ENGAGE. Daily Routines Common Core. Essential Question How can you use the strategy draw a diagram to solve multistep division problems?


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1 LESSON 4.12 Problem Solving Multistep Division Problems FOCUS COHERENCE RIGOR LESSON AT A GLANCE F C R Focus: Common Core State Standards 4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. Also 4.OA.A., 4.NBT.B.6 MATHEMATICAL PRACTICES MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. MP4 Model with mathematics. F C R Coherence: Standards Across the Grades Before Grade 4 After.OA.A.2 4.OA.A.2 5.NBT.B.5.OA.A. 4.NBT.B.6.OA.D.8 F C R Rigor: Level 1: Understand Concepts...Share and Show ( Checked Items) Level 2: Procedural Skills and Fluency...On Your Own Level : Applications...Think Smarter and Go Deeper Learning Objective Solve multistep division problems by using the strategy draw a diagram. Language Objective Students give an example of how you can use the strategy draw a diagram to solve multistep division problems. Materials Board F C R For more about how GO! fosters Coherence within the Content Standards and ematical Progressions for this chapter, see page 195J. About the Professional Development Why Teach This Problem situations often involve several pieces of information and require more than one operation to solve. When students draw bar models to visualize the information given, it is easier for them to understand the relationship between these pieces and decide which operations to use. In the problems in this lesson, students ﬁrst ﬁnd a multiple of a given number or the sum of two numbers, and then divide by another given number. Drawing bar models helps students to think through the problem. The length of each bar represents the quantities, either known or unknown, needed to solve the problem. Students will develop their skill with bar models through repeated use. In doing so, they ultimately improve their problemsolving thinking and increase their readiness for writing and solving algebraic equations to solve problems. Professional Development Videos 265A Chapter 4 Interactive Student Edition Personal Trainer on the Spot
2 Daily Routines Common Core Problem of the Day 4.12 What is the remainder of 8 5? Vocabulary Interactive Student Edition Multimedia Glossary e Common Core Fluency Fluency Builder Standard 4.NBT.B.4 Add Multidigit Whole Numbers Write the following addition problems on the board. Have students use estimation to check if their answers are reasonable. Then have students check their answers with their partners. 50, ,798 = 80,229 15, ,829 = 2,691 9,74 + 6,927 = 46,661 77, ,495 = 919,42 49, ,447 = 2,100 47, ,948 = 7,164 1 ENGAGE with the Interactive Student Edition Essential Question How can you use the strategy draw a diagram to solve multistep division problems? Making Connections Invite students to tell you what they know about using various math operations. What math operations are shown in this problem: ? addition, subtraction, and multiplication What is an example of a situation in your life where you have used addition and subtraction? Possible answer: finding the number of items you have, then subtracting the items that you gave away to your friends Learning Activity What problem are you trying to solve? the number of boxes of dish soap bottles needed to fill 4 shelves at the diner How many bottles of dish soap are in each box? 6 bottles How many shelves need to be filled with bottles of dish soap? 4 shelves How many bottles of dish soap fit on each shelf? 18 bottles Have students think about how they might solve the problem using various math operations. Literacy and ematics Choose one or more of the following activities. Have students draw a diagram showing the boxes of soap and bottles on the shelf. Have them explain one way they could solve the problem using this diagram. Have the students rewrite the problem as a short story in which they suggest a method to solve the program. How can you use the strategy draw a diagram to solve multistep division problems? 265B
