In 5th grade, you learned how to divide using models and partial quotients. Take a look at this problem.

Transcription

1 Lesson 38 Part 1: Introduction Equivalent Divide Multi-Digit Ratios Numbers Develop Skills and Strategies MAFS 6.NS.2.2 In 5th grade, you learned how to divide using models and partial quotients. Take a look at this problem. For a fundraiser, the sixth graders have 288 bags of popcorn to sell. There are 3 sixth-grade classes. If each class sells an equal number of bags, how many bags of popcorn does each class sell? Explore It Use the math you already know to solve the problem. Use a bar model to represent the problem. Fill in the whole and the number of groups What division expression represents this problem? Estimate the quotient. The quotient is around. Explain your thinking. Use your estimate. At least how many bags of popcorn should each class sell? How many bags are left to sell altogether? By each class? How many more bags can each class sell? How do you know? Explain how to find the total number of bags of popcorn each class can sell. 72 L3: L8: Equivalent Divide Multi-Digit Ratios Numbers

2 Part 1: Introduction Lesson 8 Find Out More You used partial quotients to solve the problem. divisor quotient partial quotients dividend You know that 9 groups of 3 is 27. Subtract to find how many are left You know 6 equal groups of 3 is 18. Subtract to find how many are left To find the quotient, add the partial quotients So, You can also use the division algorithm to find the quotient. This method is like partial quotients, except you need to pay attention to place value. You know the quotient is around 9. 3 HTO tens or 27 ones 18 ones 288 is 28 tens and 8 ones. There are 9 groups of 3 in tens 3 3 ones 5 27 tens. 28 tens 2 27 tens 5 1 ten 27 tens is the same as 27 ones. When you bring down the 8 ones to get 18, you are subtracting 27 from 288. There are 6 groups of 3 in ones ones. 18 ones 2 18 ones 5. There is no remainder. Reflect So, To divide 343 by 9, would you use partial quotients or the division algorithm? Explain your reasoning. L8: Divide Multi-Digit Numbers 73

3 Part 2: Modeled Instruction Lesson 8 Read the problem below. Then explore how to divide with a two-digit divisor using partial quotients or the division algorithm. A family is heading out on a car trip of 672 miles to what is known as the sixth most popular National Park, the Blue Ridge Parkway. If they travel at an average of 56 miles per hour, how long will it take to get there? Estimate It You can use compatible numbers to estimate the quotient Model It You can use partial quotients to divide. divisor quotient partial quotients dividend Model It You can use the division algorithm to divide. 56 HTO tens 112 ones 672 is 67 tens and 2 ones. There is 1 group of 56 in ten tens 67 tens 2 56 tens 5 11 tens Bring down the 2. There are 2 groups of 56 in ones ones 112 ones ones 5 ones 74 L8: Divide Multi-Digit Numbers

4 Part 2: Guided Instruction Lesson 8 Connect It Now compare the two methods of dividing to solve the problem. 2 Why does it make sense to use 66 and 6 to estimate the quotient? 3 How is writing the 1 in the division algorithm the same as writing the 1 in the partial quotients model? 4 How is writing the 56 in the division algorithm the same as writing the 56 in the partial quotients model? 5 When solving this problem with the division algorithm, how is bringing down the 2 ones like the first subtraction step in the partial quotients method? 6 How long will it take the family to drive to the park? How can you check your answer? 7 How is using the division algorithm to divide the same as using partial quotients to divide? How is it different? Try It Use what you just learned about dividing to solve these problems. Show your work on a separate sheet of paper. 8 A grandmother has $49 that she wants to give to her 14 grandchildren. How much money will each grandchild receive if they each receive an equal amount? 9 18 students collected cans for a school recycling project. If the students collected a total of 36 cans, how many cans did each student collect? L8: Divide Multi-Digit Numbers 75

5 Part 3: Modeled Instruction Lesson 8 Read the problem below. Then explore how to divide a 5-digit dividend by a 2-digit divisor. Sam s father bought a new car for $26,34. He expects to pay for it in 24 equal monthly payments. How much will Sam s father have to pay each month? Estimate It You can use compatible numbers to estimate the solution. $24, $1, Model It You can use the division algorithm to solve the problem. 24 Th HTO , ,34 is 26 thousands, 3 hundreds, and 4 ones. There is 1 group of 24 in thousand thousands 26 thousands 2 24 thousands 5 2 thousands Bring down the 3. There are no groups of 24 in 23. hundreds hundreds 23 hundreds 2 hundreds 5 23 hundreds Bring down the. There are 9 groups of 24 in tens tens 23 tens tens 5 14 tens Bring down the 4. There are 6 groups of 24 in ones ones 144 ones ones 5 ones There is no remainder. 76 L8: Divide Multi-Digit Numbers

