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“eje de simetría”?, ¿recuerdan qué actividades hicieron cuando hablaron del eje de

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WR.G 4D5/:3 1L1:/2/ /4 =1 L1461==1XJJJ 9:/>;34/4 36:1 F/H =1 6/2=1 _ WR.G

4D5/:3 1L1:/2/XJJJ 9:/>;34/4 F1:;1> F/2/> =1 6/2=1 _ E 5;:/4 21?1 F/H O.G

4D5/:3 1L1:/2/J W93: O.G 2://4 O./ 1L1:/2/4 />3> 4D5/:3>XJJJ

PU +Q3:1 L:/>;34/4 =1> 6/2=1> >;0.;/46/> /4 /= 3:?/4 /4 O./ F3E 1 ?/2;:=1>, U ^ T _

WR.G 4D5/:3 1L1:/2/ /4 =1 L1461==1XJJJ 9:/>;34/4 36:1 F/H =1 6/2=1 _ WR.G4D5/:3 1L1:/2/XJJJ 9:/>;34/4 F1:;1> F/2/> =1 6/2=1 _ E 5;:/4 21?1 F/H O.G

4D5/:3 1L1:/2/J W93: O.G 2://4 O./ 1L1:/2/4 />3> 4D5/:3>XJJJ

2U +Q3:1 L:30:15/4 .>6/?/> =1 21=2.=1?3:1 L1:1 O./ F1E1 >.514?3 ?/ 6:/> /4 6:/>J

WR.G 6/2=1> ?/P/4 L:/>;341: E /4 O.G 3:?/4 ?/P/4 Q12/:=3X

8@>H3 N2 #:014;2/ 1= 0:.L3 /4 L1:/C1>B L:/@/:/46/5/46/ O./ >/14 1=.543> ?/= 5;>53

0:1?3 escolar, y explique las reglas del juego: “Ahora uno de ustedes va a ir sumando de

?3> /4 ?3> 3 ?/ 6:/> /4 6:/>B >/0D4 /= 4D5/:3 O./ E3 ?;01B L/:3 >;4 .>1: =1 21=2.=1?3:1B =3F14 1 Q12/: 5/461=5/46/, ?;2/4 /= 4D5/:3 O./ ?/P/ >1=;: 21?1 F/H O./ >/ L:/>;341 =1

L Adaptación de “Dando saltos”, en Gálvez, G; Navarro, S; Riveros, M; Zanocco, P. (1994) :=5'.&$'.&4

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6/2=1 _J M. 235L1`/:3 3 235L1`/:1 .>1:A =1 21=2.=1?3:1 L1:1 F/:;@;21: >; >. :/>L./>61 />

=1 23::/261J k3 F3E 1 ?/2;: Q1>61 O.G 4D5/:3 ?/P/4 ==/01:B />1 >/:A =1 5/61J M; /=

235L1`/:3 O./ 43 .>1 =1 21=2.=1?3:1 =30:1 ==/01: 1 =1 5/61 >;4 /O.;F321:>/B 0141 />1

L1:6;?1B L/:3 >; /4 1=0D4 535/463 >/ /O.;F321B 0141 /= 36:3 235L1`/:3J (/>L.G> >/

;46/:215P;14 =3> L1L/=/>, O.;/4 L:;5/:3 6/4K1 =1 21=2.=1?3:1 1Q3:1 >.51:A 5/461=5/46/

.>14?3 /= 5;>53 4D5/:3 O./ /4 =1 L1:6;?1 146/:;3: E /= 36:3 F/:;@;21:A 234 =1 21=2.=1?3:1J

-.01:A4 234 6:/> 4D5/:3> ?;@/:/46/>J += @;41=B /= 0141?3: 3 0141?3:1 ?/@;4;6;F3 >/:A O.;/4

haya ganado más partidas.”

)3> 4D5/:3> 234 =3> O./ C.01:A4 >34, [B _ E cJ <34 /= 4D5/:3 [ ?/P/:A4 ==/01: Q1>61 /=

[TB 234 /= 4D5/:3 _ ?/P/:A4 ==/01: Q1>61 /= _T E 234 /= 4D5/:3 c Q1>61 /= cTJ

*'-,&&#++# *' +, -'-./"

SJ +46/> ?/ O./ =3> 1=.543> ==/F/4 1 21P3 =1 91:6/ SB L/:5;61 O./ /bL=3:/4

=;P:/5/46/ /= @.42;3415;/463 ?/ =1 21=2.=1?3:1J 91:1 1L3E1: />1 /bL=3:12;I4B

.>6/? L./?/ L/?;:=/> O./ 1F/:;0l/4 234 O.G 6/2=1 >/ /42;/4?/B 234 2.A= >/ 1L101J

9./?/ L/?;:=/> 615P;G4 O./ L:/>;34/4 F1:;1> 6/2=1> ?/ 4D5/:3> L1:1 F/: Q1>61

2.A461> 2;@:1> L./?/4 F/:>/ /4 =1 L1461==1 N/4 =1 51E3:K1 ?/ =1> 21=2.=1?3:1>

235.4/> 1L1:/2/4 Q1>61 j 2;@:1>UJ 9:/0.46/, WO.G L1>1 >; 6/2=/14 5A> ?/ 32Q3

cifras? (aparece una letra E, que indica “Error”).

[J )=/F/ 1 21P3 =1 91:6/ S ?/ =1 126;F;?1?J '= L:3LI>;63 ?/ />1 L1:6/ /> O./ =3>

1=.543> 235L:/4?14 /= L:32/?;5;/463 L1:1 L:30:151: =1 21=2.=1?3:1 ?/ 514/:1

61= O./ >/ L./?1 ;: >.514?3 /= 4D5/:3 /=/0;?3 2.1461> F/2/> >/ O.;/:1B 1 L1:6;:

?/ 2/:3J

_J +4;5/ 1 =3> 1=.543> 1 O./ /bL:/>/4B 234 >.> L:3L;1> L1=1P:1>B >. :/>L./>61 1 =1

pregunta “¿Por qué creen que aparecen />3> 4D5/:3>X”. Algunas respuestas

pueden ser: “porque va sumando de dos en dos”, “es la tabla del dos”.

