Addition with Three or More Addends

Transcription

1 ddition with hree or More ddends Objective o guide children as they solve number stories having three or more addends. epresentations eoolkit lgorithms Practice EM Facts Workshop Game Family Letters ssessment Management Common Core State Standards Curriculum Focal Points Interactive eacher s Lesson Guide eaching the Lesson Ongoing Learning & Practice ifferentiation Options 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 lgebra Goal 4] Key ctivities Children practice adding three or four numbers in a convenient order. hey solve number stories having three or more addends, including stories with missing addends. Key Vocabulary addend Playing Name hat 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 (from the Everything Math eck, if available) Children practice writing number sentences. Ongoing ssessment: Recognizing Student chievement Use Math Masters, page 451. [Number and Numeration Goal 4] Math Boxes Math Journal 1, p. 53 Children practice and maintain skills through Math Box problems. Home Link Math Masters, pp. 56 and 57 Children practice and maintain skills through Home Link activities. REINESS dding with Base-10 Blocks Math Masters, p each of number cards 1 10 and 1 each of number cards (from the Everything Math eck, if available) base-10 blocks Children explore addition using base -10 blocks. ENRICHMEN Solving ddition and Subtraction Puzzles Math Masters, pp. 58 and 59 Children solve addition and subtraction puzzles. Materials Math Journal 1, pp. 51 and 52 Home Link 2 8 transparency of Math Masters, p. 44 (optional) dvance Preparation eacher s Reference Manual, Grades 1 3 pp Lesson 147

2 Getting Started Mental Math and Reflexes Children write answers on slates as you pose higher-decade fact-extension problems. For example: 5 + = = = = = = = = = Mathematical Practices SMP1, SMP2, SMP4, SMP6, SMP8 Content Standards 3.O.8, 3.NB.2 Math Message he ostriches in the zoo had 4 clutches this year. hey laid 13 eggs, 9 eggs, 7 eggs, and 11 eggs. How many eggs were laid in all? 40 eggs Home Link 2 8 Follow-Up Unit eggs Have partners share their answers and strategies before turning in their work. 1 eaching the Lesson Math Message Follow-Up WHOLE-CLSS ISCUSSION lgebraic hinking iscuss 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? s-and-total What might a parts-and-total diagram for the problem look like? raw a parts-and-total diagram on the board and have children write the number of eggs in the s 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 in the box. Can anyone suggest a number model for the problem? Sample answer: = id 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. oes 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 ddition (the turn-around rule) and the ssociative Property of ddition, which states that numbers can be added in any order without changing the sum. 148 Unit 2 dding and Subtracting Whole Numbers

3 oes your answer make sense in the original story? yes How can you tell? he total number of eggs is more than the number in any one clutch. oes your answer make the number model true? yes Write a summary number model on the board: = 40. dding hree or Four Numbers in ny Order WHOLE-CLSS CIVIY Write additional sets of three and four numbers on the board. Children decide which order is easiest for them to find the sums. Suggestions: = 30; = = 40; = = 30; = 20; = = 30 and = 36; or = 20 and = 36 Using the Guide to Solving Number Stories (Math Masters, p. 44) WHOLE-CLSS CIVIY lgebraic hinking Guide children through the problem-solving steps for the following number story: 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? 1. What do you understand from the story? What do you want to find out? he number of books read by the third child What information do you know from the number story? total of 19 books were read. One child read 6, and another read 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? s-and-total, with 2 parts and the total known and 1 part unknown raw 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 s boxes and 19 in the 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 s, write the letter P in the third s box. sk volunteers to suggest number models for the story. Sample answer: P = 19 ate ate ime Number Stories with Several ddends continued 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? P = 54 or = 29, = P 25 eggs nswer the question: Sample answer: he 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? ? = 250 or = 130, = P nswer the question: $1.20 ime Number Stories with Several ddends 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? = nswer the question: $2.00 Sample answer: he 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. 2. Michelle drove from Houston, exas to 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? = 610 miles nswer the question: Sample answer: he first two amounts will be more than 400, so when you add the last amount, it will be more than 500. Math Journal 1, p. 51 Student Page Sample answer: he 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 P Student Page P P Lesson 149

