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Addition with Three or More Addends Objective To guide children as they solve number stories having three or more addends. www.everydaymathonline.com ePresentations eToolkit Algorithms Practice EM Facts Workshop Game™ Teaching the Lesson Key Concepts and Skills • Use basic facts to solve extended fact problems. [Operations and Computation Goal 1] • Solve addition number stories with three or more addends. [Operations and Computation Goal 2] • Use a parts-and-total diagram to solve addition number stories involving three or more addends. [Operations and Computation Goal 6] • Practice adding three or four numbers in a convenient order. [Patterns, Functions, and Algebra Goal 4] Key Activities Children practice adding three or four numbers in a convenient order. They solve number stories having three or more addends, including stories with missing addends. Key Vocabulary Family Letters Assessment Management Common Core State Standards Ongoing Learning & Practice 1 2 4 3 Playing Name That Number Math Masters, p. 451 Student Reference Book, pp. 299 and 300 per group: 4 each of number cards 0–10 and 1 each of number cards 11–20 (from the Everything Math Deck, if available) Children practice writing number sentences. Ongoing Assessment: Recognizing Student Achievement Use Math Masters, page 451. [Number and Numeration Goal 4] Curriculum Focal Points Interactive Teacher’s Lesson Guide Differentiation Options READINESS Adding with Base-10 Blocks Math Masters, p. 412 4 each of number cards 1–10 and 1 each of number cards 11–20 (from the Everything Math Deck, if available) base-10 blocks Children explore addition using base -10 blocks. ENRICHMENT Solving Addition and Subtraction Puzzles Math Masters, pp. 58 and 59 Children solve addition and subtraction puzzles. Math Boxes 2 9 Math Journal 1, p. 53 Children practice and maintain skills through Math Box problems. Home Link 2 9 Math Masters, pp. 56 and 57 Children practice and maintain skills through Home Link activities. addend Materials Math Journal 1, pp. 51 and 52 Home Link 28 transparency of Math Masters, p. 44 (optional) Advance Preparation Teacher’s Reference Manual, Grades 1–3 pp. 225–229 Lesson 2 9 147 Mathematical Practices SMP1, SMP2, SMP4, SMP6, SMP8 Content Standards Getting Started 3.OA.8, 3.NBT.2 Mental Math and Reflexes Math Message Children write answers on slates as you pose higher-decade fact-extension problems. For example: The ostriches in the zoo had 4 clutches this year. They laid 13 eggs, 9 eggs, 7 eggs, and 11 eggs. How many eggs were laid in all? 40 eggs = 11 6 = 21 16 = 51 46 9 17 = 8 + 37 = 8 + 29 67 = 8 + 59 = 15 7 8+ 88 + = 105 17 118 + = 175 57 5+ 5+ 5+ Unit eggs Home Link 2 8 Follow-Up Have partners share their answers and strategies before turning in their work. 1 Teaching the Lesson Math Message Follow-Up Total T Part Part Part Part 13 9 7 11 148 Unit 2 Adding and Subtracting Whole Numbers WHOLE-CLASS DISCUSSION Algebraic Thinking Discuss the Math Message by asking questions such as the following: ● What do you understand from the Math Message number story? We need to find out the number of eggs laid in all. We know that ostriches laid clutches of 13, 9, 7, and 11 eggs. ● What did you do to find the answer? add ● What kind of number story is this? Parts-and-total ● What might a parts-and-total diagram for the problem look like? Draw a parts-and-total diagram on the board and have children write the number of eggs in the Parts boxes. Explain that a letter can be used in place of a question mark to represent what we want to find out. Since the total number of eggs is what we want to find out, write a T in the Total box. ● Can anyone suggest a number model for the problem? Sample answer: 13 + 9 + 7 + 11 = T ● Did everyone add the numbers in the same order? Remind children that numbers in an addition problem are called addends. Can someone suggest another way to combine the addends to make the addition easier? For example, someone might first add 13 and 7, totaling 20; then add 9 and 11, also totaling 20; and finally add 20 and 20. ● Does it matter in which order the addends are written? no Explain to children that they can add the numbers in any order because of the Commutative Property of Addition (the turn-around rule) and the Associative Property of Addition, which states that numbers can be added in any order without changing the sum. ● Does your answer make sense in the original story? yes How can you tell? The total number of eggs is more than the number in any one clutch. Student Page Date Time LESSON Number Stories with Several Addends 29 ● Does your answer make the number model true? yes Write a summary number model on the board: 13 + 9 + 7 + 11 = 40. 