eJ )=/F/ 1 21P3 =1 91:6/ [ ?/ =1 126;F;?1?J Z41 F/H O./ /4 21?1 L1:/C1 Q1E1 .4

0141?3:B L:/0.46/ 1= 0:.L3 =3 >;0.;/46/, WO.G >/:;/ 4.5G:;21 >/ =/> Q;H3 5A>

?;@K2;=B =1 ?/= [ 3 =1 ?/= _XB W=1 ?/= _ 3 =1 ?/= cXB WO.G 234>/C3> =/ ?1:K14 1 1=0.;/4 1



W@

O.;/4 >/ =/ ?;@;2.=61 >.51: ?/ 6:/> /4 6:/>XB WE L1:1 1=0.;/4 1 O.;/4 >/ =/ ?;@;2.=61

>.51: ?/ c /4 cX

#&.'"J,<.#"'- '-8'<KL.<,- 8,&, '+ $#".J#&

M/0.:15/46/ F1:;3> ?/ =3> 1=.543> E1 Q14 6/4;?3 /bL/:;/42;1> 234 36:1> 21=2.=1?3:1>B E1>/1 L3:O./ =1> .>14 /4 /= >1=I4 ?/ 2=1>/ 3 /4 >. 21>1J (/ 63?1> @3:51> /> 234F/4;/46/

O./ /= 0:.L3 /bL=3:/ /= @.42;3415;/463 PA>;23 ?/ =1 21=2.=1?3:1 2353 >/ L:3L34/ /4 /=

punto 1 del apartado “Desarrollo de la sesión”.

$;/46:1> =1> L1:/C1> C./014B L:32.:/ 2;:2.=1: /46:/ /==1> L1:1 1E.?1:=/> /4 21>3 ?/ O./

6/4014 ?;@;2.=61?/> L1:1 3:014;H1:>/ 3 L1:1 235L:/4?/: =1> :/0=1> ?/= C./03J

M; =3 234>;?/:1 234F/4;/46/B .>6/? L./?/ L34/: 5/61> ?;@/:/46/> L1:1 =3> 1=.543> ?/

21?1 0:1?3\ L3: /C/5L=3B L1:1 =3> ?/ L:;5/: 0:1?3 L;?1 O./ ==/0./4 Q1>61 /= Sc 3 Sj2.14?3 C./014 234 /= 4D5/:3 _B 3 O./ ==/0./4 Q1>61 /= _T 2.14?3 C./014 234 /= 4D5/:3

cJ (/ =1 5;>51 514/:1B .>6/? L./?/ 1.5/461: =1> 5/61> L1:1 =3> 1=.543> ?/ 6/:2/:

0:1?3 / ;42=.>3 L:3L34/: 36:1> >/:;/> 4.5G:;21>J



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-34567 Y

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)3> 1=.543> 2./4614 ?/ ?3> /4 ?3> E ?/ 6:/> /4 6:/>B 5/?;146/ .4 C./03 >3P:/ .41 :/261

4.5G:;21B 234 =1 @;41=;?1? ?/ ?/>1::3==1: =1 432;I4 ?/ 5D=6;L=3J

#&;,".9,<./" *'+ ;&=8#

SJ g3:5/ /O.;L3> ?/ 6:/> 1 2.16:3 1=.543> E /46:/0./ 1 21?1 /O.;L3 .41 P3=>1 234

@;2Q1>B .41 6;:1 ?/ 21:6342;==3 numerada (ver “Orientaciones específicas”) E .41

P3=>1 234 Q1P1> N3 234 36:1> >/5;==1> 0:14?/>UJ

[J 'bL=;O./ /4 O.G 234>;>6/ /= C./03, “M/ 6:161 ?/ .41 L.=01 O./ 6:161:A ?/ :/23::/:

63?1 =1 6;:1 4.5/:1?1 ?14?3 >1=6;63> >;4 21/: /4 .41 6:15L1J +=0.;/4 ?/= /O.;L3

L34?:A .41 Q1P1 >3P:/ =1 6;:1B />1 >/:A =1 6:15L1\ 21?1 .43 ?/ .>6/?/> 6/4?:A >.

„L.=01‟, que son las fichas; a46/> ?/ O./ .>6/?/> Q1014 >1=61: 1 >. L.=01B ?/P/:A4

?/2;?;: ?/ O.G 6151`3 >/:A /= >1=63 ?/ =1 L.=01B >; >/:A ?/ ?3> 3 ?/ 6:/> />L12;3>\

?/P/:A4 L/4>1:=3 5.E P;/4 L1:1 /F;61: O./ 21;01 /4 =1 trampa”.

_J 'bL=;O./ =1 @3:51 /4 O./ >/ 3:014;H1:A 21?1 /O.;L3 L1:1 ==/F1: 1 21P3 /= C./03,

– '4 21?1 /O.;L3 ?/2;?/4 O.;G4 >/:A /= L:;5/: C.01?3: O./ L34/ =1 6:15L1J

– '= C.01?3: 1 O.;/4 =/ 6321 L34/: =1 6:15L1 23=321 .41 Q1P1 /4 2.1=O.;/:

4D5/:3 ?/ =1 6;:1?1 ?/>L.G> ?/= 2/:3J '>1 Q1P1 /> =1 6:15L1J

– )3> ?/5A> C.01?3:/> 63514 .41 @;2Q1 ?/ =1 P3=>1J 8/4 ?I4?/ />6A =1 6:15L1 E

21?1 .43 ?/2;?/ >; >. @;2Q1 :/23::/:A =1 6;:1 >1=614?3 ?/ ?3> /4 ?3> 3 ?/ 6:/> /4

6:/>J

– '4 >. 6.:43B 21?1 C.01?3: L34/ >. @;2Q1 /4 /= 4D5/:3 2/:3 E =1 Q12/ 1F14H1:

>1=614?3 ?/ ?3> /4 ?3> 3 ?/ 6:/> /4 6:/>B >/0D4 Q1E1 />230;?3J M; />230;I

b`3%+$+ $/ B<'/" 8 :=5'.&' C"+'*,+$-"(D @54=<'(+"( ="5" &$7'5+$5(' 8 +5"#"E"5 '. '% "<%"D V30/,,&-'

“Libros del Rincón”, SEP. AbbA



W"

>1=63> ?/ ?3> />L12;3>B 2.14?3 =/ 6321 >. 6.:43 >1=61 1= ?3>B 1= 2.16:3B 1= >/;> E

1>K Q1>61 >1=;: ?/ =1 6;:1J M; 21/ /4 =1 6:15L1B 43 L./?/ >/0.;:J

– <.14?3 .4 C.01?3: =30:1 >1=61: 63?1 =1 6;:1 >;4 21/: /4 =1 6:15L1B >/ O./?1 234

>. @;2Q1J M; 43B >/ O./?1 234 =1 @;2Q1 /= C.01?3: O./ L.>3 =1 6:15L1J

– <.14?3 63?3> Q14 Q/2Q3 1F14H1: >. @;2Q1B 6321 1 36:3 C.01?3: L34/: =1 6:15L1J – '= C./03 6/:5;41 2.14?3 21?1 C.01?3: Q1 L./>63 =1 6:15L1 ?3> F/2/>J

