COLEGIO OSCAR CASTRO PLANIFICACION2015ASIGNATURA: EDUCACION MATEMATICASFECHA:AGOSTO DE 2015CURSO: TERCEROS AOSA yB PROFESORA:CARMEN MUOZ URRUTIA - XIOMARA TRUJILLOOBJETIVO DE APRENDIZAJE CONTENIDO CURRICULAR INDICADOR DE LOGRO OBSERVACIONES NMEROS Y OPERACIONESOA 8D!"#$%&% '( )"!*%+,+ - $&.- , !(-$/*-/)&% 0$& 10 , !&+%& *%"1%#/2&:3 (#&+," %*%#+$&)/"+# )"+)%$y */)$4%/)3 5*%#&+," (+& !(-$/*-/)&)/4+ )"!" (+& &,/)/4+ , #(!&+,"# /1(&-#3 (#&+," -& ,/#$%/.($/2/,&, )"!"#$%&$1/& *&%& )"+#$%(/% - $&.-0$& - 10I,+$/6/)&+ #/$(&)/"+# , #( +$"%+" '( ,#)%/.+ -& &1%(*&)/4+ + 1%(*"# , -!+$"# /1(&-#73 R*%#+$&+ (+ )(+$" !&$!8$/)" '( # %6/% & (+/$(&)/4+ , )"!./+&% 1%(*"# /1(&-#9 *"%!,/" , (+&5*%#/4+ +(!:%/)&73 I-(#$%&+ y %*%#+$&+ (+& #(!& , 1%(*"# , -!+$"# /1(&-# *"% !,/" , (+& !(-$/*-/)&)/4+73 R*%#+$&+ )"+)%$&!+$ (+& !(-$/*-/)&)/4+ )"!" (+&3 &*-/)&+," -"# %#(-$&,"# , - $&.- , !(-$/*-/)&)/4+ 0$& 105109#/+ %&-/;&% )8-)(-"#3 %#"-2/+," *%".-! '( /+2"-()%+ - $&.- &*%+,/, 0$& - 10&,/)/4+ %*$/,& , 1%(*"# ,-!+$"# /1(&-#73 C%&+ (+ )(+$" !&$!8$/)" , (+& !(-$/*-/)&)/4+ ,&,& 5 ?73 R*%#+$&+ (+& !(-$/*-/)&)/4+ + 6"%!& )"+)%$&9 */)$4%/)& y #/!.4-/)&9 (#&+," (+& !&$%/; , *(+$"#73 C%&+ (+& !&$%/; , *(+$"9 *&%& ,!"#$%&% -& *%"*/,&,)"+!($&$/2&< *"% =!*-": 2 5 > @ > 5 273 R#(-2+ *%".-! , -& 2/,& )"$/,/&+&9 (#&+," -& M(-$/*-/)&)/4+ *&%& #( #"-()/4+73 R*/$+ - $&.- , !(-$/*-/)&)/4+ , !!"%/&7GEOMETRAOA 9D!"#$%&% '( )"!*%+,+ -& ,/2/#/4+ + - )"+$5$" , - $&.-> , 0$& 10510:3 %*%#+$&+," y 5*-/)&+," -&,/2/#/4+ )"!" %*&%$/)/4+ y &1%(*&)/4+ + *&%$# /1(&-#9 )"+ !&$%/&- )"+)%$" y */)$4%/)"73 )%&+," y %#"-2/+," *%".-! + )"+$5$"# '( /+)-(y&+ -& %*&%$/)/4+ y -& &1%(*&)/4+3 5*%#&+," -& ,/2/#/4+ )"!" (+(#$%&))/4+ %*$/,&7#)%/./+," y &*-/)&+," -& %-&)/4+ /+2%#& +$% -& ,/2/#/4+ y -& !(-$/*-/)&)/4+3 &*-/)&+," -"# %#(-$&,"# , - I,+$/6/)&+ #/$(&)/"+# , #( +$"%+" '( ,#)%/.+ (+&%*&%$/)/4+ + *&%$# /1(&-#73 R*%#+$&+ (+ )(+$" !