Plan de Area Matematica

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INSTITUCIÓN EDUCATIVA COLEGIO INTEGRADO PETROLEALICENCIA DE FUNCIONAMIENTO RESOLUCIÓN Nº 004444 DEL 14 DE NOVIEMBRE DE 2008.

DANE 254810000165 MUNICIPIO DE TIBU

Elaborado Por:LIC. FABIO ALONSO CUADROS

LIC. MARICELA PAREDES PABÓNLIC. LUIS OLIDES ROJAS BOHORQUEZ

Prese!ado a:ESP. JOR"UE RODR#"UEZ PABÓN

$IBU%&'()



INSTITUCIÓN EDUCATIVA COLEGIO INTEGRADO “PETROLEA”DANE 254810000165

LICENCIA DE FUNCIONAMIENTO RESOLUCIÓN Nº 004444 DEL 14 DE

NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

CON$ENIDO

1. IDENTIFICACIÓN DEL AREA

2. JUSTIFICACIÓN

3. OBJETIVOS GENERALES DEL AREA

4. FUNDAMENTACION LEGAL

5. APORTES DEL AREA AL PERFIL DE ESTUDIANTE6. MARCO TEORICO

7. ENFOQUE DEL AREA

8. FILOSOFIA DEL AREA

. ESTANDARES DE CONTENIDO

1!. FORMACION EN VALORES

11. APORTES DEL AREA A LA ESPECILIDAD DE LA INSTITUCION

12. COMPETENCIAS LABORALES.13. INDICADORES DE LOGRO CURRICULARES "RES. 2343#14. METODOLOGIA1. CRITERIOS DE EVALUACION $ EVALUACION2. PLANES ESPECIALES DE APO$O3. CRITERIOS DE VALORACION EN EL AREA4. ACTIVIDADES DEL AREA5. RECURSOS6. FORMATO PLAN DE AREA POR GRADO

BIBLIOGRAFIA

IN$RODUCCIÓN

2



INSTITUCIÓN EDUCATIVA COLEGIO INTEGRADO %PETROLEA&DANE &*)+(''''(,*

LICENCIA DE FUNCIONAMIEN$O RESOLUCIÓN N- '')))) DEL () DENOIEMBRE DE &''+MUNICIPIO DE $IBU

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*( 0( '(+*( + 0' )'*+),*-' +0 - + *-9- +--')+*+ ' 0'

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2. P+(')-+* +('-'0 ? (-(*+)'( :+)*-(

3. P+(')-+* )*- ? (-(*+)'( + )+-'(

3





NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

4. P+(')-+* '0+'*- ? (-(*+)'( + '*(

5. P+(')-+* '-'-'0 ? (-(*+)'( '0:+9'-( ? ''0*-(

(. IDEN$IFICACIÓN

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P+*0+' +0 )--- + T-9/ (+ ')+*' +0 ,+' + )'*+),*-'( 0'

(-:-+*+ -*+(-' @'-'/ :'(.

AREA IN$ENSIDAD HORARIA SEMANAL POR "RADOS

(- &- /- )- *- ,- 0- +- 1- ('- ((-MATEMATICAS 5 5 5 5 5 5 5 5 5 4 4

ASI"NA$URA "RADOS

ARITMETICA 1 5

ARITMETICA $ GEOMETRIA 6 7

ALGEBRA 8

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TRIGONOMETRIA $ GEOMETRIA ANALKTICA 1!

INTRODUCCION AL CLCULO 11

&. JUS$IFICACIÓN

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5





NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

• E0 '+( '0 -)-+*/ 0' -+-'/ 0' *-' ? +0 )+* + 0'

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6





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NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

90-:'*-'. D+ * 0'/ +0 +('00 +0 +( +'*-/ *')9- (+

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establecer las Normas Técnicas Curriculares y Pedagógicas para los niveles de la

educación preescolar, básica y media, sin que esto vaya en contra de la

autonoma de las instituciones educativas y de las caractersticas regionales, y

definir, dise!ar y establecer instrumentos y mecanismos para el me"oramiento de

la calidad de la educación, además, de dar orientaciones para la elaboración del

currculo, respetando la autonoma para organi#ar las áreas obligatorias e

introducir asignaturas optativas de cada institución&.

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NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

+(*'90++ +*+ '*-'+( -'( +(-'(/ '( ) '+00'(

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0. ENFOQUE EL AREA

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9>+*--' + 0'( -*++*'-+( + 0' +'0-'/ +( ++('- )' ---(

''+( + )++ 0 ')+*'0 + 0'( 0+?+(/ ---(/ 0+:'>+ ?

+(**' + +(*' -+-'/ +( +-/ -(*( + ' 0*' )'*+),*-' ' - +

'?' + )'+' ((*+-' 0' (-9-0-' + '++ ' 0( *+-( + *(

0( ')( +0 -)-+*.

11





NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

E +(*+ ,)9-*/ +0 +( +'*- +9+ (+ -'0 ? -,)-/ +(-(*+ 0' ' *++-' ' ')0' -)-+*( '' (+ +*+-(. D+9+

?+*'(+ ' 0' )'-< + ---( +(-* + +'*--'/ +

)-'-</ + -< ? + :+(/ ? + +(*+ (+*-/ 0' M'*+),*-' +( +0

') ),( '+'/ ?' + '?' ' +(**' ? ':-0-=' + )'+' (-*-' 0'(

),( '0*'( +'-+( +0 +(')-+*H ',0-(-(/ (*+(-(/ -*++*'-</ >--

*-/ +*.

E( -)+(--90+/ +*+(/ + (+ -(++ +(*'( + '+-='>+(

'+(-90+(/ +( +- ,*-'( + +(+'=' '*--'*-'(/ +(-'(/ +0+-'( ?

+0-9+'*+( + +)-*' ' )+> )+(-< ? )-- + +(*' -+-'/

''*+(*-'( '+'( ? + *-0-' ,*-'/ *+-+*+( ' 0:' +('(

)+*+*+( '' +0 ',0-(-( + -*++*'-< 9>+*-' + 0' +'0-'. U +'

'0 ? ' +' -< '-++ +*+(/ *'* 0' )'*+-' ) 0'( )'( ?

)+-( + '+-='>+. U' + 0'( -'0-'+( + 0' -+-' +( '?' '0 (+

@)' + 0' (0-< + 90+)'( +*( + ( -'/ ? 0' )'*+),*-'/ ++ +('' + +(+ ))-(.

E 0( L-+')-+*( C-0'+( + M'*+),*-'( (+ + :'-=' +0

0 ) * ')-( + -*+:' '0++ + *+( :'+( +>+(H

Pro3esos de a4red56a7e *'0+( ) +0 '=')-+* 0' +(0-< ?

0'*+')-+* + 90+)'(/ 0' )-'-< 0' )+0'-< ? 0' +0'9'-</

)''-< ? +>+-*'-< + +-)-+*(.

Coo3585e!os b9s53os + *-++ + + -)-+*( +(+-(

+ +('00' +0 +(')-+* )'*+),*- ? (-(*+)'( -( + 0'(

)'*+),*-'(. E(*( +(( +(+-( (+ +0'-' +0 (+-- +

+(')-+* )-/ +('-'0/ )*-/ :+)*-/ '0+'*- ? '-'-'0.

L( (-(*+)'( ( '+00( + (+ @' +- -+ +(+ 0' R+'-<

C-0'H (-(*+)'( )-(/ (-(*+)'( :+)*-(/ (-(*+)'( + )+-'/

(-(*+)'( + '*( ? (-(*+)'( '0:+9'-( ? ''0*-(.

El 3o!e!o *-++ + + 0( ')9-+*+( + +' '0 +(*-'*+ ? + 0+

' (+*- ? +(+'- '' 0' '0-'9-0-' ' 0' )'*+),*-' + '++.

12





0.( LOS ES$2NDARES DE COMPE$ENCIAS B2SICASH L( +(*,'+( (

-*+-( 9>+*-( + --' lo que debe saber y saber hacer, +(*-'*+

+H M'*+),*-'(/ C-+-'( S-'0+( ? N'*'0+(/ L+:'>+ ? C-'''(.

;QU< SON LOS ES$2NDARES DE CALIDAD= U E(*,' + '0-' +

:++'0/ +( -*+- 0' ? + )-- 90- + +)-*+ '0' (- '

+('/ +( * )0+ -+*'( ++*'*-'( (-'0+( + '0-'.

U E(*,' B,(- + C'0-' + +'-</ +( -*+- 0' ? + )--

90- + +)-*+ '0' (- 0' )'-< + +(*-'*+ )0+ 0'(

++*'*-'( (-'0+( + '0-' + ( +'-<.

;PARA QU< UNOS ES$2NDARES DE COMPE$ENCIAS B2SICAS DE

CALIDAD EN EDUCACIÓN=

P+-(' 0( -+0+( + '0-' + 0' +'-< ' 0( + *-++ ++@ *( 0(

-( ? -'( + *'( 0'( +:-+( +0 '( "'(/ 0( +(*,'+( +(+)+'

'+0 + 0' )-< + 0' +-' ? 0' -:'0' + *-'+(#.

O-+*' +0 -(+ + 0( + '+ 0( PEI/ + 00++ ' 0'( +('(

+ -(*-*-+( ' '0'=' (+' 0( -+0+( (+'0'( 0( +(*,'+(.

I0- + 0' -+*'-< ? )+>')-+* + 0' )'-< ---'0 ? *-'' + 0(

+*+(.

I)0(' 0' '0-' + )'*+-'0+(/ *+*( ? *( '?( +'*-( -(

0( (+*+( --'0 ? -'.

L( +(*,'+( ) +++*+( + +0 +( +'*-/ +)-*+ -+*--'

'(+*( + 0' +*-+-' + 0( (-(*+)'( + +'0'-< -*+( ? +*+(.

;QU< ES UNA COMPE$ENCIA= U >* + -)-+*(/ '*-*+(/

-((--+( ? @'9-0-'+( ":-*-'(/ (-'+*-'( ? )-'*-'(#/

+0'-''( +*+ ( '' '-0-*' +0 +(+)+ 0+-90+ ? (+*- + '

'*--' + *+*( +0'*-')+*+ +( ? +*'+(. P 0 *'*/ 0'

)+*+-' -)0-' +/ (+ ? ('9+ @'+.

0.& ES$RUC$URA

13





NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

L' +(**' +*'0 +9+ (+'0' ) )-) '0:( '(+*( ) (H

:'-='-< + 0( *+-(/ :'+( *+)'(/ (++-'/ -'/

-*++0'-+( ? +('00 +0 D+ '+ 0' -(-< :09'0 + -*+:'0 +0 +@'+ )'*+),*-/ +)(

(-+' *+( :'+( '(+*( '' :'-=' +0 0.

0.&.( Pro3esos >eerales. T-++ + + +0 '+-='>+/ *'0+( ) +0

'=')-+* 0' +(0-< ? 0'*+')-+* + 90+)'( 0' )-'-< 0'

)+0'-</ +0'9'-</ )''-< ? +>+-*'-< + +-)-+*(.

El ra6oa85e!o. D+ )'+' :++'0 +*++)( '=' 0' '-< +

+' -+'( + 0' )+*+ '' 00+:' ' ' 0(-<. E0 0 +

)'*+),*-'( +9+ ++ + +0 '=')-+*/ 0' ':)+*'-< ? 0'

+)(*'-< (*-*?+ -+='( ')+*'0+( + 0' '*--' )'*+),*-'.

A+),( + +(*-)0' +(*( +(( + 0( +(*-'*+(/ +( ++('- + (+

+>+-*+ + 0' )0'-< + -+(*-:'-< + >+*'( ? + '+' ' +'0'

':)+*( ? +)(*'-+( )'*+),*-'(. P'' +00 +9+ + ? (+

''+( + -+*--' -+('( )'( + '=')-+* ? )*( ++)(*'-<.

La resol?35@ 4la!ea85e!o de 4roble8as. L' ''-' '' 0'*+' ?

+(0+ 90+)'( +9+ (+ ' + 0'( --'+( +0 0 + )'*+),*-'(.

L( 0'+( + +(*- +9+ :''*-=' + 0( +(*-'*+( +('00+

@+')-+*'( ? +(*'*+:-'( '' +(0+ 90+)'( + ',*+ )'*+),*-/ 9-+

(+' + +0 ') )-() + 0'( )'*+),*-'( + *( ,)9-*( +0'-'(

+00'(. T')9- +( -)*'*+ +('00' +(-* +0+- '+' +0 +(

+ + ' (+ +(+0+ 90+)' (+ *)' ' +-(-<.

La 3o8?53a35@. M+-'*+ 0' )-'-< + -+'( (+' + 0+

)'*+),*-' 0( +(*-'*+( (0-' ( )'+' + +('. P'' +00 +0

0 +9+, -0- '*--'+( + 0+ +)-*' )-' ' 0( +),( ((

-+'( )'*+),*-'( + )' @++*+/ 0'' ? +-('.

La 5!er4re!a35@ (+ +*-++ ) 0' ''-' + '*' +0 (+*- -+'

')+*'0 ? 0' (--< 00+' '0 @+@ + )0' @-<*+(-(/ @'+

+--+(/ +*.

14





La elabora35@ eal?a35@ de 4ro3ed585e!os -)0-' +*++ ? +0-' 0(

+*( (9+ 0( '0+( (+ '?'/ -:'0)+*+ 0' 0<:-' + 0( ((*+*' ''

('9+ ' +( -'90+ +(.

0.&.&. Coo3585e!os b9s53os. T-++ + + +(( +(+-( +

+('00' +0 +(')-+* )'*+),*- ? (-(*+)'( -( + 0' )'*+),*-'.

Los 3o!e5dos b9s53os es!9 or>a56ados e s5s!e8as:

Pesa85e!o N?8r53o S5s!e8a N?8r53o. E(*+ )+*+ +0 0

' + 0( +(*-'*+( '-+' ' )+(-< (<0-' *'*( + 0(

)+(/ 0'( +0'-+( ? +'-+( + +-(*+ +*+ +00(/ ) + 0'(

-++*+( )'+'( + ++(+*'0(.

E0 +(')-+* )- (+ '-++ :''0)+*+ ? ' +0-' + 0'

)+-' + + 0( +(*-'*+( *-++ 0' *-' + +(' + 0( )+( ?

+ ('0( + *+*( (-:--'*-(.

Pesa85e!o Es4a35al S5s!e8a "eo8!r53o. E0 )+*+ :+)*- +0

0/ +9+, +)-*- ' 0( +(*-'*+( +')-' ? ''0-=' 0'( -+'+( +

0( +('-( 9--)+(-'0+( ? *--)+(-'0+(/ '( ) 0'( )'( ? -:'(

:+)*-'( + (+ @'00' + +00(. D+ 0' )-()' )'+'/ +9+ ++0+(

@+')-+*'( *'0+( ) +0 ( + *'()'-+(/ *'(0'-+( ? (-)+*'( ''

''0-=' (-*'-+( )'*+),*-'(. L( +(*-'*+( +9+, +('00' 0'

''-' + +(+*' ':)+*( )'*+),*-( '+' + 0'( +0'-+(

:+)*-'(/ '+),( + *-0-=' 0' -('0-='-</ +0 '=')-+* +('-'0 ? 0'

)+0'-< :+)*-' '' +(0+ 90+)'(.

Pesa85e!o M!r53o S5s!e8as de Med5das. E0 +('00 + +(*+

)+*+ +0 0 +9+ ' ) +(0*' 0' )+(-</ '*+ +0

+(*-'*+/ + 0( '*-9*( )+('90+( + 0( 9>+*( ? +0 *-+). A( )-()/

+9+ ' 0' )+(-< + 0( -+(( (-(*+)'(/ -'+( ? +(( + 0'

)+--<.

P+(')-+* A0+'*- ? S-(*+)'( + D'*(. E0 0 + )'*+),*-'( +9+

:''*-=' + 0( +(*-'*+( (+' ''+( + 0'*+' + '*(. L(

+(*-'*+( ? 0'( (-*'-+( ((+*-90+( + (+ ''0-=''( )+-'*+ 0'

15





NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

+0+-< (-(*+),*-' ? :'-='' '+),(/ +9+ +(*' + ''-' +

+' ? +(+*' +(*( '*( ?/ + :'( (*+-+( (+0+-' ? *-0-='

)*( +(*'(*-( '' ''0-='0( ? +('00' ? +'0' -++-'( ?+--+( ' '*- + +00(. D+ -:'0 )'+' 0( +(*-'*+( +('00', '

)+(-< :+(-' + 0( +*( ')+*'0+( + 0' 9'9-0-'.

