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 !" !"!!?

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.

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

NAME:___________________________ Math_______,Period____________

Mr.Rogove Date:__________

G8M7L8:ApproximatingIrrationalNumbers4

Independent Practice: Estimatethevalueof 22tothenearesthundredth.

Estimatethevalueof 63tothenearesthundredth.

Whichisgreater, 72 !" 8. 4?

Whichisgreater, 14 !" !"! ?

NAME:___________________________ Math_______,Period____________

Mr.Rogove Date:__________

G8M7L8:ApproximatingIrrationalNumbers5

Activating Prior Knowledge: Wecandividefractionsusinglongdivision:

411

512

Closure: Describeatleastthreewaystoapproximate 108orApproximate 25! Notes: Lesson11and13?Homeworkshouldbelesson13Problemset.NocalculatorPLEASE!!!