module 3 lessons 5 & 6 merged

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Module 3 Lesson 5 & 6 Merged.notebook 1 January 22, 2015 Jan 294:20 PM Problem Set Lesson 3

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  • Module3Lesson5&6Merged.notebook

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    January22,2015

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    ProblemSetLesson3

  • Module3Lesson5&6Merged.notebook

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    ProblemSetLesson4

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  • Module3Lesson5&6Merged.notebook

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  • Module3Lesson5&6Merged.notebook

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    MODULE3RationalNumbersTopicA:UnderstandingPositiveandNegativeLesson5:TheOppositeofaNumbersOppositeStudentOutcomes

    Studentsunderstandthat,forinstance,theoppositeof5isdenoted(5)andisequalto5.Ingeneral,theyknowthattheoppositeoftheoppositeistheoriginalnumber;e.g.,(a)=a

    Studentslocateandpositionoppositenumbersonanumberline.

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    Example1:TheOppositeofanOppositeofaNumber

    Whatistheoppositeoftheoppositeof8?Howcanweillustratethisnumberonanumberline?

    a. Whatnumberis8unitstotherightof0?

    b. Howcanyouillustratelocatingtheoppositeof8onthisnumberline?

    Whatistheoppositeof8?

    c. Usethesameprocesstolocatetheoppositeof8.Whatistheoppositeof8?

    d. Theoppositeofanoppositeofanumberis.

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    Asymbolmeanstheoppositeofanumber.

    (5)=5

    Sincetheoppositeof5isnegative5,andtheoppositeofnegative5ispositive5,then(5)=5.

    Whatistheoppositeofnegativesix?

    Whatistheoppositeoftheoppositeof10?

    Howwouldyouwritetheoppositeoftheoppositeof12?

    Whatdoesasymbolmean?

    Whatistheoppositeoftheoppositeofadebitof$12?

    Ingeneral,theoppositeoftheoppositeofanumberistheoriginalnumber;e.g.,(a)=a.

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    Exercise

    Completethetableusingthecardsinyourgroup.

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    1. Writetheoppositeoftheoppositeof10asanequation.

    2. Ingeneral,theoppositeoftheoppositeofanumberisthe___________

    3. Providearealworldexampleofthisrule.Showyourwork.

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    Closing

    Please take out your exit ticket for Lesson 5, close your binder, and complete the exit ticket. This will be collected.

    Whatistheoppositeofanoppositeofanumber?Supportyouranswerwithanexample.

    Theoppositeofanoppositeofanumberistheoriginalnumber.Theoppositeoftheoppositeofnegative6isnegative6becausetheoppositeof6is6.Theoppositeof6is6.

    Whatistherelationshipbetweenthelocationofanonzeronumberonthenumberlineandthelocationofitsoppositeonthenumberline?

    Anumberanditsoppositearelocatedthesamedistancefrom0onanumberlinebutonoppositesidesof0.

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    MODULE3RationalNumbersTopicA:UnderstandingPositiveandNegative

    Lesson6:RationalNumbersontheNumberLineStudentOutcomes

    Studentsusenumberlinesthatextendinbothdirectionsanduse0and1tolocateintegersandrationalnumbersonthenumberline.Studentsknowthatthesignofanonzerorationalnumberispositiveornegative,dependingonwhetherthenumberisgreaterthanzero(positive)orlessthanzero(negative),anduseanappropriatescalewhengraphingrationalnumbersonthenumberline.

    Studentsknowthattheoppositesofrationalnumbersaresimilartotheoppositesofintegers.Studentsknowthattworationalnumbershaveoppositesignsiftheyareondifferentsidesofzero,andthattheyhavethesamesigniftheyareonthesamesideofzeroonthenumberline.

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    What is a rational number?

    A rational number is a number that can be written as a fraction. (The denominator cannot

    be zero.)Integers, Whole Numbers, Some Decimals

    Decimals are rational when:~it terminates (ends)

    ~it repeats with a pattern

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    So what about a number like Pi?

    Pi does not terminate and it never repeats or develops a pattern. What do we call it?

    Irrationalnumberandarewrittenwithasymbol

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    Locateandgraphthenumberanditsoppositeonanumberline.

    Example1:GraphingRationalNumbers

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    Usewhatyouknowaboutthepoints,anditsopposite,tographbothpointsonthenumberlinebelow.The

    fraction,,islocatedbetweenwhichtwoconsecutiveintegers?Explainyourreasoning.

    Exercise1:

    Onthenumberline,eachsegmentwillhaveanequallengthof.Inthefraction,

    thenumeratorisandthedenominatoris.Thefractionislocated

    betweenand.

    0

    Explanation:

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    Example2:RationalNumbersandtheRealWorld

    Thewaterlevelofalakerose1.25feetafteritrained.Answerthequestionsbelowusingthediagrambelow.

    a. Writearationalnumbertorepresentthesituation.

    b. Whattwointegersis1.25betweenonanumberline?

    c. Writethelengthofeachsegmentonthenumberlineasadecimalandafraction.

    d. Whatwillbethewaterlevelafteritrained?Graphthepointonthenumberline.

    e. Aftertwoweeksofrain,thewaterlevelofthelakeistheoppositeofthewaterlevelbeforeitrained.Whatwillbethenewwaterlevel?Graphthepointonthenumberline.Explainhowyougotyouranswer.

    f. Statearationalnumberthatisnotanintegerwhosevalueislessthan1.25,anddescribeitslocationbetweentwoconsecutiveintegersonthenumberline.

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    Closing

    Please take out your exit ticket for Lesson 6, close your binder, and complete the exit ticket. This will be collected.

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