Pesa85e!o ar5a35oal S5s!e8as Al>ebra53os Aal!53os. E(*+

)+*+ +0 0 *-++ + +*' ' + 0'( '0-'-+( ),( -)*'*+(

+ 0' )'*+),*-'/ '0 +( 0' )0'-< + 0( )+0( )'*+),*-( ''

-+(( +<)+(. P +00(/ +(*+ 0 +9+ +)-*- + 0( +(*-'*+(

'-+' :+(-')+*+ ' )+(-< + '*+(/ +0'-+( ? -+(/

'( ) +('00' ( ''-' + ++(+*' ? ''0-=' (-*'-+( ?

+(**'( )'*+),*-'( )+-'*+ ()90( '0:+9'-( ? :'-'( '-''(. A(

)-()/ +9+ +('00' + +00( 0' ''-' + ''0-=' +0 ')9- + '-(

*+*( ? + *-0-=' )+0( )'*+),*-( '' +*++ ? ++(+*'

+0'-+( '*-*'*-'(.

0.&./ El 3o!e!o. T-++ + + 0( ')9-+*+( + +' '0 +(*-'*+ ?

+ 0+ ' (+*- ' 0'( )'*+),*-'( + '++. E0 *'*')-+* + 90+)'(

+( +0 *+* + (+ -*+:' +(( ? (-(*+)'(. E0 (+*- + -'

-@ *+* -++ + 0' +*-+-' + '' (-*'-< 90+)'

0*'0)+*+ 9-'' ? ++ ':' + (-:--'-< '' 0( +(*-'*+(.

E( 0' -)+(-< + (+ '-++ -'=' + +0 ( + 0'( )'*+),*-'( ? (+

+('00' ' '*-* )+*'0 +(++'*+ + --(-*-'.

0. /. FILOSOF#A

L' )'*+),*-' *-0-=' 0+:'>+ +-(/ 0'/ ? -(. S+ ++ +- + +(

0' -+-' + 0'( -*++0'-+(. E(*, +(+*+/ + +0 )++/ '*' ?

--. E( ,+' + -' 0( )+-( '' ''0-='/ +-/ 00+' ' 0'

-' * + 0 + +0 +(*-'*+ +9+ +*'(+ ? +0+-'.

E0 +( + )'*+),*-'( +9+ 00+' '0 +(*-'*+ )+-'*+ '=')-+*(

0<:-(/ ' ++-' 0 *+<- '' +('00' +*')+*+ 0 ,*- ? '(/

+'=' 0' )+*+ +0 '0) ' 9(+' (-*'-+( + 0 00+' ' )+>' (

-' ? ' @'+ '*+( ' '0: + *'' +)( )++H 0' '-< +

D-(.

16





E0 -)-+* )'*+),*- +(0'/ +( (-+' '0:( ) +0

-)-+* *--' + *-++ + + 0( )+( ? 0'( +'-+(/ ?

*(/ ) +0 -)-+* )'*+),*- +0+)+*'0/ + +(0*' + '9' (+--'0)+*+ '0:( +0+)+*( )-)( + 0' )'*+),*-' -(-0-'. E

:++'0 (+ (-+' + 0'( )'*+),*-'( + 0' +(+0' *-++ '+0

+(+-'0)+*+ -(*)+*'0/ + ' '*+ (+ +0+>' + +0 +('00 +

@'9-0-'+( ? +(*+='( '' +(0+ 90+)'( + 0' -' ,*-'/ '' ('

,:-0)+*+ +0 0+:'>+ (-)9<0-/ 0( +-)-+*( ? '0:-*)( ?/ *'/ + +0

+('00 +0 +(')-+* 0<:- )'0.

L' @-(*-' ' +*' + (-:0( ? (-:0( + -+('( (--+( ? -((-+( (9+

+0 -:+ ? 0' '*'0+=' + 0'( )'*+),*-'(.

El Pla!o5s8o (:-++ + 0'( )'*+),*-'( +( (-(*+)' + +'+( + @'

+-(*- +(+ (-+)+/ + -++-+*+ +0 @)9+ . La !area del 8a!e89!53o es

des3?br5r esas erdades 8a!e89!53as/ ?' + + -+* (+*- +(*, ()+*-' '

+00'( ? 0'( *-++ + 9+++. E(*+ ++ + 0'( -:'( :+)*-'(/ )

0'( +'-+( ? 0'( +0'-+( :+)*-'( ( +(0*' + '0:' )')-(*+-('/ *-++ -+'+( + +(9-)( :' +(+= @'? *'( +

( +(=')( +(9- + 0 (+:-)(/ ? +-(*+ *( + -

(--+' ((+@')(/ ?' + 0'( )'*+),*-'( *'(-++ 0' )+*+ @)''.

El lo>535s8o (-+' + 0'( )'*+),*-'( ( ' ')' + 0' 0<:-'/ -'

-'/ + +0 )-() -:+ ? )*/ ? + ( '*+ + ' -(-0-'

-+('0 + +:-' *'( 0'( )'( + ':)+*'-<. P+ +-- 0(

+*( )'*+),*-( )+-'*+ *)-( 0<:-(/ ? +- 0( *++)'( + 0'(

)'*+),*-'(/ ? 0( *++)'( + 0' 0<:-'/ )+-'*+ +0 +)0+ + +-+(

0<:-'(. E(*' -+*+ ++ 0' +-(*+-' + (H 0' 0<:-' +*-' ? 0'

-*-'.

L' +*-' 9(' 0' @++-' + 0'( -+'( +*+ ( '*+ + +)-('(

:++'0+( '' 00+:' ' 0(-+( +(+-'(. L' -*-' ' 0'

@++-' + 0'( -+'( +0 ) +'0 '*+ + 9(+'-+( +(+-'(

'' 00+:' ' 0(-+( :++'0+( + ' +-' ' *'( + 0' ++-+-' ?

*'(*'-+( +)-'(.

F+:+ @-= :'+( '*+( ' 0 + @? +)( ) 0<:-' )'*+),*-'(H

C,00 (--'0/ +:0'( '' +0 +)0+ + 0( '*--'+( -+('0+( ?

+-(*+-'0+(/ ? +0 ',0-(-( 0<:- +0 )* + +9' + --< )'*+),*-'.

17





NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

El or8al5s8o ++ + 0'( )'*+),*-'( ( ' +'-< + 0' )+*+

@)'' ? (-(*+ (0')+*+ + '-)'(/ +---+( ? *++)'( )

++(-+( )'0+( + (+ +(')90' ' *'( + ()90(/ + ()'-0'( )9-'( -+*'( +:0'(. L' +' + 0' )'*+),*-'

)'0-(*' '-' + 0' )+*+ @)'' + + 0'( (*-+( + +00'

+'0-=' -*+')+*+/ (- + 0' @++-' + 0'( +:0'( +0 >+: (-)9<0-

+(+*-. L'( +)(*'-+( +9+ (+ -:('(/ 9'(''( -')+*+ + 0'(

+:0'( +0 >+: +*- +(+*- + -++-+*+)+*+ + 0'( -),:++( +

'(-+)( 0( *)-( ? 0'( +0'-+(.

El 3os!r?3!55s8o (-+' + 0'( )'*+),*-'( ( ' +'-< + 0' )+*+

@)''/ ? + -')+*+ *-++ +-(*+-' +'0 '+00( 9>+*( )'*+),*-(

+ ++ (+ (*-( +-)-+*( --*( ' '*- 9>+*( -)-*-(.

E0 (**--() )'*+),*- +( )? @++*+ 0' +'::' '*-' ? (+

'?' + 0' (-0:' :+*-' (+ -*++(' 0'( --+( + 0'( '0+( 0'

)+*+ +'0-=' 0' (*-< + 0( +*( )'*+),*-(/ 0' )' )

0( :'-=' + +(**'( ? 0' '0-'-< + 0+( '. N 9'(*' + +0

)'+(* @'?' @+@ 0'( (*-+( )+*'0+(/ '' +(*-'*+ ++(-*' ' (+= +'0-='0'.

E 0' '*'0-' +0 '+0 + 0' -0(' + 0'( )'*+),*-'( *-' (-+/ +(+

0+:/ ' +*' + 0' '*'0+=' + 0'( )'*+),*-'(/ + +(+ 0'(

+(+*-'( )@ ),( ')0-'( + 0'( 0'*+''( 0'( +(+0'( -0(<-'(

)+-''(/ +(+*-'( + *-++ + +*' *'* '(+*( +*+( 0'

@-(*-'/ 0' :+(-( ? 0' ,*-' + 0'( )'*+),*-'(/ ) '(+*( -*+(/ +0

(+ "*0:'# ? +0 + "+-(*+)0:'#.

L' )-' + +'+( )'*+),*-( @' +(* ' +' -(-< + 0'(

)'*+),*-'( +(0'+( 9'(''( +H

A+*' + +0 -)-+* )'*+),*- +( +0 +(0*' + ' +0-<

@-(*<-'.

V'0' 0' -)*'-' + *-++ 0( +(( (**-( ? + -*+'-<

(-'0 + 0' +(+'=' ? +0 '+-='>+ + 0'( )'*+),*-'(.

C(-+' + +0 -)-+* )'*+),*- (*-*?+ ' @+')-+*'

*+*+ '' +0 +('00 + @'9-0-'+( + +(')-+*.

R++ + +-(*+ 0+ + -)-+*( )'*+),*-( 9,(-( +

+9+ )-' * -''.

18





C)++ ? '()- *( 0( +<)+( + *'((--< -,*-'.

R++ +0 -)'* + +'( *+0:'( *'* + 0( '(-( -0'+(

) + (( '0-'-+(. P--0+:-' ) *+* +0 @'+ )'*+),*- +(0' 0'( (-*'-+(

90+),*-'(.

0.) FUNDAMEN$OS.

0.).( F5los@53o. A *'( + 0( :')'( :'-='( + (+ +(+*' + +(*+

?+*/ (+ 9(' + *-9?' +'0 ? ++*-')+*+ ' 0' )'-< +0 (+

0*'0/ @-(*<- ? (-'0 +0 +'. D' ' + * '+00 + 0+ '

@+(-< ? *--' + 0' (-+' + +0 +('- ? + +0 *-+). A( 0'

)'*+),*-' +( -)*'*+ '' +0 +' '' + +(+ ' 0'(

++(-'+( -'( ? + ( +*.

$' + *( + +(*'( ,*-'( *--''( ++(-*')( ' )+ ++*'

,00( ? +(*-)' '0:( +(0*'(/ *'0 )*- + 0'( -++*+( +(-+(

--( (+ +-:+ '+' )'+> + +*( ? +(( )'*+),*-(.

0.).& E45s!e8ol@>53o. T+-+ + +*' + +*+ 0( -+( +0 S-(*+)'

E'*- C0)9-' +(*, +0 + +('00' + 0' +(' 0' ''-' *-' ?

''0*-' +0 +(-* -+*-/ )+-'*+ 0' '-(--< + 0( ---( ?

)*( + 0( -++*+( +(( +'*-(/ +(+ +0 ,+' + )'*+),*-'( (+

9(' -0' + +0 +' 0' ++(-' + - 0' *+' ? 0' '-( '' '(0:' +*+)-''( @'9-0-'+( ) 0'( + (+ +-++ '0 ',0-(-(/ (*+(-(/

9(+'-</ )0'-< ? (0-< + 90+)'( )+- + +-)-+*( +

*-'.

0.)./ Peda>@>53o. L' ')+*'-< +':<:-' +0 ,+' + )'*+),*-'(/ (+

+(+*' 9'(+ + 0'( ''*+(*-'( + 0' -+*+ 00')'' +'::' '*-'.

B(' ' '*-* *-' +*+ ' 0' +'::' *'--'0. D+ 0' +(+0'

'*-' +*++ +('00' +0 +(-* -+*-/ '+( 0'( +-:+-'( + 0'

(-+'. S- +(-- + 0( '(+*( ')+*'0+( +0 ,+'.

E 0' '*'0-' (+ 9(' + +0 +' (+ '-+ + 0( -)-+*(

)'*+),*-( ++('-( '' ( +('00 -*+:'0 ? '( (+ +'+ '' ++*'

(+:-' ? (0+-' (-*'-+( ? 90+)'(. T +(* (+, (-90+ '

*'( + 0' ++-+-' + '+-='>+ (--+*+ ( + )'*+-'0+(

19





NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

+*(/ +0 *'9'> + +- ? 0' +0+-< + :. L' +0'9'-< 0'

(*-< +'*-' + )'( +*'0+( + 0+ +)-*' '0 '0) '(-)-0'

0' +'0-' (-' ? 0*'0 +0 '0 *+ -*+'*'.

0.).) Ps53ol@>53os. C) 0( -( -+(' + )' -++*+ ' 0( '0*( ?

+ 0' +0-< +0 +(')-+* -'*-0 '0 +(')-+* '0* (+ 0:' ' *'(

+ '-( +( (+(-( +'(/ +0 :')' + )'*+),*-'( *-++ '

+(**' '+'' '*+-+ ' 0'( ++(-'+( ? ++*'*-'( + +(*(

+'(. A( 9(' +0 +('00 -*+:'0 +0 +' ' *'( + 0'

)+(-< + +*( ? +(( )'*+),*-( + )' *-' ?

-++*+( :'( + )0+>-' ? :++'0-'. S+: 0'( +(**'( +0

+(')-+*/ -'( + '' ? '*+-+ ' 0'( ''*+(*-'(/ (-9-0-'+(

? ++(-'+( + '' +'.

0.).* So35ol@>53os. D+(+ * + -(*' (-0<:- ? 0*'0 0' +(+'='

+ 0'( )'*+),*-'( @' (-0' +*+ 0'( (--+( )'*-'( ? 0'( *-0-*'-(*'(

0' )'*-' '-'0 --:-' ' 0( -0<(( ? (- '0-'-+( + *- ,*-/

+*+ ' ' )'*+),*-' (+(-90+ ? *-0-*'-'/ --:-' ' 0( '*+('( ? *-(. A +(*' '+*'-< + 0' +*-+*+ *-0-*'-' (+ ')'' + 0' +*+(-< +

-*- *' -)+(-< -'0H 0' + -' ' 0' +(+0' 0( +(

)+-( *+0<:-( + +*/ 0' '00'' ? +0 +'. S (

:++'0-=' + 0' (-+' '*'0 *'(*' ( '(+-' + 0( +*( ?/

(9+ */ + 0'( '0'(/ + 0'( '*--'+( +(0'+( *--''(/ @'-+

++('- -+*- +(*' *++-' @'9-*'0 +0 (-(*+)' +'*- ' +)'++ +

+('0'( ' 0'( -'-+( *+0<:-'(.

E0 -)-+* )'*+),*- +( (-+' @? ) ' '*--' (-'0 +

+9+ *++ + +*' 0( -*++(+( ? 0' '*--' +0 - ? +0 >+. C) *'

*'+' (-'0 ++ +(+(*'( ' ' )0*-0--' + -+( + -*++(+( +

+)'+*+)+*+ (:+ ? (+ +*+=' + +0 ) '*'0.

+. FILOSOF#A DEL 2REA

L' )'*+),*-' *-0-=' 0+:'>+ +-(/ 0'/ ? -(. S+ ++ +- + +(

0' -+-' + 0'( -*++0'-+(. E(*, +(+*+/ + +0 )++/ '*' ?

--. E( ,+' + -' 0( )+-( '' ''0-='/ +-/ 00+' ' 0'

-' *' + 0 + +0 +(*-'*+ +9+ +*'(+ ? +0+-'.

E0 +( + )'*+),*-'( +9+ 00+' '0 +(*-'*+ )+-'*+ '=')-+*(

0<:-(/ ' ++-' 0 *+<- '' +('00' +*')+*+ 0 ,*- ? '(/

20





+'(' 0' )+*+ +0 +(*-'*+ ' 9(+' (-*'-+( + 0 00+' ' )+>' (

-' ? ' @'+ '*+( ' '0: + *'' +)( )++H 0' '-< +

D-(.

E0 -)-+* )'*+),*- +(0'/ +( (-+' '0:( ) +0

-)-+* *--' + *-++ + + 0( )+( ? 0'( +'-+(/ ?

*(/ ) +0 -)-+* )'*+),*- +0+)+*'0/ + +(0*' + '9'

(+--'0)+*+ '0:( +0+)+*( )-)( + 0' )'*+),*-' -(-0-'. E

:++'0 (+ (-+' + 0'( )'*+),*-'( + 0' +(+0' *-++ '+0

+(+-'0)+*+ -(*)+*'0/ + ' '*+ (+ +0+>' + +0 +('00 +

@'9-0-'+( ? +(*+='( '' +(0+ 90+)'( + 0' -' ,*-'/ '' ('

,:-0)+*+ +0 0+:'>+ (-)9<0-/ 0( +-)-+*( ? '0:-*)( ?/ *'/ + +0

+('00 +0 +(')-+* 0<:- )'0.

L' @-(*-' ' +*' + (-:0( ? (-:0( + -+('( (--+( ? -((-+( (9+

+0 -:+ ? 0' '*'0+=' + 0'( )'*+),*-'(.

