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LESSON 4.11 Divide by 1-Digit Numbers FOCUS COHERENCE RIGOR LESSON AT A GLANCE F C R Focus: Common Core State Standards 4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Learning Objective MATHEMATICAL PRACTICES MP2 Reason abstractly and quantitatively. MP7 Look for and make use of structure. MP8 Look for and express regularity in repeated reasoning. Divide multi-digit numbers by 1-digit divisors. F C R Coherence: Divide multi-digit numbers by 1-digit divisors. Language Objective Materials MathBoard Standards Across the Grades Before Grade 4 After 3.OA.A.2 4.NBT.B.6 5.NBT.B.5 3.OA.B.6 F C R Rigor: Level 1: Understand Concepts....................Share and Show ( Checked Items) Level 2: Procedural Skills and Fluency.......On Your Own Level 3: Applications..................................Think Smarter and Go Deeper F C R For more about how GO Math! fosters Coherence within the Content Standards and Mathematical Progressions for this chapter, see page 195J. About the Math Professional Development MP2 Reason abstractly and quantitatively. In this lesson, students will use reasoning skills to make predictions, solve problems, and check their solutions. Guide them to see how the parts of the division algorithm are interrelated and how the operations of multiplication and division are used throughout the process. Students will need to apply previous knowledge of multiples to predict whether division problems will result in quotients with remainders. Students will also learn to recognize when a zero should be placed in a quotient. It is important that students understand the inverse relationship between multiplication and division to check their solutions Professional Development Videos 259A Chapter 4 Interactive Student Edition Personal Math Trainer Math on the Spot Animated Math Models iTools: Algebra HMH Mega Math 1 ENGAGE Daily Routines Common Core Problem of the Day 4.11 Nora used 20 blocks to build two towers. The number of blocks used to build each tower was a multiple of 4. What are possible numbers of blocks used to make the towers? Possible answer: 8 blocks and 12 blocks Vocabulary Essential Question How can you divide multidigit numbers and check your answers? Making Connections Invite students to tell you what they know about division of a two-digit number by a one-digit number. What is one way to divide 96 by 8? Possible answer: repeated subtraction or regrouping Learning Activity Interactive Student Edition Multimedia eGlossary Fluency Builder with the Interactive Student Edition What is the problem the students are trying to solve? Connect the story to the problem. Common Core Fluency Standard 4.NBT.B.6 Materials Vocabulary Cards (see eTeacher Resources) • What problem are you trying to solve? How much a bowl of spaghetti costs at the diner. • How much did the diner make in spaghetti sales? $935 • What math operation can you use to find the cost of one bowl of spaghetti? division Vocabulary Cards Use vocabulary cards to help students remember deﬁnitions for review words. Ask students to respond to a question or statement such as: The number being divided into parts is the ___. Literacy and Mathematics Choose one or more of the following activities. • Have students write their own word problem involving division by 5 and discuss how they might solve their problem. • Have students identify details in the problem that they do and do not need to solve the problem. How would you know when a problem will have a ___? remainder dividend How can you divide multidigit numbers and check your answers? Lesson 4.11 259B LESSON 4.11 2 EXPLORE 4.NBT.B.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies DO NOTon EDIT--Changes must be made through "File info"the relationship between multiplication and division. Illustrate and based place value, the properties of operations, and/or CorrectionKey=A explain the calculation by using equations, rectangular arrays, and/or area models Lesson 4.11 Name Unlock the Problem Divide by 1-Digit Numbers id you know that origami is the Japanese D art of paper folding? The goal is to create an object with folds using one sheet of paper and no scissors or glue. Unlock Unlock the the Problem Problem Students in the third, fourth, and fifth grades made 525 origami animals to display in the library. Each grade made the same number of animals. How many animals did each grade make? Example 1 Example 1 Divide. 525 ÷ 3 After students read the problem, ask: • Why do we use division to solve this problem? Possible answer: we know how many STEP 1 Use place value to place the first digit. Look at the hundreds in 525. 