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Chapter 8 Lesson 1 -1 -3 10 Story Problems About Comparing NCTM Standards 1, 2, 6, 7, 8, 9, 10 Common Core State Standards 2.OA.1, 2.NBT 5, 7 STUDENT OBJECTIVES Lesson Planner • n • n o choose the appropriate operation in addition and subtraction T situations To solve two-step word problems involving comparisons (CCRG p. CC 27) Open Ended Problem Solving / Headline Story Skills Practice and Review— Mental Math (CCRG p. CC 28–CC 30) Comparing Secret Numbers (CCRG p. CC 28) Creating and Solving Story Problems (CCRG p. CC 29) Solving More Story Problems (CCRG p. CC 30) •CCRG: Activity Master, Writing Your Own Story Problem •sticky notes •counters (optional) • LAB Masters, CCRG pp. CC 32–CC 33 (CCRG p. CC 31) Leveled Problem Solving (CCRG p. CC 31) Practice Master, CCRG p. CC 34 Intervention Activity (CCRG p. CC 31) Extension Master, CCRG p. CC 35 Extension Activity (CCRG p. CC 31) Lesson Notes Lesson 8.10-3 has been added. Use after Lesson 8.10-2. About the Lesson Lesson 8.10-3 is the third in a series of three lessons on two-step word problems. If you are using this lesson later in the year, after Chapter 10, you may want to use three-digit numbers in the classroom part of the lesson. About the Mathematics The comparison model is another way for children to think about subtraction. To compare two numbers to find their difference, children can form two separate groups of counters to represent the numbers. Then they line up the counters in the two groups, matching them one-to-one. When no more matches can be made, the counters left over in the larger number represent the difference. CC 26 Common Core Resource Guide TMG2CCRG_CH08_L10-3_TG_p26-p31.indd 26 In solving word problems involving comparing, the critical skill is identifying which operation to use. For example, if you know that Jake has 3 more marbles than Dana, and then find out that Jake has 15 marbles, how do you know whether to add or subtract the 3 to find out how many marbles Dana has? Help your children think about this by asking them to identify the larger of the two numbers. Jake has more marbles, so to find out how many Dana has, you will want to subtract the difference, 3, from Jake’s total. Chapter 8 • Lesson 10-3 12/21/10 4:06:49 PM Developing Mathematical Language Vocabulary: compare, difference, more, less, fewer While working on word problems, pair ELL students with fluent readers. Encourage children to think carefully about the meaning of sentences involving comparison words. Open-Ended Problem Solving Share this headline story with your class. Encourage children to think about all the possible numbers of cars that Jack might have, and to compare those numbers to the number that Amy and Rory have. Amy has 23 toy cars. Rory has 32 toy cars. Jack has more cars than Amy, but fewer cars than Rory. Beginning Count out 13 counters and hand them to one student. Then count out 8 counters and hand them to another student. Say, write, and read sentences comparing the counters that the two children have, “Jon has 5 more counters than Ali. Ali has 5 fewer counters than Jon.” Possible responses: Jack might have 24 cars. That is 1 more than Amy but 8 fewer than Rory. He could have 28 toy cars. That is 5 more than Amy and 5 fewer than Rory. He could have anywhere from 24 to 31 toy cars. Intermediate Have children take some counters from a pile and count them. Take 12 counters for yourself. Say, “I have 12 counters. Who has more than 12?” and then, “Who has fewer than 12?” Help children compare the number of counters they have to 12. “I have 15 counters. That is 3 more than 12.” Write some of their comparisons on the board. Advanced Have children take some counters from a pile and count them. Then ask children to compare the number of counters they have to the number that others have. “I have 3 more counters than Jon, but 2 fewer than Ali.” Write some of these sentences on the board. Skills Practice and Review Mental Math Write an addition or subtraction problem on the board. Call on