6 Part 3: Guided Instruction Lesson 8 Connect It Now answer the question and think about the division algorithm. 1 How much will Sam s father have to pay each month? Is that answer reasonable? Explain. 11 Look back at the division algorithm. What is 24 3 $1,96? 12 Suppose Sam s father decides to pay for the car in 48 monthly payments. How much would he have to pay each month? Show your work. 13 Why is it important to pay close attention to place value when dividing with the division algorithm? Try It Use what you just learned to solve these problems. Show your work on a separate sheet of paper. 14 In a year (12 months), a sports team practiced for a total of 1,35 hours. On average, how many hours did the team practice each month? 15 There are 1,891 students participating in the citywide holiday concert. A bus seats 62 students. How many buses will be needed to bring the students to the concert? L8: Divide Multi-Digit Numbers 77

7 Part 4: Guided Practice Lesson 8 Study the student model below. Then solve problems Student Model The student remembered to write a in the ones place in the quotient to show that there were no ones left. The marching band packed 3,6 cans of juice into boxes for a band competition. Each box holds 18 cans. How many boxes did the band members have to carry? Look at how you could show your work using the division algorithm. Pair/Share How could you check your answer? Solution: 17 boxes , What is a good estimate for the quotient? 16 A local bank donated 4,74 pencils to distribute to the 42 sixthgrade classes in the district. How many pencils did each class receive? Show your work. Pair/Share Does your answer make sense? Solution: 78 L8: Divide Multi-Digit Numbers

8 Part 4: Guided Practice Lesson 8 17 At an amusement park, only 18 people are allowed on a ride at the same time. There are 157 people waiting in line. How many groups will there be? Show your work. If there is a remainder, I need to decide whether to round up or down. Solution: 18 Route 8 runs a little over 2,9 miles across the United States from the New York City area to San Francisco. If you drove the entire length in 14 days, on average how many miles would you travel per day? Circle the correct answer. Pair/Share Compare the steps you each took to solve this problem. What is the whole in this problem? A B a little more than 27 miles per day a little more than 2,7 miles per day C a little more than 27 miles per day D a little more than 27 miles per day 1 Cody chose A as the correct answer. How did he get that answer? Pair/Share Talk about the problem and explain how you could get each of the answers. L8: Divide Multi-Digit Numbers 79

9 Part 5: MAFS Practice Lesson 8 Solve the problems. 1 Charlotte read a 68-page book in 16 hours last month. How many pages per hour was that? A 38 pages B 38 pages C 4 2 }} 16 pages D 3 R4 pages 2 There are 3,72 books in the school library. There are 96 sixth graders. If the sixth graders teamed up to read all the books, how many books would each sixth grader need to read? A about 4 books B 32 books C 3 72 }} 1 books D about 37 books 3 A farmer needs to pack 2,93 apples into crates to ship to supermarkets. Each crate can hold only 3 apples. Choose True or False for each statement. A The farmer needs 96 crates to ship out all the apples. True False B The farmer needs 97 crates to ship out all the apples. True False C At least one of the crates will not be filled to capacity. True False D To determine the number of crates needed, divide 2,93 by 3. True False 4 In each box, write the appropriate digit to complete the division algorithm L8: Divide Multi-Digit Numbers

10 Part 5: MAFS Practice Lesson 8 5 An elementary school received a donation of $1,. The school has 4 kindergarten classes and 3 classes each in Grades 1 through 6. Can the money be divided equally among the classes? Explain. Show your work. Answer 6 The seating capacity of a basketball stadium is 5,782. The seats are arranged in 24 sections of the same size. Any seats that are left over from the 24 sections are called priority seating. How many seats are called priority seating? Show your work. Answer Self Check Go back and see what you can check off on the Self Check on page 53. L8: Divide Multi-Digit Numbers 81