El Pla!o5s8o (:-++ + 0'( )'*+),*-'( +( (-(*+)' + +'+( + @'+-(*- +(+ (-+)+/ + -++-+*+ +0 @)9+ . La !area del 8a!e89!53o es

des3?br5r esas erdades 8a!e89!53as/ ?' + + -+* (+*- +(*, ()+*-' '

+00'( ? 0'( *-++ + 9+++. E(*+ ++ + 0'( -:'( :+)*-'(/ )

0'( +'-+( ? 0'( +0'-+( :+)*-'( ( +(0*' + '0:' )'

)-(*+-('/ *-++ -+'+( + +(9-)( :' +(+= @'? *'( +

( +(=')( +(9- + 0 (+:-)(/ ? +-(*+ *( + -

(--+' ((+@')(/ ?' + 0'( )'*+),*-'( *'(-++ 0' )+*+ @)''.

El lo>535s8o (-+' + 0'( )'*+),*-'( ( ' ')' + 0' 0<:-'/ -'

-'/ + +0 )-() -:+ ? )*/ ? + ( '*+ + ' -(-0-'

-+('0 + +:-' *'( 0'( )'( + ':)+*'-<. P+ +-- 0(

+*( )'*+),*-( )+-'*+ *)-( 0<:-(/ ? +- 0( *++)'( + 0'(

)'*+),*-'(/ ? 0( *++)'( + 0' 0<:-'/ )+-'*+ +0 +)0+ + +-+(

0<:-'(. E(*' -+*+ ++ 0' +-(*+-' + (H 0' 0<:-' +*-' ? 0'

-*-'.

L' +*-' 9(' 0' @++-' + 0'( -+'( +*+ ( '*+ + +)-('(

:++'0+( '' 00+:' ' 0(-+( +(+-'(. L' -*-' ' 0'

@++-' + 0'( -+'( +0 ) +'0 '*+ + 9(+'-+( +(+-'(

'' 00+:' ' 0(-+( :++'0+( + ' +-' ' *'( + 0' ++-+-' ?

*'(*'-+( +)-'(.

21





NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

F+:+ @-= :'+( '*+( ' 0 + @? +)( ) 0<:-' )'*+),*-'(H

C,00 (--'0/ +:0'( '' +0 +)0+ + 0( '*--'+( -+('0+( ?+-(*+-'0+(/ ? +0 ',0-(-( 0<:- +0 )* + +9' + --< )'*+),*-'.

El or8al5s8o ++ + 0'( )'*+),*-'( ( ' +'-< + 0' )+*+

@)'' ? (-(*+ (0')+*+ + '-)'(/ +---+( ? *++)'( )

++(-+( )'0+( + (+ +(')90' ' *'( + ()90(/ + (

)'-0'( )9-'( -+*'( +:0'(. L' +' + 0' )'*+),*-'

)'0-(*' '-' + 0' )+*+ @)'' + + 0'( (*-+( + +00'

+'0-=' -*+')+*+/ (- + 0' @++-' + 0'( +:0'( +0 >+: (-)9<0-

+(+*-. L'( +)(*'-+( +9+ (+ -:('(/ 9'(''( -')+*+ + 0'(

+:0'( +0 >+: +*- +(+*- + -++-+*+)+*+ + 0'( -),:++( +

'(-+)( 0( *)-( ? 0'( +0'-+(.

El 3os!r?3!55s8o (-+' + 0'( )'*+),*-'( ( ' +'-< + 0' )+*+

@)''/ ? + -')+*+ *-++ +-(*+-' +'0 '+00( 9>+*( )'*+),*-(

+ ++ (+ (*-( +-)-+*( --*( ' '*- 9>+*( -)-*-(.E0 (**--() )'*+),*- +( )? @++*+ 0' +'::' '*-' ? (+

'?' + 0' (-0:' :+*-' (+ -*++(' 0'( --+( + 0'( '0+( 0'

)+*+ +'0-=' 0' (*-< + 0( +*( )'*+),*-(/ 0' )' )

0( :'-=' + +(**'( ? 0' '0-'-< + 0+( '. N 9'(*' + +0

)'+(* @'?' @+@ 0'( (*-+( )+*'0+(/ '' +(*-'*+ ++(-*' ' (

+= +'0-='0'.

E 0' '*'0-' +0 '+0 + 0' -0(' + 0'( )'*+),*-'( *-' (-+/ +(+

0+:/ ' +*' + 0' '*'0+=' + 0'( )'*+),*-'(/ + +(+ 0'(

+(+*-'( )@ ),( ')0-'( + 0'( 0'*+''( 0'( +(+0'( -0(<-'(

)+-''(/ +(+*-'( + *-++ + +*' *'* '(+*( +*+( 0'

@-(*-'/ 0' :+(-( ? 0' ,*-' + 0'( )'*+),*-'(/ ) '(+*( -*+(/ +0

(+ "*0:'# ? +0 + "+-(*+)0:'#.

L' )-' + +'+( )'*+),*-( @' +(* ' +' -(-< + 0'(

)'*+),*-'( +(0'+( 9'(''( +H

A+*' + +0 -)-+* )'*+),*- +( +0 +(0*' + ' +0-<

@-(*<-'.

V'0' 0' -)*'-' + *-++ 0( +(( (**-( ? + -*+'-<

(-'0 + 0' +(+'=' ? +0 '+-='>+ + 0'( )'*+),*-'(.

22





C(-+' + +0 -)-+* )'*+),*- (*-*?+ ' @+')-+*'

*+*+ '' +0 +('00 + @'9-0-'+( + +(')-+*.

R++ + +-(*+ 0+ + -)-+*( )'*+),*-( 9,(-( ++9+ )-' * -''.

C)++ ? '()- *( 0( +<)+( + *'((--< -,*-'.

R++ +0 -)'* + +'( *+0:'( *'* + 0( '(-( -0'+(

) + (( '0-'-+(.

P--0+:-' ) *+* +0 @'+ )'*+),*- +(0' 0'( (-*'-+(

90+),*-'(

1. ES$ANDARES DE CON$ENIDO

DE PRIMERO A $ERCER "RADO

A0 *+)-' *+4+4 :'

PENSAMIEN$O NUMERICO SIS$EMAS NUMERICOS.

• R+161=1 (-:6-'51( 5+0 6)+41 +6 5-B+4+6*+( 16*+*( ")+5--<6/ 16*+1/

1)7'4'-<6/ 15-'-<6/ 01'0-='-<6 +6*4+ *(#.

• D+(4-91/ 1)7'41 ? 3'6*-1 (-*3'-16+( 16 6)+41(/ +6 5-B+4+6*+( 16*+*1( ?

16 5-8+4('( 4+74+(+6*'-16+(.

• D+(4-91 (-*3'-16+( + 4+23-+4+6 +0 ( + )+5-5'( +0'*-'(.

• D+(4-91 (-*3'-16+( + )+5--<6 3*-0-='651 B4'-16+( )+(.

• U(1 4+74+(+6*'-16+( 74-6-7'0)+6*+ 164+*'( ? 7-*<4-'( 7'4' +70-'4 +0 8'014 +

71(--<6 + +0 (-(*+)' + 63)+4'-<6 +-)'0.

• U(1 4+74+(+6*'-16+( 74-6-7'0)+6*+ 164+*'( ? -*<4-'( 7'4' 4+'0-='4

+23-8'0+6-'( + 36 6)+41 + 0'( 5-B+4+6*+( 36-5'5+( 5+0 (-(*+)' +-)'0.

• R+161=1 7417-+5'5+( + 0( 6)+41( "(+ 7'4/ (+ -)7'4/ +*.# ? 4+0'-16+(

+*+ +001( "(+ )'?14 23+/ (+ )+614 23+/ (+ )0*-701 5+/ (+ 5-8-(-90+ 714/ +*.#

+ -B+4+6*+( *+*(.

• R+(3+081 ? B14)301 74190+)'( + (-*3'-16+( '5-*-8'( + 1)71(--<6 ? 5+

*'()'-<.

• R+(3+081 ? B14)301 74190+)'( +6 (-*3'-16+( 5+ 8'4-'-<6 -'0.

• U(1 5-8+4('( +(*4'*+:-'( + ,0301 "+(7+-'0)+6*+ ,0301 )+6*'0# ? +

+(*-)'-<6 7'4' 4+(108+4 74190+)'( + (-*3'-16+( '5-*-8'( ? )0*-0-'*-'(.

23



C O M P E T E N C I A S

E N M A T E M Á T I C A S



NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

• I5+6*-1/ (- ' 0' 03= + 01( 5'*1( + 36 74190+)'/ 01( +(30*'51( 19*+6-51( (16 1 61

'='90+(.

• I5+6*-S1 4+:30'4-5'5+( ? 7417-+5'5+( + 0( )+( 3*-0-='651 5-B+4+6*+(

-6(*43)+6*1( 5+ ,0301 "'030'51 4'(/ ,9'1(/ 90123+( )30*-9'(+/ +*.#.

PENSAMIEN$O ESPACIAL SIS$EMAS "EOM<$RICOS.

• D-B+4+6-1 '*4-93*1( ? 7417-+5'5+( + 19>+*1( *4-5-)+6(-'0+(.

• D-93>1 ? 5+(4-91 3+471( :34'( *4-5-)+6(-16'0+( + 5-(*-6*'( 71(--16+( ?

*')'(.• R+161=1 61-16+( + @14-=16*'0-5'5/ 8+4*-'0-5'5/ '4'0+0-()1 ?

7+47+65-30'4-5'5 + 5-(*-6*1( 16*+*1( ? ( 165--<6 4+0'*-8' 16 4+(7+*1 '

5-B+4+6*+( (-(*+)'( + +++-'.

• R+74+(+6*1 +0 +(7'-1 -4365'6*+ 7'4' +(*'90++4 +0'-16+( +('-'0+(.

• R+161=1 ? '70-1 *4'(0'-16+( ? :-41( (194+ 36' :34'(.

• R+161=1 ? 8'0141 (-)+*4'( + 5-(*-6*1( '(7+*1( +0 '4*+ ? +0 -(+.

• R+161=1 16:43+6-' ? (+)+>'6=' +*+ :34'( "')70-'4/ +-#.

• R+'0-=1 16(*43-16+( ? 5-(+1( 3*-0-='651 3+471( ? :'( :+1)A*4-'(

*4-5-)+6(-16'0+( ? 5-93>1( :34'( :+1)A*4-'( 9--)+(-'0+(.

• D+('441001 @'9-0-5'5+( 7'4' 4+0'-16'4 5-4+-<6/ 5-(*'6-' ? 71(--<6 +6 +0 +('-

PENSAMIEN$O ME$RICO SIS$EMA DE MEDIDAS

• R+161=1 +6 01( 19>+*1( 7417-+5'+( '*4-93*1( 23+ (+ 73+5'6 )+5-4 "016:-*35/

,4+'/ 8103)+6/ '7'-5'5/ 7+(1 ? )'('# ?/ +6 01( +8+6*1(/ (3 '-<.

• C1)7'41 ? 145+61 19>+*1( +(+* ' '*4-93*1( )+-90+(.

• R+'0-=1 ? 5+(4-91 741+(1( 5+ )+5--<6 '*+( '49-*4'4-1( ? '0:361(

+(*'65'4-='51(/ 5+ '3+451 '0 *+*.

• A6'0-=1 ? +70-1 (194+ 0' 7+4*-6+6-' + 7'*416+( + -6(*43)+6*1( + 741+(1( 5+

)+--<.

• R+'0-=1 +(*-)'-16+( + )+5-5'( 4+23+4-5'( + 0' 4+(103-<6 + 90+)'(

+0'*-( 7'4*-30'4)+6*+ ' 0' 8-5' (1-'0/ +16<)-' ? + 0'( -+-'(.

• R+161=1 +0 3(1 5+ 0'( )':6-*35+( ? (( 36-5'5+( + )+5-5' + (-*'-16+(

'5-*-8'( ? )0*-0-'*-'(

PENSAMIEN$O ALEA$ORIO SIS$EMA DE DA$OSG

• C0'(-1 ? 14:'6-=1 5'*1( 5+ '3+451 ' 3'0-5'5+( ? '*4-93*1( ? 01( +(+*1 +6

24





*'90'(.

• I*++* 3'0-*'*-8')+6*+ '*( 4+B+4-51( ' (-*3'-16+( +0 +* +(0' .

• D+(4-91 (-*3'-16+( ++*( ' 7'4*-4 5+ 36 16>36*1 5+ '*(.• R++(+* '*( +0'*-( ' )- +6*1461 3('651 19>+*1( 164+*1(/ 7-*1:4')'(

? 5-':4')'( 5+ 9''(.

• I5+6*-S1 4+:30'4-5'5+( ? *++-'( +6 36 16>36*1 5+ '*(.

• E70-1 +(+ )- +7+4-+6-'Q 0' 71(-9-0-5'5 -)71(-9-0-5'5 + 44+6-' 5+

+8+6*1( *--'(.

• P4+5-:1 (- 0' 71(-9-0-5'5 5+ 1344+6-' + 36 +8+6*1 +( )'?14 23+ 0' + *.

• R+(3+081 ? B14)301 74+:36*'( + 4+23-+4'6 '' ( (103-<6 10+-16'4 ?

'6'0-='4 '*( +0 +* <-).

PENSAMIEN$O ARIACIONAL SIS$EMAS AL"EBRAICOS ANAL#$ICOS.

• R+161=1 ? 5+(4-91 4+:30'4-5'5+( ? 7'*416+( + 5-(*-6*1( 16*+*( "63)A4-1/

:+1)A*4-1 )3(-'0/ +6*4+ *(#.

• D+(4-91 3'0-*'*-8')+6*+ (-*3'-16+( 5+ ')9-1 ? 8'4-'-<6 3*-0-='651 +0 0+6:3'>+

6'*34'0/ 5-93>1( ? :4,B-'(.

• R+161=1 ? :+6+41 +23-8'0+6-'( +*+ ++(-+( )-'( ? 5+(4-91

<)1 ')9-'6 01( ()9101( '3623+ +0 8'014 (-:' -:3'0.

• C16(*43?1 (++-'( 63)A4-'( ? :+1)A*4-'( 3*-0-='651 7417-+5'5+( + 01(

6)+41( ? + 0'( :34'( :+)*-'(.

DE CUAR$O A QUIN$O

• A0 *+)-' 23-6*1 :'

PENSAMIEN$O NUMERICO SIS$EMAS NUMERICOS.

• I6*+474+*1 0'( B4'-16+( + 5-B+4+6*+( 16*+*1(H (-*'-16+( 5+ )+5--<6/

4+0'-16+( 7'4*+ *151/ 1-+6*+/ '=6+( ? -+(.

•

I5+6*-1 ? 3(1 )+5-5'( 4+0'*-8'( +6 5-(*-6*1( *+*(.• U*-0-=1 0' 61*'-<6 5+-)'0 7'4' +74+('4 B4'-16+( +6 -B+4+6*+( 16*+*1( ?

4+0'-161 +(*'( 51( 61*'-16+( 0' 5+ 01( +*'>+(.

• J3(*-1 +0 8'014 5+ 71(--<6 +6 +0 (-(*+)' 5+ 63)+4'-<6 5+-)'0 + 4+0'-<6 16 +0

16*+1 4+344+6*+ + 36-5' +(.

• R+(3+081 ? B14)301 74190+)'( 3?' +(*4'*+:-' 5+ (103-<6 4+23-+4' + 0'( 4+0'-16+(

? 7417-+5'5+( + 01( )+( 6'*34'0+( ? (3( +'-+(.

25







NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

• R+(3+081 ? B14)301 74190+)'( + (-*3'-16+( '5-*-8'( + 1)71(--<6/

*4'6(B14)'-<6/ 1)7'4'-<6 + -:'0'-<.

• R+(3+081 ? B14)301 74190+)'( + (-*3'-16+( + 741714 -16'0-5'5 5-4+*'/ -68+4(' ?

74153*1 5+ )+-'(.

• I5+6*-1 0' 71*+6-'-<6 ? 0' 4'5-'-<6 +6 16*+*1( )'*+),*-1( ? 61

)'*+),*-(.

• M15+01 (-*3'-16+( + 5+7+65+6-' )+5-'6*+ 0' 741714 -16'0-5'5 5-4+*' + -+('.

• U(1 5-8+4('( +(*4'*+:-'( + ,0301 ? + +(*-)'-<6 '' 4+(108+4 74190+)'( +

(-*3'-16+( '5-*-8'( ? )30*-70-'*-8'(.

• I5+6*-1/ + +0 16*+*1 + 36' (-*3'-<6/ 0' 6++(-5'5 + ,0301 +'*1 '741-)'51 ? 0 4'=16'90+ + 0( 4+(30*'51( 9*+-(.

