Module 2 – Lesson 24 Objective: Divide decimal dividends by multiples of 10, reasoning about the placement of the decimal point and making connections to a written method.

Fluency Practice – Rename Tenths and Hundredths Rename the following unit form numbers to standard form (decimal) 9 tenths 10 tenths 20 tenths 90 tenths 100 tenths 200 tenths 600 tenths 650 tenths 657 tenths 832 tenths 9 hundredths 10 hundredths 20 hundredths 90 hundredths 95 hundredths 100 hundredths 200 hundredths 900 hundredths 950 hundredths 1,000 hundredths 2,000 hundredths 5,000 hundredths 5,800 hundredths 5,830 hundredths 5,834 hundredths 2,834 hundredths =.9 = 1.0 = 2.0 =9.0 = 10.0 = 20.0 =60.0 = 65.0 = 65.7 =83.2 = .09 = .10 =.20 = .90 = .95 =1.00 = 2.00 = 9.00 = 9.50 =10.00 = 20.00 =50.00 = 58.00 =58.30 = 58.34 =28.34

Fluency Practice – Divide Decimals 15 ones ÷ 5 15 tenths ÷ 5 15 hundredths ÷ 5 12 tens ÷ 3 12 tenths ÷ 3 24 hundreds ÷ 6 24 hundredths ÷ 6 = 3 ones or 3 = 3 tenths or .3 = 3 hundredths or .03 = 4 tens or 40 = 4 tenths or .4 = 4 hundred or 400 = 4 hundredths or .04

Fluency Practice – Divide by Two-Digit Numbers 5,349 ÷ 21 6,816 ÷ 32 4,378 ÷ 51 = 254 r 15 = 213 = 85 r 43

Application Problem A long-time runner compiled her training distances in the chart below. Fill in the missing values. Runner’s Log Total Number of Miles Run Number of Days Miles Run Each Day 420 12 14.5 5 38.0 10 17 16.5 420 ÷ 12 = 35 14.5 ÷ 5 = 2.9 38 ÷ 10 = 3.8 17 X 16.5 = 280.5

Concept Development – Problem 1 54 ÷ 10 How is this written in unit form? 5 tens 4 ones What is 1 ten divided by 10? 1 one What is 5 tens divided by 10? 5 ones How do you show that using number disk? 10 ÷ 10 = 1

Concept Development – Problem 1 54 ÷ 10 What is 1 one divided by ten? (think 10 x ? = 1) 1 tenth What is 4 ones divided by 10? (think 10 x ? = 4) 4 tenths Show using number disk. Based on 5 tens divided by 10 and 4 ones divided by 10 quotients, what is the answer to 54 ÷ 10? 5.4 1 ÷ 10 = .1

Concept Development – Problem 1 54 ÷ 10 The answer is 5.4. What can you tell me about the quotient compared to the dividend? The quotient is 1 tenth as large as 54, or 54 is ten times larger than 5.4.

Concept Development – Problem 2 5.4 ÷ 10 = ? What is the unit form of the dividend? 5 ones 4 tenths What is 5 ones divided by 10? What is 4 tenths divided by 10? (Keep in mind our place value chart.) 5 tenths and 4 hundredths Show the division using number disk. 1 ÷ 10 = .1 .1 ÷ 10 = .01

Concept Development – Problem 2 5.4 ÷ 10 = ? What is the answer based on our number disk and unit form answers? (Note: Add the two answers together.) .54 What can you tell me about the quotient and the dividend? The quotient is 1 tenth as large as the dividend.

Concept Development – Problem 3 .54 ÷ 10 = ? What is the unit form of the dividend? 5 tenths 4 hundredths What is 5 tenths divided by 10? What is 4 hundredths divided by 10? (Keep in mind our place value chart.) 5 hundredths and 4 thousandths Show the division using number disk. .1 ÷ 10 = .01 .01 ÷ 10 = .001

Concept Development – Problem 3 .54 ÷ 10 = ? What is the answer based on our number disk and unit form answers? (Note: Add the two answers together.) .054 What can you tell me about the quotient and the dividend? The quotient is 1 tenth as large as the dividend. What pattern have you noticed in the last 3 problems? The numbers keep shifting one place to the right each time we divided by 10.

Concept Development – Problem 4 54 ÷ 90 How is this problem different than problem 1? The divisor is a multiple of 10 instead of a power of 10. What is a simpler problem that you know the answer to? 54 ÷ 9 = 6 and/or 54 ÷ 10 = 5.4 What is another way to look at this problem? (think decomposition) 54 ÷ 10 ÷ 9 Do you recall what 54 ÷ 10 is in problem 1? 5.4

Concept Development – Problem 4 54 ÷ 90 The answer of 5.4 is the result of 54 ÷ 10. What do we have left to do in the problem 54 ÷ 10 ÷ 9? 5.4 ÷ 9 What is 5.4 ÷ 9? (Think what can we multiply 9 by to get 5.4.) What is the unit form of 5.4 in tenths? 54 tenths What is 54 tenths divided by 9? 6 tenths What is quotient in standard form? 0.6

Concept Development – Problem 5 5.4 ÷ 90 How is this problem different than problem 2? The divisor is a multiple of 10 instead of a power of 10. What is a simpler problem that you know the answer to? 5.4 ÷ 9 = .6 and/or 5.4 ÷ 10 = .54 What is another way to look at this problem? (think decomposition) 5.4 ÷ 10 ÷ 9 Do you recall what 5.4 ÷ 10 is in problem 2? .54

