# 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

Jan294:20PM

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.

• Module3Lesson5&6Merged.notebook

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Asymbolmeanstheoppositeofanumber.

(5)=5

Sincetheoppositeof5isnegative5,andtheoppositeofnegative5ispositive5,then(5)=5.

Whatistheoppositeofnegativesix?

Whatistheoppositeoftheoppositeof10?

Howwouldyouwritetheoppositeoftheoppositeof12?

Whatdoesasymbolmean?

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

• Module3Lesson5&6Merged.notebook

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Exercise

Completethetableusingthecardsinyourgroup.

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1. Writetheoppositeoftheoppositeof10asanequation.

2. Ingeneral,theoppositeoftheoppositeofanumberisthe___________

3. Providearealworldexampleofthisrule.Showyourwork.

• Module3Lesson5&6Merged.notebook

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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.

Theoppositeofanoppositeofanumberistheoriginalnumber.Theoppositeoftheoppositeofnegative6isnegative6becausetheoppositeof6is6.Theoppositeof6is6.

Whatistherelationshipbetweenthelocationofanonzeronumberonthenumberlineandthelocationofitsoppositeonthenumberline?

Anumberanditsoppositearelocatedthesamedistancefrom0onanumberlinebutonoppositesidesof0.

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MODULE3RationalNumbersTopicA:UnderstandingPositiveandNegative

Lesson6:RationalNumbersontheNumberLineStudentOutcomes

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

Studentsknowthattheoppositesofrationalnumbersaresimilartotheoppositesofintegers.Studentsknowthattworationalnumbershaveoppositesignsiftheyareondifferentsidesofzero,andthattheyhavethesamesigniftheyareonthesamesideofzeroonthenumberline.

• Module3Lesson5&6Merged.notebook

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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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fraction,,islocatedbetweenwhichtwoconsecutiveintegers?Explainyourreasoning.

Exercise1:

Onthenumberline,eachsegmentwillhaveanequallengthof.Inthefraction,

thenumeratorisandthedenominatoris.Thefractionislocated

betweenand.

0

Explanation:

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Example2:RationalNumbersandtheRealWorld

a. Writearationalnumbertorepresentthesituation.

b. Whattwointegersis1.25betweenonanumberline?

d. Whatwillbethewaterlevelafteritrained?Graphthepointonthenumberline.

f. Statearationalnumberthatisnotanintegerwhosevalueislessthan1.25,anddescribeitslocationbetweentwoconsecutiveintegersonthenumberline.

• Module3Lesson5&6Merged.notebook

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Jan227:30AM

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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