• J3(*-1 4+:30'4-5'5+( ? 7417-+5'5+( 5+ 01( 6)+41(/ (( 4+0'-16+( ? +'-+(

• PENSAMIEN$O ESPACIAL SIS$EMAS "EOM<$RICOS.

• C1)7'41 ? 0'(-S1 19>+*1( *4-5-)+6(-16'0+( + '3+451 16 1)716+6*+( "'4'(/

0'51(# ? -+'+(.

• C1)7'41 ? 0'(-1 :34'( 9-5-)+6(-16'0+( + '3+451 (( 1)716+6*+(

",6:301(/ 8A4*-+(# ? '4'*+4(*-'(.

• I5+6*-1/ 4+74+(+6*1 ? 3*-0-=1 ,6:301( +6 :-41(/ '9+4*34'(/ -60-6'-16+(/ :34'(/

736*'( ? +(23-6'( +6 (-*3'-16+( +(*,*-'( ? -,)-'(.

• U*-0-=1 (-(*+)'( + 1145+6'5'( 7'4' +(7+-'4 01'0-='-16+( ? 5+(4-9-4

4+0'-16+( +('-'0+(.

• I5+6*-1 ? >3(*-S1 4+0'-16+( 5+ 16:43+6-' ? (+)+>'6=' +6*4+ :34'(.

• C16(*43?1 ? 5+(1)716:1 :34'( ? (<0-51( ' 7'4*-4 5+ 5--16+( ''(.

• C16>+*341 ? 8+4-1 01( 4+(30*'51( + '70-'4 *4'6(B14)'-16+( ' :34'( +6 +0 70'61

7'4' 16(*43-4 -(+(.

• C16(*43?1 19>+*1( *4-5-)+6(-16'0+( ' 7'4*-4 + ++(+*'-16+( 9-5-)+6(-16'0+( ?

73+51 4+'0-='4 +0 741+(1 *4'4-1 +6 16*+*1( 5+ '4*+/ 5-(+1 ? '-*+*'


• D-B+4+6-1 ? 145+61/ + 19>+*1( ? +8+6*1(/ 7417-+5'5+( '*4-93*1( + (+

73+5'6 )+5-4 "016:-*35+(/ 5-(*'6-'(/ ,4+'( 5+ (37+4S-+(/ 810)+6+( + 3+471(

(<0-51(/ 810)+6+( 5+ 023-51( ? '7'-5'5+( + 4+-7-+6*+(F +(( ? )'(' +

3+4 71( (<0-51(F 534'-<6 + +8+6*1( 741+(1( ')70-*35 5+ ,:0(#.

• S+0+-161 36-5'5+(/ *'* 8+6-16'0+( ) +(*'65'4-='5'(/ '7417-'5'(

'' -++*+( )+5--+(.

• U*-0-=1 ? >3(*-1 +0 ( + 0' +(*-)'-< '' +(0+ 74190+)'( 4+0'*-81( ' 0'

8-5' (1-'0/ +16<)-' ? + 0'( -+6-'(/ 3*-0-='651 4'6:1( 5+ '-'-<.

26





• U*-0-=1 -++*+( 741+5-)-+6*1( + ,0301 7'4' @'00'4 +0 ,+' + 0' (37+4S-+

+*+4-14 ? +0 8103)+6 + '0:361( 3+471( (<0-(.

• J3(*-1 4+0'-16+( 5+ 5+7+65+6-' +0 ,+' ? 8103)+6/ 4+(7+*1 ' 0'(5-)+6(-16+( 5+ :34'( ? (<0-(.

• R+161=1 +0 ( + '0:36'( )':-*+( "016:-*35/ ,+'/ 8103)+6/ '7'-5'5/

+( ? )'('/ 534'-<6/ 4'7-5+=/ *+)7+4'*34'# ? + '0:36'( + 0'( 36-5'5+( +

(+ (' '' )+- '6*-5'5+( + 0' )':6-*35 4+(7+*-8' + (-*3'-16+( '5-*-8'(

? )0*-0-'*-'(.

• D+(4-91 ? '4:3)+6*1 4+0'-16+( +6*4+ +0 7+4)+*41 ? +0 ,4+' 5+ :34'( 5-B+4+6*+(/

3'651 (+ >' 36' + +(*'( )+-'(

• PENSAMIEN$O ALEA$ORIO SIS$EMA DE DA$OSG

• R+74+(+6*1 '*( (' *'90'( ? :4,'( "7-*1:4')'(/ :4,'( + 9'44'(/

5-':4')'( + 06+'(/ 5-':4')'( -0'+(#.

• C1)7'41 5-B+4+6*+( 4+74+(+6*'-16+( 5+0 )-()1 16>36*1 5+ '*(.

• I*++* -6B14)'-<6 74+(+6*'5' + *'90'( ? :4,S'(. "7-*1:4')'(/ :4,'( +

9'44'(/ 5-':4')'( + 06+'(/ 5-':4')'( -0'+(#.• C16>+*341 ? 716:1 ' 743+9' 74+5--+( '+' + 0' 71(-9-0-5'5 + 1344+6-'

5+ ++*(.

• D+(4-91 0' )'6+4' 1)1 '++ 5-(*4-93-4(+ 0( 5-(*-6*1( '*( + 16>36*1

+ +00( ? 0' 1)7'41 16 0' )'6+4' 1)1 (+ 5-(*4-93?+6 +6 1*41( 16>36*1( 5+

'*(.

• U(1 + -6*+474+*1 0' )+5-' " )+-# ? 0' )+5-'6' ? 1)7'41 0 + --'.

•R+(3+081 ? B14)301 74190+)'( ' 7'4 *- + 16>36*1 + '*( 7418+6-+6*+( 5+

19(+48'-16+(/ 16(30*'( 1 ++-)+*(


• D+(4-91 + -*++* 8'4-'-16+( 4+74+(+6*'5'( +6 :,(.

•

P4+5-:1 '*+( + 8'4-'-<6 + 36' (+3+6-' 63)A4-'/ :+1)A*4-' 1 :,'.• R+74+(+6*1 ? 4+0'-161 '*+( 63)A4-1( 16 *'90'( ? 4+:0'( 8+4 9'0+(.

• A6'0-=1 ? +70-1 4+0'-16+( + +++-' +*+ '6*-5'5+( + 8'4'6 +6 +0

*-+)71 16 -+4*' 4+:30'4-5'5 + (-*3'-16+( +16<)-'(/ (1-'0+( ? 5+ 0'( -+6-'(

6'*34'0+(.

• C16(*43?1 -:3'05'5+( ? 5+(-:3'05'+( 63)A4-'( ) ++(+*'-<6 +

4+0'-16+( +*+ 5-(*-6*1( '*(.

27





NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

DE SE$O A S<P$IMO "RADO

A0 *+)-' (A7*-)1 :'

PENSAMIEN$O NUMERICO SIS$EMAS NUMERICOS

• R+(3+081 ? B14)301 74190+)'( + 16*+*1( + )+5-5'( 4+0'*-8'( ? 5+ 8'4-'-16+( +6

0'( )+-'(.

• U*-0-=1 6)+41( 4'-16'0+(/ + (( 5-(*-6*'( +74+(-16+( "B4'-16+(/ 4'=16+(/

5+-)'0+( 714+6*'>+(# 7'4' +(108+4 74190+)'( +6 16*+*1( 5+ )+-'.

• J3(*-1 0' +*+6(-<6 + 0' 4+74+(+6*'-<6 710-61)-'0 +-)'0 3(3'0 + 01( 6)+41(

6'*34'0+( ' 0' 4+74+(+6*'-<6 5+-)'0 3(3'0 + 0( 6)+41( 4'-16'0+(/ 3*-0-='651

0'( 7417-+5'5+( 5+0 (-(*+)' 5+ 63)+4'-<6 +-)'0.

• R+161=1 ? :+6+4'0-=1 7417-+5'5+( 5+ 0'( 4+0'-16+( +*+ 6)+41( 4'-16'0+(

"(-)A*4-'/ *4'6(-*-8'/ +*.# ? + 0'( 17+4'-16+( +6*4+ +001( "16)3*'*-8'/ '(1-'*-8'/

+*.# +6 5-B+4+6*+( *+*(.

• R+(3+081 ? B14)301 74190+)'( 3*-0-='651 7417-+5'5+( 9,(-'( 5+ 0' *+14' 5+ 6)+41(/

1)1 0'( 5+ 0' -:3'05'5/ 0'( + 0'( 5-(*-6*'( B14)'( + 0' 5+(-:3'05'5 ? 0'( + 0'

'--<6/ (3(*4'-<6/ )30*-70-'-<6/ 5-8-(-<6 ? *+-'-<.

• J3(*-S1 741+5-)-+6*1( '4-*)A*-1( 3*-0-='651 0'( +0'-16+( ? 7417-+5'5+( 5+ 0'(

+'-+(.

• F14)301 ? 4+(3+081 74190+)'( + (-*3'-16+( '5-*-8'( ? )30*-70-'*-8'(/ +6

5-B+4+6*+( 16*+*1( ? 51)-6-1( 63)A-(.

• R+(3+081 ? B14)301 74190+)'( 3?' (103-<6 4+23-+4+ + 0' 71*+6-'-<6 1

'-'-<.

• J3(*-1 +0 3(1 + 4+74+(+6*'-16+( ? 741+5-)-+6*1( + (-*3'-16+( 5+

741714-16'0-5'5 5-4+*' + -+('.

• J3(*-1 0' 7+4*-6+6-' 5+ 36 ,0301 +'*1 1 '741-)'51 + 0' (103-<6 + 36

74190+)' ? 01 4'=16'90+ 61 + 0'( 4+(73+(*'( 9*+-'(.

• E(*'90+=1 16>+*34'( (194+ 7417-+5'5+( ? 4+0'-16+( + 01( 6)+41(/ 3*-0-='651

'030'514'( 1 )*'+(.

• J3(*-S1 0' +0+-<6 5+ )A*151( + -6(*43)+6*1( 5+ ,0301 +6 0' 4+(103-<6 5+

90+)'(.

• R+161=1 '4:3)+6*1( 1)9-6'*14-1( 1)1 @+44')-+6*' 7'4' -6*+474+*'-<6 5+

(-*3'-16+( 5-8+4('( 5+ *+

28








• R+74+(+6*1 9>+*( *4-5-)+6(-16'0+( +(+ -++*+( 71(--16+( ? -(*'(.

• I5+6*-1 ? 5+(4-91 :34'( ? 3+471( :+6+4'51( 714 14 *+( 4+*1( ? *4'6(8+4('0+(

5+ 19>+*1( *--)+(-'0+(.

• C0'(-1 710:161( +6 4+0'-<6 16 (3( -+'+(.

• P4+5-:1 ? 1)7'41 0( 4+(30*'51( + '70-'4 *4'6(B14)'-+( 4:-5'(

"*4'(0'-16+(/ 41*'-16+(/ 4+T+-16+(# ? @1)1*+-'( "')70-'-16+( ?

4+53-16+(# (9+ :34'( 9-5-)+6(-16'0+( +6 (-*3'-16+( )'*+),*-'( ? +6 +0

'*+.

• R+(3+081 ? B14)301 74190+)'( + -681034+6 4+0'-16+( ? 7417-+5'5+( +(+)+>'6=' ? 16:43+6-' 3('651 ++(+6*'-16+( -('0+(.

• R+(3+081 ? B14)301 74190+)'( 3('651 )15+01( :+1)A*4-(.

• I5+6*-1 '4'*+4(*-'( 5+ 01'0-='-<6 5+ 19>+*1( +6 (-(*+)'( 5+ 4+74+(+6*'-<6

'4*+(-'6' ? :+:,'


• U*-0-=1 *6-'( ? @+44')-+6*'( '' 0' 16(*43-<6 + :34'( 70'6'( ? 3+471( 16

)+5-5'( ''(.

• R+(3+081 ? B14)301 74190+)'( + -681034+6 '*+( +('0'+( "- (+1 5+

)'23+*'(/ )''(#.

• C'0301 ,4+'( ? 810)+6+( ' *'( + 1)71(--<6 ? 5+(1)71(--<6 5+ :34'( ?

+(.

•I5+6*-1 4+0'-16+( +6*4+ 5-(*-6*'( 36-5'5+( 3*-0-='5'( 7'4' )+5-4 '*-5'5+( 5+ 0'

)-()' )':-*.

• R+(3+081 ? B14)301 74190+)'( + 4+23-+4+6 *A6-'( 5+ +(*-)'-<


• C1)7'41 + -6*+474+*1 '*( 7418+6-+6*+( 5+ 5-8+4('( B3+6*+( "+('/ +-(*'(/

*+0+8-(-<6/ +7+4-)+6*1(/ 16(30*'(/ +*+-(*'(#.• R+161=1 0' 4+0'-<6 +*+ 36 >36*1 5+ 5'*1( ? (3 ++(+*'-<.

• I6*+474+*1/ 74153=1 ? 1)7'41 + 74+(+6*'-16+( :4,S'( '5+3'5'( ''

+(+*' -+(( *-( + 5'*1(. "5-':4')'( + 9'44'(/ 5-':4')'( -0'+(.#

• U( )+5-5'( + *+65+6-' +6*4'0 ")+5-'/ )+5-'6'/ )15'# 7'4' -6*+4 +*'

1)714*')-+6*1 + >36*1 5+ '*(.

• U(1 )15+01( "5-':4')'( + ,4910/ +>+)701# 7'4' 5-(3*-4 ? ++- 71(-9-0-5'5

29





NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

+ 1344+6-' + ++*.

• C16>+*341 '+' +0 4+(30*'51 + +7+4-)+6*1 '0+'*- 3('651

741714-16'0-5'5 ? 61-16+( 9,(-'( 5+ 9'9-0-'.• R+(3+081 ? )0 90+)'( ' 7'4*-4 + 16>36*1 + 5'*1( +(+*'(

+ *'90'(/ 5-':4')'( + 9'44'(/ 5-':4')'( -0'+(.

• P4+5-:1 ? >3(*-1 4'=16')-+6*1( ? 0(-+( (' -6B14)'-<6 +(*'(*-'.


• D+(4-91 ? 4+74+(+6*1 (-*3'-16+( + 8'4-'-<6 4+0'-16'651 5-B+4+6*+(

4+74+(+6*'-16+( "5-':4')'(/ ++(-+( +9'0+( :+6+4'0-=' 5'( ? *'90'(#.

• R+161=1 +0 16>36*1 + 8'014+( 5+ '5' 36' 5+ 0'( '6*-5'5+( 8'4-'90+( 0-:'5'(

+*+ ( + (-*3'-16+( 164+*'( 5+ ')9-1 "'-'-<#.

• A6'0-=1 0'( 7417-+5'5+( + +0'-< (-*-' ? 6+:'*-8' +*+ 8'4-'90+(/ +

8'4-'-<6 0-6+'0 + 741714-16'0-5'5 5-4+*' ? + 714-16'0-5'5 -68+4(' +

16*+*1( '4-*)A*-1( ? :+)*-(.

• U*-0-=1 )*151( -6B14)'0+( "+('?1 ? +4414 / 1)70+)+6*'-<6# + 0' (103-<6 5+

+'-+(.

• I5+6*-S1 0'( '4'*+4(*-'( + 0'( 5-8+4('( :4,S'( '4*+(-'6'( "+ *(/

16*-63'(/ B14)'5'( (+:)+6*1(/ +*.# + 4+0'-<6 16 0' (-*3'-<6 23+

++(+*'

DE OC$AO A NOENO "RADO

A0 *+)-' (A7*-)1 :'


• U*-0-=1 6)+41( 4+'0+( + (( 5-B+4+6*+( 4+74+(+6*'-16+( ? +6 5-8+4(1(

*+*(.

• R+(3+081 74190+)'( ? (-)70-1 ,0301( 3('651 7417-+5'5+( ? 4+0'-16+( 5+ 01(

6)+41( 4+'0+( ? 5+ 0'( 4+0'-16+( ? 17+4'-16+( +6*4+ +00(.

• U*-0-=1 0' 61*'-<6 -+6*' 7'4' 4+74+(+6*'4 )+5-5'( + '6*-5'5+( 5+ 5-B+4+6*+(

)':-*+(.

• I5+6*-1 ? 3*-0-=1 0' 71*+6-'-<6/ 0' 4'5-'-<6 ? 0' 01:'4-*)'-<6 7'4' 4+74+(+6*'4

(-*3'-16+( )'*+),*-'( ? )'*+),*-'( ? 7'4' 4+(108+4 90+)'(

30








•C16>+*341 ? 8+4-1 7417-+5'5+( 5+ 16:43+6-'( ? (+)+>'6='( +*+ :34'(

9-5-)+6(-16'0+( ? +*+ 19>+*1( *--)+6(-16'0+( +6 0' (103-<6 5+ 90+)'(.

• R+161=1 ? 16*4'(*1 7417-+5'5+( ? 4+0'-16+( :+1)A*4-'( 3*-0-='5'( +6

5+)1(*4'-<6 5+ *+14+)'( 9,(-1( "P-*,:14'( ? T'0+(#.