5 hundreds can be shared among 3 groups without regrouping. The first digit of the groups there are and want to find how many in each group. 1 5 Divide. Share _ hundreds equally among 3qw 525 _ 3 groups. –3 3 1 hundred Multiply. _ × __ 2 5 hundreds 3 hundreds • What will the quotient represent? the number of origami animals each class made 200, so it is reasonable. Math Talk algorithm. Use Math Talk to focus on students’ understanding of the division Possible answer: increase the number in that place in the quotient. Subtract. __ – __. © Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) ©Digital Vision/Getty Images MP1 Make sense of problems and persevere in solving them. After students complete the division, ask: • Is your answer reasonable? How do you know? Possible answer: 175 is close to the estimate MATHEMATICAL PRACTICES 8 Use Repeated Reasoning At the checking step, what would you do if the number is greater than the divisor? STEP 2 Divide the hundreds. answer: there are 3 grades: third, fourth, and fifth. closer to 600 than 300 Math Talk hundreds place. quotient will be in the __ • Why do we use 3 as the divisor? Possible • Will the quotient be closer to 100 or 200? Explain. Possible answer: 200, because the dividend is Number and Operations in Base Ten—4.NBT.B.6 MATHEMATICAL PRACTICES MP2, MP7, MP8 Essential Question How can you divide multidigit numbers and check your answers? MATHEMATICAL PRACTICES 2 Check. _ hundreds cannot be shared among 3 groups without regrouping. STEP 3 Divide the tens. 17 3qw 525 –3 22 –21 1 STEP 4 Divide the ones. 22 tens Divide. Share __ equally 3 among _ groups. 3 × 7 tens Multiply. ____ 22 tens – __ 21 tens Subtract. __ 1 ten cannot be shared Check. ___ among 3 groups without ____ regrouping. ____ . 15 ones Divide. Share __ equally 175 3qw 525 –3 22 –21 15 –15 _ 0 3 among _ groups. 3 × 5 ones Multiply. ____ 15 ones – __ 15 ones Subtract. __ 0 ones Check. __ are left. 175 So, each class made __ origami animals. • How does the number you subtract cause the result to be too large? Possible answer: the Chapter 4 259 number is not large enough. • How could you increase the size of the number you subtract? Possible answer: increase the number you wrote in the quotient. MP7 Look for and make use of structure. • How could you make division of larger numbers easier? Possible answer: to divide 3-digit numbers, divide, multiply, subtract, and check starting with the first place in the quotient and continuing to the ones place. Use the same steps to divide each place in larger numbers. 4_MNLESE342217_C04L11.indd 259 2/27/14 2:23 PM Reteach 4.11 Enrich 4.11 3 2 DO NOT EDIT--Changes must be made through "File info" CorrectionKey=B DO NOT EDIT--Changes must be made through "File info" CorrectionKey=A 1 Lesson 4.11 Reteach Name What Is Left Over ? Find the “leftover” in each situation. Then use the code key to see which letters match each of your answers. Write the letters in order of the exercises to find the answer to the riddle. Divide. 766 4 6 5 1 Step1 Useplacevaluetoplacethefirstdigit. 6 766 qw Think:7hundredscanbesharedamong _ 6groupswithoutregrouping. Step3 Thereare 4tensleftover. Regroup4tens,now thereare46ones. Dividetheones. Lesson 4.11 Enrich Name Divide by 1-Digit Numbers 1 Step2 Thereis 6qw 766 26 1hundredleftover. _ 16 Regroup1hundred, nowthereare16tens. Dividethetens. Thefirstdigitisinthe hundredsplace. 1. Jude 16tens 12 12 6qw 766 16 212 _ 46ones 46 26 __ Step4 Checktomakesurethattheremainder islessthanthedivisor.Writetheanswer. 16 ______ 212 4 2 Multiply.632tens Subtract. 2. Selena has a piece of ribbon that is 130 inches long. If she wants to make bracelets that are 9 inches long, how many inches of ribbon will be left over? Divide46onesby6. 127 127 6 766 qw 26 _ 16 212 _ 46 242 4 3. Justin prepares 229 hamburgers for a company picnic. If buns come in packages of 8, how many will be left over? Multiply.637ones Subtract. _ 127 r4 6qw 766 Step5 Usemultiplicationandadditiontocheck 127 youranswer. 3 6 _ 762 1 4 _ 766 puts 6 lemons in each bag. If he has 170 lemons, how many will be left over? Divide16tensby6. 12 qw 766 6 ______ 26 4 5 4,6 4. Mrs. Bradley has $204 to divide equally between her 7 grandchildren. How many dollars will she have left over? 1 quotient divisor 5. Mr. White has 115 tulips for bouquets. He puts 9 tulips in each bouquet. How many tulips will be left over? remainder dividend 7 Divide and check. 217 868 1. 