a student for the answer. Explain that you want children to use mental math to solve the problems. If your children enjoy silent teaching, you can do this activity silently by handing the chalk to the student you wish to answer. Start by presenting problems that do not require regrouping. If children are successful, try some with regrouping in one place. At the end of the practice, ask children to share their strategies for solving these problems. Common Core Resource Guide CC 27 TMG2CCRG_CH08_L10-3_TG_p26-p31.indd 27 12/21/10 4:06:49 PM whole class 15 MIN NCTM Standards 1, 2, 6, 7, 8, 9, 10 CCSS 2.OA.1, 2.NBT.5, 7 Comparing Secret Numbers Purpose To explore problems involving comparing Introduce Without letting your children see what numbers you are writing, write three two-digit numbers on the board such as 28, 37, and 41. Cover each number with a sticky note. Label the sticky notes A, B, and C. Tell your class that these are your secret numbers. Give the following clues to the secret numbers: • A is 9 less than B As you are working with the class, look for children who are having trouble choosing an operation to solve comparing problems. During the second activity, you may be able to work more closely with these children and help them understand how to make the correct choices. • C is 13 more than A • B is 4 less than C Work with your class to rephrase each of the three clues, until you have this list: • A is 9 less than B; B is 9 more than A • C is 13 more than A; A is 13 less than C • B is 4 less than C; C is 4 more than B Problem Is there anything else we can figure out? Let children work on this for a bit. Hopefully, they will come up with more than one solution. Possible solutions include A 5 5, B 5 14, C 5 18; A 5 68, B 5 77, C 5 81. As a class, decide that you don’t have enough information to figure out the numbers. Reveal any one of the three numbers, for example, show that B = 37. Have children figure out what the other two are. Talk Math I know that B is 4 less than C. Should I add or subtract 4 from B to find C? Possible answer: C has to be greater than B, so you should add 4 to get 41. Once you know all three numbers, what questions could you ask about them? Possible answer: We could ask for the sum of the three numbers. We could ask which one is the greatest. Write a word problem using your numbers. Let children help you decide about what objects will be counted in the problem and the names you will use. Here is a sample problem for these numbers: Jesse has 13 more marbles than Sophie. Sophie has 4 fewer marbles than Dale. Dale has 37 marbles. How many marbles does Jesse have? Help children see that they can solve this problem with only two comparing sentences. Children should already realize that they have to reveal at least one number for the problem to be solvable. Discuss how you would solve this problem if you didn’t already know the secret numbers. CC 28 Common Core Resource Guide TMG2CCRG_CH08_L10-3_TG_p26-p31.indd 28 Chapter 8 • Lesson 10-3 12/21/10 4:06:49 PM Creating and Solving Story Problems pairs Materials Purpose To write and solve two-step word problems involving comparing • For each child: AM: Writing Your Own Story Problem Introduce Tell children that you want them to write their own comparing problems. Give each student a copy of Activity Master: Writing Your Own Story Problem. Go through the instructions for the page with the class. Name Date 6Xi^k^inBVhiZgM 6Xi^k^inBVhiZg NCTM Standards 1, 2, 6, 7, 8, 9, 10 CCSS 2.0A 1, 2.NBT 5, 7 Writing Your Own Story Problem Master: Writing Your Own Story Problem, each student writes a comparison story problem. When the word problem is complete, children should fold the top edge of the paper down to the dotted line on the activity master to hide the solution. You may need to demonstrate how to fold the paper. Next, children exchange papers with a partner and solve the problem they get on a separate piece of paper. They can check their work by unfolding the paper to see the solution. Choose 3 secret numbers. A B Which secret number will you tell? Write a question you can ask about your numbers. After you write your story, fold the top edge of your paper down to the dotted line to cover the answers. Write a story problem about your numbers. 