3 LESSON OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and DO NOT EDITChanges be made through Filetoinfo equations with a symbolmust for the unknown number represent the problem, distinguishing multiplicative comparison from CorrectionKey=B additive comparison. 2 EXPLORE PROBLEM SOLVING Unlock the Problem Problem Solving Multistep Division Problems Essential Question How can you use the strategy draw a diagram to solve multistep division problems? MATHEMATICAL PRACTICES MP4 Model with mathematics. After students read the problem, discuss what they need to find. Point out that this is a twostep problem and that they will need to draw a diagram for each step to help solve it. How does making a diagram help you? Operations and Algebraic Thinking 4.OA.A.2 Also 4.OA.A., 4.NBT.B.6 MATHEMATICAL PRACTICES MP1, MP4, MP5 Unlock Unlock the the Problem Problem Lucia picked times as much corn as Eli. Together, they picked 96 ears of corn. Eli wants to divide the number of ears he picked equally among 8 bags. How many ears of corn will Eli put in each of the 8 bags? Possible answer: it helps to organize the information and helps me decide what operation to use. Read the Problem What does the first bar model represent? the total number of ears of corn when Lucia picked times as many ears of corn as Eli What do I need to find? of corn that I need to find the number of ears will go in each bag. What does the second bar model represent? the total number of ears of corn Eli picked in equal groups when divided into 8 bags answers: use inverse operations or work backward ELL Strategy: Cooperative Grouping Differentiated Instruction Pair students and have them explain to a partner how to draw a bar model to show 10 = 0. Guide students to complete the task using their language proficiency level: Beginning:Draw a bar model. Show 10 = 0. Intermediate: Have students complete the sentence frame: Bar models help me see. Advanced: Explain how bar models help you solve problems. Students practice listening to one another and repeat the information the others shared. I can draw bar models to visualize the information given. First, I will model and compare to find the number of ears of corn that Eli picked. What information do I need to use? times as much corn as Eli. Lucia picked _ Lucia s ears of corn. The Together they picked _ Image Credits: (t) Heath Robbins/Getty Images MP6 Attend to precision. What equation could you write to represent the number of ears of corn in each bag? Possible answer: 8 = What name might you give to the way you checked your answer in Exercise 2? Possible Solve the Problem Eli s number of ears Eli picked are divided equally 96 4 = 8 bags. among _ number of parts How will I use the information? Then I will model and divide to find how many ears of corn Eli will put in each bag. I will make a bar model for each step to divide visualize the information. Then I will _ to find the number of ears Eli picked and divide to find the number for each bag. _ ears of corn 1. How many ears of corn will Eli put in each bag? answer: I can multiply the number of ears in 2. How can you check your answers? Possible each bag by the number of bags ( 8 = ) and multiply the number of parts in the model by the number of ears picked (4 = 96). Chapter Meeting Individual Needs 4_MNLESE42217_C04L12.indd 265 Reteach 4.12 Enrich 4.12 DO NOT EDITChanges must be made through "File info" CorrectionKey=B DO NOT EDITChanges must be made through "File info" CorrectionKey=B 2 1 Reteach 10/1/14 2:2 PM Differentiated Instruction Enrich Problem Solving Multistep Division Problems It s a Riddle! There are 72 third graders and 84 fourth graders going on a field trip. An equal number of students will ride on each of 4 buses. How many students will ride on each bus? Solve each problem. Look for the answer in the riddle below and write the letter of the problem on the line. Not all letters will be used. Read the Problem I need to find the number of students who will ride on each bus. Maria takes photos at the circus and 72 photos on her vacation. If each page in her scrapbook can hold 6 photos, how many pages can Maria fill? R José uses flowers for each corsage he makes. He has orders for 18 corsages each from two different stores. How many flowers will he need? Y Taren makes 62 chocolate chip cookies and 74 oatmeal cookies. If she places 8 cookies on a plate for the bake sale, how many plates will Taren need? N Chan and his two sisters make and sell jewelry. They sell each piece of jewelry for $9 and agree to share the money equally. If they sell 8 pieces of jewelry in all, how much money will each person receive? I can model the number of students in all using a bar model. 