4qw 217 3 4 _ 868 259 Chapter 4 Chapter Resources © Houghton Mifflin Harcourt Publishing Company 4_MNLEAN343092_C04R11.indd 25 Differentiated Instruction 328 r1 657 2. 2qw 328 3 2 _ 656 1 1 _ 657 4-25 1,210 r3 3. 7q w 8,473 1,210 3 7 __ 8,470 1 3 __ 8,473 Reteach 1 2 3 4 5 6 7 8 G F E L A N S T What flies around all day but never goes anywhere? FLAGS Chapter Resources © Houghton Mifflin Harcourt Publishing Company 11/13/14 11:31 AM 4_MNLEAN343092_C04E11.indd 26 4-26 Enrich 17/02/14 11:15 PM Example 2 Division is extended to include 4-digit dividends. Students will also begin to understand when to place a zero in the quotient. • How is division with a 4-digit dividend different from division of smaller dividends? Possible answer: I need to begin with There are 8,523 sheets of origami paper to be divided equally among 8 schools. How many sheets of origami paper will each school get? Example 2 Divide. 8,523 ÷ 8 STEP 1 Use place value to place the first digit. Look at the thousands in 8,523. 8 thousands can be shared among 8 groups without regrouping. The first digit of the quotient will be thousands place. in the __ STEP 2 Divide the thousands. STEP 3 Divide the hundreds. STEP 4 Divide the tens. STEP 5 Divide the ones. 1,065 sheets of So, each school will get _ origami paper. the thousands place to see if I can divide thousands or need to regroup. 1, 0 6 5 r 3 8qw 8, 5 2 3 − 8 0 5 − 0 5 2 − 4 8 4 3 − 4 0 3 • In Step 3, why do you place a zero in the hundreds place? Possible answer: since 5 hundreds cannot be shared equally among 8 groups without regrouping, I must write a zero in the hundreds place in the quotient. Connect Discuss how to check division. • How will you know if your answer to a division problem is correct when you check by multiplication and addition? Possible answer: 3 sheets left. There will be _ if the result of the multiplication and addition matches the dividend, the answer to the division is correct. connect Division and multiplication are inverse operations. You can use multiplication to check your answer to a division problem. Multiply the quotient by the divisor. If there is a remainder, add it to the product. The result should equal the dividend. Divide. Check. quotient divisor → 1,065 r3 → 8qw 8,523 ← remainder ← dividend ← quotient ← divisor 1,065 × 8 __ 8,520 + 3 __ 8,523 ← remainder ← dividend The check shows that the division is correct. 260 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) Houghton Mifflin Harcourt Place a zero in the quotient when a place in the dividend cannot be divided by the divisor. DEEPER MP3 Construct viable arguments and critique the reasoning of others. Work together with students to make a list on the board of division errors. At the end of the lesson, have students write a division exercise and purposely make an error in dividing. Then exchange with a partner to see if the partner can ﬁnd the error. ELL Strategy: Identify Relationships • Display a color-coded division problem, as shown below. Visual / Logical Partners Advanced Learners • Provide students with the following problems. 2qw 128 2qw 6,926 5qw 8,250 5qw 700 • Ask students to analyze the problems to determine how to tell without dividing if there will be a remainder. • Provide students with the following problems. 9qw 171 19 2qw 243 27 9qw 612 68 • Ask students to analyze the problems to determine a method for knowing, without dividing, if there will be a remainder when the divisor is 9. Possible answer: if the divisor is 9 and the sum of the digits of the dividend is 9, there will be no remainder. divisor dividend quotient remainder product difference Divide. 1 0 2r1 8qw 81 7 −8 ____ 0 1 − 0 ____ 17 − 16 ____ 1 Check. 102 × 8 ___ 816 + 1 ___ 817 • Have students solve several division problems. Then have them use the correct terms as they explain the steps in their solution and in their check. Lesson 4.11 260 DO NOT EDIT--Changes must be made through "File info" CorrectionKey=A Name 3 EXPLAIN Share Share and and Show Show MATH BOARD 1. Ollie used 852 beads to make 4 bracelets. He put the Share and Show same number of beads on each bracelet. How many beads does each bracelet have? Check your answer. MATH BOARD Divide. The first problem connects to the learning model. Have students use the MathBoard to explain their thinking. 