Concept Development – Problem 5 5.4 ÷ 90 The answer of .54 is the result of 5.4 ÷ 10. What do we have left to do in the problem 5.4 ÷ 10 ÷ 9? .54 ÷ 9 What is .54 ÷ 9? (Think what can we multiply 9 by to get .54.) What is the unit form of .54 in hundredths? 54 hundredths What is 54 hundredths divided by 9? 6 hundredths What is quotient in standard form? 0.06

Concept Development – Problem 6 .54 ÷ 90 How is this problem different than problem 3? The divisor is a multiple of 10 instead of a power of 10. What is a simpler problem that you know the answer to? .54 ÷ 9 = .06 and/or .54 ÷ 10 = .054 What is another way to look at this problem? (think decomposition) .54 ÷ 10 ÷ 9 Do you recall what .54 ÷ 10 is in problem 3? .054

Concept Development – Problem 6 .54 ÷ 90 The answer of .054 is the result of .54 ÷ 10. What do we have left to do in the problem .54 ÷ 10 ÷ 9? .054 ÷ 9 What is .054 ÷ 9? (Think what can we multiply 9 by to get .54.) What is the unit form of .054 in thousandths? 54 thousandths What is 54 thousandths divided by 9? 6 thousandths What is quotient in standard form? 0.006

Concept Development – Problem 7 54 ÷ 900 What is a simpler problem that you know the answer to? 54÷ 9 = 6 and/or 54 ÷ 100 = .54 What is another way to look at this problem? (think decomposition) .54 ÷ 100 ÷ 9 What is 54 ÷ 100? .54 What is .54 ÷ 9? (Think of this as 54 hundredths) .06

Concept Development – Problem 8 5.4÷ 900 What is a simpler problem that you know the answer to? 5.4÷ 9 = .6 and/or 5.4 ÷ 100 = .054 What is another way to look at this problem? (think decomposition) 5.4 ÷ 100 ÷ 9 What is 5.4 ÷ 100? .054 What is .054 ÷ 9? (Think of this as 54 hundredths) .006

Exit Ticket 1. Divide A. 27.3 ÷ 3 = ____ B. 2.73 ÷ 30 = _____ C. 273 ÷ 300 = _____ 2. If 7.29 ÷ 9 = 0.81, then the quotient of 7.29 ÷ 90 is ______________. Use the place value reasoning to explain the placement of the decimal point.

End of Module Activities Problem Set Exit Ticket Homework

Problem Set 1. Divide. Show the division in two steps. The first two have been done for you. A. 1.2 ÷ 6 = 0.2 B. 1.2 ÷ 60 = (1.2 ÷ 6) ÷ 10 = 0.02 C. 2.4 ÷ 4 = _____ D. 2.4 ÷ 40 = ______________ E. 14.7 ÷ 7 = _____ F. 14.7 ÷ 70 = ______________ G. 3.4 ÷ 2 = ______ H. 3.4 ÷ 20 = _______________ I. 0.45 ÷ 9 = ______ J. 0.45 ÷ 90 = _______________ K. 3.45 ÷ 3 = _____ L. 34.5 ÷ 300 = ______________ 2. Use place value reasoning and the first quotient to compute the second quotient. Explain your thought. A. 46.5 ÷ 5 = 9.3 46.5 ÷ 50 = __________ B. 0.51 ÷ 3 = 0.17 0.51 ÷ 30 = __________ C.29.4 ÷ 70 = 0.42 29.4 ÷ 7 = ___________ D. 13.6 ÷ 40 = 0.34 13.6 ÷ 4 = ___________

Problem Set 3. Twenty (20) polar bears live at the zoo. In four weeks, they eat 9,732.8 pounds of food altogether. Assuming each bear is fed the same amount of food, how much food is used to feed one bear for a week? Round your answer to the nearest pound. 4. The total weight of 30 bags of flour and 4 bags of sugar is 42.6 kg. If each bag of sugar weighs 0.75 kg, what is the weight of each bag of flour?

Homework 1. Divide. Show the division in two steps. The first two have been done for you. A. 1.8 ÷ 6 = 0.3 B. 1.8 ÷ 60 = (1.8 ÷ 6) = 0.3 ÷ 10 = 0.03 C. 2.4 ÷ 8 = ______ D. 2.4 ÷ 80 =______________ E. 14.6 ÷ 2 = ______ F. 14.6 ÷ 20 = _____________ G. 0.8 ÷ 4 = _______ H. 80 ÷ 400 = _____________ I. 0.56 ÷ 7 = _______ J. 0.56 ÷ 70 = _____________ K. 9.45 ÷ 9 = ______ L. 9.45 ÷ 900 = ____________ 2. Use place value reasoning and the first quotient to compute the second quotient. Explain your thought. A. 65.6 ÷ 80 = 0.82 65.6 ÷ 8 = __________ B. 2.5 ÷ 50 = 0.65 2.5 ÷ 5 = ___________ C. 19.2 ÷ 40 = 0.48 19.2 ÷ 4 = __________ D. 39.6 ÷ 6 = 6.6 39.6 ÷ 60 = _________

Homework Chris rode his bike along the same route every day for 60 days. He logged that he had gone exactly 127.8 miles. A. How many miles did he bike each day? Show your work to explain how you know. B. How many miles did he bike over the course of two weeks? 4. 2.1 liters of coffee were equally distributed to 30 cups. How many milliliters of coffee were in each cup?