– a141 /= C.01?3: O./ >/ O./?1 234 5A> @;2Q1>J

*'-,&&#++# *' +, -'-./"

SJ <.14?3 63?3> =3> L1:6;2;L146/> ?/ 21?1 /O.;L3 Q1E14 L./>63 =1 6:15L1 .41 F/HB

Q101 .41 L1.>1 L1:1 ==/F1: 1 21P3B ?/ 514/:1 P:/F/B .41 L./>61 /4 235D4B 234

=1 @;41=;?1? ?/ O./ /4 =1> >;0.;/46/> :34?1> =3> 1=.543> L./?14 5/C3:1: >.>/>6:16/0;1> ?/ C./03J 91:1 /==3B .>6/? L./?/ L=146/1: =3 >;0.;/46/,

– WY1E 1=0.41 514/:1 ?/ /F;61: O./ =1 L.=01 21;01 /4 =1 6:15L1XB WO.G

>.0/:/42;1> Q1:K14 1 36:3> C.01?3:/> L1:1 =30:1: O./ =1 L.=01 :/23::1 63?1 =1

6;:1 >;4 21/: /4 =1 6:15L1X

– Wk O.G >.0/:/42;1> L./?/4 Q12/: para poner “buenas trampas”? Es decir, ¿en

O.G 4D5/:3 3 4D5/:3> 234F;/4/ L34/: =1 6:15L1 L1:1 1>/0.:1:43> ?/ O./ =1

L.=01 21;01 /4 /==1X

[J Z41 F/H O./ =3> /O.;L3> Q1E14 235L1:6;?3 />6:16/0;1>B 2346;4D14 C.014?3 Q1>61

O./ 21?1 C.01?3: Q1E1 L./>63 =1 6:15L1 ?3> F/2/>J

_J 91:1 2/::1: =1 >/>;I4B L:3L3401 1= 0:.L3 =1> >;0.;/46/> L:/0.461>B =1> 2.1=/> 43

6;/4/4 O./ >/: 2346/>61?1> 4/2/>1:;15/46/ /4 />61 >/>;I4B >;43 O./ L./?/

dejarlas como “preguntas para pensar” con la finalidad de que para la próxima vez

O./ C./0./n a “La pulga y las trampas”, tengan mejores estrategias tanto para

23=321: =1> 6:15L1> 2353 L1:1 /F;61: 21/: /4 /==1>,

– M; ?/2;?3 O./ =1 L.=01 >1=6/ ?/ ?3> /4 ?3> 1 L1:6;: ?/= 2/:3B W/4 O.G 4D5/:3>

F1 1 21/: >;/5L:/XB WO.G 61P=1 ?/ 5.=6;L=;21: ?1 />3> 4D5/:3> 2353

:/>.=61?3X

– M; ?/2;?3 O./ =1 L.=01 >1=6G ?/ 6:/> /4 6:/> 1 L1:6;: ?/= 2/:3B W/4 O.G 4D5/:3>

F1 1 21/: >;/5L:/XB WO.G 61P=1 ?/ 5.=6;L=;21: ?1 />3> 4D5/:3> 2353

:/>.=61?3X



WC

– k >/ =1 L.=01 >1=61:1 ?/ 2;423 /4 2;423 1 L1:6;: ?/= 2/:3B W/4 O.G 4D5/:3> F1 1

21/: >;/5L:/XB WO.G 61P=1 ?/ 5.=6;L=;21: ?1 />3> 4D5/:3> 2353 :/>.=61?3X

#&.'"J,<.#"'- '-8'<KL.<,- 8,&, '+ $#".J#&)1 6;:1 ?/ 21:6342;==3 6/4?:A 14361?3> =3> 4D5/:3> ?/= T 1= _TJ )3> />L12;3> /46:/ =3>

4D5/:3> ?/P/4 ?/ >/: ?/ 2.16:3 2/46K5/6:3>J )1 6;:1 6/4?:A 1L:3b;51?15/46/ .4 5/6:3

?/ =1:03 L3: 2;423 2/46K5/6:3> ?/ 142Q3J M; =3 234>;?/:1 234F/4;/46/B /4 F/H ?/ .>1:

21:6342;==3 L./?/ ?;P.C1: =1 6;:1 /4 /= L;>3J M/ :/O.;/:/ ?/ .41 6;:1 L3: /O.;L3J

@ A " C W Y Z _ L b A@ AA A" AC AW AY AZ A_ AL Ab "@…

$;/46:1> =3> /O.;L3> C./014B L:32.:/ 2;:2.=1: /46:/ /==3> L1:1 1E.?1:=/> /4 21>3 ?/ O./

6/4014 ?;@;2.=61?/> L1:1 3:014;H1:>/ 3 L1:1 235L:/4?/: =1> :/0=1> ?/= C./03J '> 5.E

L:3P1P=/ O./ 1= L:;42;L;3 =3> 1=.543> 43 Q1014 .>3 ?/ 4;40.41 />6:16/0;1 4; L1:1 /=/0;: /=

6151`3 ?/= >1=63 4; L1:1 23=321: =1 6:15L1B =3 2.1= L./?/ @1F3:/2/: O./ L;/:?14 234 2;/:61

@:/2./42;1J 9/:5;61 O./ C./0./4 2353 /==3> L./?14B L3>6/:;3:5/46/B 2353 >/ ;4?;21 /4

“Desarrollo de la sesión”, usted podrá hacer una pausa para que los alumnos compartan

>.> />6:16/0;1> E 6/4014 51E3:/> /=/5/463> L1:1 0141:J



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)3> 1=.543> Q12/4 >.51> >.2/>;F1> 1 L1:6;: ?/ .4 4D5/:3 ?1?3B 5/?;146/ .4 C./03 234

