ENGAGE NY MODULE 1LESSON 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 , , , and .

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 42 0. 4 8

-0 0 4 -0 4 08 -08 0

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 43 0. 4 2

-0 0 4 -0 3 12 -12 0

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

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

APPLICATION PROBLEMJose 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?

Jose’s $

$2.82 ? $1.43

oranges pineapples change

$20

$15.75

$20 - $1.43 - $2.82 = $15.75

pineapples

?

$15.75 ÷ 5 =15 ones ÷ 5 + 75 hundredths ÷ 5=3 ones + 15 hundredths =$3.15

Each pineapple costs $3.15.

CONCEPT DEVELOPMENT - PROBLEM 1

Solve 1.7 ÷ 2 using disks on your place value chart.

• 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.

Ones Tenths 0 2 1 . 7 -0 1 7

CONCEPT DEVELOPMENT - PROBLEM 1

Solve 1.7 ÷ 2 using disks on your place value chart.

• 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?

Ones Tenths Hundredths

0 8 2 1 . 7 -0 1 7 -1 6 1

CONCEPT DEVELOPMENT - PROBLEM 1

Solve 1.7 ÷ 2 using disks on your place value chart.

• 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.)

Ones Tenths Hundredths

0 . 8 5 2 1 . 7 0 -0 1 7 -1 6 1 0 - 1 0 0

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.