• A70-1 ? >3(*-S1 4-*+4-1( + 16:43+6-'( ? (+)+>'6=' +*+ *4-,6:301( + 0'

4+(103-<6 ? B14)30'-<6 + 90+)'(.

• U(1 4+74+(+6*'-16+( :+1)A*4-'( 7'4' 4+(108+4 ? B14)30'4 74190+)'( +6 0'(

)'*+),*-'( ? +6 1*4'( -(-0-'(


• G+6+4'0-=1 741+5-)-+6*1( + ,0301 8,0-51( 7'4' +616*4'4 +0 ,+' + 4+:-16+(

70'6'( ? +0 8103)+6 + (<0-(.

• S+0+-161 ? ( *-'( + -(*)+*( '' )+- 016:-*35+(/ ,+'( +

(37+4S-+(/ 810)+6+( ? ,6:301( 6-8+0+( + 74+-(-<6 '-'(.

•

J3(*-1 0' 7+4*-6+6-' + 3*-0-='4 36-5'5+( 5+ )+5-5' +(*'65'4-='5'( +6 (-*3'-16+(*1)'5'( 5+ 5-(*-6*'( -+-'(.


• R+161=1 <)1 5-B+4+6*+( )'6+ '( + 74+(+6*'-<6 + -6B14)'-<6 73+5+6

14-:-6'4 5-(*-6*'( -*++*'-+(.

• I*++* '6'0*-' ? 4*-')+6*+ -6B14)'-<6 +(*'5(*-' 7418+6-+6*+ + 5-8+4('(

B3+6*+( "74+6('/ 4+8-(*'(/ *+0+8-(-<6/ +7+4-)+6*1(/ (30*'(/ +*+-(*'(.

• I*++* ? 3*-0-=1 +*( + )+5-'/ )+5-'6' ? )15' ? +70--*1 (3(

5-B+4+6-'( +6 5-(*4-93-16+( + 5-(*-6*' 5-(7+4(-<6 ? '(-)+*'.

• S+0+-161 ? ( '0:361( )A*151( +(*'5(*-1( '5+3'51( '0 *- + 74190+)'/

+ -6B14)'-<6 ? '0 6-8+0 + 0' +('0' + 0' 23+ +(*' (+ ++(+6*' "61)-6'0/ 145-6'0/

5+ -6*+48'01 1 5+ '=<#.

• C1)7'41 4+(30*'51( + +7+4-)+6*( '0+'*-( 0( 4+(30*'51( 74+8-(*1( 714

36 )15+01 )'*+),*-1 9'9-0(*-'.

• R+(3+081 ? B14)301 74190+)'( (+0+-16'651 -6B14)'-<6 4+0+8'6*+ + 16>36*1(

+ 5'*1( 7418+6-+6*+( + B3+6*+( 5-8+4('(. "74+6('/ 4+8-(*'(/ *+0+8-(-<6/

+7+4-)+6*1(/ (30*'(/ +*+-(*'(#.

• R+161=1 *+65+6-'( + (+ +(+*' + 16>36*1( + 8'4-'90+(

+0'-''(.

• C'00 7419'9-0-5'5 + +8+6*1( (-)0+( (' )*( 5-8+4(1( "0-(*'51(/

31





NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

5-':4')'( + ,4910/ *-'( 5+ *+#.

• U(1 16+7*1( 9,(-1( 5+ 7419'9-0-5'5 "+(7'-1 )3+(*4'0/ +8+6*1/ -65+7+65+6-'/

+*.#.


• I5+6*-S1 4+0'-16+( +*+ 7417-+5'5+( 5+ 0'( :4,'( ? 7417-+5'5+( 5+ 0'(

+3'-16+( '0:+9'-'(.

• C16(*43?1 +74+(-16+( '0:+94'-'( +23-8'0+6*+( ' 36' +74+(-<6 '0:+94'-' ''.

• U(1 741+(1( -653*-81( ? 0+6:3'>+ '0:+94'-1 7'4' B14)30'4 ? 716+4 ' 743+9'

>+*'(.• M15+01 (-*'-+( + 8'4-'-<6 16 B36-16+( 0-<)-'(.

I5+6*-S1 5-B+4+6*+( )A*151( '' (103-16'4 (-(*+)'( + +3'-16+( 0-+'0+(.

• A6'0-=1 0( 741+(1( -6S6-*1( + (39?'+6 + 0'( 61*'-16+( 5+-)'0+(.

• I5+6*-1 ? 3*-0-=1 5-B+4+6*+( )'6+ '( + 5+6-4 ? )+5-4 0' 7+65-+6*+ + 36' 348'

23+ 4+74+(+6*' + +0 70'61 '4*+(-'61 (-*3'-16+( + 8'-'-<.

• I5+6*-1 0' 4+0'-<6 +6*4+ 01( ')9-1( +6 01( 7'4,)+*41( 5+ 0' ++(+6*'-<6

'0:+94'-' + 36' B')-0-' + B36-16+( ? 0( ')9-1( + 0'( :4,'( 23+ 0'(

++(+*'.

• A6'0-=1 + 4+74+(+6*'-16+( :4,'( '4*+(-'6'( 01( 1)714*')-+6*( + ')9-1

+ B36-16+( +(+'( 7+4*+6+-+6*+( ' B')-0-'( + B36-16+( 710-6<)-'(/

4'-16'0+(/ +716+6-'0+( ? 0:'*)-'(

DE DECIMO F UNDECIMO

A0 *+4)-6'4 365-)1 :4'51

NIEL DE (' A ((


A'0-=', ++(+*'-+( +-)'0+( + 0( )+( +'0+( ''

-++-' +*+ '-'0+( + -'-'0+(.

R++, 0' +(-' + -)0+*-* + 0( )+( '-'0+( ' *'(

+ )*( )-(/ :+)*-( ? '0:+9'-(.

32





C)'', ? *'(*', 0'( -+'+( + 0( )+( "+*+(/

'-'0+(/ +'0+(# (( +0'-+( ? +'-+( "(-(*+)'( )-(#.

U*-0-=', ':)+*( + 0' *+' + )+( '' >(*--' +0'-+( +

-0' )+( '*'0+(.

E(*'90++, +0'-+( ? -++-'( +*+ -++*+( *'-+( +

)+( +'0+( '' +-- (9+ ( ( + ' (-*'-< ''.


I+*--', 0'( -+'+( + 0'( '( + 0( 9+( 9*+-( )+-'*+

*+( "0:-*-'0 ? *'(+('0# + ? -0-.

I+*--', ''*+(*-'( + 0'0-='-< + 9>+*( :+)*-( +

(-(*+)'( + ++(+*'-< '*+(-'' ? *( "0'+(/ +(-(/#.

R+(0+, 90+)'( + 0( + (+ (+ 0'( -+'+( :+)*-'( +

-:'( <-'( + )'+' '0:+9'-'.

U(', ':)+*( :+)*-( '' +(0+ ? )0' 90+)'( +

*+*( )'*+),*-( ? + *'( -+-'(.

D+(-9-, ? )+0', +<)+( +-<-( +0 ) +'0 ('

+0'-+( ? -+( *-:)*-'(.

R++, ? +(-9-, '( 0:'+( :+)*-(.


D-(+', +(*'*+:-'( '' '9' (-*'-+( + )+--< + +-+'

:'( + +-(-< +(+-(.

R+(0+, ? )0', 90+)'( + -0' )+--+( +-''(

'' '*-9*( *'0+( ) +0-' ? +(-'.

33





NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

J(*--', +(0*'( 9*+-( )+-'*+ +(( + '-)'-<

(+(-'/ ':( + '-'-< ? 0)-*+( + (-*'-+( + )+--<.

C)'', +(*-( +-+*+( + )+-( + C)-'-<

J(*--', -++-'( +-+*+( + 0( )+-( + +(*-( -(+'(

+ +0 ,)9-* +(0'.

D-(+', ++-)+*( '0+'*-( "+ 0'( -+-'( (-'(/ '*'0+(

(-'0+(# '' +(*-' 90+)' +:*'.


D+(-9-, *++-'( + (+ 9(+' + >*( + '-'90+(

+0'-''(.

I*++*', -+( 9,(-'( +0'-''( +0 )'+> + -)'-<

") 90'-</ )+(*'/ '-'90+/ +(*':' ? ',)+*#.

U(', )+(-')+*+ '0:'( )+-'( + +*'0-='-</ 0'0-='-</

-(+(-< ? +0'-< "++*-0+(/ '*-0+(/ +*'0-'/ -(*'-'/ ':/

'-'='/ '-'=' ? )'0-'.

I*++*', +*( + 9'9-0-' --'0 + -+++-' +

++*(.

R+(0+, ? )0', 90+)'( (' +*( 9,(-( + *+ ?

9'9-0-' ")9-'-+(/ +)*'-+(/ +('- )+(*'0/ )+(*+

'0+'*-/ )+(*+ ++)0'=')-+*#.

P, -++-'( ' '*- +0 +(*- + )+(*'( 9'9-0(*-'(.


U*-0-= 0'( *-'( + '-)'-< + +(( ---*( )-(.

I*++* 0' -< + +-'' ) '=< + ')9- ? ) '0 + 0'

+-+*+ + 0' *':+*+ ' ' ' ? +('00 )*( '' @'00' 0'(+-''( + '0:'( -+( 9,(-'( + *+*( )'*+),*-( ?

)'*+),*-(.

A'0-= 0'( +0'-+( ? -+'+( +*+ 0'( ++(-+( '0:+9'-'( ? 0'(

:,-' '( + -+( 0-<)-'( ? '-'0+( ? + (( +-''(.

M+0 (-*'-+( + '-'-< +-<-' -+( *-:)*-'( +

-*++* ? *-0-= (( +-''(.

34





('. FORMACION EN ALORES

T +*+ +(+ ( ,+' + -)-+* +9+ )+ ' -+-'

'-' ? +( *'+' -)*'*(-)' 0' +(+'=' '+-='>+ + 0( '0+( + +

-)+' -(*'-' (+ 0*-' + 0( @:'+( ? (*+-)+*+ (+ *'0++ +(+

0( 0'=( + ')-(*' + (+ :++' + 0' +(+0' + +(+ -*+')9- + -+'(/

0*' ? -)-+*.

D+(+ +0 ,+' + )'*+),*-'( (+ ++ -- :' '-+' + '0+( + (+

'*-0'' *'( -(-0-'( ? (+ *'(+('0-='' ?+*( )

E'-< (+'0 ? C(*-< + C-'''/ E'-< ')9-+*'0/ +'-<

'' 0' +)'-' +*+ *(.

L( '0+( + (+ ++ )+*' +(+ +0 '+-='>+ + 0'( )'*+),*-'( (H

LA SOLIDARIDAD '0 -)-'0 ' 0' @' + )(*' 9+( +(0*'( + 0'(

-+('( '*--'+( +(*'( + +0 ,+'.

LA $OLERANCIA +( +(+ 0'( '0'( + 0'(+ + +(' -*+'-< 0' -+(-'

+ +('0-'+( + '++)( ' '+*' 0'( -++-'( ? ' ('' 9++--

+ +00'(.EL RESPE$O + +0 *'9'> + +- (+ *'0++, +(*+ '0 + 0' )+-' +

)+(*+ (-+'-< @'-' 0'( +:0'( ? '*( + '0' +(*'90+-( '' +0

'+' +('00 + 0( ))+*( +':<:-(.

LA PERSEERANCIA +(*+ '0 (+ )++ + 0' )+-' + (+ *'=' )+*'(

? (+ 0@' @'(*' '0'='0'(/ (+ + + ,*-' ' 0' @' + ' (0-< '

(-*'-+( 90+)-'( + ( 0'*+'/ *')9- ' (+ +(+='

'++ '0:-*) 00+:' ' 0' (0-< + +>+--

LA DISCIPLINA +(*+ '0 (+ + + ,*-' ' (+ ''*' )'(/ (+

(-:+ -+*'-+( (+ )0+ '(( ++*+)-'( '' '++ -+*

+*/ '0:-*) '' +'0-=' '0-+ '=')-+* 0<:- )'*+),*-.

LA RESPONSABILIDADG +( )? -)*'*+ '0 ))+* + '()-

+(*'-' 0'( (++-'( + 0'( )-(-+(/ 9'(/ ++(-+( ?

(+*-)-+*( :++' + 0' +('/ +0 +*/ 0' -' + 0( +),(. T')9- ' 0'

@' + )0- ' '9'0-' 0 +)+'.

LA AU$ONOM#A/ ''-' ---'0 ? 0+*-' '' -0- +(('90+)+*+

(9+ 0' (0-< + (-*'-+( 90+)-'( + 0' )'*+),*-' ? + *(

*+*(. E(*' -)0-' '*--'-< + 0' *)' + +-(-+( '' 9('

'0*+'*-'( '+''( ' 0' +'0-' + +)-*' ' (0-< ' +(*-+(

0'*+''(.

35





NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

((. APOR$ES DEL AREA A LA ESPECILIDAD DE LA INS$I$UCION

B(' ' )+> +''-< +0 +(*-'*+ +' @'-' +0 CULTIVO $COSECA DE PALMA DE ACEITE (+ +*++ +(*'90++ '( 9'(+( + +0 ,+'

+ )'*+),*-'(/ + 0+ +)-*' ( -0(-< + +0 ') 0'9'0 + ' )'+'

+--+*+ ? )+*+*+.

C +00 +0 * 9'@-00+ '++, ' '0' ? ' (+ :+(* + ( - *'9'>

+ -0(-+ , -)0(' ')9-( + 9++-- + 0' -(*-*-< ? + 0' )-'

+ P+*<0+'/ + +('00' ( ?+* + -'.

C 0' E'-< M+-' T-' (+ +*++ + +0 +(*-'*+ '-+'

-)-+*( + '* '0 )'+> + '0)' '-'' + *( (( +((

) -+/ 0*-/ )'*+-)-+*/ '/ (+@' +*+ *'(

L'( *-9-+( +0 ,+' ( 0'( (-:-+*+(H

P'' )+- ? '+' *++( '' 0' (-+)9' + 0' '0)' *-0-='

0'( -'+( +0 ,+' +0 (-(*+)' )*- +-)'0.

L' +(*'(*-' '' +'0-=' +(*-( + -< (9+ +0 0*- ?(+@' + 0' '0)' + '+-*+.

0' :+)+*' '' +0'9' 0'( )'( +0 *++/ )--+ 0' -(*'-' +

(+ +9+ *++ '' (+)9' 0' '0)'/ '+),( +)-*+ *'=' *')( +

+)-*+ 0' *-0-='-< +0 +('- *-0-='90+ +0 ,+' + (-+)9'.

L( (-(*+)'( + )+'-</ ) +0 >* + 0( )+( '*'0+('' 0' '*--'-< + 0( 0*-( + 0' '0)' + '+-*+.

*-0-=' 0'( )+-'( + *-+)/ )'('/ ''-' '' +0 0*- ? (+@'

+ 0' '0)' + '+-*+.

L'( '-+(/ '=+(/ -+( '0-,0'( ' 0' +'*--' + 0(

0*-( + '0)' + '+-*+. A+),( -0?+ 0' +:0' + *+( -+*' +

-+('.

(&. COMPE$ENCIAS LABORALES

E +0 )' +0 +(' + ++ ' +'-< + '0-' + --+ ' 0(

><++( +0 I(*-*-< E'*-' C0+:- I*+:' P+*<0+' '-- )+*+-'(

36





0'9'0+( ? 0'+( + 0+( +)-*' +0 +>+-- 0+ + 0' -'''/ 0'

(+-< + +(*-( ' -+0+( ),( +0+'( ? ' )'? ? )+> -(+-< +

+0 ) +0 *'9'>/ +0 ,+' + )'*+),*-'( +*++ )' ' 0( +(*-'*+( (0')+*+ :-*-')+*+ (- *'0( + @+')-+*'( + 0+( +)-*'

+(+)+'(+ )+*+*+)+*+ ? ''*'(+ '0 ) *-.

E0 +* + )+*+-' +:09' (<0 0'( ''-'+( ++-'( '' +0

+>+-- + ' '*--' +(-'0/ (- *')9- >* +

)*')-+*(/ '0*' + ',0-(-(/ *)' + +-(-+(/ *'()-(-< +

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+(('9-0-' +0 ') 0' )+(-< +0 +(+* 0' >(*--' 0' -+-' +*+

*(.

37





NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

COMPETENCIA INTERPERSONALESH +(*' )+*+-' 9(')(

+' (+ +0'-+ -*++('0 )+*+ ( *'9'> *'+ ---'0/

+- + (+' *- '*+ 0( 0-*( ('9-+ (+ 9+ 0+ + -*+'*' *( '' 9*++ +(0*'( +(*' )+*+-' (+ +('00' + +(--+(

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0'( +0'-+( -*++('0+(.

