2nd grading - exponential and logarithmic

8/18/2019 2nd Grading - Exponential and Logarithmic

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La Consolacion University PhilippinesCity of Malolos, Bulacan

BASIC EDUCATION DEPARTMENTScholastic Year 2013 – 2014

Understandin !y Desin Unit Plan

Unit TitleE"ponential #Loarith$ic %&nctions

Quarter Unit Plan ' ( Second

Curriculum rea Mathe$atics I) Year !e"el %o&rth *ear#e"elo$e% &y Mr+ Marco Rhonel M+

E&se!io Time 'rame ,- Days

STA.E '/ Desired Res&lts ( O&tco$esLEARNIN. STANDARDS/

Content Stan%ar%( The learner %emonstrates )no*le%+e an% s)ills relate%to e$onential functions-

.erformance Stan%ar%s( The learner in the lon+ term an% on his/her o*n, *ill&e a&le to ma)e soun% u%+ments an% $re%ictions an%ta)e a$$ro$riate actions in situations that in"ol"ea$$lications of e$onential an% lo+arithmic functions-

End&rin Understandins 0EU1s2 Essential 3&estions 0E31s2

• Some mathematical functions can &e +enerate%&y eaminin+ $atterns an% relationshi$s of a+i"en set of %ata-

• The in"erse of a +i"en function can &e +reat tool

in n%in+ solutions to the function

• !o+arithms are other form of e$ressin+e$onents

• !imits connect a%"ance% al+e&ra an% &asic

calculus

• o* %o $atterns hel$ us re$resent, analye,ma)e $re%ictions, an% %ra* an% ustifyconclusions from set %ata

• o* can *e use $atterns to communicate

mathematical i%eas

• o* %o $atterns, relations, an% functions hel$ usun%erstan% our *orl%

• o* %o $ro$erties of lo+arithm hel$ us sim$lify

e$ressions an% sol"e e$onential e5uations

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Trans4er .oal6 *ant my stu%ents to learn the conce$ts of e$onential an% lo+arithmic functions an% its a$$lication for real7life

situations-5no6lede S7ills )al&e InterationThe st&dents 6ill 7no6 the4ollo6in/

1- 6n"erse 'unctions2- 8$onential 'unctions3- 9ra$h of 8$onential

'unctions4- !o+arithmic 'unctions:- !a*s of !o+arithms;- !o+arithmic 85uation


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Evidence at the Level o4 Understandin/ !earners shoul% &e a&le to %emonstrate un%erstan%in+ &y co"erin+ si =;> facets of un%erstan%in+(

EXPLANATION#iscuss the %enition an% characteristics of a function-

Criteria/ Clear, Coherent

INTERPRETATION#escri&e an% inter$ret $ro$erties of a function-

Criteria/ 6llustrati"e, Clear, Creati"e

APPLICATION

.erforms the %iDerent o$erations an% $roce%ures inten%e% for function relate%

$ro&lems-

Criteria/ ele"ant, ccurate, $$ro$riate

PERSPECTIVE#e"elo$ insi+hts on $erformin+ functions *ithin a com$any

Criteria/ E$en7min%e%, Sensiti"e, Meanin+ful

EMPATHY

Manifest the im$ortance of accuracy an% analytical thin)in+ in sol"in+ function

relate% $ro&lems-

Criteria/ Un$reu%ice%, ele"ant, 8"i%ent

SELF-KNOWLEDGE

Sho*s un%erstan%in+ on follo*in+ the ste$s in sol"in+ %iDerent function relate%

$ro&lems-

Criteria/ eFecti"e, ele"ant, 8"i%ent

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R&!ric 4or Per4or$ance Tas7/

CateoriesO&tstandin

082Satis4actory

092Developin

0,2Beinnin

0'2Ratin

Reso&rce4&lness and 3&alityo4 :or7 09;


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STA.E 9/ Teachin and Learnin E"perience 0Learnin Plan2

Day '

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S&!>ectMatter

.resentation of .erformance Tas)

Re4erence

Re$ar7s

)al&eInteration

E$en7min%e%ness, Coo$eration Materials

Trans$arency, E.