72 What information do I need to use? 72 There are third graders and 84 fourth graders. There will be 4 buses. I can model the number of buses and divide to find the number of students on each bus. I will make a bar model for each step. I will add 72 and 84 to find the total number of students. I will divide by 4 to find how many students will ride on each bus students will ride on each bus. iranda has 180 beads for making jewelry. She buys 0 more M beads. She wants to store the beads in a case with 6 sections. She wants to put the same number of beads in each section. How many beads should Miranda put in each section? L Mr. Davis sells sleeping bags. He has 0 red sleeping bags and 26 green sleeping bags to put on shelves. Each shelf can hold 8 sleeping bags. How many shelves can he fill? T Keisha bought 10 bags of apples. There are 15 apples in each bag. If Keisha repacks the apples into 5 bags, how many apples will be in each bag? E Linh orders 16 blueberry muffins and cranberry muffins from a bakery. The bakery places 8 muffins in each package. How many packages will Linh have to pick up? $175 7 shelves 17 plates 70 beads 2. Carmen and Wayne sell 25 birdhouses at a craft fair. They share the money equally. If each birdhouse costs $14, how much money will Carmen and Wayne each receive? 108 flowers So, I 16 pages How will I use the information? 1. C Solve the Problem What do I need to find? ll 20 students at Polk School eat lunch at the same time. One A day 19 students were absent. If 8 students sit at each table in the lunchroom, how many tables were used that day at lunch? 0 apples 5 packages $114 Which city has no people? E 2 tables 265 Chapter 4 Chapter Resources 4_MNLEAN4092_C04R12.indd Reteach L 7 E 5 Chapter Resources 11/1/14 11:7 AM 4_MNLEAN4092_C04E12.indd 28 C 16 T 0 R I 175 C 16 I 175 T 0 Y 17 Enrich 11/1/14 11:40 AM
4 266 Try Another Problem There are 8 dinner rolls in a package. How many packages will be needed to feed 64 people if each person has 2 dinner rolls? Read the Problem What do I need to find? I need to find the number of packages of rolls needed. What information do I need to use? Each of 64 people gets 2 rolls. Each package of rolls has 8 rolls. How will I use the information? I will make a bar model for each step to visualize the information. Then I will multiply to find the total and divide to find the number of packages of rolls needed.. How many packages of rolls will be needed? 16 packages 4. How did drawing a bar model help you solve the problem? Possible answer: it helped me to see the relationships between the numbers and decide what operations I needed to use to solve the problem. Solve the Problem I can draw bar models to visualize the information given and then decide how to find the number of packages of rolls needed. First, I will model and multiply to find the total number of rolls needed Talk Then, I will model and divide to find how many packages are needed for that many rolls. MATHEMATICAL PRACTICES 1 Analyze What other method could you have used to solve the problem? Possible answer: I could have divided 64 by 8 and then multiplied by 2. (t) VStock/Alamy Try Another Problem After students read the problem, give them an opportunity to describe the situation and discuss how the two parts of the problem are related. What should your first model represent? the total number of rolls needed if each person has 2 rolls What should the second model represent? the total number of rolls divided into packages of 8 How are the models alike? Possible answer: they both represent the total number of rolls needed. How are the models different? Possible answer: in the first model, you find the total when you know the parts; in the second model, you divide the total into equal parts to find out how many parts. Have volunteers give their answers to Exercise 4. Talk Use Talk understanding of alternate problem solving strategies. How could you have first used the information that there are 8 dinner rolls in a package and 64 people to feed? Possible answer: divide 64 by 8 to find how many packages of rolls are needed if each person has 1 roll. What would your second step need to be? Possible answer: multiply the number of packages by 2 because each person has 2 rolls. Would you get the same answer if you follow these steps? Possible answer: yes; 64 8 = 8 and 2 8 = 16 You may suggest that students place completed Try Another Problem graphic organizers in their portfolios. Advanced Learners Visual / Logical Partners Write the following equation