=1 21=2.=1?3:1B 234 =1 @;41=;?1? ?/ ?/>1::3==1: >.> Q1P;=;?1?/> ?/ 2A=2.=3 5/461=J

#&;,".9,<./" *'+ ;&=8#

8@>H3 12 '46:/0./ 1 21?1 1=.543 .41 21=2.=1?3:1 E /bL=;O./ =1 L:;5/:1 L1:6/ ?/ =1

126;F;?1?,

1U 9:/>;34/4 =1> >;0.;/46/> 6/2=1> /4 /= 3:?/4 /4 O./ F3E 1 ?/2;:=1>, P ^ N _


4D5/:3 1L1:/2/XJJJ 9:/>;34/4 F1:;1> F/2/> =1 6/2=1 _ E 5;:/4 21?1 F/H O.G

4D5/:3 1L1:/2/J W93: O.G 2://4 O./ 1L1:/2/4 />3> 4D5/:3>XJJJ

PU +Q3:1 L:/>;34/4 =1> 6/2=1> >;0.;/46/> /4 /= 3:?/4 /4 O./ F3E 1 ?/2;:=1>, N ^ P _


4D5/:3 1L1:/2/XJJJ 9:/>;34/4 F1:;1> F/2/> =1 6/2=1 _ E 5;:/4 21?1 F/H O.G

4D5/:3 1L1:/2/J W93: O.G 2://4 O./ 1L1:/2/4 />3> 4D5/:3>XJJJ

8@>H3 N2 #:014;2/ 1= 0:.L3 /4 L1:/C1>B L:/@/:/46/5/46/ O./ >/14 1=.543> ?/= 5;>53

grado escolar, y explique las reglas del juego: “Ahora yo voy a decir un nú5/:3 234 /= O./

63?3> F14 1 /5L/H1:J MI=3 .43 ?/ .>6/?/> .>1:A =1 21=2.=1?3:1J '= 36:3 ;:A >.514?3

5/461=5/46/B ?/ ?3> /4 ?3> 3 ?/ 6:/> /4 6:/>B >/0D4 E3 >/ =3> ;4?;O./\ ?;:A /= 4D5/:3

O./ ?/P/ >1=;: 21?1 F/H O./ >/ L:/>;341 =1 6/2=1 _J M. 235L1`/:3 3 235L1`/:1 .>1:A =121=2.=1?3:1 L1:1 F/:;@;21: >; >. :/>L./>61 /> =1 23::/261J k3 F3E 1 ?/2;: Q1>61 O.G 4D5/:3

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?/P/4 ==/01:B />1 >/:A =1 5/61J M; /= 235L1`/:3 O./ 43 .>1 =1 21=2.=1?3:1 =30:1 ==/01: 1 =1

5/61 >;4 /O.;F321:>/B 0141 />1 L1:6;?1B L/:3 >; /4 1=0D4 535/463 >/ /O.;F321B 0141 /=

36:3 235L1`/:3J (/>L.G> >/ ;46/:215P;14 =3> L1L/=/>, O.;/4 L:;5/:3 6/4K1 =1 21=2.=1?3:1

1Q3:1 >.51:A 5/461=5/46/ .>14?3 =3> 5;>53> 4D5/:3> O./ /4 =1 L1:6;?1 146/:;3: E /=

36:3 F/:;@;21:A 234 =1 21=2.=1?3:1J -.01:A4 234 6:/> 4D5/:3> ?;@/:/46/>J += @;41=B /= 0141?3:o ganadora definitivo será quien haya ganado más partidas.” El juego se desarrolla en dos

535/463>B ?/ =1 >;0.;/46/ 514/:1,

1U *3?1> =1> L1:/C1> L1:6/4 ?/= 4D5/:3 c E F14 1 ;: >.514?3 ?/ [ /4 [J )1> L1:/C1>

?/ L:;5/: 0:1?3 ?/P/4 ==/01: Q1>61 /= 4D5/:3 [cJ )1> L1:/C1> ?/ >/0.4?3 0:1?3

?/P/:A4 ==/01: Q1>61 /= 4D5/:3 _cJ )1> L1:/C1> ?/ 6/:2/: 0:1?3 ?/P/:A4 ==/01:

Q1>61 /= ecJ M/ ;46/:215P;14 =3> L1L/=/>B L1:6/4 ?/= 5;>53 4D5/:3 E ==/014 1=

5;>53 4D5/:3J

PU *3?1> =1> L1:/C1> L1:6/4 ?/= 4D5/:3 h E F14 1 ;: >.514?3 ?/ _ /4 _J )1> L1:/C1>

?/ L:;5/: 0:1?3 ?/P/4 ==/01: Q1>61 /= 4D5/:3 [jJ )1> L1:/C1> ?/ >/0.4?3 0:1?3

?/P/:A4 ==/01: Q1>61 /= 4D5/:3 c[J )1> L1:/C1> ?/ 6/:2/: 0:1?3 ?/P/:A4 ==/01:

Q1>61 /= hTJ M/ ;46/:215P;14 =3> L1L/=/>B L1:6/4 ?/= 5;>53 4D5/:3 E ==/014 1=

5;>53 4D5/:3J

*'-,&&#++# *' +, -'-./"

SJ )=/F/ 1 21P3 =1 91:6/ S ?/ =1 126;F;?1?J '= L:3LI>;63 ?/ />1 L1:6/ /> O./ =3>

1=.543> 235L:/4?14 /= L:32/?;5;/463 L1:1 L:30:151: =1 21=2.=1?3:1 ?/ 514/:1

61= O./ >/ L./?1 ;: >.514?3 /= 4D5/:3 /=/0;?3 2.1461> F/2/> >/ O.;/:1B 1 L1:6;:

?/ .4 4D5/:3 ?;>6;463 ?/ 2/:3J

[J )=/F/ 1 21P3 =1 91:6/ [ ?/ =1 126;F;?1?J Z41 F/H O./ /4 21?1 L1:/C1 Q1E1 .4

0141?3:B L:/0.46/ 1= 0:.L3 =3 >;0.;/46/, WO.G >/:;/ 4.5G:;21 >/ =/> Q;H3 5A>

?;@K2;=B =1 ?/ >.51: ?/ ?3> /4 ?3> 1 L1:6;: ?/= cXB W3 =1 ?/ >.51: ?/ 6:/> /4 6:/> 1

L1:6;: ?/= hXB WO.G 234>/C3> =/ ?1:K14 1 1=0.;/4 1 O.;/4 >/ =/ ?;@;2.=61:1 /= L:;5/: C./03XB WE L1:1 1=0.;/4 1 O.;/4 >/ =/ ?;@;2.=61:1 /= >/0.4?3 C./03X



WZ

#&.'"J,<.#"'- '-8'<KL.<,- 8,&, '+ $#".J#&

$;/46:1> =1> L1:/C1> C./014B L:32.:/ 2;:2.=1: /46:/ /==1> L1:1 1E.?1:=/> /4 21>3 ?/ O./

6/4014 ?;@;2.=61?/> L1:1 3:014;H1:>/ 3 L1:1 235L:/4?/: =1> :/0=1> ?/= C./03J

M; =3 234>;?/:1 234F/4;/46/B .>6/? L./?/ L34/: 5/61> ?;@/:/46/> L1:1 =3> 1=.543> ?/21?1 0:1?3\ ?/ =1 5;>51 514/:1B .>6/? L./?/ 1.5/461: =1> 5/61> L1:1 =3> 1=.543> ?/

