Engage NY Math Module 2

Lesson 23: Divide three- and four-digit dividends by two-digit divisors resulting in two- and three-digit quotients, reasoning about the decomposition of successive remainders in each place value.

Divide Decimals 6 tens ÷ 3 =

› Say the division sentence in unit form and state the quotient.6 tens ÷ 3 = 2 tens

› Say the division sentence in decimal form and state the quotient.60 ÷ 3 = 20

Divide Decimals 6 tenths ÷ 3 =

› Say the division sentence in unit form and state the quotient. 6 tenths ÷ 3 = 2 tenths

› Say the division sentence in decimal form and state the quotient. 0.6 ÷ 3 = 0.2

6 hundredths ÷ 3 = › Say the division sentence in unit form and state

the quotient. 6 hundredths ÷ 3 = 2 hundredths

› Say the division sentence in decimal form and state the quotient. 0.06 ÷ 3 = 0.02

Divide Decimals 9 thousands ÷ 3 =

› Say the division sentence in unit form and state the quotient. 9 thousands ÷ 3 = 3 thousands

› Say the division sentence in decimal form and state the quotient. 9,000 ÷ 3 = 3,000

9 hundreds ÷ 3 = › Say the division sentence in unit form and state

the quotient. 9 hundreds ÷ 3 = 3 hundreds

› Say the division sentence in decimal form and state the quotient. 900 ÷ 3 = 300

Divide Decimals 9 hundredths ÷ 3 =

› Say the division sentence in unit form and state the quotient. 9 hundredths ÷ 3 = 3 hundredths

› Say the division sentence in decimal form and state the quotient. 0.09 ÷ 3 = 0.03

9 tenths ÷ 3 = › Say the division sentence in unit form and state

the quotient. 9 tenths ÷ 3 = 3 tenths

› Say the division sentence in decimal form and state the quotient. 0.9 ÷ 3 = 0.3

Rename Tenths and Hundredths State the following numbers as decimals.

› 1 tenth 0.1

› 2 tenths 0.2

› 3 tenths 0.3

› 8 tenths 0.8

› 9 tenths 0.9

Rename Tenths and Hundredths› 10 tenths

1› 11 tenths

1.1› 19 tenths

1.9› 20 tenths

2› 30 tenths

3› 80 tenths

8› 90 tenths

9› 100 tenths

10

› 200 tenths 20

› 1 hundredth .01

› 2 hundredths .02

› 3 hundredths .03

› 8 hundredths .08

› 9 hundredths .09

› 10 hundredths .10

› 20 hundredths .20

› 3 hundredths .30

› 90 hundredths .90

› 100 hundredths 1

› 200 hundredths 2

› 900 hundredths 9

› 1,000 hundredths 10

› 2,000 hundredths 20

• State the following numbers as decimals.

Divide by Two-Digit Numbers• In your notebooks, solve the following

problems. Check your answers with multiplication.• 650 ÷ 16• 40 R 16• 16 x 40 = 640 + 10 = 650

• 740 ÷ 32• 23 R 4• 23 x 32 = 736 + 4 = 740

• 890 ÷ 27• 32 R 26• 32 x 27 = 864 + 26 = 890

Application Problem• The rectangular room measures 224 square

feet. One side of the room is 14 feet long. What is the perimeter of the room?

Multiples of 1414 -- 128 -- 242 -- 356 -- 470 -- 584 -- 698 -- 7

(16 x 2) + (14 x 2) =

32 + 28 =60 feet

The perimeter of the room is 60 feet.

224 ft.²

14 2241

-14

84

6

84 0

14 feet

?

Concept Development – Problem 1

• 6,247 ÷ 29• Can we divide 6 thousands by 29?

• Not without changing them to 60 hundreds

• We will think about 62 hundreds, which we can divide into 29 groups. Divide 62 hundreds by 29. Show how to estimate 62 hundreds divided by 29.• 60 hundreds ÷ 30 = 2 hundreds

• Record 2 in the hundreds place of the quotient.• What is 2 hundreds x 29?

• 58• How many hundreds are remaining?

• 4 29 6,2472

-5 8

4

Concept Development – Problem 1

• 6,247 ÷ 29• Decompose (regroup those 4 hundreds into 40 tens

plus the 4 tens in the whole. How many tens is that?• 44 tens

• Now we must divide 44 tens by 20. Show me how you estimate 44 ÷ 29.• 30 tens ÷ 30 = 1 ten

• What is 1 ten x 29?• 29 tens

• 44 tens – 29 tens is a remainder of?• 15 tens

• Can we divide again or must we decompose?

