Engage NY Math Module 2

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 • State the following numbers as decimals. • 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

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? ? 224 ft.² 14 feet Multiples of 14 14 -- 1 28 -- 2 42-- 3 56-- 4 70-- 5 84-- 6 98 -- 7 (16 x 2) + (14 x 2) = 32 + 28 = 60 feet 6 1 14 224 The perimeter of the room is 60 feet. -14 84 84 0

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 2 29 6,247 -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. 1 2 29 6,247 -5 8 4 4 2 9 1 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 1 5 2 1 5 x 2 9 1 9 3 5 + 4 3 0 0 2 3 5 + 1 2 6 2 4 7 2 29 6,247 -5 8 4 2 9 4 1 5 7 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. Multiples of 52 52-- 1 104-- 2 156 -- 3 208 -- 4 260 -- 5 312 -- 6 364 -- 7 416 -- 8 468 -- 9 Check your answer by multiplying. 8 2 R 25 8 2 x 5 2 1 6 4 + 4, 1 0 0 4, 2 6 4 + 2 5 4, 2 8 9 • 52 4,28 9 -4 16 9 12 - 104 25 How many 52s are in 129? Use your chart to find the closest multiple without going over. How many 52s are in 428? Use your chart to find the closest multiple without going over.

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. Multiples of 63 63 -- 1 126 -- 2 189 -- 3 252 -- 4 315 -- 5 378-- 6 441 -- 7 504 -- 8 567 -- 9 Check your answer by multiplying. 1 0 5 x 6 3 3 1 5 + 6, 3 0 0 6, 615 + 3 4 6, 64 9 1 0 5 R 34 • 636,64 9 -6 3 3 4 9 - 315 34 How many 63s are in 66? Use your chart to find the closest multiple without going over. How many 63s are in 34? Use your chart to find the closest multiple without going over. How many 63s are in 349? Use your chart to find the closest multiple without going over.

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 64

End of Lesson Activities Debrief Problem Set Homework Exit Ticket

Exit Ticket

Problem Set Divide, then check using multiplication. • 4,859 ÷ 23 • 7,242 ÷ 34 • 9,152 ÷ 29 • 4,368 ÷ 52 • 3,164 ÷ 45 • 4,424 ÷ 63

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 Divide, then check using multiplication. • 9,962 ÷ 41 • 6,691 ÷ 28 • 2,409 ÷ 19 • 1,495 ÷ 45 • 2,625 ÷ 32 • 5,821 ÷ 62

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.

Engage NY Math Module 2