6/:2/: 0:1?3 / ;42=.>3 L:3L34/: 36:1> >/:;/> 4.5G:;21>J



W_

"#$%&' ( " $'&# *' +, -'-. "0 “La pulga y las trampas I.”2

-34567 1U

,8&'"*.9,:'- '-8'&,*#-

)3> 1=.543> 2./4614 ?/ ?3> /4 ?3>B ?/ 6:/> /4 6:/>B Q1>61 ?/ 2;423 /4 2;423B 5/?;146/ .4

C./03 >3P:/ .41 :/261 4.5G:;21B 234 =1 @;41=;?1? ?/ ?/>1::3==1: =1 432;I4 ?/ 5D=6;L=3 E ?/

?;F;>3: 235D4J

#&;,".9,<./" *'+ ;&=8#

)1 126;F;?1? >/ 3:014;H1 ?/ =1 5;>51 514/:1 2353 >/ L=146/1 /4 =1 F/:>;I4 7B 234 =1>

>;0.;/46/> 53?;@;212;34/>,

SJ '= C.01?3: O./ 23=321 =1 6:15L1 L34/ ?3> 6:15L1> 1 =1 F/HJ

[J El jugador que hace saltar a “la pulga”, /=;0/ >1=63> ?/>?/ ?3> Q1>61 2;423

/>L12;3>J

*'-,&&#++# *' +, -'-./"

SJ <.14?3 63?3> =3> L1:6;2;L146/> ?/ 21?1 /O.;L3 Q1E14 L./>63 =1 6:15L1 .41 F/HBQ101 .41 L1.>1 L1:1 ==/F1: 1 21P3B ?/ 514/:1 P:/F/B .41 L./>61 /4 235D4B 234

=1 @;41=;?1? ?/ O./ /4 =1> >;0.;/46/> :34?1> =3> 1=.543> L./?14 5/C3:1: >.>

/>6:16/0;1> ?/ C./03J 91:1 /==3B .>6/? L./?/ L=146/1: =3 >;0.;/46/,

– WY1E 1=0.41 514/:1 ?/ /F;61: O./ =1 L.=01 21;01 /4 =1> ?3> 6:15L1>XB WO.G

>.0/:/42;1> Q1:K14 1 36:3> C.01?3:/> L1:1 =30:1: O./ =1 L.=01 :/23::1 63?1 =1

6;:1 >;4 21/: /4 4;40.41 6:15L1X

– ¿Y qué sugerencias pueden hacer para poner “buenas trampas”X '> ?/2;:B W/4

O.G 4D5/:3> 234F;/4/ L34/: =1> 6:15L1> L1:1 1>/0.:1:43> ?/ O./ =1 L.=01

21;01 /4 /==1>X

[J Z41 F/H O./ =3> /O.;L3> Q1E14 235L1:6;?3 />6:16/0;1>B 2346;4D14 C.014?3 Q1>61

O./ 21?1 C.01?3: Q1E1 L./>63 =1> 6:15L1> ?3> F/2/>J



WL

_J 91:1 2/::1: =1 >/>;I4B L=146/G 4./F15/46/ =1> L:/0.461> ?/= L.463 S ?/ />6/

1L1:61?3B L./> /> 5.E L:3P1P=/ O./ =3> 1=.543> Q1E14 1@;41?3 >.> />6:16/0;1>J

#&.'"J,<.#"'- '-8'<KL.<,- 8,&, '+ $#".J#&

$;/46:1> =3> /O.;L3> C./014B L:32.:/ 2;:2.=1: /46:/ /==3> L1:1 1E.?1:=/> /4 21>3 ?/ O./

6/4014 ?;@;2.=61?/> L1:1 3:014;H1:>/ 3 L1:1 235L:/4?/: =1> :/0=1> ?/= C./03J

'4 =3 O./ >/ :/@;/:/ 1 =1> />6:16/0;1> L1:1 /F;61: 21/: /4 =1> 6:15L1>B =3> 1=.543> 6;/4/4

que elegir un número (el “tamaño del salto”) que no sea divisor de ninguno de lo>

4D5/:3> /=/0;?3> 2353 6:15L1>J 93: 36:1 L1:6/B 2.14?3 >/ 6:161 ?/ L34/: =1> 6:15L1>B />

L3>;P=/ P=3O./1: 63?3 /= :/23::;?3 ?/ =1 L.=01 >; >/ L34/4 =1> 6:15L1> /4 4D5/:3> O./

@3:514 L1:6/ ?/ ?;>6;461> >/:;/>\ L3: /C/5L=3B >; /= 6151`3 ?/ =3> >1=63> L./?/ ?/ ?/ [ 1 c

/>L12;3>B /46342/> L./?/4 L34/:>/ =1> 6:15L1> /4 4D5/:3> 2353 /= j E /= ScB ?/ />61

514/:1 21/:A4 =1> L.=01> O./ >1=6/4 ?/ [ /4 [B ?/ _ /4 _B ?/ e /4 e E ?/ c /4 cJ 9/:3/>61 />6:16/0;1 ?;@K2;=5/46/ 1L1:/2/:A ?/ ;45/?;163B >/ 234>6:.E/ 0:1?.1=5/46/ 1 6:1FG>