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(+' ''= + -*+'*' +0 ) +*+- +('00' @'9-0-'+( ?

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(-+' ' -(-< *-'/ @'9-0-'+( '' :+(*-' ? )'+>' -)'-< ? +(( +(('9-0-'.

COMPETENCIA EMPRESARIALESH L'( )+*+-'( +)+('-'0+( +

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(/. INDICADORES DE DESEMPEO

BASICA PRIMARIA

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S)' ? +(*' :-*

38





I+*--' 0' ++' >* + 1! +0+)+*(

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'00' 0( '*+( + )+

39





NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

D-++-' 0( -*+-( + --(-9-0-'

'00' 0( --(+( + )+

'00' +0 )-) ) )0*-0 ? +0 ),-) ) --( + >*+ )+(

C?ar!o

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40





'00' +0 ),-) ) --( ? +0 )-) ) )0*-0 + >*

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BASICA SECUNDARIA

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A0-' 0( '0:-*)( + 0' '--< ? ((*'-< + '-'-( + 0'

(0-< + 90+)'(

41





NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

A0-' 0( '0:-*)( + 0' )0*-0-'-< ? --(-< + '-'-( + 0'

(0-< + 90+)'(

R++ +0 *+* +'0 + 0( )+( +-)'0+( U*-0-=' 0( +-)'0+( '' +(0+ 90+)'(

S4!58o

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R++(+*' '+>'( +''( + +0 0' + +''( '*+(-''(

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42





D' ' +---< +*' + ,0:+9'

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43





NOVIEMBRE DE 2008

MUNICIPIO DE TIBU

MEDIA OCACIONAL

. D358o

I+*--' )':-*+( + (+ ++(+*' + +*+( T'=' +*+( ? +*+)-' ( -+-< ? )':-*

D-9>' +*+( + (+:' -)+(-< + --++ (0 + ( -+-<

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0' -'0 (+ ++*' + ''*+ '

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Ud358o

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44





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45





NOVIEMBRE DE 2008MUNICIPIO DE TIBU

(). ME$ODOLO"#A

L' +'-< )'*+),*-' +0 +(*-'*+ +9+ +(*' '*-0''/ +0 +)+ ?

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+(( + +-++ ' '(+(' +('0-='' +0 +*+ '-)' +

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1. N5el 5!rod?3!5o. L' )*-'-< +( -)*'*+ '*+ +0 +*+

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46





E 0' +(+'=' + 0' )'*+),*-' (+ +9+ +)0+' )*( ,*-(/ '*-(

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(*.( CRI$ERIOS DE EALUACION

47






E +0 ,+' + )'*+),*-'( (+ *+, + +*' 0( -*+-( + +'0'-<

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48





A0'=' *( 0( +(+)+( +(*( (- '*--'+( )0+)+*'-'(.

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49






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63




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A*+'0'-<C@+'0'-<+*++'0'-<

AREAH MATEMATICAS NIVEL PRIMARIA GRADO PRIMERO


64





PERIODO: $ERCERO

UNIDAD $EM2$ICA

ES$ANDARES CURRICULARES DESEMPEOS

INDICADORES DE DESEMPEO ME$ODOLO"#A RECURSOS DID2C$ICOS

CRI$ERIOS PROCEDIMIEN$OS PARA

EALUAR ELAPRENDIZAJE


N)+( -'0+(

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AREAH MA$EMA$ICAS NIVEL PRIMARI GRADO Pr58ero

INTENSIDAD ORARIA SEMANAL DOCENTE LUIS OLIDE ROJAS BOHORQUEZ

PERIODO: CUAR$O

65





UNIDAD $EM2$ICA



DESEMPEOME$ODOLO"#A

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AREAH MA$EMA$ICAS NIVEL PRIMARI GRADO SE"UNDO


PERIODO: PRIMERO

66





UNIDAD $EM2$ICA



DESEMPEOME$ODOLO"#A

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AREAH ORQUEW MA$EMA$ICAS NIVEL PRIMARIA GRADO Se>?do.INTENSIDAD ORARIA SEMANAL 5 ORAS DOCENTE LUIS OLIDE ROJAS BOH

PERIODO: PRIMERO

67





UNIDAD $EM2$ICA ES$ANDARES CURRICULARESDESEMPEOS

INDICADORES DEDESEMPEO

ME$ODOLO"#ARECURSOS

DID2C$ICOSCRI$ERIOS PROCEDIMIEN$OS

PARA EALUAR EL APRENDIZAJEES$ANDAR COMPE$ENCIA

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AREAH MA$EMA$ICAS NIVEL PRIMARIA GRADO SE"UNDOINTENSIDAD ORARIA SEMANAL 5 ORAS DOCENTE LUIS OLIDE ROJAS

PERIODO: se>?do

UNIDAD $EM2$ICA ES$ANDARES CURRICULARES DESEMPEOS ME$ODOLO"#A

68







DESEMPEO DID2C$ICOS PARA EALUAR ELAPRENDIZAJE


CON$ANDO MUL$IPLIANCO

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A*+'0'-<C@+'0'-<

+*++'0'-<

AREAH MA$EMA$ICAS NIVEL PRIMARIA GRADO SE"UNDO

INTENSIDAD ORARIA SEMANAL 5 ORAS DOCENTE LUIS OLIDE ROJAS BOHORUEZ

TERCERO

70





UNIDAD$EM2$ICA



DESEMPEOME$ODOLO"#A

RECURSOSDID2C$ICOS


CON$ANDO MUL$IPLIANCO

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REAH MA$EMA$ICAS NIVEL PRIMARIA GRADO SE"UNDOINTENSIDAD ORARIA SEMANAL 5 ORAS. DOCENTE LUIS OLIDE ROJAS

PERIODO: CUAR$O


71






RECURSOSDID2C$ICOS

CRI$ERIOS PROCEDIMIEN$OSPARA EALUAR EL APRENDIZAJE


REPAR$IENDO DIIDENDO

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AREAH MA$EMA$ICAS NIVEL PRIMARIA GRADO $ERCERO

INTENSIDAD ORARIA SEMANAL 5 ORAS DOCENTE LUIS OLIDE ROJAS BOHORQUEZ.

PERIODO: PRIMERO


72






RECURSOSDID2C$ICOS



NUM<RICO

CONOZCAMOS LOSNMEROS NA$URALES CON

LA ADICIÓN LASUS$RACCIÓN

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73









AREAH MA$EMA$ICAS NIVEL PRIMARIA GRADO $ERCEROINTENSIDAD ORARIA SEMANAL 5 ORAS DOCENTE LUIS OLIDE ROJAS BOHORQUEZ

PERIODO: $ERCER

UNIDAD $EM2$ICA



DESEMPEOME$ODOLO"#A

RECURSOSDID2C$ICOS


REPARTIENDO$UDIVIDIENDO.

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AREAH MA$EMA$ICAS NIVEL PRIMARIA GRADO $ERCERO

76






PERIODO: CUARTO

UNIDAD $EM2$ICAES$ANDARES CURRICULARES


DESEMPEOME$ODOLO"#A RECURSOS DID2C$ICOS


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AREAH MATEMATICAS NIVEL SECUNDARIA GRADO QUINTO

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82





UNIDAD $EM2$ICA



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AREAH M MATEMATICAS NIVEL SECUNDARIA GRADO QUINTOINTENSIDAD ORARIA 5 SEMANAL DOCENTE FABIO ALONSO CUADROS

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UNIDAD $EM2$ICA



DESEMPEO ME$ODOLO"# A RECURSOS D ID2C$ICOSCRI$ERIOS PROCEDIMIEN$OS


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AREAH MATEMATICAS NIVEL SECUNDARIA GRADO QUINTO

INTENSIDAD ORARIA SEMANAL DOCENTE FABIO ALONSO CUADROS

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UNIDAD $EM2$ICA



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AREAH MATEMATICAS NIVEL SECUNDARIA GRADO SE;TO

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UNIDAD $EM2$ICA


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AREAH MATEMATICAS NIVEL SECUNDARIA GRADO SE;TOINTENSIDAD ORARIA SEMANAL 5 ORAS DOCENTE FABIO ALONSO CUADROS

87





PERIODO: SEGUNDO



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AREAH MATEMATICAS NIVEL SECUNDARIA GRADO CSE;TO

INTENSIDAD ORARIA SEMANAL 5 ORAS DOCENTE FABIO ALONSO CUADROS

PERIODO: TERCERO

UNIDAD $EM2$ICA



DESEMPEOME$ODOLO"# A RECURSOS D ID2C$ICOS


88







CRITERIOS Y PROCEDIMIENTOS PARAEVALUAR EL APRENDIZAJE

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2articipación en las acti'idades

PRIMER: PERIODO

AREAH MATEMATICAS NIVEL SECUNDARIA GRADO CSEPTIMO


90





PRIMER: SEGUNDO



DESEMPEOME$ODOLO"#A RECURSOS DID2C$ICOS


91

UNIDAD $EM2$ICA ES$ANDARES CURRICULARES DESEMPEOS INDICADORES DEDESEMPEO

ME$ODOLO"#A RECURSOS DID2C$ICOS CRI$ERIOS PROCEDIMIEN$OSPARA EALUAR EL APRENDIZAJEES$ANDAR COMPE$ENCIA

N)+( +*+(

NUMEROS ENTEROS• A)0-'-< +0

>* + 0('*'0+(.

• R+0'-< ? + +0( W.

• A--< ? ((*'-<+ )+( W.

• P-+'+( + 0''--< +

)+( W.• E'-+( '-*-'(.

MULTIPLICACIÓN $DIVISIÓN DE Z• M0*-0-'-< ?

--(-< +)+( W.

• P-+'+( + 0')0*-0-'-< +0( W

• E'-+()0*-0-'*-'(.

• L( P0-)-( ?(-:( +':'-<.

POTENCIACIÓN $RADICACIÓN. EN LOSENTEROS.

T'9'> 0( )+( +'0+(+ (( -++*+(++(+*'-+(.

R+(+0 ? )0 90+)'(*-0-=' +0'-+( ?-+'+(? @'-+ +'-+( )+( +*+(.

U( +(*'*+:-'( + ,00 +'-)'-< (+: 0'(-*'-</ '' +(0+90+)'( + ()' ?)0*-0-'-<.

R++(+* -++*+((-*'-+( *+-'-< ?'-'-<.

R+(*'90++, 0' +0'-<+-(*+*+ +*+ +0 >* +0( '*'0+( ? 0( +*+( ?D+('00'' @'9-0-'+( + +0,00 ? '0-'-< + 0'(+'-+( 0( )+(+*+(.

U(', 0'( +:0'( ''+*+)-' +0 * ? +0-+*+ + ( +*+(/ ''+(0+ 90+)'( + 0+)'*+),*-.

A0-'' 0'( -+'+( +*+-'-< ? '-'-< ''+(0 + 9 0+)'( ?(-)0--' ++(-+(. A0-'' 0' '*)' ?+(')-+* 0<:- + 0'(0-< + 90+)'( ''+' +(-* )+*-*-.

E+*' '--+( +*+)+( +*+(.I+*--' 0'( -+'+( +0' '--< +*+ +*+(.'00' 0' -++-' +*+)+( +*+(.R+(+0+ +'-+( '-*-'(+ 0( +*+(.

D+('00' +'-+( +*+)0*-0-'-+( ? --(-+(+ +*+(.I+*--' 0( 0-)-( ?(-:( + ':'-< +-++*+( + >+ - -()'*+),*-( +*+ +*+(.R+(+0+ +'-+( 0-+'0+()0*-0-'*-'( +--+*+(+*+(.

I*++*' 0'( -+'+( +*+-'-< ? '-'-< ++>+--( ,*-(.

R+'0-=' 0'( '*--'+( +0'(+ *+-+ + +*' 0'(+)+'-+( ''(.

E(--<.

E0-'-<.

E>+)0--'-<.D+('00 + *'00++( ? *'9'>(---'0+( ? *'9'>( :'0+(.

D+('00 + :'( + *'9'>.

C(0*'(.

T'90+( ? '-0-'+(.

M0.

A*--'+()0+)+*'-'(.

S*b'+

S'0' + C)*.

I*+( '0 (0*' ? ')0-' *+)'(-(*( + 0'(+ +(*(.

P+9'( +(-*'( 0-9 '9-+*.

R+'0-='-< + )+(' +' ?+9'*+(.

A,0-(-( + -*++*'-< 9>+*-' + 0'(+9'( +(-*'(.

P'*--'-< + 0'( '*--'+(

AREAH MATEMATICAS NIVEL SECUNDARIA GRADO SEPTIMO






N)+(R'-'0+(

NUMEROSRACIONALES• E0 >* + 0(

)+('-'0+(.

• E+(-< +-)'0+ 0( )+('-'0+(.

• O+ + 0('-'0+(.

ADICION $SUSTRACIONDE RACIONALES• P-+'+( + 0'

'--< +'-'0+(.

• A--< ?((*'-< +0( '-'0+(.

• E'-+('-*-'(.

T'9'> 0( )+( +'0+(+ (( -++*+(++(+*'-+(.

R+(+0 ? )0 90+)'('0-' -+'+( + 0(N)+( ? + (( +'-+(.

I+*- -' ? +0'-' 0()+( '-'0+( + 0(-++*+( *+*( +0)+-. E+*'' '--+( ?((*'-+( + )+('-'0+(/ +-+ ?@'-+ ( + 0'(-+'+( +(+*-'(.

I*++*'' ? +(0+,+'-+( '-*-'( + 0('-'0+( ? 90+)'( + 0'(-0'.

U*-0-=', 0' +'*--' ? +0+(')-+* 0<:- + 0'(0-< + 90+)'( '''-'=' 0( -)-+*(

I+*--' ? 9-' +0 >*+ 0( )+( '-'0+( +0' +*'.E+(' + )' +-)'0 ''-< ? -++('.'+ ( + 0'( +---+('' +(*'90++ + +*++-)'0+(.

I+*--' 0'( -+'+( +0' '--< + 0( '-'0+(.E+*' +'-+( +'--< ? ((*'-< '-'0+(.

I *++ *' ? +(+ 0++'-+( '-*-'( + 0('-'0+(.J(*--' +-)-+*( ''+(0+ +'-+( '-*-'( ''*- + 0'( -+'+(

R+'0-=' 0'( '*--'+( +0'(+ *+-+ + +*' 0'(+)+'-+( ''(

E(--<.

E0-'-<.

E>+)0--'-<.D+('00 + *'00++( ? *'9'>(---'0+( ? *'9'>( :'0+(.

D+('00 + :'( + *'9'>.

C(0*'(.

T'90+( ? '-0-'+(.

M0.

A*--'+()0+)+*'-'(.

S*b'+

S'0' + C)*.

I*+( '0 (0*' ? ')0-' *+)'( -(*( + 0'(+ +(*(.

P+9'( +(-*'( 0-9'9-+*.

R+'0-='-< + )+(' +'? +9'*+(.

A,0-(-( + -*++*'-<9>+*-' + 0'( +9'(

+(-*'(.

P'*--'-< + 0'('*--'+(.



PERIODO: TERCERO

UNIDAD $EM2$ICA



DESEMPEOME$ODOLO"#A

RECURSOSDID2C$ICOS


92





N)+( R'-'0+(

G+)*-

MULTIPLICACIÓN $DIVISIÓN DERACIONALES• M0*-0-'-< +

'-'0+( ?-+'+(.

• D--(-< +'-'0+(.

POTENCIAS $ RAICESEN LOS RACIONALES.• P*+-'-< ? ((

-+'+(.•

R'-'-<P-+' -*':<-'

C'00', +)+* ?,+' + -:'( 0''( '*'( + )(--< ?+()(--< +-:'(.

. P+)+* ? ,+'( +-:'( 0''(.

.C0'(--'' 0:(+ +0'-< ((-+'+(.

T'9'> 0( )+( +'0+(+ (( -++*+(++(+*'-+(.

E+* 0' -++-' +*+0( )+( '-'0+( ? 0(-'-'0+('0 ++(+*'0( + )'+-)'0.

R++(+* -++*+((-*'-+( *+-'-< ?'-'-<.

R+(+0 ? )0 90+)'('0-' -+'+( + 0(N)+( ? + (( +'-+(.

E0- +0 +-)-+* ''@'00' +0 +)+* ? ,+' +-:'( 0''(.

R+= 0( 0:( ? 0(0'(--.

R+= 0' -++-' +*+ +0+)+* ? ,+'.

E+*'' +'-+( +*( ? -+*+( +)+( ' -'0+( ?++, (-*'-+( + 0'('0+( +)0+'0'(.

I*++*''/ 0'*+'' ?+(0+, +'-+()0*-0-'*-'( + 90+)'(*--'(.