&$!8$/)" '( # %6/% & (+/$(&)/4+ , %*&%$/)/4+ + *&%$# /1(&-#9(#&+," 6/)03 C%&+ (+ )(+$" !&$!8$/)" ,&,& (+&,/2/#/4+73 R-&)/"+&+ -& !(-$/*-/)&)/4+ )"+ -& ,/2/#/4+9 ($/-/;&+," (+&!&$%/; , *(+$"#9 y -& ,#)%/.+ )"+ 5*%#/"+# +(!:%/)3 A*-/)&+ -& %-&)/4+ /+2%#& +$% -& ,/2/#/4+ y -& !(-$/*-/)&)/4++ -& %#"-()/4+ , *%".-!$&.- , !(-$/*-/)&)/4+ 0$& 105109#/+ %&-/;&% )8-)(-"#OA 10R#"-2% *%".-! %($/+&%/"# + )"+$5$"# )"$/,/&+"#9 '( /+)-(y&+ ,/+%"/+2"-()%+ - )(&$%" "*%&)/"+# A+" )"!./+&,M",-&+ -& &,/)/4+ , ,"# " !8# +B!%"#9 ($/-/;&+," !&$%/&-)"+)%$" " %*%#+$&)/"+# */)$4%/) y %1/#$%&+ - *%")#" + 6"%!& #/!.4-/)&73 M",-&+ -& #(#$%&))/4+ , ,"# +B!%"#9($/-/;&+," !&$%/&- )"+)%$" " %*%#+$&)/"+# */)$4%/) y %1/#$%&+ - *%")#" + 6"%!& #/!.4-/)&73 F"%!(-&+ (+ )(+$" *&%& #(!&% 9 (+ )(+$" *&%& %#$&%9 (+& 0/#$"%/& *&%& !(-$/*-/)&% y "$%& 0/#$"%/& *&%& ,/2/,/%73 U$/-/;&+ *&%& #"-()/"+&% -& "*%&)/4+ &*%"*/&,&:- (+& #$%&$1/& *%"*/&- -& #$%&$1/& *"% ,#)"!*"#/)/4+(#&+," - &-1"%/$!" )"%%#*"+,/+$F%&))/"+#OA 11D!"#$%&% '( )"!*%+,+ - 6%&))/"+# , (#" )"!B+: 1C?9 1C>9 1C29 2C>9 >C?:3 5*-/)&+," '( (+& 6%&))/4+ %*%#+$& -& *&%$ , (+ $"," 9 , !&+%& )"+)%$&9 */)$4%/)&9 /!.4-/)&9, 6"%!& !&+(&- yC" )"+ #"6$D&% ,()&$/2"3 ,#)%/./+," #/$(&)/"+#9 + -)(&-# # *(, (#&% 6%&))/"+#3 )"!*&%&+," 6%&))/"+# , (+ !/#!"$","9 , /1(&- ,+"!/+&,"%I+,/)&+ )&%&)$%E#$/) )"!(+# , ,/6%+$# 6%&))/"+#9 ($/-/;&+," !&$%/&- )"+)%$" yC" %*%#+$&)/"+# */)$4%/)3 R-&$&+ #/$(&)/"+# , -& 2/,& )"$/,/&+& + - )(&-# # ($/-/;&+ F%&))/"+#3 C"+6))/"+&+ )"+ !&$%/&- )"+)%$" 6%&))/"+# *"% !,/" , )"%$#9 ,".-)# y )"-"%/,"9 -"# ,+"!/+&+ y ,!(#$%&+ '( - *&%$# #"+ /1(&-#73 R*%#+$&+ 6%&))/"+# #/!.4-/) , !&+%& )"+)%$& y */)$4%/)&73 D+"!/+&+ y %1/#$%&+ 6%&))/"+# *"% !,/" , %*%#+$&)/"+# */)$4%/)3 C"!*&%&+ 6%&))/"+# )"+ - !/#!" ,+"!/+&,"%9 ($/-/;&+," !",-"# , !&$%/&- )"+)%$"73 M",-&+ )"+ (+& !$86"%& - #/1+/6/)&," ,- +(!%&,"% y ,-,+"!/+&,"% y -" 5*-/)&+ )"+ %*%#+$&)/"+# 1%86/)3 I,+$/6/)&+ - +(!%&,"% y - ,+"!