?/ F1:;3> C./03>B L3: /==3 /> L:3P1P=/ O./ /4 />61 >/>;I4 =3> 1=.543> 43 >/14 5.E

>;>6/5A6;23> 1= :/>L/263B L/:3 >/0.:15/46/ >/ 1L:3b;51:A4 3 /5L/H1:A4 1 ;46.;: =1>

/>6:16/0;1> 0141?3:1>\ 14K5/=3> 1 /bL=3:1: ?;>6;461> L3>;P;=;?1?/> E 1 L34/:=1> 1 L:./P1B

1.4 2.14?3 >/ /O.;F3O./4J



Wb

"#$%&' ( ")$'&# *' +, -'-./"0 “El rompecabezas I”J -34567 11

,8&'"*.9,:'- '-8'&,*#-

)3> 1=.543> :/1=;H1:A4 6:14>@3:512;34/> 0/35G6:;21> .6;=;H14?3 .4 :35L/21P/H1>B 234 =1

@;41=;?1? ?/ ?/>1::3==1: >. L/:2/L2;I4 0/35G6:;21J

#&;,".9,<./" *'+ ;&=8#

g3:5/ /O.;L3> ?/ 6:/> 1 2.16:3 1=.543>B L:32.:14?3 O./ >/14 ?/ ?;>6;463> 0:1?3>J

'46:/0./ 1 21?1 1=.543 .41 Q3C1 ?/ 23=3: 234 /= :35L/21P/H1> ;5L:/>3J 9:32.:/

/46:/01: Q3C1> ?/ ?;>6;463 23=3: /4 21?1 /O.;L3B 1>K =3> 1=.543> L3?:A4 ;46/:215P;1: >.>

L;/H1> L1:1 O./ >. :35L/21P/H1> 6/401 ?;>6;463> 23=3:/>J (G .4 6;/5L3 L1:1 O./ 21?1

1=.543 :/23:6/ >. L:3L;3 :35L/21P/H1>\ 1L3E/ 1 =3> 1=.543> O./ :/O.;/:14 1E.?1B L./>

>; 43 :/23:614 23::/2615/46/ 6/4?:A4 ?;@;2.=61?/> ?/>L.G> L1:1 1:51: =1> @;0.:1> O./ >/

=/> >3=;2;6/4J

SJ Z41 F/H O./ =3> 1=.543> Q1E14 :/23:61?3 / ;46/:215P;1?3 >.> L;/H1> L1:1 6/4/:

?/ ?;>6;463> 23=3:/>B LK?1=/> O./ @3:5/4 =1> @;0.:1> O./ /==3> O.;/:14J (G .46;/5L3 L1:1 O./B ?/ 514/:1 =;P:/B /bL=3:/4 =3 O./ L./?/4 Q12/: 234 />/

:35L/21P/H1>J

[J '46:/0./ 1 21?1 /O.;L3 ?3> @36323L;1> 234 =3> 53?/=3> O./ >/ 5./>6:14 /4

L5WQ>@4 1B L1:1 O./ =3> 1=.543> =1> :/L:3?.H214SSJ

_J '46:/0./ .41 Q3C1 P=1421 1 21?1 1=.543 E L/015/463 E =AL;2/> ?/ 23=3:/> L1:1

21?1 /O.;L3J <1?1 1=.543 @3:51:A .41 @;0.:1 234 >.> L;/H1> ?/= :35L/21P/H1>

NL./?/4 .>1: /= 4D5/:3 ?/ L;/H1> O./ /==3> O.;/:14U E =1 L/01:A4 /4 =1 Q3C1J <34

AA 8%G</'/( )3%+$+( $/ 03( N&>*3( $/ `/T)3 7*+)5&)3(P C"+'*,+$-"(D @5$*'5 J5"&4D 1/,*/)+*F+ $/ 4$5,+,&-'

;R>0&,+H [:T&,3? "@@CQ 9 C"+'*,+$-"(D K'/<.&4 J5"&4D 1/,*/)+*F+ $/ 4$5,+,&-' ;R>0&,+H [:T&,3? "@@AH



Y@

=3> 23=3:/> L3?:A4 ?;P.C1: .4 @34?3 L1:1 >. @;0.:1 3 10:/01: =3> /=/5/463> O./

/==3> O.;/:14J

eJ #:014;2/ .41 /bQ;P;2;I4 ?/ =1> 235L3>;2;34/> ?/ =3> 1=.543>J

*'-,&&#++# *' +, -'-./"

SJ $;/46:1> =3> 1=.543> :/23:614 /= :35L/21P/H1>B 1L:3F/2Q/ /= 535/463 L1:1 O./

;?/46;@;O./4 =1> @;0.:1> O./ =3 235L34/4 L=146/14?3 =1> >;0.;/46/> L:/0.461>,

W<.A461> L;/H1> 6;/4/ /= :35L/21P/H1>XB WO.G @;0.:1> :/23432/4XB W2.A463>

6:;A40.=3> Q1EXB W2.A463> 2.1?:1?3> Q1EXB W2I53 >/ ==151 =1 @;0.:1 O./ 43 />

6:;A40.=3 4; 2.1?:1?3X

[J )3> 1=.543> /bL=3:14 /= :35L/21P/H1> @3:514?3 =1> @;0.:1> O./ /==3> 5;>53>

?;>/`/4J

_J +L3EA4?3>/ /4 =3> 53?/=3> ?/ =1> g;0.:1> SB =3> 1=.543> 6:1614 ?/ :/L:3?.2;:

21?1 .43 ?/ =3> 53?/=3>J

eJ g3:514 =1 @;0.:1 O./ /==3> O.;/:1> E =1 L/014 /4 =1 Q3C1 P=1421J

cJ M/ 3:014;H1 .41 /bL3>;2;I4 234 =1> L:3?.22;34/> ?/ 63?3> =3> 1=.543>J

#&.'"J,<.#"'- '-8'<KL.<,- 8,&, '+ $#".J#&

)3> 53?/=3> O./ >/ 3@:/2/4 6;/4/4 ?;>6;463> 0:1?3> ?/ 235L=/C;?1?, /4 1=0.43> ?/ /==3>

>/ 5./>6:14 63?1> =1> @;0.:1> O./ 235L34/4 1= 53?/=3B 1>K 2353 =1 L3>;2;I4 ?/ 21?1 .41

?/ =1> @;0.:1>\ 5;/46:1> O./ /4 36:3> >I=3 >/ 5./>6:14 1=0.41> ?/ =1> @;0.:1> O./ =3>

235L34/4B />63 /> 234 =1 ;46/42;I4 ?/ O./ Q1E14 ?;>6;463> 0:1?3> ?/ ?;@;2.=61?