Activities

Daily Ro&tine

O!>ective(s/ To $resent the $erformance tas) to the stu%ents an% manifest the"alues of o$en7min%e%ness an% coo$eration amon+ the +rou$ mem&ers-

• Interaction/ The teacher *ill $resent the nature of the $erformance tas) an% *ill+i"e eam$les if there is an a"aila&le material- ules, $roce%ures an% contents

*ill &e %iscusse%- The class *ill &e %i"i%e% into t*o to three +rou$s- llo* them toas) 5uestions for them to &e +ui%e% accor%in+ly-

Day ,

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S&!>ectMatter

#enition of 6n"erse 'unctionsRe4erence

Basic Calculus &y 9-Marcelo

Re$ar7s

)al&eInteration

$$reciation of 9o%s CreationMaterials

!a$to$, !C#

Activities

Daily Ro&tine

O!>ective(s/ %ene in"erse functions

• Interaction/ !et the stu%ents rea% the selection 9enesis in e"erse story- Thestu%ents *ill %iscuss their un%erstan%in+ a&out the selection rea% an% ans*er the+ui%e 5uestions- Then, they *ill conecture the relationshi$ of the 9enesis ine"erse story *ith the to$ic 6n"erse 'unctions-

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Day 9

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S&!>ectMatter

6n"erse 'unctionsRe4erence


Re$ar7s

)al&eInteration


!a$to$, !C#, Chal)&oar%

Activities

Daily Ro&tine

O!>ective(s/ 'in% the in"erse of a function +i"en a set of or%ere% $airs

• Interaction/ The teacher *ill use the %e%ucti"e a$$roach- Ste$s in n%in+ forthe in"erse of a function *ill &e $ro"i%e%- !et the stu%ents sol"e on their o*n an%try to lan% on the in"erse- Try to %etermine in *hat ste$ of the *ay the stu%ents*ent *ron+ an% try to correct misconce$tions if there are-

•Assess$ent/ 'ormati"e =The stu%ents *ill n% for the in"erse of the +i"en set of functions>

Day 8

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S&!>ectMatter

6n"erse 'unctionsRe4erence


Re$ar7s

)al&eInteration


!C#, !a$to$, Chal)&oar%

Activities Daily Ro&tine

O!>ective(s/ Gerify if the com$ute% in"erse of a function is correct &y a$$lyin+the conce$t of com$osition of functions

• Interaction/ !et the stu%ents recall the conce$t of Com$osition of 'unctions- !etthem cite the ste$s in n%in+ for the com$osition of 'unctions- The stu%ents after*hich *ill su&stitute the com$ute% in"erse *ith the ori+inal $ro&lem usin+ thecom$osition of functions- !et them see *hat the ans*ers *ill &e an% %ra*conclusion from it-

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• Assess$ent/ 'ormati"e =By $air, they *ill +i"e each other eam$les for them tosol"e an% they *ill chec) the *or) of their $air->

Day ?

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S&!>ect

Matter 6n"erse 'unctions

Re4ere

nce

Basic Calculus &y 9-

Marcelo Re$ar7s

)al&eInteration

onestyMaterials


Activities

Daily Ro&tine

• O!>ective(s/ To measure stu%ents com$etencies on in"erse functions throu+hsummati"e assessment

• Assess$ent/ Summati"e =6n%i"i%ual Qui, 6n"erse 'unctions>

Day @

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S&!>ectMatter

#enition of 8$onential'unctions

Re4erence


Re$ar7s

)al&eInteration

#iDerentiatin+ +oo% from &a%Materials



O!>ective(s/ %ene e$onential functionsH %istin+uish *hich amon+ the +i"enfunctions are e$onential

Interaction/ The teacher *ill +i"e t*o sets of eam$les, one is for an eam$le of an e$onential function an% one for non7eam$les- !et the stu%ents choose*hether *hich is an eam$le an% not an eam$le- 'or non7eam$les, let themstate the reason &ehin%-

• Assess$ent/ 'ormati"e =9i"en a set of eam$les, they *ill choose *hich are

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eam$les an% non7eam$les, for non7eam$les they ha"e to state the reason>

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Day

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S&!>ectMatter

Sol"in+ for the Ieros of8$onential 'unctions

Re4erence


Re$ar7s

)al&eInteration

$$reciatin+ ootsMaterials


Activities

Daily Ro&tine

O!>ective(s/ %etermine an% a$$ly the $rocess on ho* to sol"e for the eros ofe$onential functions

• Interaction/ The teacher *ill use the %e%ucti"e metho%- e *ill $resent theste$s in sol"in+ the eros of e$onential functions- !ater, he *ill %emonstrate onho* to a$$ly the conce$t in *or% $ro&lems-

