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Order of Operations ACTIVITY ACTIVITY 2.9 Investigative A Fairly Ordered Operation 2.9 SUGGESTED LEARNING STRATEGIES: Close Reading, Think Order of Operations Aloud, Marking the Text, Summarize/Paraphrase/Retell, Quickwrite My Notes Activity Focus • Order of Operations Ayana and Zachary Wilson are excited about going to the Pace County Fair. General admission to the fair is $8.00 per person. Materials It covers visiting exhibits and some entertainment. Tickets for • No special materials are needed. rides and games must be bought separately. Food and drinks are purchased at the concession stands. A ride ticket costs $3.00. Chunking the Activity 1. Ayana loves to make lists of things to do to prepare for an #1 #8 #12 activity. She made the following list for the morning of the fair. #2–4 #9 #13 #5 #10 #14 To Do Order #6–7 #11 #15 Comb my hair 8 Take a shower 2 Paragraph Close Reading, Brush my teeth 1 Think Aloud, Marking the Text, Eat breakfast 6 Summarize/Paraphrase/Retell Put my clothes on 3 1 Quickwrite After the students 10 Buy my tickets for the fair give the order of the steps it is Put on my shoes 5 very important that they explain Put on my socks 4 why the order of the steps is Ride to the fair 9 important. Get money out of piggy bank 7

a. TEACHER TO YYou could have students Order the steps as you think Ayana will complete them. TEACHER Answers may vary. Sample answer: See table above. wwrite each step on a ststickyicky nnoteote or an index card so b. Explain why the order of steps is important. they can easily play around with Answers may vary. Sample answer: Some things have to be done before others, such as putting on socks before shoes. the order of the steps before 2. Ayana plans to go on 5 rides. She wrote the numerical entering the order in the student

© 2010 College Board. All rights reserved. expression 8 + 5 × 3 to represent the cost of her rides and book. admission to the fair. 2 Close Reading, Guess and a. What is the total cost of Ayana’s admission to the fair and the rides she wishes to go on? Check, Quickwrite The intent of $23 this question (and the next two) is to show a need for an agreement b. Do you think her expression represents this total cost? on the order in which operations Explain. should be performed. After com- Answers may vary. Sample answer: Yes, if you multiply ﬁ rst. pleting this ﬁ rst set of questions, Unit 2 • Operations with Numbers 115 students will learn that multiplication should be performed before

Unit 2 • Operations with Numbers 115

1115-122_SB_MS1_2-9_TE.indd15-122_SB_MS1_2-9_TE.indd 111515 22/3/10/3/10 66:32:05:32:05 PMPM 1115-122_SB_MS1_2-9_TE.indd 116 1 5 - 1 2 2 _ S Check, Quickwrite Quickwrite Check, Quickwrite Check, Quickwrite Check, 6 5 4 3 ACTIVITY written isimportant. that thewayexpressions are Students shouldalsodetermine should comebefore addition. determine thatmultiplication developed. and subtractingcontinuestobe of order ofoperationsforadding question, students’understanding addition. multiplication isperformedbefore should beabletoexplainthat B 116 _ Close Reading, Guess and and Guess Reading, Close and Guess Reading, Close Debrief and Guess Reading, Close M S 1 SpringBoard _ 2 - 9 _ T E . i n Students should d 2.9 d