234>;?/:14?3 O./ 615P;G4 L./?/ Q1P/: ?;@/:/42;1> /4 =1> Q1P;=;?1?/> ?/ =3> 1=.543>J



YA

&#$8'<,%'9,-



Y"

L.;=&,- 1



YC

"#$%&' ( ")$'&# *' +, -'-./"0 “,H`7@E3 @E A3>D3”1NJ -34567 1N

,8&'"*.9,:'- '-8'&,*#-

)3> 1=.543> 3P6;/4/4 :/>.=61?3> 1L:3b;51?3>B 5/?;146/ .4 C./03 >3P:/ .41 :/261

4.5G:;21B 234 =1 @;41=;?1? ?/ ?/>1::3==1: >.> Q1P;=;?1?/> ?/ 2A=2.=3 5/461=J

#&;,".9,<./" *'+ ;&=8#

g3:5/ /O.;L3> ?/ ?3> 1 6:/> 1=.543>B /46:G0./=/> /= 516/:;1= E /bL=;O./ =1> :/0=1> ?/=

C./03,

+46/> ?/ ;4;2;1: /= C./03B ?/P/4 :/F3=F/: =1> 61:C/61> E 23=321:=1> >3P:/ =1 5/>1B

.41 >3P:/ =1 36:1 E 234 /= 23=3: Q12;1 1P1C3J

'4 21?1 /O.;L3 >/ L34/4 ?/ 12./:?3 >3P:/ O.;G4 ;4;2;1 /= C./03J

R.;/4 /5L;/H1 /= C./03 6351 .41 @;2Q1 ?/ =1 P3=>1 E =1 L34/ >3P:/ 2.1=O.;/:

4D5/:3 ?/ =1 6;:1J

'= 5;>53 C.01?3: =/F1461 .41 61:C/61 E 1= F/: /= 23=3: >\Z5D@?37H3 ?/P/ ?/2;:2.A463 >.51: 3 2.A463 :/>61: 1= 4D5/:3 ?34?/ />6A >. @;2Q1 L1:1 21/: /4

2.1=O.;/: 4D5/:3 O./ />6G /4 =1 @:14C1 ?/= 23=3: O./ =/ >1=;IJ

Si dice “más”, mueve su ficha Q12;1 =1 ?/:/2Q1B 61463> =.01:/> 2353 /= 4D5/:3

que dijo. Si dice “menos”, la mueve Q12;1 =1 ;HO.;/:?1J 93: /C/5L=3B >; ?;Co “más

cinco”, mueve su ficha 2;423 =.01:/> Q12;1 =1 ?/:/2Q1\ >; ?;C3 “menos tres”, mueve

>. @;2Q1 6:/> =.01:/> Q12;1 =1 ;HO.;/:?1J

M; /= C.01?3: =30:1 21/: /4 =1 @:14C1 ?/= 23=3: O./ =/ >1=;I /4 =1 61:C/61 O./ >/

=/F146IB >/ O./?1 234 =1 @;2Q1\ >; 43B =1 ?/F./=F/ 1 =1 P3=>1J

<1?1 61:C/61 O./ >/ 6351 >/ L34/ ?/ 4./F3 ?/P1C3 ?/ =1> ?/5A>J

A" `3%+$+ $/ B<'/" 8 :=5'.&' C"+'*,+$-"(D @54=<'(+"( ="5" &$7'5+$5(' 8 +5"#"E"5 '. '% "<%"D V30/,,&-'

“Libros del Rincón”. SEP.



YW

91:1 2346;4.1:B 36:3 C.01?3: 23=321 .41 @;2Q1 >3P:/ 2.1=O.;/: 4D5/:3 ?/ =1 6;:1 E

=/F1461 36:1 61:C/61J

a141 /= C.01?3: O./ =30:/ :/.4;: 5A> @;2Q1> ?/>L.G> ?/ 2;423 :34?1>J

*'-,&&#++# *' +, -'-./"

SJ <.14?3 63?3> =3> /O.;L3> Q1E14 C.01?3 ?3> :34?1>B Q101 .41 L1.>1 L1:1 ==/F1: 1

21P3B ?/ 514/:1 P:/F/B .41 L./>61 /4 235D4 234 =1 @;41=;?1? ?/ O./ /4 =1>

>;0.;/46/> :34?1> =3> 1=.543> L./?14 5/C3:1: >.> />6:16/0;1> ?/ C./03J 91:1 /==3B

.>6/? L./?/ L=146/1: =3 >;0.;/46/,

– WY1E 1=0.41 514/:1 rápida de saber si deben decir “más” o “menos” cuando

>1214 =1 61:C/61X – WY1E 1=0.41 514/:1 :AL;?1 ?/ 21=2.=1: 2.A463 >/ ?/P/ 1F14H1: 3 :/6:32/?/:

