Number Stories Objective To guide children as they use change diagrams to help solve change number stories. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Use basic facts to solve extended fact problems. [Operations and Computation Goal 1] Use and explain strategies to solve addition and subtraction number stories. [Operations and Computation Goal 2] Solve change-to-more and change-to-less multidigit addition and subtraction number stories using change diagrams. [Operations and Computation Goal 6] Write number models for addition and subtraction number stories. [Patterns, Functions, and Algebra Goal 2] Key Activities Children review the Guide to Solving Number Stories and use change diagrams to solve change-to-more and change-to-less number stories. Ongoing Assessment: Informing Instruction See page 127. 1 4 2 3 Playing Number-Grid Difference Student Reference Book, p. 301 Math Masters, pp. 21 and 452 per partnership: 4 each of number cards 0 9 (from the Everything Math Deck, if available), calculator, counters Children practice finding differences on the number grid. Math Boxes 2 5 Math Journal 1, p. 41 Children practice and maintain skills through Math Box problems. Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 3. [Number and Numeration Goal 1] Home Link 2 5 Math Masters, p. 46 Children practice and maintain skills through Home Link activities. READINESS Changing the Calculator Display Math Masters, pp. 21, 45, and 47 transparency of Math Masters, p. 45 (optional) calculator Children complete calculator puzzles. ENRICHMENT Writing and Solving Number Stories Math Journal 1, p. 40 Math Masters, pp. 45 and 407 Student Reference Book, pp. 212 and 213 Children make up and solve change number stories. Key Vocabulary change diagram change-to-more number story deposit change-to-less number story withdraw trade-first algorithm Materials Math Journal 1, pp. 39 and 40 Home Link 2 4 Math Masters, pp. 406 and 409 transparency of Math Masters, p. 409 (optional) Number-Grid Poster or Class Number Line calculator (optional) Advance Preparation Teacher s Reference Manual, Grades 1 3 pp. 84 89 Lesson 2 5 123
Getting ed Mental Math and Reflexes Pose questions like the following. Consider demonstrating the answers on the Number-Grid Poster or Class Number Line. Is 18 closer to 10 or 20 20 Is 21 closer to 20 or 30 20 Is 188 closer to 180 or 190 190 Is 105 closer to 100 or 110 Same distance away Is 450 closer to 400 or 500 Same distance away Is 2,777 closer to 2,770 or 2,780 2,780 Mathematical Practices SMP1, SMP2, SMP3, SMP4, SMP5, SMP6, SMP7, SMP8 Content Standards 3.NBT.2 Math Message Madeline had $38 in her bank account. She deposited another $15. How much money was in her account then $53 Home Link 2 4 Follow-Up Unit Review the answers. Have children discuss the strategies they used to solve the parts-and-total number stories. 1 Teaching the Lesson Math Message Follow-Up WHOLE-CLASS DISCUSSION Name Date Time Diagrams 38 +15 Teaching Aid Master Math Masters, p. 409 Have children tell which label they put in the unit box. dollars or $ Invite them to share the strategies they used to solve the Math Message problem. Solving a -to-more Number Story (Math Masters, pp. 406 and 409) WHOLE-CLASS DISCUSSION Algebraic Thinking Refer to the Guide for Solving Number Stories as you work through the steps in the problem-solving process for the Math Message story. Be sure that children know the meaning of deposit. 1. What do you understand from the Math Message story Think. What do you want to find out The new amount of money in Madeline s account What do you know from reading the story Madeline had $38 in her bank account and she deposited $15 more. 2. What will you do SOLVING What do you have to do to find the new amount of money in Madeline s account Add 38 and 15 What kind of number story is this If no one mentions it, remind children about change-to-more number stories from second grade. Display a change diagram. To support English language learners, consider creating a change diagram poster similar to the parts-and-total diagram poster in the Part 3 activity in Lesson 2-4. ELL 405-412_451_456_465_EMCS_B_MM_G3_U02Proj_576957.indd 409 4/8/11 10:20 AM 124 Unit 2 Adding and Subtracting Whole Numbers