1 1 6 Continued ® With this With Students Mathematics with Meaning 115-122_SB_MS1_2-9_SE.indd 116 116 continued ACTIVITY ™ SpringBoard Level 1 2.9 My Notes ® Order ofOperations A FairlyOrderedOperation Mathematics withMeaning™ 5. multiplication should fi performed be containing addition both and multiplication operation the of Mathematicians have agreed that evaluating when an expression 4. b. a. 6. not fi Th b. a. 3. eday of fair the Ayana both realized that and had they Zachary addition. Ayana, becausemultiplicationmustbeperformedbefore is correct. expressions havedifferentvaluesanditisnotclearwhich Answers mayvary. Sampleanswer: Yes, becausethe the costofthe Explain. hisrides? her admission ticket it use and to or represent rides can Zachary AyanaCan expression the use 8 Explain. mathematical expression to represent two diff Is it aproblem that Ayana both same the used and Zachary to represent total the costof hewishesto go rides the on. is now left expression 100 $5 for fair the sheputs so bank. it Ayana inherpiggy wrote the fair. Th Ayana bank. She has$100inherpiggy took $60out to go to the 5 rides in the aft inthe 5 rides intends onZachary going on morning inthe 8rides and gured into food costof the going to fair. the subtract ﬁ Answers mayvary. Sampleanswer: Yes, youcanaddor Explain. youDo hisexpression think represents total cost? this What total isthe costof Zachary’s rides? Explain. youDo herexpression think represents total amount? this What total isthe amount left $45 Answers mayvary. Sampleanswer: Yes, ifyouaddﬁ $39 Work Quickwrite, Backward Check, and SUGGESTED LEARNING STRATEGIES: Close Reading, Guess Level1 enherdadgave her$5allowance. She not does needthis inherbank. rst andtheanswerissame. - ernoon. Heernoon. wrote expression the 8 60 + 5to represent amount the of money that inAyana’s bank? piggy + rst. 5 × 3to represent costof the erent costs? + 5 rst. × 3 22/3/10 6:32:06 PM / 3 / 1 0

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2 © 2010 College Board. All rights reserved. _ S B b. a. 9. three sacks.She gave then Ayana eachasack. and Zachary more bagsof 6granola bars, sharing evenly them into same the barsthe evenly into three sacks. She same didthe thing with three snacks to fair. the She took abag of 6granola bars and divided Ayana and Zachary’s mom neededto some take decidedthey Aft 8. orderperformed inthe appear they inwhich from left subtraction, operations the of addition and subtraction should be When evaluating anumerical expression with addition and Th b. a. 7. Aloud, the Marking Text, Summarize/Paraphrase/Retell Think Work Quickwrite, Check, and Guess Backward, SUGGESTED LEARNING STRATEGIES: Close Reading, Order ofOperations A FairlyOrderedOperation _ inkabout order the operations inwhich should performed. be M er that Zachary decidedto only take er that $60to fair. the Zachary S number of granola bars. each sack, he said the expression hesaid sack, the each 6 When Ayana how many asked Zachary granola bars were in Ayana’s bank or the amount left Does the expression the Does 100 amount of money now left It representstheamountin Ayana’s bank:100 Zachary wrote expressionZachary the 100 andfood, admission to fair, the and hetook $5out for asouvenir. bank. He has$100inhispiggy took $60outZachary for rides, 1 _ 2 how Zachary derived hisexpression.how Zachary How many granola bars were actually ineach bag? Explain answer. less than 1whole granola bar. Explain how shearrived at this Ayana evaluated expression the and said bagcontained the Explain. youDo hisexpression think represents total amount? this What total isthe amount left 6 bars Explanations mayvary. Sampleanswer:8bars; Answers mayvary. Sampleanswer:6 not addwhenyoutakesomethingaway. Answers mayvary. Sampleanswer:No,becauseyoushould $35 - 9 _ T E . i n ÷ d d 3

= 1 1 2;2 7 × 4bagsofbars - inhisbank. 60 + inZachary’s bank? Explain. inZachary’s bank? piggy 5represent amount the left - ÷ 60 3 = 8. × + ÷ 4represented the 5to represent the 3 × - 4 60 = to right. 6 + 5 ÷ 12 = 45. = in .5. Unit 2• Operations withNumbers My Notes ACTIVITY continued 117 12/16/09 5:57:12PM 2.9 Unit 2 •Oeain ihNmes •Operations with Numbers TEACHER TO Paragraph volleyball. game, suchassoccer, chess,or to therulesbywhichtheyplaya properties andorder ofoperations students connectmathematical makes theexpression true. ses andthensubtractingfrom 100 Paragraph tion todothisproblem. which todoadditionandsubtrac- abouttheorderjust learned in that enclosing60 8 st 7 ACTIVITY 9 Summarize/Paraphrase/Retell write write and division. multiplication towhich perform in theorder in deciding practice TEACHER ud Guess and Check, Quick- Check, and Guess Quick- Check, and Guess This question gives students gives students question This en ts Students willusewhatthey Some studentsmaysee A After Question7would be agoodtimetohave b c Close Reading, Reading, Close Reading Close 2.9 + Continued 5inparenthe- 22/3/10 6:32:07 PM 117 / 3 / 1 0