/+&,"% , (+& 6%&))/4+OA 12G+%&%9 ,#)%/./% y %1/#$%&% *&$%"+# +(!:%/)"#9 (#&+," (+& 2&%/,&, , #$%&$1/ + $&.- ,- 1009 , !&+%& !&+(&- yC" )"+ #"6$D&% ,()&$/2"D#)%/.+ -& %1-& , (+ *&$%4+ %*$/$/2",&,"9 /+)-(y+," - *(+$" , *&%$/,&9/+,/)&+ )4!" #/1( - *&$%4+73 I,+$/6/)&+ -& %1-& , (+ *&$%4+ , )%)/!/+$" )+,+$C,#)+,+$ y 5$/+,+ -"# ? *"# #/1(/+$# ,- *&$%4+73 U./)&+ y 5*-/)&+ 2&%/"# *&$%"+# , )%)/!/+$" )+,+$#C ,#)+,+$# +(+& $&.-& , 1009 , 6"%!& 0"%/;"+$&-92%$/)&- y ,/&1"+&-73 C"!*&%&+ *&$%"+# +(!:%/)"# , )"+$" , 2 + 29 , 5 + 59 , 10 + 109 , 25 + 25 y , 100 + 100 + 6"%!&)+,+$C,#)+,+$73 R*%#+$&+ (+ *&$%4+ )+,+$C,#)+,+$ ,&," +6"%!& )"+)%$&9 */)$4%/)& y #/!.4-/)&73 C%&+ y %*%#+$&+ (+ *&$%4+ , )%)/!/+$"7 )+,+$C ,#)+,+$ + 6"%!& )"+)%$&9 */)$4%/)& y #/!.4-/)&9 y,#)%/.+ -& %1-& &*-/)&,&73 S"-()/"+&+ (+ *%".-!&9 ($/-/;&+," *&$%"+# , )%)/!/+$")+,+$#C,#)+,+$#73 I,+$/6/)&+ y ,#)%/.+ *&$%"+# , )%)/!/+$" )+,+$#C,#)+,+$# + - +$"%+"73 I,+$/6/)&+9 ,#)%/.+ -& %1-& y )"!*-$&+ *&%$# 6&-$&+$# , (+ *&$%4+ , )%)/!/+$" )+,+$C,#)+,+$ ,&,"OA 13R#"-2% )(&)/"+# , (+ *" '(/+2"-()%+ &,/)/"+# y #(#$%&))/"+# y (+ #E!."-" 1"!:$%/)" '( D#)%/.+ y 5*-/)&+ (+& "*%&)/4+ /+2%#& )"+ &y(,& , -%-&)/"+# +(!:%/) + (+& 6&!/-/& , "*%&)/"+#9 *"% =!*-"9 F9 G y 1> + %*%#+$ (+ +B!%" ,#)"+")/,"9 + 6"%!& */)$4%/)& y #/!.4-/)& ,- 0 &- 10076"%!& )"+)%$&9 */)$4%/)& y #/!.4-/)&:R#(-2+ (+& )(&)/4+9 &*-/)&+," #$%&$1/ )"!" :- +#&y" y %%"%- ($/-/;&% -& "*%&)/4+ /+2%#& + 6"%!& )"+)%$&9 */)$4%/)& y #/!.4-/)&7A 1D#)%/./% -& -")&-/;&)/4+ , (+ ".=$"+ (+ !&*& #/!*- " )(&,%E)(-&D#)%/.+ (+ !&*& #+)/--"< *"% =!*-"9(+ !&*& , 6&+$E&,- +$"%+"73 O$"%1&+ -$% " +B!%"# & - )"-(!+ y 6/- + (+& )(&,%E)(-&,9 *"% =!*-"9 F 5 573 SH&-&+ -(1&%# + (+& )(&,%E)(-& & *&%$/% , - )"-(!+ y 6/- ($/-/;&+," -$% " +B!%"#73 E+)(+$%&+ -(1&%# + (+ !&*& ,- $#"%"73 D#)%/.+ -& .B#'(,& , (+ $#"%" " (+2/&= /!&1/+&%/"9 /+,/)&+," %6%+)/ 5*%#&, )"+ -$% y +B!%"#< *"%=!*-": A?9 C29 $)I3 A,/2/+&+ 6/1(% -&."