11 NAME DATE PERIOD Lesson 5 Reteach Divide Multi-Digit Numbers When one number is divided by another, the result is called a quotient. The dividend is the number that is divided and the divisor is the number used to divide another number. Example Find Estimate or R The quotient is 19 R22. Exercises Find each quotient. Divide each place-value position from left to right. Since = 22 and 22 < 3, 22 is the remainder Copyright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use , , , Course 1 Chapter 3 Compute with Multi-Digit Numbers 45

12 NAME DATE PERIOD Lesson 5 Extra Practice Divide Multi-Digit Numbers Find each quotient R R R R R R R R R R R R R R7 Course 1 Chapter 3 Compute with Multi-Digit Numbers

13 NAME DATE PERIOD Lesson 7 Reteach Divide Decimals by Whole Numbers When you divide a decimal by a whole number, place the decimal point in the quotient above the decimal point in the dividend. Then divide as you do with whole numbers. Example 1 Find Estimate: 9 9 = 1.97 Place the decimal point directly above the decimal point in the dividend Divide as with whole numbers =.97 Compared with the estimate, the quotient is reasonable. Example 2 Find Estimate: 1 1 = 1 Copyright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use..715 Place the decimal point Annex a zero to continue dividing =.715 Compared with the estimate, the quotient is reasonable. Exercises Divide Course 1 Chapter 3 Compute with Multi-Digit Numbers 49

14 NAME DATE PERIOD Lesson 7 Extra Practice Divide Decimals by Whole Numbers Divide. Round to the nearest tenth if necessary Course 1 Chapter 3 Compute with Multi-Digit Numbers

15 Part 3: Modeled Instruction Lesson 1 Read the problem below. Then explore how to divide by decimals. Olympic National Park is 28.5 miles from Forks, Washington. It took the Pearce family.75 hours to drive there. What was their average speed, in miles per hour? Estimate It You can estimate the quotient miles is close to 3 miles..75 hours is close to 1 hour. The average speed is about 3 miles 4 1 hour. Model It Since the fraction bar means division, you can write the division problem as a fraction to understand how to divide by decimals To get a whole number divisor, multiply.75 by 1. The decimal point moves 2 places to the right. If you multiply the denominator by 1, you also have to multiply the numerator by , is equivalent to 2, The divisor has two decimal places. Moving the decimal point 2 places to the right to get a whole number is the same as multiplying the divisor by 1. If you multiply the divisor by 1, you have to do the same to the dividend L1: Multiply and Divide Decimals

16 Part 3: Guided Instruction Lesson 1 Connect It Use what you know about equivalent fractions and division to solve the problem. 9 Look at Estimate It. About how many miles per hour is their average speed? 1 Look at Model It. Why do you multiply.75 by 1? 11 Why do you have to multiply 28.5 by 1? 12 What is the Pearce family s average speed? 13 Does your answer make sense? Explain how you know. 14 Explain how to divide when the divisor is a decimal. Try It Use what you just learned about dividing by decimals to solve these problems. Show your work on a separate sheet of paper. 15 At a craft fair, Emily made $52.5 selling paper flowers. If she sold the flowers for $.75 each, how many paper flowers did she sell? 16 Every day Marco puts $.25 cents into a jar for savings. One day he counted his money and found he had $ How many days had he been saving? L1: Multiply and Divide Decimals 97

17 Part 4: Modeled Instruction Lesson 1 Read the problem below. Then explore how to divide decimals using an algorithm. The average walking speed is 3.4 miles per hour. How many hours would it take to walk from Boston to Seattle, a distance of 3,2.22 miles? Estimate It You can estimate the quotient. 3.4 miles per hour is about 3 miles per hour. 3,2.22 miles is about 3, miles. 3, miles 4 3 miles per hour 5 number of hours Model It You can think about equivalent fractions to understand the division algorithm. 3, , , , L1: Multiply and Divide Decimals

18 Part 4: Guided Instruction Lesson 1 Connect It Use what you know about equivalent fractions and dividing by decimals to solve the problem. 17 Look at Estimate It. About how many hours would it take to walk from Boston to Seattle? 18 Look at the fractions in Model It. Why do you multiply the numerator and denominator by 1? 19 Explain how moving the decimal point one place to the right is the same as multiplying the numerator and denominator of the fraction. 2 How many hours would it take to walk from Boston to Seattle? And, how can your estimate help you decide where to place the decimal point? 21 How do you divide by decimals? Try It Use what you just learned to solve these problems. Show your work on a separate sheet of paper. 22 Annette had a 24-karat gold necklace that weighs 2.3 grams. She sold it for $ What was the price per gram of her necklace? 23 At maturity, a stalk of corn is inches tall. It took hours to reach that height. What was the rate of growth per hour? L1: Multiply and Divide Decimals 99