1. José bought milk for 35 cents, apple juice for 55 cents, grape juice for 45 cents, and orange juice for 65 cents. How much money did he spend? Total T Part Adding Three or Four Numbers 35 + 65 + 55 + 45 = T $2.00 Answer the question: Part Part 35 55 45 65 Number model: WHOLE-CLASS ACTIVITY Part (unit) Check: How do you know your answer makes sense? in Any Order Sample answer: The answer has to be more than 100 cents because only two of the amounts add up to at least 100, so all four must be more than that. Write additional sets of three and four numbers on the board. Children decide which order is easiest for them to find the sums. Suggestions: 2. Michelle drove from Houston, Texas to Total Wichita, Kansas. On the first day, she drove 245 miles. On the second day, she drove 207 miles. On the third day, she drove 158 miles and arrived in Wichita. How many miles did she drive in all? 9 + 8 + 21 9 + 21 = 30; 30 + 8 = 38 T Part Part Part 245 207 158 Number model: 245 + 207 + 158 = T 610 miles 15 + 25 + 18 15 + 25 = 40; 40 + 18 = 58 Answer the question: (unit) 8 + 13 + 7 + 22 8 + 22 = 30; 13 + 7 = 20; 30 + 20 = 50 Check: How do you know your answer makes sense? 16 + 14 + 1 + 5 16 + 14 = 30 and 30 + 1 + 5 = 36; or 14 + 1 + 5 = 20 and 20 + 16 = 36 so when you add the last amount, it will be more than 500. Sample answer: The first two amounts will be more than 400, Math Journal 1, p. 51 Using the Guide to Solving WHOLE-CLASS ACTIVITY EM3MJ1_G3_U02_30-54.indd 51 12/29/10 4:35 PM Number Stories Total (Math Masters, p. 44) 19 Algebraic Thinking Guide children through the problem-solving steps for the following number story: Part Over the summer, 3 children read a total of 19 books. One child read 6 books, and another child read 9 books. How many books did the third child read? 6 Part Part 9 P 1. What do you understand from the story? ● What do you want to find out? The number of books read by the third child Student Page Date Time LESSON ● What information do you know from the number story? A total of 19 books were read. One child read 6, and another read 9. Number Stories with Several Addends 29 3. Zookeepers watched a clutch of 54 python eggs. On the first day, 18 eggs hatched. On the next day, 11 more hatched. How many eggs did not hatch? Total 54 Number model: 18 + 11 + P = 54 or 18 + 11 = 29, 54 − 29 = P 2. What could you do to find the number of books read by the third child? Find the total number of books read by the two children, then subtract that sum from the total number of books read. ● ● ● What kind of a number story is this? Parts-and-total, with 2 parts and the total known and 1 part unknown Draw a parts-and-total diagram on the board, or display a transparency of Math Masters, page 44, and have children write 6 and 9 in the Parts boxes and 19 in the Total box. Remind children that a letter can be used to represent what we want to find out. In this case, since we don’t know one of the Parts, write the letter P in the third Parts box. Ask volunteers to suggest number models for the story. Sample answer: 6 + 9 + P = 19 Answer the question: continued Part Part Part 18 11 P 25 eggs (unit) Check: How do you know your answer makes sense? Sample answer: The amount of unhatched eggs has to be less than the total amount of 54. More than 20 hatched so less than 30 have not hatched. 