shells on the board. ( + ) = ( ) = Have students revisit their bar models and solutions for the problems on pages Then have partners choose the appropriate shell and write an equation for each problem. Finally, ask partners to write and solve a word problem that would fit the following shell. ( ) = Sample word problem: Jan has 8 apples. She eats 2 of them and then shares the remaining apples equally among horses. How many apples does each horse get? (8 2) = 12; 12 apples COMMON ERRORS Error The bar model that represents a relationship is not drawn correctly. Example In the Try Another Problem, students may show only one bar labeled 64 for the total in the first model. Springboard to Learning Remind students to check that they have used all the information given for the first step. Each person gets 2 rolls, so the model should show
5 DO NOT EDITChanges must be made through File info CorrectionKey=A EXPLAIN Share Share and and Show Show Unlock the Problem MATH BOARD 1. A firehouse pantry has 52 cans of vegetables and 74 cans of soup. Each shelf holds 9 cans. What is the least number of shelves needed for all the cans? Share and Show MATH First, draw a bar model for the total number of cans. BOARD Use Talk to focus on students understanding of how to check MATHEMATICAL PRACTICES 1 Evaluate How could you check to see that your answer is correct? Possible answer: multiply 9 14 to check that it is 126 and then subtract 74 and check that the result is 52. WRITE Show Your Work What are two pairs of inverse operations? 14 shelves are needed to hold all of the cans. So, _ addition and subtraction; multiplication and division 2. Use the checked exercises for Quick Check. Students should show their answers for the Quick Check on the Board. 1 RtI RtI Differentiate Instruction with Reteach 4.12 Personal Trainer 4.OA.A.2 RtI Tier 1 Activity (online) that will fit on a shelf is 18, which is double 9, the number of shelves needed would be half as many, or What if 18 cans fit on a shelf? What is the least number of shelves needed? Describe how your answer would be different. 7 shelves; possible description: since the number of cans (t) VStock/Alamy a student misses the checked exercises. Julio s dad bought 10 dozen potatoes. The potatoes were equally divided into 6 bags. How many potatoes are in each bag? 20 potatoes 4. At the garden shop, each small tree costs $125 and each large tree costs $225. How much will small trees and 1 large tree cost? DEEPER MP4 Model with mathematics. Challenge students to write an equation for each step in Exercise 1. Then solve for the unknowns. Possible equations: = n, n 9 = z, n is 126 and z is 14 For Exercise 2, students who recognize that twice as many cans will fit on a shelf should reason that half as many shelves are needed. $600 Chapter 4 Lesson 12 4_MNLESE42217_C04L12.indd Chapter operations and work backward Then Talk Finally, divide to find the number of shelves needed. an answer. What are some strategies you can use to check your answer? Possible answer: use inverse If If Choose a strategy you know. Then, draw a bar model to show the number of shelves needed. 52 Quick Check Quick Check Underline important facts. Next, add to find the total number of cans. The first problem connects to the learning model. Have students use the Board to explain their thinking. Talk Use the Problem Solving Board /27/14 4:9 PM
6 MATHEMATICAL PRACTICES ANALYZE On Your Own DIFFERENTIATED INSTRUCTION Fruit Peach Apple Plum Personal Trainer 9. Ryan bought 8 dozen bandages for the track team firstaid kit. The bandages were divided equally into 4 boxes. How many bandages are in each box? 268 Ms. Johnson bought 6 bags of balloons. Each bag has 25 balloons. She fills all the balloons and puts 5 balloons in each bunch. How many bunches can she make? 0 bunches An adult s dinner costs $8. A family of 2 adults and 2 children pays $26 for their dinners. How much does a child s dinner cost? Explain. $5; possible explanation: subtract the cost of the adult meals from the total to find the cost of 2 children s meals. Divide by 2 to find the cost of one child s meal. MATHEMATICAL PRACTICE 5 Communicate Use the table at the right. Maria bought 80 ounces of apples. She needs 10 apples to make a pie. How many apples will be left over? Explain. 