in the drawing.

Concept Development - Problem 3 17 ÷ 4 = _____ Look at this problem; what do you notice? Turn and share with your partner. In fourth grade we recorded the remainder as r1. What we have we done today that lets us keep sharing the remainder? We can trade it for tenths or hundredths and keep dividing in between our groups. Now solve this problem using the place value chart with your partner. Partner A will draw the number disks and Partner B will solve using the standard algorithm. Compare your work. Match each number in the algorithm with its counterpart in the drawing. 17 ÷ 4 = 4.25

Concept Development - Problem 4 22 ÷ 8 = _____ Now solve this problem using the place value chart with your partner. Partner B will draw the number disks and Partner A will solve using the standard algorithm. Compare your work. Match each number in the algorithm with its counterpart in the drawing. 22 ÷ 8 = 2.75

Concept Development - Problems 5 - 6 In your journal, solve the following problems using the standard algorithm. When you are finished, compare your answers with your neighbor. 7.7 ÷ 4 = _____ 7.7 ÷ 4 = 1.925 0.84 ÷ 4 = _____ 0.84 ÷ 4 = 0.21

Problem Set, Debriefing, Exit Ticket, and Homework Complete Problem Set in small groups. Check answers and discuss difficulties. Handout Exit Ticket and independently. Handout Homework.