2 1 3 4 qw 8 5 2 − 8 0 5 − 4 1 2 − 1 2 0 Math Talk Use Math Talk to focus on students’ understanding of how to use multiplication to check a division problem. • What operation undoes division? multiplication • How can you use multiplication to undo division? Possible answer: start with the result of 1 Rt I If a student misses the checked exercises Then Differentiate Instruction with • Reteach 4.11 • Personal Math Trainer 4.NBT.B.6 • RtI Tier 1 Activity (online) On Your Own If students complete the checked exercises correctly, they may continue with the remaining exercises. COMMON ERRORS COMMON ERRORS Error Students do not place a zero in the quotient. Example 12 r 1 8qw 8 1 7 ∙ 8 ____ 1 7 ∙1 6 ___ 1 Springboard to Learning Demonstrate that you cannot divide 1 ten into 8 groups. Explain that a 0 fills the tens place in the quotient to show that there are 0 tens. Then regroup the 1 ten to divide 17 ones. 261 Chapter 4 Possible answer: multiply the quotient by the divisor. If the product equals the dividend, the quotient is correct. Math Talk MATHEMATICAL PRACTICES 7 Identify Relationships How could you check to see if your quotient is correct? Divide and check. 197 2. 2qw 394 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) Houghton Mifflin Harcourt 2 © Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) Houghton Mifflin Harcourt Quick Check 3 1 2 1 3 × 4 8 5 2 213 beads. So, each bracelet has _ dividing, the quotient, and multiply by the divisor. If the quotient is correct, the product should be the dividend. Use the checked exercises for QuickCheck. In Exercise 3, make sure students place a zero in the tens place in the quotient. In Exercise 4, make sure students place the first digit in the hundreds place. Check. 197 × 2 _ 394 401 r1 3. 2qw 803 401 × 2 _ 802 + 1 _ 803 862 4. 4qw 3,448 177 r1 6. 4qw 709 177 × 4 _ 708 + 1 _ 709 89 7. 3qw 267 862 × 4 _ 3,448 On On Your Your Own Own Divide and check. 408 5. 2qw 816 8. 408 × 2 _ 816 89 × 3 _ 267 DEEPER The flower shop received a shipment of 248 pink roses and 256 red roses. The shop owner uses 6 roses to make one arrangement. How many arrangements can the shop owner make if he uses all the roses? 84 arrangements Chapter 4 • Lesson 11 4_MNLESE342217_C04L11.indd 261 261 13/02/14 4:11 PM MATHEMATICAL PRACTICES COMMUNICA5&t1&34E7&3&tCONSTRUCT ARGUMENTS OqnakdlRnkuhmf¤@ookhb`shnmr OqnakdlRnkuhmf¤@ookhb`shnmr 4 ELABORATE Use the table for 9–11. 9. The Craft Store SMARTER Four teachers bought 10 origami books and 100 packs of origami paper for their classrooms. They will share the cost of the items equally. How much should each teacher pay? Item $210 10. MATHEMATICAL 5 Communicate Six students shared equally the PRACTICE cost of 18 of one of the items in the chart. Each student paid $24. What item did they buy? Explain how you found your answer. Price Origami Book $24 each Origami Paper $6 per pack Origami Kit $8 each WRITE Problem Solving • Applications MATHEMATICAL PRACTICES SMARTER Math Show Your Work For Exercise 9, students need to use data from the table to solve this multistep problem. origami kits; possible explanation: first, I found how much they spent altogether: $24 × 6 = $144. Then, I tried Math on the Spot Video Tutor dividing $144 by 8 to see if they bought the origami kits. 144 ÷ 8 = 18, so they bought 18 of the origami kits. Use this video to help students model and solve this type of Think Smarter problem. 11. Ms. Alvarez has $1,482 to spend on origami paper. How many packs can she buy? Math on the Spot videos are in the Interactive Student Edition and at www.thinkcentral.com. 247 packs DEEPER Evan made origami cranes with red, blue, and yellow paper. The number of cranes in each color is the same. If there are 342 cranes, how many of them are blue or yellow? © Houghton Mifflin Harcourt Publishing Company • Image Credits: (t) Houghton Mifflin Harcourt 12. 228 cranes 13. SMARTER On Monday 336 fourth graders went on a field trip to a local park. The teachers divided the students into 8 groups. Use a basic fact. Estimate the number of students in each group. Show your work. 32 ÷ 8 = 4, so 320 ÷ 8 = 40. About 40 students will be in each group. 262 DIFFERENTIATED INSTRUCTION D INDEPENDENT ACTIVITIES MP5 Use appropriate tools strategically. Encourage students to explain completely how they decided what computations they needed to do to solve the problem and how they used the result of the computations to answer the question. SMARTER Students who are not able to explain how the estimate in Exercise 13 shows that the answer is reasonable may not truly understand why they are asked to estimate an answer before they complete the division. 