%&, *"% "$%& *%#"+& + (+& )(&,%E)(-&9 & *&%$/% , %6%+)/ 5*%#&,)"!" B >OA 15D!"#$%&% '( )"!*%+,+ -&%-&)/4+ '( 5/#$ +$% 6/1(% >D y6/1(% 2D:3 )"+#$%(y+," (+& 6/1(%& >D & *&%$/%, (+& %, A*-&+$/--&J3 ,#*-1&+," -& 6/1(%& >DD#)%/.+ - 6/1(% 2D '( 6"%!&+ - %,# A*-&+$/--J , 6/1(% >D )"!" )(."#9 *&%&--*E*,"#9 )/-/+,%"# y )"+"#9,#&%!8+,"-3 D#)%/.+ 6/1(% >D )"!" )(."#9 *&%&--*E*,"#9 )/-/+,%"# y )"+"# , &)(%," & #(# )&% &%/#$ y 2:%$/)#73 R-&)/"+&+ %,# , 6/1(% >D )"+ - 6/1(% 2D )"%%#*"+,/+$#73 R)"+")+ 6/1(% >D , &)(%," & 2/#$ , ,"# ,/!+#/"+#73 A%!&+ (+& 6/1(%& >D9 *"% =!*-" (+ )(." yC" (+ *&%&--*E*,"9 & *&%$/% , (+& %, $%&;&,&OA 1FD#)%/./% )(."#9 *&%&--*E*,"#9#6% )"+"#9 )/-/+,%"# y */%8!/,# , &)(%," & -& 6"%!& , #(# )&% y I,+$/6/)&+ y ,+"!/+&+ 6/1(% 2D )"!"*&%$ , 6/1(% >D )"+)%$"# ,- +$"%+"73 C-/6/)&+ 6/1(% 2D7- +B!%" , &%/#$ y 2:%$/)#7 3 E-&."%&+ (+& 6/1(%& ,&,& + (+ 1"*-&+"9 )"+ - *&%$# , (+$&+1%&!& yC" %)"%$#73 E-&."%&+ 6/1(% 2D + 6"%!& */)$4%/)&9 ($/-/;&+," (+& !&$%/; , *(+$"#73 E-&."%&+ (+ )(&,%&,"9 *-1&+,"(+& 0"=& , *&*-73 D/.(=&+ 6/1(% (#&+," *&*- )(&,%/)(-&," " , *(+$"#OA 1GR)"+")% + - +$"%+" 6/1(% 2D '( #$8+ $%-&,&, %6-=&, y %"$&,R)"+")+ 6/1(% 2D %6-=&, $%-&,&, y %"$&, + 6/1(% 2D ,- +$"%+"9 -$% , /!*%+$&9 #H&-# ,$%8+#/$"9 $)73 F"%!&+ 6/1(% %6-=&, y $%-&,&, + - 1"*-&+"9 + *&*- )(&,%/)(-&," " (#&+," /+#$%(!+$"# 1"!:$%/)"#73 F"%!&+ 6/1(% 2D .8#/) %"$&, #/+," (+" , #(# 2:%$/)# - )+$%" , %"$&)/4+ y ($/-/;&+," *-&+$/--&73 D/.(=&+ 6/1(% 2D %6-=&, $%-&,&, y %"$&, (#&+," /+#$%(!+$"# 1"!:$%/)"# )"!" -& %1-& y-& #)(&,%&7OA 1KD!"#$%&% '( )"!*%+,+ - )"+)*$" , 8+1(-":3 /,+$/6/)&+," =!*-"# , 8+1(-"#+ - +$"%+"3 #$/!&+," -& !,/,& , 8+1(-"#9(#&+," )"!" %6%+$ 8+1(-"# ,?5L y , M0LE-&."%&+ (+ 8+1(-" %)$"9 *-1&+," (+& 0"=& , *&*- #1B+ /+#$%())/4+73 C"+6))/"+&+ (+ 8+1(-" %)$" y , ?5L73 I,+$/6/)&+ 8+1(-"# + 6/1(% 2D ,- +$"%+"73 I,+$/6/)&+ 8+1(-"# + 6/1(% >D ,- +$"%+"73 R)"+")+ 8+1(-"# + 6/1(% 2D ,- +$"%+"9 !