88(+ 8dbbdc8dgZGZhdjgXZ<j^YZ Activity Master: Writing Your Own Story Problem Talk Math Concept Alert How do you know whether to add or subtract? Possible answer: I just think about which number is supposed to be greater. If the number I want to find is less than the number I know, I subtract. If the number I want to find is greater than the number I know, I add. Share Ask children to share any strategies they have developed for solving these problems. Children may also want to share problems they thought were funny or especially tricky. You can keep this collection of story problems for children to use for practice. Since the solutions are included, children will be able to practice independently. Chapter 8 • Lesson 10-3 C Write some sentences comparing the numbers. © School Specialty Task Write your own story problem. Using Activity '% B>C As children are working, check to see that they are writing problems with enough information to be solvable. For example, if they don’t include a comparison sentence that mentions one of the numbers, it may not be possible to find that number later. Common Core Resource Guide CC 29 individuals Solving More Story Problems LAB Masters, 20 CCRG pp. CC 32–CC 33 MIN Purpose To write comparison sentences and to solve two-step word problems NCTM Standards 1, 2, 6, 7, 8, 9, 10 CCSS 2.OA 1, 2.NBT 5, 7 involving comparisonsPurpose To solve two-step word problems involving putting together and taking apart Lesson Activity Book Master, CCRG p. CC 32 Chapter 8 Lesson Name Lesson Activity Book Master, CCRG p. CC 33 Answer each question. Show your work. Date/Time 10-3 Story Problems About Comparing NCTM Standards 1, 2, 6, 7, 8, 9, 10 Common Core State Standards 2.OA 1, 2.NBT 5, 7 4. Bevfound23plasticbottles. Tomfound9fewerplastic bottles.Thetwochildren recycledallthebottlesthey found.Howmanybottlesdid theyrecycle? Sample work is shown. Evan has 22 baseball cards. Drew has 41 more cards than Evan. Evan 37 1. Circle the name of the person who has more baseball cards. 2. How many baseball cards does Drew have? Show your work. Possible response: Drew has 63 cards. Drew has 41 more cards than Evan, so Drew has 22 + 41 = 63 cards. 2 moreflowers © School Specialty © School Specialty Answer your question. Show your work. Kerry Jo Eric HowmanyflowersdidKyleplant? 15 7 + 8 = 15 HowmanymoreflowersdidMaya plant? 13 Possible solutions are shown. 6. F indthreedifferentsolutions tothisproblem. Possible response: How many baseball cards do Evan and Drew have in all? Evan and Drew have 85 cards altogether. 22 + 63 = 85 cards Howmanybottlesdidthey recycle? 37 bottles 9 + 4 = 13 Challenge 3. Write another question about the baseball cards. 14 23 – 9 = 14 23 + 14 = 37 bottles 5. Kyleplanted7rosesand8 tulips.Mayaplanted9roses and4tulips.Howmanymore flowersdidKyleplantthan Maya? Drew Sample work is shown. HowmanybottlesdidTomfind? Kerryhas21moreraisins thanJo.Erichas12fewer raisinsthanKerry.Howmany raisinsdoeseachhave? Solution 1 Solution 2 Solution 3 31 10 19 41 20 29 51 30 39 NOTE: Your child is learning to solve story problems involving comparisons. Play a game where you and your child guess numbers from clues, such as, “My number is 18 more than 53.” CC 32 Common Core Resource Guide TMG2CCRG_CH08_L10-3_LAB_p32-p33.indd 32 Common Core Resource Guide CC 33 12/21/10 1:19:12TMG2CCRG_CH08_L10-3_LAB_p32-p33.indd PM 33 12/21/10 1:19:12 PM Teaching Notes for LAB Master, CCRG Page CC 32 Teaching Notes for LAB Master, CCRG Page CC 33 Problem 1 guides children to make sense of what they are reading by having them identify the person with the greater number of baseball cards. Then, they answer one question about the problem and write another question that could be answered from the information in the problem. Encourage children to start each problem by looking for a number