Write a question mark in the box to represent what you want to find out. Point out that the total amount of money in Madeline s bank account changed to more. Write 38 in the box and +15 on the line. Have volunteers write number models for the story on the board (See margin.) 3. Answer the question. Madeline now has $53 in her account. Have children share their solution strategies. Some children may have used mental computation to find the sum. Possible Solution Strategies First add the tens: 30 + 10 = 40. Then add the ones: 8 + 5 = 13. Finally, add the two parts: 40 + 13 = 53. Add the second addend to the first addend in parts (tens and ones): 38 + 10 = 48; 48 + 5 = 53. Add the first addend to the second addend in parts (tens and ones): 15 + 30 = 45; 45 + 8 = 53. Take 2 from 15, leaving 13. Add the 2 to the 38 to get 40. 40 is an easy number to work with. Add 13 to 40: 40 + 13 = 53. 4. Check. Does your answer make sense How do you know Go back to the question in the number story. Have you answered it yes How do you know your answer is reasonable The total amount of money should be more because Madeline added money to her account. Does your answer make the number model true yes Write a summary number model on the board: 38 + 15 = 53. Possible number models: 38 + 15 = 38 15 + 38 = + 15 NOTE Lesson commentaries often include examples of solution strategies. This does not mean that children must be comfortable with all the strategies. Children benefit from hearing strategies that others have used. Help children choose a strategy that works for them. Solving a -to-less Number Story ELL PROBLEM SOLVING WHOLE-CLASS Algebraic Thinking Pose the following number story: José had $76 in his bank account. He withdrew $29. How much money was in his bank account then Be sure children know the meaning of the words withdraw and withdrew. Write the words on the board to support English language learners. Guide children through the problem-solving steps: 1. What do you understand from the story What do you want to find out The new amount of money in José s bank account What do you know from listening to the story José had $76 in his bank account. He withdrew $29. 2. What will you do What could you do to find out how much money José has in the bank Sample answer: Subtract 29 from 76. 76-29 Lesson 2 5 125
Date LESSON 2 5 Time For each number story, write in the change diagram for the number you want to find. Then write the numbers you know in the diagram. Next, write a number model. Finally, solve the problem and write the answer. 1. Ahmed had $22 in his bank account. For his birthday, his grandmother deposited $25 for him. How much money is in his bank account now 22 + 25 = Answer the question: $47 Sample answer: The end number has to be greater than the start and change numbers. 2. Omar had $53 in his piggy bank. He used $16 to take his sister to the movies and buy treats. How much money is left in his piggy bank 53 16 = or 16 + = 53 Answer the question: $37 Sample answer: The answer has to be less than $53. 3. Cleo had $37 in her purse. Then Jillian returned $9 that she borrowed. How much money does Cleo have now 37 + 9 = Answer the question: $46 Sample answer: It s more than $37, since $9 was added. Math Journal 1, p. 39 EM3MJ1_G3_U02_30-54.indd 39 Student Page Number Stories: -to-more and -to-less 22 +25 53 16 37 +9 Unit dollars Links to the Future The counting-up and trade-first methods for subtraction will be reviewed in Lesson 2-8. Date 254 255 NOTE Some children may need to act out their solution strategies. Make sure the Number-Grid Poster or Class Number Line is available to them. LESSON 2 5 Time 4. Audrey had $61 in her bank account. She withdrew $48 to take on vacation. How much is left in her account 61 48 = or 48 + = 61 Answer the question: $13 Sample answer: Audrey has $13 left from $61 because she withdrew $48. Try This Number Stories continued 5. Trung had $15 in his piggy bank. After his birthday, he had $60 in his bank. How much money did Trung get as birthday presents 15 + = 60 or 60 15 = Answer the question: $45 Sample answer: The answer has to be more than 15 and less than 60. 6. Nikhil had $40 in his wallet when he went to the carnival. When he got home, he had $18. How much did he spend at the carnival 40 18 = or 18 + = 40 Answer the question: $22 1_ Sample answer: Nikhil spent a little more than 2 of his money. $22 is about right. 40 Math Journal 1, p. 40 Student Page 61 15 40 48 60 18 12/29/10 4:35 PM What kind of a number story is this change-to-less number story Display a change diagram. Write a question mark in the box to represent what we want to find out. Point out that the total amount of money in José s bank account changed to less. Write 76 in the box and 29 on the line. Have volunteers write number models for the story on the board. Possible number models 76-29 = 76 29 29 + = 76-29 + 76 3. Answer the question. $47 is now in the bank account. Have children share their solution strategies. Possible Solution Strategies Some children may remember and use the trade-first algorithm from second grade. They may ask themselves: Are there enough tens and ones in 76 so that I can subtract 2 tens and 9 ones No, there aren t enough ones, so I need to trade a ten for more ones. Other children may try counting up: What number added to 29 will give me 76 If I add 1 to 29, I m at 30, which is an easy number to work with. 30 + 46 = 76, and 1 + 46 = 47. Others may try counting up and then backing out the extra. For example, I ll try adding 50 to 29 because 50 is an easy number to work with. 50 + 29 = 79. 