&y"%# y !+"%# , M0L y 8+1(-"# + 2D ,- +$"%+"9 !&y"%#y !+"%# , ?5L73 E#$/!&+ 8+1(-"# , ?5L y , M0L y )"!*%(.&+9 !/,/:+,"-"#MEDICI!NOA 1ML%/+$%*%$&% -E+ , $/!*" yC&-+,&%/"#S)(+)/&+ 2+$"# + - $/!*"73 L+/+$%*%$&+ 0"%&%/"# ,/2%#"# y )%"+"1%&!3 C%&+ (+ )&-+,&%/" '( /+)-(y ,E ,-& #!&+&9 6)0 /!*"%$&+$# y 6)0 *%#"+&-#73 D!(#$%&+ - *" ,- $/!*" , &)(%," & &)$/2/,&,# *%#"+&-# #/1+/6/)&$/2OA 20L% y %1/#$%&% - $/!*" + 0"%!,/ 0"% )(&%$"# , 0"%& y !/+($"# + %-"=# &+8-"1"# y ,/1/$&-#D#)%/.+ -& *"#/)/4+ , -"# *(+$%"# *&%& !,/ 0"% )(&%$"# , 0"%&9 0"% y !/+($"# + %-"=# &+8-"1"#73 L+ - $/!*" )"+ /+$%2&-"# , !,/0"% )(&%$"# , 0"%&9 0"% y !/+($"# ($/-/;&+," %-"=# &+8-"1"# y ,/1/$&-#73 M/,+ - $/!*" $%&+#)(%%/,"73 U$/-/;&+ !,/, , $/!*" *&%& /+,/)&%2+$"#OA 21D!"#$%&% '( )"!*%+,+ -*%E!$%" , (+& 6/1(%& %1(-&% /%%1(-&%:3 !/,/+," y %1/#$%&+," - *%E!$%", 6/1(% ,- +$"%+" + - )"+$5$" , -& %#"-()/4+ , *%".-!3 ,$%!/+&+," - *%E!$%" , (+M/,+ - *%E!$%" , 6/1(% *-&+3 H&--&+ - *%E!$%" , %)$8+1(-"# y )(&,%&,"# & *&%$/% , - *%"*/,&,# , #(# -&,"#3 C&-)(-&+ - *%E!$%" , %)$8+1(-"# y )(&,%&,"# " -&,"#, #$"#)(&,%&," y , (+ %)$8+1(-"OA 22D!"#$%&% '( )"!*%+,+ -& !,/)/4+ ,- *#" A1 y N1J:3 )"!*&%&+," y "%,+&+," ,"# " !8#".=$"# & *&%$/% , #( *#" , !&+%&/+6"%!&-3 (#&+," !",-"# *&%& 5*-/)&% -&%-&)/4+ '( 5/#$ +$% 1%&!"# yN/-"1%&!"#3 #$/!&+," - *#" , ".=$"# , (#")"$/,/&+"9 (#&+," %6%+$#3 !/,/+," y %1/#$%&+," - *#" ,".=$"# + +B!%"# y + 6%&))/"+#, (#" )"!B+9 + - )"+$5$" , -&%#"-()/4+ , *%".-!E-/1+ ".=$"# , #( +$"%+" *&%& ($/-/;&%-"# *&%& ,$%!/+&% - *#" , ".=$"# , (#" )"$/,/&+"73 C"!*&%&+ ".=$"# , (#" )"$/,/&+"9 ($/-/;&+," (+& .&-&+;&73 E#$/!&+ - *#" , 6%($ B$/-#9 !)"$ &+/!&-#9 (#&+," (+ %6%+$9 y 6(+,&!+$&+ #( -))/4+73 E5*-/)&+ )4!" 6(+)/"+& (+& .&-&+;&73 R-&)/"+&+ ".=$"# ,- +$"%+" y &+/!&-# , &)(%," & #( *#" y 6(+,&!+$&+ -& #"-()/4+73 C&-)(-&+ - *#" , ".=$"# & *&%$/% , ,&$"# )"+")/,"# ,-*#" , (+/,&,# , (+ ".=$" A1 " N1J ($/-/;&+," (+ *&$%4+3 R-&)/"+&+ !,/, , *")" y , !