Algebra II Lesson for Calculator Overflow/Underflow Using ...

AlgebraIILessonforCalculatorOverflow/UnderflowUsingLogarithms appliedtotheUILCalculatorApplicationsContest

LessonGoal:Tohavestudentslearnhowuselogarithmsinworkingwithvery largenumbersandnumbersclosetozero. Time:1classperiod Course:AlgebraII TEKSAddressed: AlgebraII(2)(A)Foundationsforfunctions.Thestudentunderstandsthe importanceoftheskillsrequiredtomanipulatesymbolsinordertosolveproblems andusesthenecessaryalgebraicskillsrequiredtosimplifyalgebraicexpressions andsolveequationsandinequalitiesinproblemsituations.Thestudentisexpected tousetoolsincludingfactoringandpropertiesofexponentstosimplifyexpressions andtotransformandsolveequations.

Overview: Thestudentswilllearnhowtosolvefornumbersthataretoolargeforthecalculator andhowtosolvefornumbersthataretooclosetozeroforthecalculatortohandle.

MaterialsNeeded:

1. ScientificorGraphingCalculator(TI-83orTI-84) 2. Exampleproblems(attached) 3. Practiceproblems(attached) 4. AnswerKey(attached)

Procedures:

ProvidestudentswiththeExampleProblemspaper.

Aftergoingoverbothexamples,givethestudentstheworksheetover

practiceproblems.

Havestudentscompletethepracticeproblemstherestoftheperiodor

assignashomeworkandroundeachanswertothreesignificantdigits.

Assessment:

Calculatoroverflow/underflowworksheet

CalculatorUnderflowExample

Find980,311-62,053onacalculator.Ifyoutypein980311^(-62053)onaTI- 83orTI-84theanswergivenis0.Thisisbecauseyourcalculatorcannot handlenumbersveryclosetozero.Usinglogarithmsandalgebrawecan solveforthisanswer.Onthestatecalculatortestin2011questionnumber 28asks: 11I-28Whatis980,311-62,053?

Letx=980,311-62,053 Takethecommonlogarithmofbothsides

logx=log(980,311-62,053) Usetheexponentpropertyoflogarithms.

logx=-62,053log(980,311) Type-62,053log(980,311)intothecalculator

logx=-371,782.1026...

Subtract(-371,783)from-371,782.1026...togetanumberbetween0and1.

(-371,783)-(-371,782.1026...)=0.89741171... logx=0.89741171... 10logx=100.89741171... x=7.896083095...

Roundto3decimalplaces. Write7.90x10-371,783(Anumberveryclosetozero)

CalculatorOverflowExample Find83,946950,637onyourcalculator.Ifyoutype83946^950637intotheTI- 83orTI-84calculator,theanswergivenisERR:OVERFLOWbecausethe numberistoolargeforthesecalculatorstohandle.Usingthepropertiesof logarithmsandalgebra,wecansolveforthecorrectanswer.OntheTMSCA statecalculatorcontestin2011questionnumber28is: 11E-28Whatis83,946950,637?

Letx=83,946950,637 Takethecommonlogarithmofbothsides.

logx=83,946950,637 Usethepropertyoflogarithmsforexponents.

logx=950,637log(83,946) Type950637log(83946)intothecalculator.

logx=470916.5887... Subtract470916from470916.5887...toget0.58866699...

logx=0.58866699... 10logx=100.58866699... x=3.878528526... Roundto3decimalplaces. Write3.88x10470,916(Averylargenumber)

Overflow/UnderflowPracticeProblems

1. 09G-37Calculate0.0942-48285

2. 09I-37.Calculate720575912

3. 10B-36Whatis57,893453,562?

4. 10G-36Whatis349,441-902,521?

5. Whatis777888?

6. Whatis888-999?

Overflow/UnderflowAnswers

1. 8.96x1049,537 2. 3.82x1028,718 3. 1.58x102,160,146 4. 4.80x10-5,003,012 5. 4.94x102566 6. 3.43x10-2946

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