they know or can find. Then they should look for a number compared to the number they know. Ongoing Assessment Children who are not sure what operation to use may need more help with interpreting comparison statements. Children who have difficulty finding a place to start may need more help with logical reasoning and reading comprehension. Challenge Problem In this problem, children are not given any of the numbers they are looking for. They will have to choose a value for one of the numbers, and then figure out the other two from that value. Encourage children to investigate the solutions they find and look for patterns. Reflect and Summarize the Lesson There are 12 bicycles in the rack. 7 are blue. The rest of the bicycles in the rack are red. How many more blue bicycles than red bicycles are in the rack? Possible answer: I know that there are 12 bicycles and that 7 of them are blue. That means that 5 bicycles are red. That means that there are 2 more blue bicycles than red bicycles. CC 30 Common Core Resource Guide TMG2CCRG_CH08_L10-3_TG_p26-p31.indd 30 Chapter 8 • Lesson 10-3 12/21/10 4:06:50 PM Leveled Problem Solving Sami found 16 golf balls at the park. Mark found 7 fewer golf balls than Sami. Basic Level How many golf balls did Mark find? Mark found 9 golf balls. On Level Kofi found 12 more than Mark. How many golf balls did Kofi find? Kofi found 21 golf balls. Practice Master, CCRG p. CC 34 Name Extension Master, CCRG p. CC 35 Practice Lesson Lesson10-3 34 Date Above Level Rona found three fewer golf balls than Sami and Mark put together. How many did Rona find? Mark found 9. Together Sami and Mark found 25. That means that Rona found 23 golf balls. Name Extension Lesson 10-3 Date Solving Story Problems with Comparing Stories with Many Steps Solve the problem. Solve the problem. Sample work is shown. 1. Anna ate 26 carrot sticks. Anna ate 13 more carrot sticks than Bret. Bret ate 18 fewer carrot sticks than Dana. Carly ate 15 fewer carrot sticks than Dana. Eliot ate 10 more carrot sticks than Carly. Show your work. Sample work is shown. 1. Emma buys 3 shirts at one store and 2 shirts at another store. She buys 1 more shirt than Gail did. How many shirts does Gail buy? Gail buys 4 shirts. Show your work. Emma buys: 3 1 2 5 5 shirts Gail buys: 5 2 1 5 4 shirts Who else ate the same number of carrot sticks as Anna? Eliot 2. Julio reads 9 books this summer. Kate reads 3 fewer books than Julio. Together, how many books do they read? Together they read 15 books. ate the same number of carrot sticks as Anna. Show your work. Julio: 9 books 2. Five friends were jumping rope. Anna jumped 48 jumps. Anna jumped 31 fewer jumps than Dana. Bret jumped 32 fewer jumps than Carly. Eliot jumped 8 more jumps than Carly. Dana jumped 23 more jumps than Bret. Kate: 9 2 3 5 6 books Together: 9 1 6 5 15 books Wes has 3 more marbles. Wes: 8 1 8 5 13 marbles © School Specialty How many more marbles does Wes have than Luc? Show your work. © School Specialty 3. Wes has 5 marbles in his hand and 8 marbles in his pocket. Luc has 10 marbles. Bret ate 26 2 13 5 13. Dana ate 13 1 18 5 31. Carly ate 31 2 15 5 16. Eliot ate 16 1 10 5 26. Eliot ate the same number as Anna. Show your work. Anna jumped 48 jumps. Dana jumped 48 1 31 5 79 jumps. How many jumps did Eliot jump? Bret jumped 79 2 23 5 56 jumps. 96 Carly jumped 56 1 32 5 88 jumps. Eliot jumped jumps. Eliot jumped 88 1 8 5 96 jumps. Luc: 10 marbles CC 34 Common Core Resource Guide TMG2CCRG_CH08_L10-3_Practice_p34.indd 34 Anna ate 26 carrot sticks. Common Core Resource Guide 12/21/10 2:13:22 PM Intervention Activity TMG2CCRG_CH08_L10-3_Extension_p35.indd 35 CC 35 12/20/10 6:07:20 PM Extension Activity Number Match Stories About Comparing Give children index cards. Have them make several pairs of cards: one with a number, such as 9, and the other with a comparison clue to the number, such as “4 less than 13,” or, “5 more than 4.” Check their pairs of cards. Then have them play a memory game with the cards. Children lay out all the cards face down, and then turn two