4. Carl has $2.50 for juice or milk at lunch. On each of 2 days, he buys grape juice for 45 cents. On the third day, he buys milk for 40 cents. How much money does he have left? Number model: TotalTotal 250 Part Part Part Part 45 45 40 P 45 + 45 + 40 + ? = 250 or 45 + 45 + 40 = 130, 250 − 130 = P Answer the question: $1.20 (unit) Check: How do you know your answer makes sense? Sample answer: The answer has to be less than $2.50. He spent more than $1.00 so he’ll have less than $1.50 left. Math Journal 1, p. 52 EM3MJ1_G3_U02_30-54.indd 52 12/29/10 4:35 PM Lesson 2 9 149 Home Link Master Name Date HOME LINK Time NOTE Some children may suggest 19 - 6 + 9 = P. Although children will not Three or More Addends 29 Family Note be introduced to grouping symbols until Unit 7, accept this number model and write it with parentheses: 19 - (6 + 9) = P. Explain that the addition fact inside the parentheses is calculated first, then the sum is subtracted from 19 to find the missing part. Other children may suggest 2 separate number models: 6 + 9 = 15, then 19 - 15 = P. This is also acceptable. This Home Link provides practice in looking for combinations that make addition easier. Guide your child to look for combinations that add up to 10, 20, 30, 40 and so on. Then add the rest of the numbers. Please return this Home Link to school tomorrow. Remember that when you add: The numbers can be in any order. Some combinations make the addition easier. 3. What is the answer? The third child read 4 books. Have children share their solution strategies. Add. Write the numbers in the order you added them. Tell someone at home why you added the numbers in that order. Sample answers: Example: 2. 1. 6 + 18 + 14 = 50 50 5 + 17 + 25 + 3 = 38 I added in this order: I added in this order: 55 + + 25 25 + + 17 17 + +3 6 + 14 + 18 125 + 13 + 75 = 213 3. 15 + 6 + 14 + 5 = 4. Go back to the question in the number story. Does the answer make sense? yes How can you tell? The number of books the third child read has to be less than the number of books read by all three children. 40 I added in this order: I added in this order: 125 + 75 + 13 15 + 5 + 6 + 14 70 4. 33 + 22 + 8 + 7 = ● 5. 150 + 215 + 300 + 50 + 200 = 915 I added in this order: Does your answer make the number model true? yes Write a summary number model on the board: 6 + 9 + 4 = 19. I added in this order: 33 + 7 + 22 + 8 150 + 50 + 300 + 200 + 215 Solving Number Stories Math Masters, p. 56 EM3MM_G3_U02_036-063.indd 56 1/5/11 3:41 PM PARTNER ACTIVITY Having Three or More Addends PROBLEM PRO PR P RO R OBL BLE B LE L LEM EM SO S SOLVING OL O LV LV VIN ING (Math Journal 1, pp. 51 and 52) Links to the Future Algebraic Thinking Give partners time to work on the journal pages. Circulate and use guiding questions such as those modeled in this lesson. Then bring the class together to share solution strategies. As you discuss strategies, fill in the displayed parts-and-total diagram. The use of parentheses in number models is introduced in Unit 7. Recognizing that numeric expressions can have different values depending on the order in which operations are carried out is a Grade 3 Goal. Evaluating numeric expressions containing grouping symbols and inserting grouping symbols to make number sentences true is a Grade 4 Goal. Home Link Master Name HOME LINK 29 Date Playing Name That Number Time Three or More Addends 2 Ongoing Learning & Practice continued (Math Masters, p. 451; Student Reference Book, pp. 299 and 300) Solve these number stories. 6. Nico’s baby brother has a basket of wooden blocks. 18 blocks are red, 15 are blue, and 22 are yellow. How many red, blue, and yellow blocks are in the basket? Number model: 18 + 15 + 22 = T Answer the question: 55 Total T Part Part Part 18 15 22 blocks Total 7. Marianna has 3 days to read a 58-page book. She read 17 pages on Monday and 22 pages on Tuesday. How many more pages does she need to read to finish the book? 58 17 + 22 + P = 58 or 17 + 22 = 39, 58 - 39 = P SMALL-GROUP ACTIVITY Part Part Part 17 22 P Children practice writing number sentences by playing Name That Number. For game directions, see Student Reference Book, pages 299 and 300. Have children record the number sentence(s) from their best round on Math Masters, page 451. Encourage children to write each of their calculations on separate lines. Number model: Answer the question: 19 pages Ongoing Assessment: Recognizing Student Achievement 8. Make up a number story with three or more addends. Answers vary. Answer the question: (unit) [Number and Numeration Goal 4] Check. Does my answer make sense? Math Masters, p. 57 150 Use Math Masters, page 451 to assess children’s progress toward writing equivalent names for numbers. Children are making adequate progress if they write a number sentence using at least two of the five faceup cards and the target card as the sum or difference. Some children may write number sentences using more than two cards or more than one operation. Number model: EM3MM_G3_U02_036-063.indd 57 Math Masters page 451 12/29/10 5:57 PM Unit 2 Adding and Subtracting Whole Numbers Math Boxes 2 9 Student Page INDEPENDENT ACTIVITY (Math Journal 1, p. 53) Date Time LESSON 29 䉬 Math Boxes Use addition or subtraction to solve these problems on your calculator. Enter Change to How? 1. Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 2-5 and 2-7. The skill in Problem 6 previews Unit 3 content. 3,291 10,538 12,201 Home Link 2 9 (Math Masters, pp. 56 and 57) 39 49 72 INDEPENDENT ACTIVITY out 42 65 203 204 Fill in the tag. Write at least 5 names for that number. 4. Answers vary. A 500 PROBLEM PR PRO P RO R OB BLE BL LE L LEM EM SO S SOLVING OL O LV VIN IN IN NG G Rule Subtract 7 Answers vary. 18, 19, 264 In 5,639, the 5 means . Fill in the circle next to the best answer. 3. Home Connection Children look for number combinations to solve addition problems having three or more addends. 24 909 in 7 17 32 14 ⫹500 ⫺3,000 291 10,138 ⫺400 15,201 ⫹3,000 409 “What’s My Rule?” in out 2. B 5,000 C 50 D 5 18 19 Jack answered 29 questions. José answered 37 questions. How many fewer questions did Jack answer than José? Quantity 5. 37 8 29 ? Difference 3 Differentiation Options yardstick ruler thermometer thermometer Height of the ceiling yardstick ruler Length of your thumb Temperature Quantity questions 14 15 Which tool would you use to measure the following? 6. 258 Math Journal 1, p. 53 READINESS Adding with Base-10 Blocks INDEPENDENT ACTIVITY 5–15 Min (Math Masters, p. 412) To explore addition using a concrete model, have children solve addition problems with base-10 blocks. Children generate three addends by turning over three cards. They represent each addend by placing longs and cubes on Math Masters, page 412. The problem 14 + 5 + 6 = ? might be represented as shown in the margin. Encourage children to look for combinations that make tens. ENRICHMENT Solving Addition and SMALL-GROUP ACTIVITY 14 + 5 + 6 = ? Teaching Master Name LESSON 29 䉬 5–15 Min Subtraction Puzzles Date When children understand what to do, they work in small groups to solve the remaining puzzles. Volunteers may share their solution strategies. Math Masters, page 59 provides additional blank puzzles for children to complete. Time Addition and Subtraction Puzzles Study the examples. Can you figure out what must be done to solve this type of puzzle? Example 1: Example 2: SUBTRACT (Math Masters, pp. 58 and 59) To apply children’s understanding of addition and subtraction, have them solve the puzzles on Math Masters, page 58. Ask children to study the examples on the page and tell what must be done to solve this kind of puzzle. Add going across, and subtract going down. The final sum and final difference are the same: This means there is a “check number” for each puzzle. 14 + 6 + 5 = ? 20 + 5 = 25 A D D 27 8 15 3 12 5 SUBTRACT 35 18 A D D 17 40 46 20 9 20 37 86 29 57 Solve these addition and subtraction puzzles. 1. 2. 3. SUBTRACT A D D 48 18 12 8 36 10 66 20 A D D 46 22 8 14 6 8 2 30 20 5. 55 40 95 28 8 36 27 32 59 Answers vary. 6. SUBTRACT A D D A D D 10 Make up addition and subtraction puzzles of your own. 4. SUBTRACT SUBTRACT SUBTRACT SUBTRACT A D D A D D Math Masters, p. 58 Lesson 2 9 151 Name HOME LINK 29 Date Time Three or More Addends continued Solve these number stories. 6. Nico’s baby brother has a basket of wooden blocks. 18 blocks are red, 15 are blue, and 22 are yellow. How many red, blue, and yellow blocks are in the basket? Total Part Part Part Number model: Answer the question: blocks Total 7. Marianna has 3 days to read a 58-page book. She read 17 pages on Monday and 22 pages on Tuesday. How many more pages does she need to read to finish the book? Part Part Part Number model: Answer the question: pages Copyright © Wright Group/McGraw-Hill 8. Make up a number story with three or more addends. Number model: Answer the question: (unit) Check. Does my answer make sense? 57