Module 2 – Lesson 26

1. Objective: Divide decimal dividends by two-digitdivisors, estimating, quotients, reasoning about the placement of the decimal point, and making connections to a written method. Module 2 – Lesson 26

2. Fluency Practice – Rename Tenths and Hundredths • 10 tenths 90 hundredths • 90 tenths 97 hundredths • 93 tenths 100 hundredths • 100 tenths 900 hundredths • 800 tenths 970 hundredths • 483 tenths 1,000 hundredths • 365 tenths 5,946 hundredths • 9 hundredths 8,000 hundredths • 10 hundredths 8,417 hundredths = .90 = 1.0 = 9.0 = .97 = 9.3 = 1.00 = 10.0 = 9.00 = 80.0 = 9.70 = 10.00 = 48.3 = 36.5 = 59.46 = 80.00 = .09 = 0.10 = 84.17

3. Fluency Practice – Divide Decimals by Multiples of 10 • 1.2 ÷ 3 = • 1.2 ÷ 30 = • 9.6 ÷ 3 = • 9.6 ÷ 30 = • 8 ÷ 4 = • 8 ÷ 40 = • 0.45 ÷ 5 = • 0.45 ÷ 50 = 0.4 0.04 3.2 0.32 2 0.2 0.09 0.009

4. Fluency Practice – Estimate the Quotient • 15.4 ÷ 32 = (Think unit form.) • 154 tenths ÷ 32 • Round the divisor first and then find a multiple of 30 close to 154 tenths. • Divisor = 30 and dividend 150 tenths or 15.0 • Write a new division equation to find the estimated quotient. • 150 tenths ÷ 30 or 15.0 ÷ 30 = 5 tenths = .5 • Try the following problems. (Estimate the quotient.) • 2.53 ÷ 43 • 29.8 ÷ 31 • 15.98 ÷ 78 2.40 ÷ 40 = 0.06 30 ÷ 30 = 1 16.0 ÷ 80 = .2

5. Concept Development – Problem 1 & 2 • 904 ÷ 32 and 456 ÷ 16 • Estimate the quotient • 904 divided by 32 is about 30 and 456 divided by 16 is about 30. • Solve the above problem using the standard algorithm. 2 8 r 8 2 8 r 8 32 904 16 456 -64 -32 4 26 6 13 - 256 - 128 8 8

6. Concept Development – Problem 1 & 2 • What can you say about 904 ÷ 32 and 456 ÷ 16? • The quotients are equal. • Does this mean they are equivalent? • Not necessarily because the dividend and divisor are different. • How can we determine if they are equivalent? • We need to divide it farther down to determine if they are truly equivalent. We can do this by adding the decimal point in and zeros to the right of the decimal. • Where is the decimal point located? • After the last digit (ones place value) in each dividend.

7. Concept Development – Problem 1 & 2 • Let’s continue with our division problem. • Think of 9040 tenths and 4560 tenths. 2 .2 2 8 Are the two problems equivalent? 8 5 .5 32 904 .00 16 456 .0 -64 -32 No, because the problem on the left is 28.25 and the number on the right is 28.5. 4 6 26 13 - 256 - 128 8 0 8 0 - 6 4 - 8 0 16 0 0 -160 0 Note: Decimal point moves straight up.

8. Concept Development – Problem 3 • 834.6 ÷ 26 • Estimate the quotient and then solve using the standard algorithm. • What is your estimate? • 810 ÷ 30 = 27 • What is the actual quotient? • 32.1 • Does you answer make sense? • Yes, because it is fairly close to the estimate. • How can we check to make sure the quotient is correct? • Complete the opposite function of the original problem which is multiplication. 3 2 .1 26 834.6 -78 4 5 - 52 2 6 - 2 6 0

9. Concept Development – Problem 3 • Check your work. • Does the product match the dividend? • Yes the dividend and product are equal. 32.1 x 26 1926 +6420 834.6