6 apples; possible explanation: first, I found how many apples Maria bought: 80 5 = 16. Then, I found how many apples will be left: = 6. There will be 6 apples left over. 8. DEEPER Taylor has 16 tacks. She buys 2 packages of 6 tacks each. How many garage sale posters can she put up if she uses 4 tacks for each poster? 22 posters bandages Average weight 6 ounces 5 ounces 2 ounces INDEPENDENT ACTIVITIES (r) James Porter/Brand X Pictures/Getty Images 4 5 ELABORATE On Your Own After students complete the problems, invite volunteers to share with the class the solution strategies they used. Exercise 5 requires students to use higher order thinking skills to solve a multistep problem involving two operations. on the Spot Video Tutor Use this video to help students model and solve this type of Think Smarter problem. on the Spot videos are in the Interactive Student Edition and at MP5 Use appropriate tools strategically. Encourage students to explain all the steps they needed to take to solve the problem in Exercise 7. Personal Trainer Be sure to assign Exercise 9 to students in the Personal Trainer. It features an animation to help them model and answer the problem. For this item, students will need to use both multiplication and division to solve the problem. Students who answer 2 for the problem forgot to multiply the number of bandages by 12 first, since the problem states that Ryan had 8 dozen bandages. EVALUATE Formative Assessment Activities Dividend Rolls! Differentiated Centers Kit Literature The Thirst Quencher Games Divide to Win Essential Question Using the Language Objective Reflect Have students give an example to answer the Essential Question. How can you use the strategy draw a diagram to solve multistep divison problems? Possible answer: I can use bar models to help me solve each step of a multistep problem. Students complete purple Activity Card 9 by dividing digit numbers by 1digit divisors. Students read about using division to find the number of bottles to fill a vending machine. Students practice dividing digit numbers to find quotients in given range. Journal WRITE Write a twostep problem that you can solve using the strategy draw a diagram. Explain how you can use the strategy to find the solution. 268
7 Practice and Homework 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 section to determine student s understanding of content for this lesson. Encourage students to use their Journals to record their answers. Problem Solving Multistep Division Problems Check students drawings. Solve. Draw a diagram to help you. 1. There are trays of eggs. Each tray holds 0 eggs. How many people can be served if each person eats 2 eggs? Think: What do I need to find? How can I draw a diagram to help? 45 people can be served. 2. There are 8 pencils in a package. How many packages will be needed for 28 children if each child gets 4 pencils? Practice and Homework COMMON CORE STANDARD 4.OA.A.2 Use the four operations with whole numbers to solve problems. Multiply to find the total number of eggs. Divide to find how many people can be served 2 eggs. 14 packages of pencils. There are boxes of tangerines. Each box has 9 tangerines. The tangerines will be divided equally among 9 classrooms. How many tangerines will each classroom get? 1 tangerines 4. WRITE Write a twostep problem that you can solve using the strategy draw a diagram. Explain how you can use the strategy to find the solution. Check students work. Chapter Chapter 4
8 Lesson Check (4.OA.A., 4.NBT.B.6) 1. Gavin buys 89 blue pansies and 86 yellow pansies. He will plant the flowers in 5 rows with an equal number of plants in each row. Draw a bar model to help you find how many plants will be in each row A pet store receives 7 boxes of cat food. Each box has 48 cans. The store wants to put the cans in equal stacks of 8 cans. Draw a bar model to help you find how many stacks can be formed 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 Spiral Review (4.OA.A., 4.NBT.B.5, 4.NBT.B.6). What product does the model show? 4. Mr. Hatch bought 4 roundtrip airplane tickets for $417 each. He also paid $50 in baggage fees. How much did Mr. Hatch spend? 64 $1, Mae read 976 pages in 8 weeks. She read the same number of pages each week. How many pages did she read each week? pages 6. Yolanda and her brothers shared a box of 156 toy dinosaurs. About how many dinosaurs did each child get? Possible answer: about 40 dinosaurs FOR MORE PRACTICE GO TO THE Personal Trainer 270
One Way Draw a quick picture.
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