79 is 3 more than 76, so 50 is 3 more than I should have added. 50-3 = 47. 4. Check. Does your answer make sense How do you know Go back to the question in the number story. Have you answered it reasonably yes How do you know The amount of money at the end should be less than the original amount because money was taken out. Does your answer make the number model true yes Write a summary number model on the board: 76-29 = 47. Solving Number Stories (Math Journal 1, pp. 39 and 40) PARTNER ELL PROBLEM SOLVING Algebraic Thinking Partners work on the two journal pages. Ask guiding questions like the ones modeled in the previous sections. Because English language learners may not be familiar with the piggy bank context, clarify what a piggy bank is. Then bring the class together and share solution strategies. As children share ideas, fill in the change diagram that you have displayed. EM3MJ1_G3_U02_30-54.indd 40 12/29/10 4:35 PM 126 Unit 2 Adding and Subtracting Whole Numbers
Possible Solution Strategies Problem 1: Use partial sums. Problem 2: Take 10 away from 53 to get 43. Then count back 6 more to get 37. Problem 3: Use complements of 10. Think of 9 as 3 + 6. Add 3 to 37. 37 + 3 = 40. Then add the rest. 40 + 6 = 46. Problem 4: Use the counting-up method. Count up from 48 to 61. For each Try This problem, the and amounts are known; the is not known. Children may find it helpful to ask themselves, Did the amount go up or down If it changed to more, something was added. If it changed to less, something was subtracted. Problem 5: Which number, added to 15, will give me 60 Problem 6: Counting up from 18 takes how much to get to 40 From 18 to 20 is 2. Then from 20 to 40 is 20. 20 + 2 = 22. 2 Ongoing Learning & Practice Ongoing Assessment: Informing Instruction Watch for children who are having difficulty solving the Try This problems. Remind them of the calculator problems they solved in Lesson 2-2. For example, think of $15 + = $60 as follows: Enter 15 into the calculator. Add or subtract a number so the calculator displays 60. What will you do Add 45. NOTE There is not necessarily one kind of diagram that goes with a given problem. The best diagram for a child to use depends on the way the child thinks about the problem. Initially, diagrams are provided to expose children to the different ways of modeling a problem so that they will begin to develop resources to use for solving problems. Playing Number-Grid Difference (Student Reference Book, p. 301; Math Masters, pp. 21 and 452) PARTNER Children practice finding differences on the number grid by playing Number-Grid Difference. For detailed instructions, see Lesson 1-8 or page 301 in the Student Reference Book. Children may record several rounds on Math Masters, page 452 or on a half-sheet of paper. Math Boxes 2 5 (Math Journal 1, p. 41) INDEPENDENT Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 2-7 and 2-9. The skill in Problem 6 previews Unit 3 content. Ongoing Assessment: Recognizing Student Achievement Math Boxes Problem 3 Use Math Boxes, Problem 3 to assess children s ability to express the value of digits in a given number. Children are making adequate progress if they are able to complete the problem correctly. Some children may be able to identify the value of digits in larger numbers. [Number and Numeration Goal 1] Date LESSON 2 5 1. Use addition or subtraction to complete these problems on your calculator. Enter to How 366 66 894 2,894 3,775 3,175 27,581 28,581 1,000 3. 2,345 the 2 means Math Boxes the 3 means 2,000 300 40 the 4 means the 5 means 5 Student Page 300 2,000 600 18, 19, 264 5. Lily had 33 rings in one box and 29 in another. How many did she have in all 62 rings 18 19 Time 2. What s My Rule in out in Rule 10 14 21 25 32 36 56 60 Answers vary. Add 4 4. Write 5 names in the 120-box. 120 Sample answers: 60 60 1,120 1,000 125 5 10 12 one hundred twenty out 203 204 14 15 6. How many squares are shaded Fill in the oval for the best answer. 33 29 12 7 9 5 256 257 Math Journal 1, p. 41 Lesson 2 5 127