10. Concept Development – Problem 4 • 48.36 ÷ 39 • Estimate the quotient and then solve using the standard algorithm. • What is your estimate? • 40 ÷ 40 = 1 • What is the actual quotient? • 1.24 • Does you answer make sense? • Yes, because it is fairly close to the estimate. • How can we check to make sure the quotient is correct? • Complete the opposite function of the original problem which is multiplication. 1 .2 39 48.36 .4 -39 3 9 - 78 15 6 - 156 0

11. Concept Development – Problem 4 • Check your work. • Does the product match the dividend? • Yes the dividend and product are equal. 1.24 x 39 1116 +3720 48.36

12. Concept Development – Problem 5 • 8.61 ÷ 41 • Estimate the quotient and then solve using the standard algorithm. • What is your estimate? • 8.0 ÷ 40 = .2 • What is the actual quotient? • .21 • Does you answer make sense? • Yes, because it is fairly close to the estimate. • How can we check to make sure the quotient is correct? • Complete the opposite function of the original problem which is multiplication. .2 41 8.61 1 -82 1 4 - 41 0

13. Concept Development – Problem 5 • Check your work. • Does the product match the dividend? • Yes the dividend and product are equal. .21 x 41 021 + 840 8.61

14. Application Problem • Find the whole number quotient and remainder of the following two expressions: • 201 ÷ 12 __ 729 ÷ 45 (Use >, <, or = to complete the sentence. 1 1 6 6 .2 .7 > 45 12 201.00 729.0 -45 -12 5 9 1 27 8 - 270 - 72 9 9 0 0 - 8 4 - 9 0 6 0 0 - 60 0

15. End of Lesson Activities • Debrief • Problem Set • Exit Ticket • Homework

16. Exit Ticket • 1. Estimate. Then, divide using the standard algorithm and check. • a) 45.15 ÷ 21 • b) 14.95 ÷ 65 • 2. We learned today that division expressions that have the same quotient and remainders are not necessarily equal to each other. Explain how this is possible.

17. Problem Set • 156 ÷ 24 and 102 ÷ 15 both have a quotient of 6 and a remainder of 12. • (a) Are the division expressions equivalent to each other? Use your knowledge of decimal division to justify your answer. • (b) Construct your own division problem with a two-digit divisor that has a quotient of a 6 and a remainder of 12 but is not equivalent to the problems in 1(a).

18. Problem Set • Divide, then check your work with multiplication. • 36.14 ÷ 13 62.79 ÷ 23 12.21 ÷ 11 6.89 ÷ 13 • 249.6 ÷ 52 24.96 ÷ 52 300.9 ÷ 59 30.09 ÷ 59 • The weight of 72 identical marbles is 183.6 grams. What is the weight of each marble? Explain how you know the decimal point of your quotient is placed reasonably. • Cameron wants to measure the length of his classroom using his foot as a length unit. His teacher tells that it takes him 92 steps. How long is Cameron’s foot in meters? • A blue rope is three times as long as a red rope. A green rope is 5 times as long as the blue rope. If the total length of the three ropes is 508.25 meters, what is the length of the blue rope?

19. Homework • 1. Create two whole number division problems that have a quotient of 9 and a remainder of 5. Justify which is greater using decimal division. • 2. Divide, then check your work with multiplication. • a) 75.9 ÷ 22 b) 97.28 ÷ 19 c) 77.14 ÷ 38 d) 12.18 ÷ 29 • 3. Divide • a) 5,224 ÷ 43 b)1,908 ÷ 36 • 4. Use the quotients in Problem 3 to write the quotients for the following. Explain how you decided where to place the decimal in the quotient. • a) 522.4 ÷ 43 and 52.24 ÷ 43 b) 190.8 ÷ 36 and 19.08 ÷ 36

20. Homework • 5. The height of Burj Dubai, the tallest in the world (2013), has a total of 162 stories. If the building is 828 meters tall, about how many meters tall is each story? • 6. Elaine has a desktop that is 4.5 feet by 5.5 feet, and she is going to cover it with patches of wallpaper that each measure 18 inches wide and 24 inches long. • How many patches will Elaine need to cover the entire desktop? Justify your answer.