cards face up. If the cards match they get to take the pair and go again. If they don’t match, they turn both cards face down again. Challenge children to write comparison word problems using three-digit numbers. If you like, you can make extra copies of Activity Master: Writing Your Own Problems for children to use. Give children access to base-ten blocks to support both writing and solving the problems. Chapter 8 • Lesson 10-3 TMG2CCRG_CH08_L10-3_TG_p26-p31.indd 31 Common Core Resource Guide CC 31 12/21/10 4:06:50 PM Chapter 8 Lesson Name Date/Time 10-3 Story Problems About Comparing NCTM Standards 1, 2, 6, 7, 8, 9, 10 Common Core State Standards 2.OA 1, 2.NBT 5, 7 Evan has 22 baseball cards. Drew has 41 more cards than Evan. 1. Circle the name of the person who has more baseball cards. Evan Drew 2. How many baseball cards does Drew have? Show your work. 3. Write another question about the baseball cards. © School Specialty Answer your question. Show your work. NOTE: Your child is learning to solve story problems involving comparisons. Play a game where you and your child guess numbers from clues, such as, “My number is 18 more than 53.” CC 32 Common Core Resource Guide TMG2CCRG_CH08_L10-3_LAB_p32-p33.indd 32 12/21/10 1:18:54 PM Answer each question. Show your work. 4. Bev found 23 plastic bottles. Tom found 9 fewer plastic bottles. The two children recycled all the bottles they found. How many bottles did they recycle? How many bottles did they recycle? bottles bottles 5. Kyle planted 7 roses and 8 tulips. Maya planted 9 roses and 4 tulips. How many more flowers did Kyle plant than Maya? How many bottles did Tom find? How many flowers did Kyle plant? How many more flowers did Maya plant? more flowers Challenge 6. F ind three different solutions to this problem. © School Specialty Solution 1 Kerry has 21 more raisins than Jo. Eric has 12 fewer raisins than Kerry. How many raisins does each have? Solution 2 Solution 3 Kerry Jo Eric Common Core Resource Guide CC 33 TMG2CCRG_CH08_L10-3_LAB_p32-p33.indd 33 12/21/10 1:18:55 PM Name Date Practice Lesson Lesson10-3 34 Solving Story Problems with Comparing Solve the problem. 1. Emma buys 3 shirts at one store and 2 shirts at another store. She buys 1 more shirt than Gail did. Show your work. How many shirts does Gail buy? Gail buys shirts. 2. Julio reads 9 books this summer. Kate reads 3 fewer books than Julio. Show your work. Together, how many books do they read? books. 3. Wes has 5 marbles in his hand and 8 marbles in his pocket. Luc has 10 marbles. How many more marbles does Wes have than Luc? Wes has Show your work. © School Specialty Together they read more marbles. CC 34 Common Core Resource Guide TMG2CCRG_CH08_L10-3_Practice_p34.indd 34 12/21/10 2:13:33 PM Name Date Extension Lesson 10-3 Stories with Many Steps Solve the problem. 1. Anna ate 26 carrot sticks. Anna ate 13 more carrot sticks than Bret. Bret ate 18 fewer carrot sticks than Dana. Carly ate 15 fewer carrot sticks than Dana. Eliot ate 10 more carrot sticks than Carly. Show your work. Who else ate the same number of carrot sticks as Anna? ate the same number of carrot sticks as Anna. 2. F ive friends were jumping rope. Anna jumped 48 jumps. Anna jumped 31 fewer jumps than Dana. Bret jumped 32 fewer jumps than Carly. Eliot jumped 8 more jumps than Carly. Dana jumped 23 more jumps than Bret. Show your work. © School Specialty How many jumps did Eliot jump? Eliot jumped jumps. Common Core Resource Guide CC 35 TMG2CCRG_CH08_L10-3_Extension_p35.indd 35 12/21/10 2:27:55 PM Name Date Activity ActivityMaster MasterX Writing Your Own Story Problem Choose 3 secret numbers. A B C Write some sentences comparing the numbers. Which secret number will you tell? Write a question you can ask about your numbers. After you write your story, fold the top edge of your paper down to the dotted line to cover the answers. CC 36 Common Core Resource Guide © School Specialty Write a story problem about your numbers. Common Core Resource Guide CC 37 TMG2CCRG_CH08_L10-3_TN_p37.indd 37 12/21/10 4:07:50 PM