concept development: irrational numbers: and do...
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NAME:___________________________ Math_______,Period____________
Mr.Rogove Date:__________
G8M7L8:ApproximatingIrrationalNumbers1
Learning Objective:Wewilluserationalapproximationtogetamoreaccuratedecimalexpansionofirrationalnumbers.(G8M7L8)Concept Development: IrrationalNumbers:NumbersthathaveinfinitedecimalexpansionsandDONOThaverepeatingblockofdigits.Example: 3, 22
Non-Example:!! , 12.25
UsingRationalApproximationtoGettheDecimalExpansionofSquareRoots
Rationalapproximationusesasequenceofrationalnumberstogetcloserandclosertoagivennumbertoestimatethevalueofthenumber.-Beginbydeterminingtheintegersthatthesquarerootliesbetween.-Thendeterminewhichintervaloftenthsthatthenumberbelongs.-Thendeterminewhichintervalofhundredthsthenumberbelongs.WecanuserationalapproximationtocompareirrationalnumbersExample:Whichnumberisgreater: 65 !" !"!!?
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NAME:___________________________ Math_______,Period____________
Mr.Rogove Date:__________
G8M7L8:ApproximatingIrrationalNumbers2
Guided Practice: StepstoFindingtheValuesofSquareRoots1.Determinewhichtwointegersthesquarerootisbetween.2.Userationalapproximationtodeterminewhichintervaloftenthsthenumberfallsbetween.3.Userationalapproximationtodeterminewhichintervalofhundredthsthenumberfallsbetween.4.Ifnecessarymaketherequestedcomparison.Estimatethevalueof 28tothenearesthundredth.
Estimatethevalueof 17tothenearesthundredth.
Estimatethevalueof 91tothenearesthundredth.
Estimatethevalueof 78tothenearesthundredth.
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NAME:___________________________ Math_______,Period____________
Mr.Rogove Date:__________
G8M7L8:ApproximatingIrrationalNumbers3
Whichisgreater, 50 !" !"#!" ?
Whichisgreater, 59 !" !"#!! ?
Placethefollowingonanumberline:38 , 43 , 47 , 203 , 6. 15 , 538
6.06.16.26.36.46.56.66.76.86.97.0
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NAME:___________________________ Math_______,Period____________
Mr.Rogove Date:__________
G8M7L8:ApproximatingIrrationalNumbers4
Independent Practice: Estimatethevalueof 22tothenearesthundredth.
Estimatethevalueof 63tothenearesthundredth.
Whichisgreater, 72 !" 8. 4?
Whichisgreater, 14 !" !"! ?
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NAME:___________________________ Math_______,Period____________
Mr.Rogove Date:__________
G8M7L8:ApproximatingIrrationalNumbers5
Activating Prior Knowledge: Wecandividefractionsusinglongdivision:
411
512
Closure: Describeatleastthreewaystoapproximate 108orApproximate 25! Notes: Lesson11and13?Homeworkshouldbelesson13Problemset.NocalculatorPLEASE!!!