4 Name ate ime HOME LINK Family Note Links to the Future he 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. Name ate ime HOME LINK hree or More ddends 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? = nswer the question: blocks 8. Make up a number story with three or more addends. nswers vary. hree or More ddends his 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. hen add the rest of the numbers. Please return this Home Link to school tomorrow. Remember that when you add: he numbers can be in any order. Some combinations make the addition easier. dd. Write the numbers in the order you added them. ell someone at home why you added the numbers in that order. Sample answers: Example: = = = 70 nswer the question: Home Link Master Math Masters, p. 56 Home Link Master 55 Check. oes my answer make sense? Marianna has 3 days to read a 58-page book. She read 17 pages on Monday and 22 pages on uesday. How many more pages does she need to read to finish the book? P P = 58 or = 39, = P nswer the question: 19 pages Math Masters, p = = = NOE Some children may suggest = P. lthough children will not 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: = 15, then = P. his is also acceptable. 3. What is the answer? he third child read 4 books. Have children share their solution strategies. 4. Go back to the question in the number story. oes the answer make sense? yes How can you tell? he number of books the third child read has to be less than the number of books read by all three children. oes your answer make the number model true? yes Write a summary number model on the board: = 19. Solving Number Stories Having hree or More ddends (Math Journal 1, pp. 51 and 52) PRNER CIVIY lgebraic hinking Give partners time to work on the journal pages. Circulate and use guiding questions such as those modeled in this lesson. hen bring the class together to share solution strategies. s you discuss strategies, fill in the displayed parts-and-total diagram. 2 Ongoing Learning & Practice Playing Name hat Number (Math Masters, p. 451; Student Reference Book, pp. 299 and 300) SMLL-GROUP CIVIY Children practice writing number sentences by playing Name hat 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. Ongoing ssessment: Recognizing Student chievement PROBLEM SOLVING Math Masters page 451 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 and Numeration Goal 4] 150 Unit 2 dding and Subtracting Whole Numbers

5 Math Boxes (Math Journal 1, p. 53) INEPENEN CIVIY Mixed Practice Math Boxes in this lesson are linked with Math Boxes in Lessons 2-5 and 2-7. he skill in Problem 6 previews Unit 3 content. ate 2 9 Math Boxes 1. Use addition or subtraction to solve these problems on your calculator. Enter Change to How? , ,000 10,538 10, ,201 15,201 3,000 Student Page 18, 19, 264 ime 2. What s My Rule? in out nswers vary. in Rule Subtract 7 out Home Link (Math Masters, pp. 56 and 57) INEPENEN CIVIY Home Connection Children look for number combinations to solve addition problems having three or more addends. 3 ifferentiation Options REINESS dding with Base-10 Blocks (Math Masters, p. 412) PROBLEM SOLVING INEPENEN CIVIY 5 15 Min 3. In 5,639, the 5 means. Fill in the circle next to the best answer. 500 B 5,000 C Jack answered 29 questions. José answered 37 questions. How many fewer questions did Jack answer than José? Quantity 37 8 questions Quantity ifference Math Journal 1, p. 53? Fill in the tag. Write at least 5 names for that number. nswers vary. 6. Which tool would you use to measure the following? yardstick ruler thermometer emperature Height of the ceiling Length of your thumb thermometer yardstick ruler o explore addition using a concrete model, have children solve addition problems with base-10 blocks. Children generate three addends by turning over three cards. hey represent each addend by placing longs and cubes on Math Masters, page 412. he problem =? might be represented as shown in the margin. Encourage children to look for combinations that make tens. ENRICHMEN Solving ddition and Subtraction Puzzles (Math Masters, pp. 58 and 59) SMLL-GROUP CIVIY 5 15 Min o apply children s understanding of addition and subtraction, have them solve the puzzles on Math Masters, page 58. sk children to study the examples on the page and tell what must be done to solve this kind of puzzle. dd going across, and subtract going down. he final sum and final difference are the same: his means there is a check number for each puzzle. 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 =? =? = 25 Name ate ime 2 9 ddition and Subtraction Puzzles Study the examples. Can you figure out what must be done to solve this type of puzzle? Example 1: Example 2: SUBRC Solve these addition and subtraction puzzles SUBRC SUBRC Make up addition and subtraction puzzles of your own SUBRC SUBRC eaching Master 10 SUBRC SUBRC nswers vary. SUBRC Math Masters, p. 58 Lesson 151

6 Name ate ime HOME LINK hree or More ddends 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? nswer the question: blocks 7. Marianna has 3 days to read a 58-page book. She read 17 pages on Monday and 22 pages on uesday. How many more pages does she need to read to finish the book? nswer the question: pages 8. Make up a number story with three or more addends. Copyright Wright Group/McGraw-Hill nswer the question: Check. oes my answer make sense? 57