A0-'' 0'( -+'+( +*+-'-< ? '-'-< '-'0+( '' +(0+

90+)'( ? (-)0- -' ++(-+(.

F)+*'' +0 -*+(/ 0'+(('9- 0- ' ? 0 ''-(--< + @'9-0-'+( -'( + '* ' 0 '=')-+ * 0<:- )'*+),*-/ )0'>+*'(/ -++-'(/+-+( '' 0' (0-<+ 90+)'(.R++, 0( 0:( ?0( 0'(--'.

E+*' )0*-0-'-< +)+( '-'0+(.R++ ? '0-' +0 ( +0'( -+'+( + 0')0*-0-'-< + '-'0+(.E+*' --(-< + )+('-'0+(.

I*++*' ? R+(+0++'-+( )0*-0-'*-'(.J(*--' +-)-+*( ''+(0+ +'-+( ' '*- + 0'( -+'+(.

I*++*' 0'( -+'+( +*+-'-< ? '-'-< ++>+--( ,*-(.'00' 0' @-*+(' + * -':0 +*,:0/-( 0( '*+*(.

R+'0-=' 0'( '*--'+( +0'(+ *+-+ + +*' 0'(+)+'-+( ''(.

E+*' +0 ,+' ? +)+* + 0:.

E(--<.

E0-'-<.

E>+)0--'-<.D+('00 + *'00++( ? *'9'>(---'0+( ? *'9'>( :'0+(.

D+('00 + :'( + *'9'>.

C(0*'(.

T'90+( ? '-0-'+(.

M0.

A*--'+()0+)+*'-'(.

S*b'+

S'0' + C)*.

I*+( '0 (0*' ? ')0-' * +)'( -(* ( + 0'(+ +(*(.

P+9'( +(-*'( 0-9 '9-+*.

R+'0-='-< + )+(' +' ?+9'*+(.

A,0-(-( + -*++*'-< 9>+*-'+ 0'( +9'( +(-*'(.

P'*--'-< + 0'( '*--'+(



PERIODO: CUARTO

93





UNIDAD $EM2$ICA



DESEMPEOME$ODOLO"#A

RECURSOSDID2C$ICOS


PREALGEBRA

ESTADISTICA

VARIABLES $E;PRESIONES ALGEBRAICAS^V'-'90+ ):++'0-='-<.

^V'0 )- +++(-+('0:+9'-'(.

^T)-( (+)+>'*+(+ ++(-+((+)+>'*+(.

^R+(0-< +90+)'(.

.R+0+-< ?*'90'-< + '*(.

.M+-'( + *++-'+*'0. M+-''-*)*-'/M'/ )+-''.

T'9'> 0( )+( +'0+(+ (( -++*+(++(+*'-+(.

R++(+* -++*+((-*'-+( *+-'-< ?'-'-<.

S- )+ ' ' ++(-<'0:+9'-'/ (? ''= +E*' *'( +-'0+*+(.

R++ 0' -++-' +*+90'-< ? )+(*'.

E0-' +0 +-)-+* ''@'00' 0'( )+-'( + *++-'+*'0.

I*++*''/ ++('' ?+(0+, )0'(:+)*-'( + +0 0+:'>+'0:+9'-.

E(*'90++, (+ +9++(9- + 90+)'+*'+, '*( +*-+*+( +0+-' + 90+)' ?+(9='' -9>( ''++(+*' (-*'-+(.

U*-0-='' +'*--' ? +0+(')-+* 0<:- + 0'(0-< + 90+)'( '' +0+('00 + )+*+-'(-*-'.

S0-'' 90+)'(*+*'0-='( +-0 ' ' -'90 +(+(*'(*-'(.

R++(+*', )+- +' *'90' + ++-'( >* + '*(.

I *++*' '- '9 0+('0:+9'-'( + -++*+(*+*( :+)*-(.E+*' +0 '0 )-+ ++(-+( '0:+9'-'(.R+'0-=' +'-+( 9,(-'(+*+ ++ (-+((+)+>'*+(.

I+*--' + 90+)' 0('*( -( ?+(- ? ++(' 0'+0'-< +*+ +00( (' ?+(0-+ +'-+(.

R+'0-=' 0'( '*--'+( +0'(+ *+-+ + +*' 0'(+)+'-+( ''(.

P0'*+' +-)-+*( ''(0 -' 90+)'(*+*'0-='( +-0' '- '9 0+(+(*'(*-'(.

E(--<.

E0-'-<.

E>+)0--'-<.D+('00 + *'00++( ? *'9'>(---'0+( ? *'9'>( :'0+(.

D+('00 + :'( + *'9'>.

C(0*'(.

T'90+( ? '-0-'+(.

M0.

A*--'+()0+)+*'-'(.

S'0' + C)*.

I*+( '0 (0*' ? ')0-' *+)'( -(* ( + 0'(+ +(*(.

P+9'( +(-*'( 0-9 '9-+*.

R+'0-='-< + )+(' +' ?+9'*+(.

A,0-(-( + -*++*'-< 9>+*-'+ 0'( +9'( +(-*'(.

P'*--'-< + 0'('*--'+(.

AREAH MATEMATICAS NIVEL SECUNDARIA GRADO OC$AO

INTENSIDAD ORARIA SEMANAL 5 ORAS DOCENTE MMARICELA PAREDES PABÓN

PERIODO: PRIMERO

UNIDAD $EM2$ICA



DESEMPEOME$ODOLO"#A

RECURSOSDID2C$ICOS


94





LOS CONJUN$OSNUM<RICOS.C>*( )-(-+'+( ?+'-+( 9,(-'(.

EPRESIONESAL"EBRAICAS.C0'(--'-< +++(-+('0:+9'-'(.T)-( (+)+>'*+(.O+'-+( ++(-+('0:+9'-'(.

PER#ME$RO 2REA DE RE"IONESPLANASP+)+* + -:'(0''( +' + -:'( 0''(

CONCEP$OSB2SICOS DEES$AD#S$ICAP90'-<M+(*'V'-'90+(T'90'( + ++-'(

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3Interpreto analítica críticamentein"ormación estadísticapro'enientede di'ersas "#entes(prensa, re'istas,tele'isión, e-perimentos,cons#ltas,entre'istas%

COMPE$ENCIAS BASICAS

U*-0-= 0( )+( +'0+( +(( -++*+( ++(+*'-+? + -+(( *+*( + 0'(0-< + (-*'-+(90+),*-'(.C(*? ++(-+('0:+9'-'( + -*++*'(-*'-+( 90+),*-'(.U(' -(*-*( +-)-+*('' +(0+ (-*'-+(90+)'( + -0' +0,00 + +)+* ? ,+'(

COMPETENCIAS CIUDADANAS Cono/co #tili/o estrateiascreati'as para sol#cionarcon"l ictos% COMPETENCIAS LABORALESEsc#c.a la in"ormación, opinión ar#mentos de otros so+re #nas it#ación determinada contri+#e a dar sol#ciones%

A0-' + -*++*' 0'(-+'+( + 0( -++*+(>*( )-( + 0'S0-< + 90+)'(.

C'00' +)+* ? ,+' ++:-+( 0''(.

I+*--'/ 0'(--/ @'00' +-*++*' +0 '0 )- +' E+(-< A0:+9'-'.

D-(-0-' ? +(('9-0-'+ 0( +(+)+(+(-+*+( ' 0''(-:'*'.

cD+*+)-' 0' +*++-' +*++-' + )+' >* )- '? 0( (9>*( +0>* + 0( )+(+'0+(.

.I+*--' ? '0-' 0(>*( )-( + 0'(0-< + +'-+(.

c E+(' ? *'-+-'( '( + )'+9'0 '0 0+:'>+ (-)9<0-.

c R++ 0'( ++(-+('0:+9'-'( ? ( 0'(--'-</+ -+*--' ? (-)0--'*)-( (+)+>'*+(.

c '00' +0 ,+' + +:-+(0''( ? +0 0)+ +(<0-( :+)*-(.

.C)++ +*(9,(-( + 0' +(*'(*-'

M+(*' -*+( ? ':' ++0 +('00 + 0'( -(*-*'('*--'+(.

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2articipación en las acti'idades%

Responsa+ilidad en la presentación decompromisos asinados%

Desarrollo de las #ías de aprendi/a0e Desempe5o en los conc#rsos matem!ticos

AREA M MATEMATICAS NIVEL SECUNDARIA GRADO OC$AO


PERIODO: SEGUNDO

UNIDAD $EM2$ICA



DESEMPEOME$ODOLO"#A

RECURSOSDID2C$ICOS


95









FAC$ORIZACION

FRACCIONESAL"EBRAICAS

$EOREMA DEPI$A"ORAS DE$HALES

MEDIDAS DECEN$RALIZACION DISPERSIÓNM+-' A-*)*-'M+-' P+'' M+-''M'

D+(-'-< +(*,' D+(-'-< *-'V'-'='

R+= +/-++*+( )'+'( ++(+*' 0'-)'-</ ++' -:+ ' -(*-*'(-*++*'-+(

I*++* ''0*-' ?*-')+*+-)'-< +(*'(*-'+-+*+ +-+('( +*+("+('/ +-(*'(/*+0+-(-</

++-)+*(/(0*'(/ +*+-(*'(#.

3Interpreto #tili/oconceptos de media,mediana moda e-plicito s#s di"erenciasen distri+#ciones dedistinta dispersión asimetría%

S+0+- ? (','0:( )*(+(*'(*-( '+'((+: +0 * - +-)'-<.

COMPE$ENCIA B2SICAS

R++ + -*++*' 0(-(*-*( +(( +'*-='-<.

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COMPE$ENCIASCIUDADANAS

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U*-0-=' ? +0-' 0( '(( +'*-='-< + 0'+()(--< +0-)-(.

A0-' +0 T++)' +P-*,:'( ? *++)' +T@'0+( + 0' (0-< +*-,:0(.

U*-0-=' 0'( )+-'( ++*'0-='-< + -(+(-<),( '+'' + 0' +(0-<+ ' (-*'-< 90+)'.

C)++ 0' -0+-' +*-++ '0:( +*( +0' +(*'(*-' '' '+(+(*' ' 0' +-' + +<)+

F'*-=' 0-)- '

A0-' 0' '*-='-< + 0'(-)0--'-< + '-+('0:+9'-'(.

R+(+0+ +'-+( '-+( '0:+9'-'( ++>+--( ,*-(.

R+(+*' 0' --< ? 0('*+( + @'+ (()'+(.

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a las e'al#aciones aplicadas

a+leros a#-iliares%

e-to #ía%



Internet







Desarrollo de las #ías de aprendi/a0e Desempe5o en los conc#rsosmatem!ticos

AREA M MATEMATICAS NIVEL SECUNDARIA GRADO NOENO


PERIODO: PRIMERO


98






RECURSOSDID2C$ICOS



POTENCIACIÓNC+*P-+'+( A0-'-+(

RADICACIONC+*P-+'+(O+'-+( '-'0+(

RACIONALIWACIONC+*P-+'+( A0-'-+(

CONCEPTOSBSICOS DEESTADKSTICAP90'-<M+(*'V'-'90+(T'90'( + ++-'(

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Identi"ico #tili/o lapotenciación laradicación pararepresentar sit#acionesmatem!ticas nomatem!ticas%

Res#el'o "orm#lopro+lemas seleccionandoin"ormación rele'anteen con0#ntos de datospro'enientesde "#entes di'ersas%(prensa, re'istas,tele'isión, e-perimentos,cons#ltas,entre'istas)%

COMPE$ENCIA B2SICAS3Simpli"icar e-presiones cone-ponentes radicales, aplicandos#s propiedades%3Racionali/a n#meradores denominador en e-presiones conradicales%

3Reconoce e interpreta conceptos+!sicos de la estadísticaCOMPETENCIA CIUDADANA

A:)+* ? +9'* (9+-0+)'( + 0' -' *--'' +0( + -(*-*( ++@( -(*-*( '0+( +*' + 0-* += 0( )+>+(':)+*(/ '( --' 0( )(.COMPETENCIAS LABORALESR+(+* 0'( -+'( ++(''( 0( *(/'+ (+' -++*+( + 0'()'(.

R+(+0+ +'-+( )+( +'0+(/ S-)0--'++(-+( )-'( ?'0:+9'-'( '-'0+(.

c R++ L'( -+'+( ?+0'-+( :+)*-'( ++0'-< '0 *++)' + T@'0+(

I+*--' + -*++*' 0'(-+'+( + 0( '-'0+(

*-0-=''( + 0' (0-< ++>+--( ? 90+)'(.

R+'0-=' + )' :'-='' ?+(('90+ +0 *'9'> +(+ 0+ + + +0 ,+'.

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Racionali/a reales en e0erciciospr!cticos%

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9,(-( + 0' +(*'(*-'

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PERIODO: SEGUNDO

UNIDAD $EM2$ICA


DESEMPEOS INDICADORES DEDESEMPEO ME$ODOLO"#A RECURSOSDID2C$ICOS CRI$ERIOS PROCEDIMIEN$OSPARA EALUAR EL APRENDIZAJEES$ANDAR COMPE$ENCIA

99





ECUACIONESLINEALES

SISTEMAS DEECUACIONESS-(*+)'( ++'-+( 22M*( + (0-<

SEMEJANZAS R'=+( P-+(R'=< + ((+:)+*(S+:)+*(

-'0+( R+*'(*''( ''0+0'(T++)' + T@'0+(P0:( (+)+>'*+(

DISTRIBUCION DEFRECUENCIASDATOS AGRUPADOS$ GRFICOSESTADKSTICOS

Recono/co contrastopropiedades relacioneseom$tricas#tili/adas endemostración deteoremas +!sicos(2it!oras ales)%

Identi"ico di"erentesm$todos para sol#cionarsistemas de ec#acioneslineales%

Con0et#ro 'eri"icopropiedades deconr#encias seme0an/asentre "i #ras+idimensionales entreo+0etos tridimensionalesen la sol#ción depro+lemas%

COMPETENCIA BASICAS-Sol#cionara, r!"ica analíticamente ec#acioneslineales con dos 'aria+lesaplicando correctamente losm$todos 'istos en modelosmatem!ticos%3Recono/co #so la seme0an/ade tri!n#los para sol#cionarpro+lemas%COMPETENCIA CIUDADANASDem#estro Capacidad deadaptación al r#po, tra+a0o en

e&#ipo, toma de decisiones,creati'idad, sol#ción de2ro+lemas, &#e me permitanadaptarme al medio am+iente enel &#e 'i'o% (Com#nidadEd#cati'a : .oar)% COMPETENCIAS LABORALESM'*+: +'( ? 0-)-()- (-*- ++(*- ? )-( -)0+)+*(+('0+(.

7#sti"ico procedimientospara resol'er e0ercicios &#etenan ec#aciones deradicales

2lantea ec#aciones &#esatis"acen condicionesdadas

2ropone sol#cionasit#aciones por medio desistemas de ec#acioneslineales

Res#el'e sistemas deec#aciones ;-; #sandodistintos procedimientos

Identi"ico #so criterios deseme0an/a para resol'erpro+lemas%

Di"erencio #so ta+las de"rec#encias en la sol#ciónde #na sit#ación pro+lema

Identi"ica es+o/a la pendiente p#ntos de corte de #naec#ación lineal%Relaciona las pendientes derectas paralelas operpendic#lares%

Reconoce como lineal #naec#ación de primer rado condos 'aria+les%

Interpreta la sol#ción r!"ica de#n sistema de dos ec#aciones

lineales con dos 'aria+les%

Res#el'e analíticamente #nsistema de dos ec#acioneslineales con dos 'aria+les%

Res#el'o sit#aciones pro+lemaen #na distri+#ción de datosar#pados no ar#pados

E-posición%E-plicación%Constr#cción paso a paso delconocimientoE0empli"icación%Desarrollo s#stentación detalleresra+a0os indi'id#ales ra+a0o cooperati'oDesarrollo de #ías deaprendi/a0e%Conc#rsos matem!ticoCons#ltas%

Sociali/ación de las correcciones alas e'al#aciones aplicadas

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DESEMPEOME$ODOLO"#A

RECURSOSDID2C$ICOS


10 0





FUNCIONCUADRAICADe"iniciónElementos de #na par!+olaDe"inición de ec#aciónc#adr!ticaSol#ciones de la "#nciónc#adr!ticaAn!lisis de las raíces de#na ec#ación c#adr!tica2ro+lemas de aplicación

2O6IEDROS<C6ASIFICACI*N =2RO2IEDADES.

MEDIDAS DEENDENCIA CENRA62ARA DAOSA4RU2ADOS = DAOSNO A4RU2ADOSMedia aritm$ticaMedia ponderadaMedianaModa

Represento r!"icamente"#nciones lineales,c#adr!ticas cú+icas ela+oro modelos para s#est#dio%

Uso representacioneseom$tricas para resol'er "orm#lar pro+lemas enlas matem!ticas enotras disciplinas%

Interpreta #tili/aconceptos de media,mediana moda e-plicas#s di"erencia endistri+#ciones

COMPETENCIA BÁSICAReconocer e interpretar los distintosprocesos de "actori/ación en lasol#ción de c#adr!ticas.

