Engage NY Module 1

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

2. SPRINT – MULTIPLY BY EXONENTS • This Sprint will help students build automaticity in multiplyingdecimals by , , , and .

3. 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 0

4. 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 0

5. 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 0

6. 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 0

7. 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

8. Concept Development - Problem 1 • Solve 1.7 ÷ 2 using disks on your place value chart. 0 2 1 . 7 -0 1 7 • 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.

9. Concept Development - Problem 1 • Solve 1.7 ÷ 2 using disks on your place value chart. 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?

10. Concept Development - Problem 1 • Solve 1.7 ÷ 2 using disks on your place value chart. 0 . 8 5 2 1 . 7 0 -0 1 7 -1 6 1 0 - 1 0 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.)

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

12. 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.

13. 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

14. 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

15. 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

16. 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.