•

Assess$ent/ 'ormati"e =6n%i"i%ual, let the stu%ents sol"e for the eros ofe$onential functions +i"en>

Day -

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S&!>ectMatter

Sol"in+ for Ieros of8$onential 'unctions

Re4erence


Re$ar7s

)al&eInteration

onestyMaterials


Activities

Daily Ro&tine

• O!>ective(s/ To measure stu%ents com$etencies on Sol"in+ Ieros of 8$onential'unctions throu+h summati"e assessment

• Assess$ent/ Summati"e =6n%i"i%ual Qui, 'in%in+ the Ieros of 8$onential'unctions>

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Day

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S&!>ectMatter

'in%in+ for the Coor%inates of8$onential 'unctions

Re4erence


Re$ar7s

)al&eInteration

There are many *ays to sol"ea $ro&lem

Materials


Activities

Daily Ro&tine

• O!>ective(s/ Sol"e for the an% y coor%inates of a +i"en e$onential function

• Interaction/ !et the stu%ents recall ho* to n% the coor%inates of a linearfunction- Use the conce$t recalle% in n%in+ the coor%inates of e$onentialfunctions-

• Assin$ent/ Jhat is the %iDerence &et*een n%in+ the coor%inates of a linear

function an% an e$onential function Cite eam$les to su$$ort your ans*ers

Day ';

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S&!>ectMatter

9ra$hin+ 8$onential 'unctionsRe4erence


Re$ar7s

)al&eInteration

8"erythin+ has its ri+htful$lace on 8arth

Materials


Activities

Daily Ro&tine

• O!>ective(s/ 9ra$h e$onential functions an% %escri&e their $ro$erties

• Interaction/ fter com$utin+ the coor%inates from the $re"ious %iscussion, letthe stu%ents recall ho* to +ra$h linear e5uations- fter +ettin+ the +ra$h let thestu%ents %escri&e the +ra$h they *ere a&le to ma)e-

• Assess$ent/ 'ormati"e =6n%i"i%ual, let the stu%ents ma)e %escri$tions on the+ra$hs they *ere a&le to +enerate>

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Day ''

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S&!>ectMatter

6nter$retin+ the 9ra$h of8$onential 'unctions

Re4erence


Re$ar7s

)al&eInteration

!oo) &eyon% *hat our eyes cansee

Materials

Activities

Daily Ro&tine

• O!>ective(s/ 6nter$ret the 9ra$h of the 8$onential 'unction +enerate%

• Interaction/ 'rom the stu%ents +ra$h of the %iDerent )in%s of e$onentialfunctions, let them +i"e inter$retation to the +ra$hs an% %ra* certainconclusions-

• Assess$ent/ 'ormati"e =.air, ma)e u%+ments &ase% on the +i"en +ra$h of

e$onential functions>

Day ',

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S&!>ectMatter

Sol"in+ .ro&lems in"ol"in+8$onential 'unctions

Re4erence


Re$ar7s

)al&eInteration

There are many *ays of sol"in+a $ro&lem

Materials


Activities

Daily Ro&tine

• O!>ective(s/ sol"e $ro&lems in"ol"in+ 8$onential functions

• Interaction/ The teacher *ill em$loy %e%ucti"e metho%- The ste$s an%$rocesses use% to sol"e $ro&lems *ill &e $resente% an% %emonstrate% to thestu%ents- fter *hich, the stu%ents *ill use it in sol"in+ $ro&lems in"ol"in+e$onential functions-

• Assess$ent/ 'ormati"e =&y +rou$, Qui +ame on sol"in+ $ro&lems in"ol"in+e$onential functions>

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Day '9

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S&!>ectMatter

8$onential 'unctionsRe4erence


Re$ar7s

)al&eInteration

onestyMaterials


Activities

Daily Ro&tine

• O!>ective(s/ To measure stu%ents com$etencies on 8$onential 'unctionsthrou+h summati"e assessment

• Assess$ent/ Summati"e =6n%i"i%ual Qui, 8$onential 'unctions>

Day '8

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S&!>ect

Matter

#enition of !o+arithmic

'unctions

Re4ere

nce

Basic Calculus &y 9-

Marcelo Re$ar7s

)al&eInteration

Searchin+ for truthMaterials


Activities

Daily Ro&tine

• O!>ective(s/ %ene lo+arithmH com$are an% contrast lo+arithm an% e$onentialfunctions

• Interaction/ !et the +o to the li&rary to research some articles on lo+arithm an%e$onential functions- !et the stu%ents com$are an% contrast the %iDerentconce$ts an% i%eas they *ere a&le to solicit from the learnin+ resource center-

• Assess$ent/ 'ormati"e =6n%i"i%ual, Genn #ia+ram an% 9ra$hic Er+anier>

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Day '?