()0" *#" )"+ %#*)$" & ".=$"# y &+/!&-# , *")" y , !()0" *#"7DATOS Y PROBABILIDADESOA 2>R&-/;&% +)(#$ y )-/6/)&% y "%1&+/;&% -"# ,&$"# ".$+/,"# + $&.- y 2/#(&-/;&%-"# + 1%86/)"# , .&%%&7R1/#$%&+ /+6"%!&)/4+ +(!:%/)& , ,&$"# + $&.- , )"+$"73 E5*-/)&+ - &$%/.($" (#&," *&%& - %1/#$%" , ,&$"# + (+ 1%86/)"73 E-&."%&+9 *&%& (+& #%/ , ,&$"# ,&,"#9,/6%+$# 6"%! , %1/#$%"9 *"% !,/" , (+& -/#$&9 (+& $&.-&9 (+& $&.-& ,)"+$" y (+ 1%86/)" , .&%%&73 R)"-)$&+ /+6"%!&)/4+ y %1/#$%&+ -"# ,&$"# ".$+/,"# *"% !,/" , (+& -/#$&9 (+& $&.-& , )"+$" y + 1%86/)"# , .&%%&OA 2?R1/#$%&% y "%,+&% ,&$"# ".$+/,"#, =(1"# &-&$"%/"# )"+ ,&,"# y!"+, +)"+$%&+," - !+"%9 -!&y"% y #$/!&+," - *(+$" !,/"+$% &!."#7R&-/;&+ =(1"# &-&$"%/"# )"+ ,&,"# , ,/6%+$# 6"%! A)(."#9 $$%&,%"# ( "$%"#J y !"+, %1/#$%&+," -"# %#(-$&,"# + $&.- , )"+$" y ,/&1%&! , *(+$"73 R"$(-&+ - $&.- , )"+$" y ,/&1%&! , *(+$"73 I+,/)&+ - !+"%9 - !&y"% y - *(+$" !,/"73 E5$%&+ /+6"%!&)/4+ , $&.- , )"+$"7OA 25C"+#$%(/%9 -%/+$%*%$&% */)$"1%&! y 1%86/)"# , .&%%& #/!*- )"+ #)&-&9 + . & /+6"%!&)/4+ %)"-)$&,& " ,&,&E-&."%&+ */)$"1%&! y 1%86/)"# , .&%%& *&%& %*%#+$&% (+& #%/ , ,&$"#9 (#&+," (+& )"%%#*"+,+)/&< *"% =!*-":2 & 19 5 & 1 ( "$%"#73 D#)%/.+ y 5*-/)&+ - *&%$# , (+ */)$"1%&!& y , (+1%86/)" , .&%% ,&,": - $E$(-"9 -"# =#9 -"# %4$(-"# y -.&%%3 E-&."%&+ (+ 1%86/)" , .&%% *&%& (+ %1/#$%" , ,&$"# ,&,"# y *%"*/"#9 /+,/)&+," - $E$(-"9 -"# =# y -"# %4$(-"# y1%&6/)&+," - .&%%3 A*-/)&+ (+& #)&-& )"+2+/+$ *&%& -"#=# , (+ 1%86/)" , .&%% )"+ #)&-&9 , &)(%," & -"# ,&$"# ,/#*"+/.-#< *"%=!*-": 2 & 19 5 & 1 ( "$%"#73 E5*-/)&+ ,&$"# %*%#+$&,"# + 1%86/)"# , .&%%& y + */)$"1%&!3 R#*"+,+ *%1(+$ , &)(%," & (+ 1%86/)"9 (+& $&.-& "(+& -/#$& , ,&$"# ,&,"#OA 2FR*%#+$&% ,&$"# (#&+," ,/&1%&! , *(+$"#7D#)%/.+ (+ ,/&1%&!& , *(+$"#73 R"$(-&+ (+ ,/&1%&!& , *(+$"#73 R1/#$%&+ /+6"%!&)/4+ +(!:%/)& , ,&$"# + ,/&1%&! , *(+$"73 R#*"+,+ *%1(+$ , &)(%," & (+ 1%86/)" , *(+$"#