Name Date Time HOME LINK 2 5 Family Note Home Link Master Number Stories Today your child learned about another diagram that helps organize the information in a number story. It is called a change diagram. For more information, see pages 254 and 255 in the Student Reference Book. 254 255 Please return this Home Link to school tomorrow. For each number story, write in the change diagram for the number you want to find. Write the numbers you know in the diagram. Then, write a number model and the answer. Finally, write how you know that each answer makes sense. 1. Marcus had $25 in his wallet. He spent $16 at the store. How much money was in Marcus s wallet then 25-16 = or 16 + = 25 Answer the question: $9 (unit) 2. Jasmine had $35. She earned $14 helping her neighbors. How much money did she have then 35 + 14 = Answer the question: $49 (unit) Sample answer: The answer has to be more than $35 since Jasmine earned $14 more. 25-16 Sample answer: Marcus spent $16 so the answer has to be less than $25. 35 +14 Home Link 2 5 (Math Masters, p. 46) INDEPENDENT Home Connection Children use change diagrams to solve change-to-more and change-to-less number stories. Because change diagrams might not be familiar to parents, you may want to send home the Student Reference Book. 3 Differentiation Options READINESS Changing the Calculator Display (Math Masters, pp. 21, 45, and 47) PARTNER 5 15 Min Math Masters, p. 46 EM3MM_G3_U02_036-063.indd 46 18 +20 38 11/9/10 9:37 AM Algebraic Thinking To explore number stories involving a change to more or a change to less, have children complete the calculator puzzles on Math Masters, page 47. Children use a number grid to help them figure out the answers. They should check their answers on calculators. When children have finished the page, briefly discuss how they solved the problems. If you have children do this activity prior to the lesson, consider making a transparency of Math Masters, page 45 and using the number sentences from Math Masters, page 47 to demonstrate a change diagram. (See the example for Problem 1 in the margin.) Name Date Time LESSON 2 5 Changing the Calculator Display Solve the calculator problems. Use a number grid to help. Check your answers on a calculator. Write a number model to show what you did. Example: How can you change 24 to 35 Add 11 1. How can you change 18 to 38 2. How can you change 30 to 80 3. How can you change 21 to 63 4. How can you change 97 to 45 24 11 35 18 20 38 30 50 80 21 42 63 97 52 45 5. How can you change 100 to 62 Teaching Master 100 38 62 Add 20 Add 50 Add 42 Subtract 52 Subtract 38 ENRICHMENT Writing and Solving Number Stories (Math Journal 1, p. 40; Math Masters, pp. 45 and 407; Student Reference Book, pp. 212 and 213) PARTNER 15 30 Min PROBLEM SOLVING Algebraic Thinking To apply children s understanding of changeto-more and change-to-less number stories, have them write their own number stories in which the and numbers are known, but the is not given. (See Problems 5 and 6 on journal page 40 for sample problems.) Children can use information from the Vending Machine Posters on pages 212 and 213 in the Student Reference Book. You may wish to compile the number stories into a class book. Math Masters, p. 47 128 Unit 2 Adding and Subtracting Whole Numbers
Name Date Time HOME LINK 2 5 Number Stories Family Note Today your child learned about another diagram that helps organize the information in a number story. It is called a change diagram. For more information, see pages 254 and 255 in the Student Reference Book. Please return this Home Link to school tomorrow. 254 255 For each number story, write in the change diagram for the number you want to find. Write the numbers you know in the diagram. Then, write a number model and the answer. Finally, write how you know that each answer makes sense. 1. Marcus had $25 in his wallet. He spent $16 at the store. How much money was in Marcus s wallet then Answer the question: (unit) 2. Jasmine had $35. She earned $14 helping her neighbors. How much money did she have then Answer the question: (unit) Copyright Wright Group/McGraw-Hill 46
Name Date Time Guide to Solving Number Stories 1. What do you understand from the story Read the story. What do you want to find out What do you know 2. What will you do Add Subtract Multiply Divide Draw a picture Make tallies Use counters or base-10 blocks Use a number grid or number line Make a table Draw a diagram Write a number model 3. Answer the question. Solve the problem. Record your work. Write the answer with the units. 4. Check. Does your answer make sense How do you know Copyright Wright Group/McGraw-Hill 406