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P M 1115-122_SB_MS1_2-9_TE.indd 118 1 5 - 1 2 2 _ S Summarize/Paraphrase/Retell Text, the Marking Aloud, Think Representations Representations the numbersentences. using numbersotherthan2with choose. Studentsmaywanttotry through 9inanyorder they putting thenumbersfrom 1 p. 137,#59–63 UNIT 2PRACTICE p. 122,#1–6 CHECK YOURUNDERSTANDING Suggested Assignment 0 Paragraph ACTIVITY have studentsmaketheirown To extendthisactivity, youmight horizontal, vertical,ordiagonal. out thattherow ofthree canbe division toplaythegame.Point subtraction, multiplicationand order ofoperationsforaddition, to usetheirknowledgeofthe mative questionthatasksstudents game cards on3 B 118 _ M Guess and Check, Create Check, and Guess S 1 SpringBoard _ 2 - 9 _ T E . i n Close Reading, Reading, Close d 2.9 d

1 1 8 × Continued This isasum- 3grids, ® Mathematics with Meaning 115-122_SB_MS1_2-9_SE.indd 118 118 Answers mayvary. Sample answers shown. continued ACTIVITY Tic-tack-two gamecard Add orsubtractfromleft • Multiply ordividefromleft • Evaluate expressionswith • Do calculationsinside • operation. Theorderis: expressions withmorethanone a setofrulesforevaluating The ACADEMIC VOCABULARY 3 8 4 to right. to right. exponents. parentheses ﬁ order ofoperations ™ SpringBoard Level 1 2.9 9 5 1 My Notes rst. ® Order ofOperations A FairlyOrderedOperation Mathematics withMeaning™ 6 2 7 is of multiplication and division are evaluated from left 10. to right. operations of addition and subtraction are evaluated also from left an follow subtraction, multiplication, and division, it so isimportant to Numerical expressions can contain operations the of addition, 22222 22222 2 22222 22222 22222 22222 22222 22222 22222 use the order the use of operations. Play game this with members the of your group. Remember to done forbeen you. wins. Anexample, isnot which avalue on game the card, has your Tic-Tack-Two card. Th a row. When you get anumber, put an Xover that number on endofthe row. the You can an use operation more than once in with any operation sign: To play, should person each fi was handed aTic-Tack-Two game card and score this sheet. At fair the Ayana one used ticket to play Tic-Tack-Two. She Guess and Check, Create Representations Create Check, and Guess Aloud, Marking the Text, Summarize/Paraphrase/Retell, SUGGESTED LEARNING STRATEGIES: Close Reading, Think Level1 ÷ + × × × × + + ÷ + order of operations 2 + + - × × × + - + - 2 + to avoid confusion. Th e fi , - ll in the spacesbetween2s ll inthe the ÷ - ÷ + × - + ÷ ÷ + , rst player to get three inarow × , or 2 ÷ to equal the number at - ÷ ÷ ÷ - + + ÷ - - e operations 2 to right. Th ======22/3/10 6:32:09 PM e / 9 8 7 6 5 4 3 2 1 0 3

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2 © 2010 College Board. All rights reserved. _ S B c. b. 11. Retell, Work Quickwrite Check, and Backward, Guess Think Aloud, the Marking Text, Summarize/Paraphrase/ SUGGESTED LEARNING STRATEGIES: Close Reading, Order ofOperations a. A FairlyOrderedOperation

_ M S the followingthe unusual. target very to be decidedto join AyanaZachary inagame of darts. Th the graythe region of target. the in that region of target. the of Zachary’s Both landed darts in on target the are points the aplayer gets for that each dart lands playerEach gets to throw two at darts target. the Th 1 _ 2 and multiplication? agreed upon evaluating when an expression with exponents What doyou order isthe think that mathematicians have same score asAyana did? have to evaluate expression this that so hewould get the Zachary expressed hisscore as2 Zachary his Zachary’s score? evaluate 3 Answers mayvary. Sampleanswer:Hewouldhaveto 18 Exponents mustbeevaluatedbeforemultiplication. Ayana expressed hisscore as3 - 9 _ T E . i n d d