5 EVALUATE Formative Assessment Essential Question Using the Language Objective Differentiated Centers Kit Activities Dividend Rolls! Literature The Thirst Quencher Games Divide to Win Reﬂect Have students write a note to an absent student to answer the Essential Question. How can you divide multidigit numbers and check your answers? Possible answer: I use the steps to divide, then I multiply the quotient by the divisor and add any remainder. If the result is the same as the dividend, my answer is correct. (BNFT Students complete purple Activity Card 9 by dividing 3-digit numbers by 1-digit divisors. Students read about using division to ﬁnd the number of bottles to ﬁll a vending machine. Students practice dividing 3-digit numbers to ﬁnd quotients in given range. Math Journal WRITE Math Josey got an answer of 167 r4 for 3qw 505 . Explain and correct Josey’s error. Lesson 4.11 262 Practice and Homework Lesson 4.11 Name Divide by 1-Digit Numbers COMMON CORE STANDARD—4.NBT.B.6 Use place value understanding and properties of operations to perform multi-digit arithmetic. Practice and Homework Divide and check. Use the Practice and Homework pages to provide students with more practice of the concepts and skills presented in this lesson. Students master their understanding as they complete practice items and then challenge their critical thinking skills with Problem Solving. Use the Write Math section to determine student’s understanding of content for this lesson. Encourage students to use their Math Journals to record their answers. 318 2qw 636 26 03 22 16 216 0 1. 318 × 2 157 r3 2. 4qw 631 636 113 r2 3. 8qw 906 157 × 4 628 + 3 631 113 × 8 904 + 2 906 Problem Problem Solving Solving Use the table for 4 and 5. 4. The Briggs rented a car for 5 weeks. What was the cost of their rental car per week? $197 5. The Lees rented a car for 4 weeks. The Santos rented a car for 2 weeks. Whose weekly rental cost was lower? Explain. Rental Car Costs Family Lee Total Cost $632 Brigg $985 Santo $328 Lees; possible explanation: Lees, $632 ÷ 4 = $158; Santos, $328 ÷ 2 = $164; $158 < $164 © Houghton Mifflin Harcourt Publishing Company 6. Math Josey got an answer of 167 r4 for 3qw WRITE 505 . Explain and correct Josey’s error. Check students’ work. Chapter 4 Extend the Math Activity Choose a Strategy for Dividing Materials MathBoard, index cards (6 for each pair of students), base-ten blocks In this chapter, students have used different strategies to divide by 1-digit divisors with up to 4-digit dividends. This activity will help students summarize and apply the strategy that is most efﬁcient for them to use to divide. Sample Division. Write this division on the board, and ask volunteers to give different strategies they could use to divide. Ask the volunteers to demonstrate their strategy. 5qw 5,055 Possible strategies: • mental math • Use base-ten blocks • Distributive Property • partial quotients • Use place value and steps: divide, multiply, subtract, check (algorithm) 263 Chapter 4 263 Have pairs write each of the strategies they named and also “Use a basic fact and a pattern” on an index card. Write 10 exercises with 3- or 4- digit dividends and 1-digit divisors on slips of paper, turn the slips face down, and play this game. Strategy Race • Partners take turns turning over a slip of paper. Both students write the exercise on their MathBoard. • Each partner chooses a different strategy on the index cards and uses that strategy to complete the division. • Partners analyze which strategy was more efﬁcient and why. • Partners continue until each student has had the opportunity to “race” with each strategy. Lesson Check (4.NBT.B.6) 1. Write an expression that can be used to check the quotient of 646 ÷ 3. 2. There are 8 volunteers at the telethon. The goal for the evening is to raise $952. If each volunteer raises the same amount, what is the minimum amount each needs to raise to meet the goal? Continue concepts and skills practice with Lesson Check. Use Spiral Review to engage students in previously taught concepts and to promote content retention. Common Core standards are correlated to each section. Possible answer: (215 × 3) + 1 $119 Spiral Review (4.OA.A.3, 4.NBT.B.5, 4.NBT.B.6) 3. What product is shown by the model? 4. The computer lab at a high school ordered 26 packages of CDs. There were 50 CDs in each package. How many CDs did the computer lab order? 5. Write a division problem whose quotient has its first digit in the hundreds place. Possible answer: 306 ÷ 2 1,300 CDs 6. Sharon has 64 fluid ounces of juice. She is going to use the juice to fill as many 6-ounce glasses as possible. She will drink the leftover juice. How much juice will Sharon drink? 4 fluid ounces © Houghton Mifflin Harcourt Publishing Company 5 × 17 = 85 FOR MORE PRACTICE GO TO THE 264 Personal Math Trainer Lesson 4.11 264