• We need to decompose 15 tens into 150 ones, plus the 7 ones in our whole.

29 6,2472

-5 8

4

4

1

2 91 5

Concept Development – Problem 1

• 6,247 ÷ 29• Now we have 157 ones divided by 29. How do we

estimate 157 ÷ 29?• 150 ÷ 30 = 5

• What is 5 x 29?• 145

• How many are remaining?• 12

• What does the 12 represent?• How many are left over after dividing 6,247 into 29 groups.

• Check your answer using multiplication.• What is 215 x 29?

• 6,235• 6,235 + 12= ?

• 6,247

2 1 5x 2 9 1 9 3 5

+ 4 3 0 06 2 3 5

+ 1 26 2 4 7

29 6,2472

-5 8

4

4

1

2 91 5 7

5

1 4 5 1 2

Concept Development – Problem 1

• 6,247 ÷ 29

Concept Development – Problem 2

• 4,289 ÷ 52• Complete this problem in your math

journal. Begin by listing your multiples for 52.

8

-4 16 12

52 4,28 9

Multiples of 5252 -- 1

104 -- 2156 -- 3208 -- 4260 -- 5 312 -- 6364 -- 7416 -- 8468 -- 9

How many 52s are in 428? Use your chart to find the closest multiple without going over.

R 25

Check your answer by multiplying.

8 2x 5 2

1 6 4+ 4, 1 0 0

4, 2 6 4+ 2 54, 2 8 9

9

How many 52s are in 129? Use your chart to find the closest multiple without going over.

2

- 104 25

Concept Development – Problem 2

• 4,289 ÷ 52• You can also think about solving this problem by first

estimating, solving, and checking with multiplication.

Concept Development – Problem 3

• 6,649 ÷ 63• Complete this problem in your math

journal. Begin by estimating or listing your multiples for 63.

1

-6 33

63 6,64 9

Multiples of 6363 -- 1

126 -- 2189 -- 3252 -- 4315 -- 5 378 -- 6441 -- 7504 -- 8567 -- 9

How many 63s are in 66? Use your chart to find the closest multiple without going over.

R 34

Check your answer by multiplying.

1 0 5x 6 3

3 1 5+ 6, 3 0 0

6, 6 1 5+ 3 46, 6 4 99

How many 63s are in 34? Use your chart to find the closest multiple without going over.

0

- 315 34

4

How many 63s are in 349? Use your chart to find the closest multiple without going over.

5

Concept Development – Problem 3

• 6,649 ÷ 63• You can also think about solving this problem by first

estimating, solving, and checking with multiplication.

Concept Development – Problem 4• 3,164 ÷ 45

• Solve this problem independently. Do all three steps independently. When you are finished, check your answers with someone at your table.

45 3, 1 6 4

End of Lesson Activities

DebriefProblem SetHomeworkExit Ticket

Exit Ticket

Problem Set

4,859 ÷ 23 

7,242 ÷ 34

9,152 ÷ 29 

4,368 ÷ 52 

3,164 ÷ 45

4,424 ÷ 63

Divide, then check using multiplication.

Problem Set Mr. Riley baked 1,692 chocolate cookies. He sold them

in boxes of 36 cookies each. How much money did he collect if he sold them all at $8 per box?

 

1,092 flowers are arranged into 26 vases, with the same number of flowers in each vase. How many flowers would be needed to fill 130 such vases?

The elephant’s water tank holds 2,560 gallons of water. After two weeks, the zookeeper measures and finds that the tank only has 1,934 gallons of water left. If the elephant drinks the same amount of water each day, how many days will a full tank of water last?

Homework Task

9,962 ÷ 41

6,691 ÷ 28 

2,409 ÷ 19

1,495 ÷ 45 

2,625 ÷ 32 

5,821 ÷ 62

Divide, then check using multiplication.

Homework Task A political gathering in South America held 788

people. Each of South America’s 14 countries were equally represented. The remaining people were guests from the United States. How many guests were from the United States?

  A chocolate company is packaging 32 ounces of

caramels into reusable, plastic cups. When a shipping box is filled with these caramel packages, it weighs 49 pounds 8 ounces.

 › How many caramel filled cups are in the box?

 › Use your remainder to find the weight of each

plastic cup.