beforehemultiplies. 1 1 9 3 3 2 3

+ 2 × 3 3 2 3 . What didAyana get for 2 . Explain how hewould e numbers ey ey found Unit 2• Operations withNumbers My Notes ACTIVITY continued 119 12/16/09 5:57:18PM 2.9 Unit 2 •Oeain ihNmes •Operations with Numbers a ACTIVITY multiplication. nents mustbeevaluatedbefore question istoshowthatexpo- write Quick- Work Backward, Check, and Guess Paraphrase/Retell, Summarize/ Text, the Marking Close Reading, Think Aloud, Aloud, Think Reading, Close b )Theintentofthis (b, c) 2.9 Continued 22/3/10 6:32:10 PM 119 / 3 / 1 0

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P M 1115-122_SB_MS1_2-9_TE.indd 120 1 5 - 1 2 2 _ S with parentheses. practice evaluatinganexpression Summarize/Paraphrase/Retell Text, the Marking Aloud, Think Paragraph which operationsare performed. theses canchangetheorder in question istoshowhowparen- Summarize/Paraphrase/Retell Text, the Marking Aloud, Think Backward Backward Backward c b Paragraph ACTIVITY B 120 _ M Guess and Check, Work Check, and Guess Work Check, and Guess S 1 SpringBoard _ 2 - 9 _ T E . i n This questionprovides The intentofthis Close Reading, Reading, Close Reading, Close d 2.9 d

1 2 0 Continued ® Mathematics with Meaning 115-122_SB_MS1_2-9_SE.indd 120 120 continued ACTIVITY ™ SpringBoard Level 1 2.9 My Notes ® Order ofOperations A FairlyOrderedOperation Mathematics withMeaning™ 13. completing operations those outside grouping the symbols. operations inside grouping the symbols should completed be before involving grouping symbols, such asparentheses or brackets, the Mathematicians have agreed that inevaluating an expression b. a. 12. numbers and operations performed fi to be T heir father explained that parentheses can placed around be the a way to change order the an inwhich expression isevaluated. As drove they home from fair, the wondered ifthere Zachary was from fair. the Part of menu the isshown below. T he Wilsons decideto stop at arestaurant on way the home ride. $3.00 per tickets for morning inthe 8rides and aft inthe 5 rides evaluated insuch away costof the asto buying give Zachary Add parentheses to expression the 8 juices, and two pizza value meals. Th (8 eWilsons order one hamburger value meal, four apples, two + Find total the costof family’s the Show meal. your work. Write an expression to fi Retell, Work Check, and Backward Guess Think Aloud, the Marking Text, Summarize/Paraphrase/ SUGGESTED LEARNING STRATEGIES: Close Reading, $32 8 Level1 5) + (4 × 3 + 2) × 2 + Pf^lik%%%%%%%%%%%%%%%%%%%%%% 8ggc\j%%%%%%%%%%%%%%%%%%%%%%% ?fdX[\Jflg%%%%%%%%%%%%%%%% Al`Z\ JXcX[%%%%%%%%%%%%%%%%%%%%%%%% G`qqX%%%%%%%%%%%%%%%%%%%%%%%% SNACKS ?XdYli^\i#Jflg#Al`Z\%%%%%%%% G`qqX#Pf^lik#Al`Z\%%%%%%%%%%%% VALUE MEALS 2 %%%%%%%%%%%%%%%%%%%%%%%% × 6 nd the totalnd the costof family’s the meal. + 5 /%'' -%'' +%'' )%,' )%'' )%'' ,%'' *%'' rst. × 3 so that 3so it can be ernoon ernoon at 22/3/10 6:32:12 PM / 3 / 1 0