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S&!>ectMatter

Chan+in+ 8$onential'unctions to !o+arithmic'unctions an% Gice7Gersa

Re4erence


Re$ar7s

)al&e

Interation'lei&ility

Materi

als!C#, !a$to$, Chal)&oar%

Activities

Daily Ro&tine

• O!>ective(s/ Chan+e 8$onential to !o+arithmic 'unctions an% !o+arithmic to8$onential 'unctions

• Interaction/ 9i"e set of 8$onential 'unctions an% !o+arithmic 'unctions to thestu%ents, let them com$are the t*o sets of eam$les an% try to see as to ho*they can chan+e e$onential to lo+arithmic an% "ice "ersa-

• Assin$ent/ ns*er $a+e 13< of your tet&oo)

Day '@

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S&!>ectMatter

.ro$erties of !o+arithm 1 an% 2Re4erence


Re$ar7s

)al&eInteration

ccuracyMaterials


Activities

Daily Ro&tine

• O!>ective(s/ enumerate an% %ene the %iDerent $ro$erties of lo+arithms

• Interaction/ 9i"e eam$les of the !o+arithms an% their $ro$erties, let thestu%ents %isco"er the $ro$erty or rule &y synthesiin+ the set of eam$les$resente%-

• Assess$ent/ Summati"e =8ercise, let the stu%ents ans*er the set of eam$les+i"en>

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Day '

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S&!>ectMatter

.ro$erties of !o+arithm 3 an% 4Re4erence


Re$ar7s

)al&eInteration

ccuracyMaterials


Activities

Daily Ro&tine



• Assess$ent/ 'ormati"e =By .air, ns*er the $ule +i"en usin+ the 3r% an% 4th

$ro$erty>

Day '-

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S&!>ectMatter

.ro$erties of !o+arithm=.ro%uct K Quotient>

Re4erence


Re$ar7s

)al&eInteration

ccuracyMaterials


Activities

Daily Ro&tine



• Assess$ent/ 'ormati"e =By +rou$, +i"en an eam$le, share to the *hole classho* %i% your +rou$ lan% on a $articular ans*er>

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Day '

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S&!>ectMatter

.ro$erties of !o+arithm =.o*eran% oot>

Re4erence


Re$ar7s

)al&e

Interation

ccuracyMateri

als


Activities

Daily Ro&tine



•

Assess$ent/

Day ,;

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S&!>ectMatter

Sim$lifyin+ !o+arithmic'unctions

Re4erence


Re$ar7s

)al&eInteration

Sim$licity is &eautyMaterials


Activities

Daily Ro&tine

• O!>ective(s/ Transform e$an%e% lo+arithm into sin+le lo+arithm &y a$$lyin+ the%iDerent $ro$erties of lo+arithm

• Interaction/ ecall the %iDerent $ro$erties +o"ernin+ !o+arithms, let thestu%ents choose *hat $ro$erty shoul% they use for the $articular eam$le +i"enfor them to sol"e-

• Assess$ent/ Summati"e =in%i"i%ual *or), ans*er $a+e 140 letter B>

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Day ,'

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S&!>ectMatter

8$an%in+ !o+arithmic'unctions

Re4erence


Re$ar7s

)al&e

Interation

ccuracyMateri

als


Activities

Daily Ro&tine

• O!>ective(s/ Transform sin+le lo+arithm into e$an%e% lo+arithm usin+ the%iDerent $ro$erties of lo+arithm

• Interaction/ ecall the %iDerent $ro$erties +o"ernin+ !o+arithms, let thestu%ents choose *hat $ro$erty shoul% they use for the $articular eam$le +i"enfor them to sol"e-

• Assess$ent/ Summati"e =6n%i"i%ual *or), ans*er $a+e 140 letter >

Day ,,

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S&!>ectMatter

8"aluatin+ !o+arithmic'unctions

Re4erence


Re$ar7s

)al&eInteration

Self78"aluationMaterials


Activities

Daily Ro&tine

• O!>ective(s/ 8"aluate lo+arithmic functions usin+ the %iDerent $ro$erties oflo+arithm