19 NAME DATE PERIOD Lesson 8 Reteach Divide Decimals by Decimals When you divide a decimal by a decimal, multiply both the divisor and the dividend by the same power of ten. Then divide as with whole numbers. Example 1 Find Estimate: 1 5 = 2 Multiply by 1 to make a whole number Place the decimal point Divide as with whole numbers Multiply by the same number, Annex a zero to continue divided by 5.2 is Compare the quotient with the estimate. Check = 1.14 Copyright The McGraw-Hill Companies, Inc. Permission is granted to reproduce for classroom use. Example 2 Find Place the decimal point Divide. - 4 Multiply each by Write a zero in the dividend - 1 and continue to divide. 4.9 divided by.2 is Check = 4.9 Exercises Divide Course 1 Chapter 3 Compute with Multi-Digit Numbers 51

20 NAME DATE PERIOD Lesson 8 Extra Practice Divide Decimals by Decimals Divide Course 1 Chapter 3 Compute with Multi-Digit Numbers

21 Part 5: Guided Practice Lesson 1 Study the student model below. Then solve problems The student multiplied as with whole numbers and used estimation to place the decimal point. Student Model The greatest skateboarding speed recorded is mph by Roger Hickey in 199. If he could keep up that speed for 15 minutes or.25 hour, how far could he go? Look at how you can use estimation to place the decimal point. 15 minutes is of an hour, and rounds up to 8, so I can 1 4 expect my answer to be about of 8, or Pair/Share What is another way to determine where to put the decimal point? Since I know that the answer is going to be around 2, the decimal point belongs after the 19. Solution: miles, which is about 2 miles. Can you estimate the product? 24 By the age of 21, the best violinists and pianists will have practiced at least 1, hours. If you practice an instrument 45 minutes (or.75 hours) a day for days, the length of a year, how many hours will you have practiced? Show your work. Pair/Share Without doing any multiplication, how can you tell whether the answer will be greater or less than hours? Solution: 1 L1: Multiply and Divide Decimals

22 Part 5: Guided Practice Lesson 1 25 When the Dixon family traded in their old car, it had 53,79 miles on it. They had the car for 8.25 years. On average, how many miles did they drive per year? Show your work. How many decimal place values are there in the divisor? Solution: 26 In 197, a record 1.5 inches of rain fell in one minute at Basse Terre, Guadeloupe in the Caribbean. At this rate, how much rain fell in 3 seconds or.5 of a minute? Circle the letter of the correct answer. A 3 inches Pair/Share How could you check your answer? Will the answer be greater than or less than 1.5 inches? B C.75 inch.75 inch D 3 inches Evan chose D as the correct answer. How did he get that answer? Pair/Share Does Evan s answer make sense? L1: Multiply and Divide Decimals 11

23 Part 6: MAFS Practice Lesson 1 Solve the problems. 1 In 1892 a world record was set. France s M. Garisoain walked on stilts for 4.97 miles from Bayonne to Biarritz, France, at an average speed of 7.1 miles per hour. How long did it take him to walk that distance? A B C D 7 hours 7 hours.7 hour.7 hour 2 Maria walks a round-trip of.75 mile to school every day. How many miles will she walk in 4.5 days? A B C D.3375 mile miles miles miles 3 Mika babysat for the Tylers for 3.5 hours. They gave her $ How much did she make per hour? A B C D $.75 per hour $7.5 per hour $9.8 per hour $13.33 per hour 12 L1: Multiply and Divide Decimals

24 Part 6: MAFS Practice Lesson 1 4 Look at each expression. Is it equivalent to ? Select Yes or No for expressions A E. A Yes No B Yes No C Yes No D Yes No E Yes No 5 One of Mr. Edward s students answered the following problem on her homework Part A Explain to Mr. Edwards whether or not the student got the question correct, and explain the reason why. Part B Use the multiplication algorithm to find the answer to the same question ? Show your work. Answer Self Check Go back and see what you can check off on the Self Check on page 53. L1: Multiply and Divide Decimals 13