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ProblemSetLesson3

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ProblemSetLesson4

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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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