Identi"icar anali/ar elcomportamiento de la "#nciónc#adr!tica para aplicarla en pro+lemasdonde se emplea este tipo de "#nción,#tili/o los di"erentes m$todos pararesol'er #na ec#ación c#adr!tica%

Interpretar las medidas decentral i/ación e-p lica s#sdi"erencias%

COMPETENCIA CIUDADANASMe com#nico a tra'$s del di!looconstr#cti'o con los otros(Com#nicati'a), re#lar emociones,'alorar 6as di"erencias (Emociones)c#idar el +ienestar de otros, respetar alotro (Interadora)COMPETENCIAS LABORALESS+0+- 0( )'*+-'0+( ++-+ '' +0 +('00 +' *'+' '-<.

Identi"ico anali/o elcomportamiento de la "#nciónc#adr!tica para aplicarla enpro+lemas donde se empleaestetipo de "#nción, #tili/o losdi"erentes m$todos para resol'er#na ec#ación c#adr!tica

Anali/ar el comportamiento típico deal#nas 'aria+les con la a#da delas "#nciones est#diadas, Identi"icarla estr#ct#ra de #na "#nciónc#adr!tica, #tili/ar los di"erentesm$todos para resol'er #na ec#aciónc#adr!tica

Identi"ica la "#nción c#adr!tica

Res#el'e c#al&#ier ec#aciónc#adr!tica #sando la "orm#la eneralo por medio del m$todo de"actori/ación c#ando este seaposi+le%

Constr#e la ta+la de 'alores de #na"#nción c#adr!ticapara reali/ar s# ra"ica

Identi"ica las características de lospoliedros%

Clasi"ica poliedros en re#lares eirre#lares

Utili/a la medida de tendenciacentral o de dispersión m!sadec#ada para dar sol#ción asit#aciones pro+lemas



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UNIDAD $EM2$ICA



DESEMPEOME$ODOLO"#A

RECURSOSDID2C$ICOS


10 1











IDEN$IDADES$RI"ONOM<$RICAS

I+*-'+(T-:)*-'(F')+*'0+(

R+-'(-+*+(P-*':-'( D+)(*'-< +I+*-'+(

I+*-'+( '' 0'

()' ? 0' '--< +,:0(

I+* -'+( '',:0( 90+( ?)+-(

ECUACIONES$RI"ONOME$RICAS

R++ 0' +(-' +-)0+*-* + 0()+( '-'0+( '*'( + )+0()-(/ :+)*-(? '0:+9'-(.

D+(-9+ ? )+0'+<)+( +-<-(+0 ) +'0 ('

+0'-+( ? -+(*-:)*-'(.

COMPETENCIA BÁSICAS

Comprende el concepto deidentidad trionom$trica reconoce cada #na de ellas paradarle aplicación a la resol#ción depro+lemas%

COMPETENCIA CIUDADANASIdenti"icar dilemas de la 'ida enlas &#e entran en con"l icto el +ieneneral el +ien partic#larBanali/o opciones de sol#ción,

considerando s#s aspectospositi'os neati'os%

COMPETENCIAS LABORALESDetermino las ca#sas de loscon"lictos elimpacto &#e $stos tienen en lasdi"erentespersonas%

R+ = ? '0-+-)-+*( '0:+9'-( ?*-:)*-( '' +(0+ (-*'-+( 90+)'( + 0'*-:)+*'.

A'0-= -)'-< +:-(*''+ *'90'( '' :++'0-=' +-) -+*( + 0 '+)(*'-< + -+*-'+(*-:)*-'(.

E+* '0+( )-('' )9' + (++(-+( *-:)*-'( ( +-'0+*+(

U( -+'+( + >*()-( '' *'()' ' ++(-< *-:)*-'+ *' +-'0+*+.

R+(+0 +'-+(* -:)* -'( ''(0-' (-*'-+(90+)'



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AREA M MATEMATICAS NIVEL SECUNDARIA GRADO DECIMO


PERIODO: CUAR$O


10 5






RECURSOSDID2C$ICOS



TRIGONOMETRKA ANALITICA

D-(*'-' +*+ (*(L+' +*'E'-< + 0' 0+'+*'P+-+*+ + 0' +*'

SECCIONESCONICASL' P',90'L' E0-(+L' -++-'L' -90'

E(*'90++ +0'-+( ? -++-'( +* +-+('( *'-+( +)+( +'0+( ''+-- (9+ ( ( +' (-*'-< ''.

R+(+0 90+)'(+ 0( + (+ (+

0'( -+'+(:+)*-'( + -:'( <-'( )+- +*'()'-+(+ 0'(++(+*'-+('0:+9'-'( + +('(-:'(.

COMPE$ENCIA B2SICASR++ 0'( 0'(+( +(+-+( <-'(.

E0-' +0 +-)-+* '':'-' -++-'(/',90'(/ +0-(+( + @-90'(.

P0'*+' +-)-+*( ''(0-' 90+)'(*+*'0-='( ?++(+*'0( :,-')+*+.

COMPETENCIA CIUDADANAS

Arg!"#$% & '"()$%*%(r" '+,"!)* '" ,)-+') "# ,%* " "#$r)#"# /%# +/$% ", (+"#g"#"r), & ", (+"#)r$+/,)rr"/%#%/+"#'% ,%*!"3%r"* )rg!"#$%*)* *")# '+*$+#$%* ) ,%*!%*.COMPETENCIAS LABORALES

Identifico alternativas

para manejar y resolver

Los conflicto

C'00' -(*'-' + (*( + +0 0' '*+(-'.

U(' -(*-*( >*()-( '' +(0+ 90+)'( + *+*(:+)*-( ? + '-'-+(.

D+*+)-' 0' +'-< + ''<-' ' '*- + (+(--< :+)*-' ?+'0-=' ( ++(+*'-< + +00' '*+(-'.

I+*--' ''*+(*-'( +0'0-='-< + 0' +*' ? + 0'-++-'.

'00' +0 +)+* + -+((0:( ' '*- + 0'++(-< + 0' -(*'-'+*+ ( *(.

D+*+)-' 0' +'-< + '+*' ''( -+*' (''*+(*-'( + +00'.

I+*--' 0' +-+*+ + '

+*' + ' )0' +0--*'+ -)0-*'.

E-posición%E-plicación%Constr#cción paso a paso delconocimientoE0empli"icación%Desarrollo s#stentación detalleresra+a0os indi'id#ales ra+a0o cooperati'oDesarrollo de #ías deaprendi/a0e%

Conc#rsos matem!ticoCons#ltas%Sociali/ación de las correcciones alas e'al#aciones aplicadas

Identi"ica la ec#ación de #nacanónica a partir de s# descripcióneom$trica%

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AREA M MATEMATICAS NIVEL SECUNDARIA GRADO UNDECIMO


PERIODO: PRIMERO

UNIDAD $EM2$ICA



DESEMPEOME$ODOLO"#A

RECURSOSDID2C$ICOS


10 6





CONJUN$OSNUM<RICOSC>* + 0('*'0+(C>* + 0(+*+(C>* + 0('-'0+(C>* + 0(-'-'0+(C>* + 0(+'0+(

IN$ERALOS A!"#$%&' C#$$()&' S#*"(!"#$%&' S#*"+#$$()&

INECUACIONES

I +' -+(L-+'0+(

I+'-+(C,'*-'(

I+'-+( +'0 '9(0*

C)'', ?*'(*', 0'(-+'+( + 0()+( "+*+(/'-'0+(/ +'0+(#((+0'-+( ?+'-+("(-(*+)'( )-(#

U(' 0( )+(+'0+( + 0' (0-<+ 9 0+)'( ?+>+--( +-0' 0'(+0'-+( + +/0( -*+'0( ? 0('0:-*)(

COMPE$ENCIA B2SICASR++ ? -++-' 0(+*( '(-'( ' 0()+( +'0+(

A:)+*' +-)-+*(? +(+(*'( ' 90+)'(0'*+'(

P+ (0-+( '90+)'( + -0++ ? +(-:'0'+(


Contri+#o a &#e los con"l ictosentre personas entre r#pos semane0en de manera pací"i ca constr#cti'a mediante la aplicaciónde estrateias +asadas en eldi!loo la neociación%

COMPETENCIAS LABORALESIndao los ar#mentos, e'idencias .ec.os&#e lle'an a los otros a pensar oe-presarsede #na determinada "orma

D+*+)-' +0 >*()- '0 + +*+++ 0'(0-< + 90+)'+-'.

R+(+0+ +>+--( +-+(( >*( )-(+ -+*--' +0 *+* +0)-().

C)++ +0 +* +-*+'0 .

R++(+*' 0' (0-< + '

-+'-< ' )'+' +>*/ + -*+'0 ?:,-')+*+.

I+*--' ' >*)- +(+ 0'(0-< + 90+)'+*+)-'

R+(+0+ 90+)'( + 0')'*+),*-' ? + '*,(-+-'( ? ++ ' +> * ) -

+*+++ ( (0-<.

P0'*+' ? (0-'-+'-+( +('*-('+ --+(''(

D+('00' +>+--( ''+*' (0-< '90+)'( -+'-+(



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PERIODO: SE"UNDO

UNIDAD $EM2$ICA



DESEMPEOME$ODOLO"#A

RECURSOS

DID2C$ICOS

CRI$ERIOS PROCEDIMIEN$OS


10 7





SUCESIONES

T)- (-) +' (+(-<

CLASIFICACIÓN DESUCESIONES

S+(-< C+-+*+S+(-+(D++-+*+(S+(-+( '*''(

(+-)+*+S+(-+( '*''(I+-)+*+

L#MI$E DE UNASUCESIÓN DEUNA SUCESIÓN

U*-0-=', ':)+*(+ 0' *+' +)+( '' >(*--' +0'-+(+ -0')+( '*'0+(.

D+(-9-, ?)+0',+<)+(

+-<-( +0 )+'0 ('+0'-+( ?-+(*-:)*-'

COMPETENCIA BÁSICASE+*' 0( *)-(:++'0+( +0 >* +(+(-+(

R++ ? -++-' 0'(-++*+( 0)-*+( +-+( *-:)*-'(.

J(*--' +(0*'(9*+-'( '' +*+)-'0)-*+( + 0'( (+(-+(


Utili/o distintas "ormas dee-presión para promo'er de"ender los derec.os .#manosen mi conte-to escolar com#nitario%

COMPETENCIAS LABORALESInteractúo con otros a#n&#e no loscono/ca pre'iamente, paraen"rentar #na tarea o sit#ación%

J(*--' +(0*'(9*+-'( '' +*+)-'*)-( :++'0+( +(+(-+(.

D+*+)-' +0 *- +(+(-+( (+: +0 '(0 ')+-*+.

D+('00' +>+--( ''

+*' (0-< '90+)'( + (+(-+(

D+*+)-' +0 *)- (-)+ ' (+(-< ' '*- +(( +0+)+*(.

E+*' 0( +0+)+*( +' (+(-< ' ( *)-(-)

C 0'(- - ' - ++ *+((+(-+( + '+ ' ((''*+(*-'(



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Responsa+ilidad en l a presentación decompromisos asinados%


PERIODO: $ERCERO

UNIDAD $EM2$ICA



DESEMPEOME$ODOLO"#A

RECURSOSDID2C$ICOS


10 8





FUNCIONESMA$EMA$ICAS

C+*( B,(-(

,&$*(- )#R#.$#-#/%(+"//( /+"/'

C(-#- )#

/+"&/#-'

A."+(+"/ )#/+"&/#-

FUNCIONES

POLINOMICAS,/+"/ L"/#(,/+"/ A/,/+"/ C()$%"+(,/+ "/ (&$ (!-&%&,/+"/ E-+(&/()(

R++, ?+(-9-, '( ? 0:'+( :+)*-(.

E(*'90+=+0'-+( ?-++-'( +*+-++*+( *'-+(+ )+( +'0+('' +-- (9+ (( + ' (-*'-<

''.


R++ 0'( 0'(+( +-+( 0-<)-'(.

P0'*+' +-)-+*('' (0-' 90+)'(*+*'0-='( ?++(+*'0(:,-')+*+.


Anali/o críticamente lasdecisiones, acciones # omisiones&#e se toman en el !m+itonacional o internacional &#ep#eden enerar con"l ictos oa"ectar los derec.os .#manos%

COMPETENCIAS LABORALESContri+#o para &#e los miem+rosdel e&#ipo aporten a la sol#ciónde los pro+lemas colecti'os%

C0'(--' -+(

T'9'>' )+0()'*+),*-( ++('00' +0 +(')-+*)-.

P0'*+' +-)-+*('' (0-' 90+)'(

*+*'0-='( ?++(+*'0(:,-')+*+.

D-++-' ' +0'-< +' -<

R++(+*' -+()'*+),*-' +)0+'-++*+( +:-(*(

'00' )-- ? ': + '-<

M'+>' +(*'*+:-'( + 0'(0-< + 90+)'( -+(.



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PERIODO: CUAR$O

10 9





UNIDAD $EM2$ICA



DESEMPEOME$ODOLO"#A

RECURSOSDID2C$ICOS


CALCULODIFERENCIAL EIN$E"RAL

D+-'' + '-<. I+)+*

+0'*-. F<)0'(

9,(-'( + 0'

+-'-<. D+-''(

'' -+(*-:)*-'(.

CALCULOINTEGRAL.

I*+:'0 +' -<.

I*+:'0+--'.

C,00 +-*+:'0+- )#"/")(-'

,$*(- !-"+(- )#"/%#$(+"/'

I/%#$(#- )#/+"&/#-%$"&/&*%$"+(-

M+0', (-*'-+(+V'-'-< +-<-' -+(* -:)*- '( +-*++* ? *-0-=(( +-''(.

I*++* 0' -<+ +-'' )'=< + ')9- ?) '0 + 0'+-+*+ + 0'*':+*+ ' ' '? +('00 )*('' @' 00' 0'(+-''( + '0:'(-+( 9,(-'( +*+*()'*+),*-( ? )'*+),*-(.


A0-' -(*-*( )*( ?-+'+( ++-'( ++0 ,00 + +-''( +-*+:'0+(

COMPETENCIA CIUDADANASComprendo la importancia de lade"ensa del medio am+iente, tantoen el ni'el local como lo+al, participo en iniciati'as a s# "a'or%

COMPETENCIAS LABORALESDetermino las ca#sas de loscon"lictos elimpacto &#e $stos tienen en lasdi"erentespersonas%

C)++ ? (' +0+* + +-'' +' -<.

E*' +-''( ++ (+- + '-< ''.

U*-0-= 0'( *-'( +

'-)'-<+ +(( ---*()-(.

I*++*' ? '00' ,+'()+-'*+ -*+:'0+(

J(*--' 0( '(( ++('00' + 0' +(0-<+ 90+)'

I*++*' +0 +* ++-''.

J(*--' 0' '0-'9-0-'+ 0( -++*+( )*(+ +-'-<

A0-' -(*-*( )*( ?-+'+( ++-'( ++0 ,00 + -*+:'0+(.

E-posición%E-plicación%Constr#cción paso a paso delconocimientoE0empli"icación%Desarrollo s#stentación detalleresra+a0os indi'id#ales ra+a0o cooperati'oDesarrollo de #ías deaprendi/a0e%Conc#rsos matem!ticoCons#ltas%Sociali/ación de las correcciones alas e'al#aciones aplicadas

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BIBLIO"RAF#A

CANO/ C')-0 E-+ ? *(. L:( M'*+),*-(. M''0 + '?

-,*-. M G'b-00. S'*' F + B:*,/ 18.

M--(*+- + E'-< N'-'0. L+? :++'0 + E'-<. L+? 115.

M':-(*+-/ 14.

M--(*+- + E'-< N'-'0. R+(0-< N)+ 2343. M':-(*+-.

J- 5 + 16.

DE GUWMAN/ M-:+0. O:'-='-< + E(*'( I9+')+-'( '' 0'

+'-</ 0' -+-' ? 0' 0*'. T++-'( ? ++-+-'( -''( +

+'-< )'*+),*-'/ 11.

DE WUBIRKA/ M-:+0. T'*' + P+'::' +*'0. P+(')-+* ?

A+-='>+H 0( -(*)+*( +0 -)-+*. F'-< A09+* M+'-.

S'*' F + B:*,/ 1.

CENTENO R./ G(*' +* '0. N+' M'*+),*-' C(**-' 1!Y ? 11Y.

L-9( ? 0-9(H S'*' F + B:*,/ 17.

CAJAMARCA RE$ CARLOS ENRIQUE. A++ ' +'(+ ' (+ ? ' 9'.

4 +--<. C'0-/ 2!!3.

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