• Interaction/ The stu%ents *ill e"aluate the !o+arithmic 'unctions usin+ the rstfour $ro$erties in *hich they shoul% assi+n "alue to the lo+arithmic function$ro"i%e% they meet the re5uirements of the $ro$erties- This *ill &e %one in a%isco"ery a$$roach metho%

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• Assess$ent/ 'ormati"e =By .air, ans*er the *or)sheet +i"en that in"ol"ese"aluatin+ lo+arithms>

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Day ,9

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S&!>ectMatter

Sol"in+ !o+arithmic 'unctionsRe4erence


Re$ar7s

)al&eInteration

8"ery $ro&lem can &e sol"e% in%iDerent *ays

Materials


Activities

Daily Ro&tine

• O!>ective(s/ Sol"e for the roots/eros of the +i"en lo+arithmice5uations/functions

• Interaction/ !et the stu%ents n% the eros of the lo+arithmic functions usin+their $re"ious )no*le%+e on sol"in+ for the eros or roots of e$onentialfunctions-

•

Assess$ent/ Summati"e =Qui on Ieros of 8$onential 'unctions>

Day ,8

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S&!>ectMatter

#enition of !imits of 'unctionsan% !imit Theorems 1, 2, an% 3

Re4erence


Re$ar7s

)al&eInteration

8"ery $erson has his/herlimitations

Materials



• O!>ective(s/ 6%entify an% %ene the limit theoremsH %etermine the limits of the+i"en functions &y a$$lyin+ the theorems

• Interaction/ The teacher *ill %isclose the meanin+ of limits since it is the rsttime the stu%ents *ill encounter the to$ic- fter *hich, the teacher *ill +i"e setof eam$les for !imit Theorems, let the stu%ents +enerate the limit &y loo)in+unto the eam$les $resente% to them-

• Assess$ent/ 'ormati"e =&y +rou$, ma)e a sim$le son+ on their un%erstan%in+

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of the limits of functions>

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Day ,?

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!imit Theorems 4, :, an% ;Re4erence


Re$ar7s

)al&eInteration


Materials


Activities

Daily Ro&tine

• O!>ective(s/ 6%entify an% %ene the limit theoremsH %etermine the limits of the+i"en functions &y a$$lyin+ the theorems

• Interaction/ The teacher *ill %isclose the meanin+ of limits since it is the rsttime the stu%ents *ill encounter the to$ic- fter *hich, the teacher *ill +i"e setof eam$les for !imit Theorems, let the stu%ents +enerate the limit &y loo)in+unto the eam$les $resente% to them-

• Assess$ent/ Summati"e =ns*er $a+es 1;2 – 1;4 of the tet &oo)>

Day ,@

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S&!>ectMatter

!imit Theorems


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• Assess$ent/ Summati"e =ns*er $a+es 1;:71;; of the tet &oo)>

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Day ,

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S&!>ectMatter

8"aluatin+ !imits &y 'actorin+Re4erence


Re$ar7s

)al&eInteration


Materials


Activities

Daily Ro&tine

• O!>ective(s/ 8"aluate the limits usin+ factorin+ metho%

• Interaction/ !et the stu%ents recall the conce$t of factorin+- 9i"e them in$utson ho* to sol"e or e"aluate limits usin+ the factorin+ theorem-

• Assess$ent/ Summati"e =ns*er $a+e 1;@ of the tet &oo)>

Day ,-

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S&!>ectMatter

8"aluatin+ !imits &yConu+ation

Re4erence


Re$ar7s

)al&eInteration


Materials


Activities

Daily Ro&tine

• O!>ective(s/ 8"aluate the limits usin+ conu+ate metho%

• Interaction/ !et the stu%ents recall the conce$t of conu+ation- 9i"e them in$utson ho* to sol"e or e"aluate limits usin+ the conu+ation theorem-

• Assess$ent/ Summati"e =ns*er $a+e 1;A of the tet &oo)>

.re$are% &y( Lote% &y(

Mr+ MARCO RONEL MA.NO EUSEBIO Mr+ )IR.ILIO NU.UID BANTI.UE

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Teacher of Mathematics Su&ect rea Coor%inator, Mathematics, Science, an%Com$uter

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2nd grading - exponential and logarithmic

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