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2 © 2010 College Board. All rights reserved. _ S B parentheses. inplace ofcan used be parentheses, usually on outside the of parentheses fi called to fair. the haveshe and lef Zachary t of $60that the took each with them they • • • • hadleft and Zachary When Ayana arrived home shewanted to f igure out how much she 14. Paraphrase/Retell, Representations Create SUGGESTED LEARNING STRATEGIES: Summarize/ Order ofOperations A FairlyOrderedOperation _ M S a numerical expression using order of operations. evaluating expressions. steps the involved Describe insimplifying mathematicians have agreed upon an order of operations for numerical expressionSince every should have only one value, Notice parentheses the within parentheses. T arehese 60 Th bought a$5souvenir.Zachary She played 2games and heplayed 1at game. $3per morningthe and af inthe 5rides ternoon at ride. $3per She went on went atotal of and 5rides on Zachary in 8rides paid $8for sheand Zachary anBoth admission ticket. Step 4: Step 3: Evaluateallexpressionsinvolvingexponents. Step 2: Evaluateallexpressionsinparentheses. Step 1: 1 e following expression represents total the amount of money _ 2 nested parenthesesnested × - 9 2 _ T E - to right. Complete alladditionandsubtractioninorderfromleft left toright. Complete allmultiplicationanddivisioninorderfrom . i rst. Notice that too [2 n d d

1 8 2 1 of the money they took to fair. of the money they the + ((8 . You must always work innermost the + 5) + brackets 5) × 3 have Brackets used. been + (1 + 2) × 3 + 5] Unit 2• Operations withNumbers My Notes ACTIVITY continued 121 12/16/09 5:57:24PM 2.9 Unit 2 •Oeain ihNmes •Operations with Numbers Summarize/Paraphrase/Retell Text, the Marking Aloud, Think d ACTIVITY Paragraph evaluated. a numericalexpression canbe describing theorder inwhich and comeupwithasetofsteps together facts theyhavelearned that asksstudentstoputallofthe This isasummativequestion Close Reading, Reading, Close 2.9 Continued 22/3/10 6:32:13 PM 121 / 3 / 1 0

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P M ACTIVITY 2.9 Order of Operations ACTIVITY 2.9 Continued continued A Fairly Ordered Operation

e Summarize/Paraphrase/ SUGGESTED LEARNING STRATEGIES: Close Reading, Retell, Create Representations Think Aloud, Marking the Text, Summarize/Paraphrase/ This question provides practice My Notes Retell, Guess and Check, Work Backward using nested parentheses. 15. Ayana started to evaluate the expression. Finish her work. Notice that parentheses around a single number can be dropped Suggested Assignment without changing any values. CHECK YOUR UNDERSTANDING 60 × 2 - [2 × 8 + ((8 + 5) + 5) × 3 + (1 + 2) × 3 + 5] p. 122, #7–12 60 × 2 - [2 × 8 + ((13) + 5) × 3 + (1 + 2) × 3 + 5] UNIT 2 PRACTICE 60 × 2 - [2 × 8 + (18) × 3 + (3) × 3 + 5] p. 137, #64 60 × 2 - [2 × 8 + 18 × 3 + 3 × 3 + 5]

60 × 2 - [16 + 54 + 9 + 5] 60 × 2 - [16 + 54 + 9 + 5] 60 × 2 - 84 1. 0 120 - 84 36 2. 40 3. 5 CHECK YOUR UNDERSTANDING 4. 80 Write your answers on notebook paper. Insert parentheses when needed to make the Show your work number sentence true. 5. 8 Simplify using order of operations. 7. 11 + 8 × 4 = 43 6. 17 1. 18 - 12 ÷ 2 × 3 8. 5 × 2 + 3 = 25 7. No parentheses are needed. 2. 9 × 4 + 8 ÷ 2 9. 16 × 4 - 4 × 4 = 0 8. 5 × (2 + 3) = 25 3. 2 × (8 + 2) ÷ 4 Use parentheses and the symbols +, -, ×, and ÷ 9. 16 × (4 - 4) × 4 = 0 4. (1 + 3)2 × 5 to make each number sentence true. 10. 7 ____ 3 ____1 ____1 = 9 10. Answers may vary. Sample 5. 4 × 42 ÷ (56 ÷ 8 × 3) 11. answer: 7 + (3 - 1) × 1 = 9 6. 4 × 22 + 1 10 ____ 5 ____ 5 ____ 2 =10 12. MATHEMATICAL Give some reasons why 11. Answers may vary. Sample REFLECTION mathematicians had to answer: 10 + (5 - 5) × 2 agree on an order of operations to be used 12. Answers may vary. Sample to simplify a numerical expression. © 2010 College Board. All rights reserved. answer: Situations such as those in this lesson can result in confusion when writing an expression unless there is understanding about how to write expressions and how to interpret them.

122 SpringBoard® Mathematics with Meaning™ Level 1

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