L1:1 ==/01: 1= 23=3: O./ ;4?;21 =1 61:C/61X

[J Z41 F/H O./ =3> /O.;L3> Q1E14 235L1:6;?3 />6:16/0;1>B 2346;4D14 C.014?3 Q1>61

O./ 21?1 C.01?3: Q1E1 L./>63 >. @;2Q1 2;423 F/2/>J

_J 91:1 2/::1: =1 >/>;I4B L=146/G 4./F15/46/ =1> L:/0.461> ?/= L.463 S ?/ />6/

1L1:61?3B L./> /> 5.E L:3P1P=/ O./ =3> 1=.543> Q1E14 1@;41?3 >.> />6:16/0;1>J

#&.'"J,<.#"'- '-8'<KL.<,- 8,&, '+ $#".J#&

)1 6;:1 ?/ 21:6342;==3 ?/P/ 6/4/: =1> >;0.;/46/> 21:126/:K>6;21>, ?/P/ />61: 4.5/:1?1 ?/= S

1= [TB ?/P/ 5/?;: j 2/46K5/6:3> ?/ 142Q3 L3: S 5/6:3 ?/ =1:03B 234 ?;F;>;34/> 21?1 c

2/46K5/6:3>J <1?1 2.16:3 4D5/:3> >/ ;=.5;414 234 .43 ?/ />63> 23=3:/>, :3C3B 1H.=B F/:?/B

151:;==3 E 41:14C1J

1 N P M T V S Y O 1U 11 1N 1P 1M 1T 1V 1S 1Y 1O NU

&3C3 +H.= 8/:?/ +51:;==3 "1:14C1



YY

'= C./03 ?/ 61:C/61> />6A @3:51?3 L3: ST 61:C/61> 234 .4 2K:2.=3 ?/ 23=3:J (/P/ Q1P/: ?3>

61:C/61> L3: 21?1 .43 ?/ =3> >;0.;/46/> 23=3:/>,

&3C3 +H.= 8/:?/ +51:;==3 "1:14C1

$;/46:1> =3> /O.;L3> C./014B L:32.:/ 2;:2.=1: /46:/ /==3> L1:1 1E.?1:=/> /4 21>3 ?/ O./

6/4014 ?;@;2.=61?/> L1:1 3:014;H1:>/ 3 L1:1 235L:/4?/: =1> :/0=1> ?/= C./03J

'> ;5L3:6146/ O./ .>6/? 6/401 /4 234>;?/:12;I4 O./ 43 >/ 6:161 ?/ 3P6/4/: .4 :/>.=61?3

/b1263B >;43 ?/ 1L:3b;51:>/ 1 .4 :1403 4.5G:;23B /4 />6/ 21>3B 1 =3> 4D5/:3>

235L:/4?;?3> /4 .4 23=3:J 93: /==3B 14;5/ 1 =3> 1=.543> 1 Q12/: =3> 2A=2.=3>

:AL;?15/46/B />3 =/ ?1:A 51E3: /532;I4 E ?;415;>53 1= C./03\ 1?/5A>B >/0.:15/46/

/==3> Q12/4 1L:3b;512;34/> ?/ 514/:1 @:/2./46/ /4 2;/:61> 126;F;?1?/> ?/ =1 F;?1 ?;1:;1J

'>61> 126;F;?1?/> ?/ 2A=2.=3 5/461= =/> >/:A4 D6;=/> 615P;G4 /4 =1 />2./=1B 2.14?3 >/

6:161B L3: /C/5L=3B ?/ />6;51: >; /= :/>.=61?3 3P6/4;?3 234 .41 2./461 />2:;61 /> 23::/263 3

43J



YZ

"#$%&' ( ")$'&# *' +, -'-./"0 “A ver quién llega”1PJ -34567 1P

,8&'"*.9,:'- '-8'&,*#-

+ L1:6;: ?/ .4 4D5/:3 ?1?3B =3> 1=.543> P.>214 /= 235L=/5/463 1?;6;F3 L1:1 3P6/4/: 36:3

4D5/:3B 5/?;146/ .4 C./03 234 21=2.=1?3:1B 234 =1 @;41=;?1? ?/ ?/>1::3==1: >.>

Q1P;=;?1?/> ?/ 2A=2.=3 5/461=J

#&;,".9,<./" *'+ ;&=8#

8@>H3 12 '46:/0./ 1 21?1 1=.543 .41 21=2.=1?3:1 E />2:;P1B E1 >/1 /4 /= L;H1::I4 3 /4

.41 Q3C1 =3 >;0.;/46/, Sh m nnn o [cJ 'bL=;O./ =1> :/0=1> ?/= C./03,

1U “Se trata de escribir el primer número en la calculadora (el 17) y sumarle otro

4D5/:3B /= O./ .>6/?/> 2:/14B ?/ 514/:1 61= O./ ==/0./4 1= 4D5/:3 [cB O./

obtengan como resultado el 25. Quien lo logre en el primer intento, gana.”

PU '= 1=.543 3 1=.541 O./ >/1 /= L:;5/:3 /4 3P6/4/: /= 4D5/:3B ?/P/:A /bL=;21: 1=

0:.L3 O.G Q;H3 L1:1 ==/01: 1= 4D5/:3 [cJ )3> ?/5A> Q12/4 /4 >. L:3L;1

21=2.=1?3:1 />/ 5;>53 L:32/?;5;/463 L1:1 F/: >;B /@/26;F15/46/B >/ 3P6;/4/ /=4D5/:3 P.>21?3J

8@>H3 N2 #:014;2/ 1= 0:.L3 /4 L1:/C1>B L:/@/:/46/5/46/ O./ >/14 1=.543> ?/= 5;>53

grado escolar, y explique las reglas del juego: “Ahora, al interior de cada pareja, uno de

.>6/?/> F1 1 L:3L34/: /= 4D5/:3 ;4;2;1=B E3 ?;:G /= 4D5/:3 ?/ ==/01?1 N/= :/>.=61?3 ?/ =1

>.51U\ ?/P/4 6/4/: 2.;?1?3 /4 O./ /= 4D5/:3 ;4;2;1= >/1 5/43: 1= 4D5/:3 ?/ ==/01?1J '=

36:3 5;/5P:3 ?/ =1 L1:/C1 ?/P/:A /42346:1:B /= 4D5/:3 O./B >.51?3 1= 4D5/:3 ;4;2;1=B 43>

L/:5;61 3P6/4/: /= 4D5/:3 ?/ ==/01?1J *;/4/ >I=3 ?3> 3L3:6.4;?1?/> L1:1 /42346:1:=3J M;

=3 =30:1B >/ 14361 .4 L.463B >; >/ /O.;F321 /= L.463 /> L1:1 >. 235L1`/:3 3 235L1`/:1

AC Adaptación de “De la suma y un sumando, al otro sumando”, en Gálvez, 7Q f+2+**3? 1Q c&2/*3(? [Q

k+'3,,3? ;H hAbbWi :=5'.&$'.&4 *"+'*,+$-"( -4. -"%-<%"&45"D [&'&()/*&3 $/ 4$5,+,&-' $/ VO&0/H



Y_

?/ L1:/C1J (/>L.G> >/ ;4F;/:6/4 =3> L1L/=/>J -.01:A4 /4 6361= 32Q3 L1:6;?1>J '= 0141?3: 3

ganadora definitivo será quien haya obtenido el mayor número de puntos.”

'>2:;P1 /4 /= L;H1::I4 3 /4 .4 21:6/= /= 4D5/:3 ?/ ==/01?1 L1:1 21?1 0:1?3 />23=1:,

f 9:;5/: 0:1?3, (/P/4 ==/01: 1= [TJ

f M/0.4?3 0:1?3, (/P/4 ==/01: 1= _TJ

f */:2/: 0:1?3, (/P/4 ==/01: 1= cTJ

*'-,&&#++# *' +, -'-./"

SJ +46/> ?/ O./ =3> 1=.543> ==/F/4 1 21P3 =1 91:6/ SB L/:5;61 O./ /bL=3:/4

=;P:/5/46/ /= @.42;3415;/463 ?/ =1 21=2.=1?3:1J 91:1 1L3E1: />1 /bL=3:12;I4B

.>6/? L./?/ L/?;:=/> O./ 1F/:;0l/4 234 O.G 6/2=1 >/ /42;/4?/B 234 2.A= >/ 1L101J

9./?/ L/?;:=/> 615P;G4 O./ L:/>;34/4 F1:;1> 6/2=1> ?/ 4D5/:3> L1:1 F/: Q1>612.A461> 2;@:1> L./?/4 F/:>/ /4 =1 L1461==1 N/4 =1 51E3:K1 ?/ =1> 21=2.=1?3:1>

235.4/> 1L1:/2/4 Q1>61 j 2;@:1>UJ 9:/0.46/, WO.G L1>1 >; 6/2=/14 5A> ?/ 32Q3

cifras? (aparece una letra E, que indica “Error”).

[J )=/F/ 1 21P3 =1 91:6/ S ?/ =1 126;F;?1?J '= L:3LI>;63 ?/ />1 L1:6/ /> O./ =3>

1=.543> 235L:/4?14 =1> :/0=1> ?/= C./03J '4 21>3 ?/ O./ =3 234>;?/:/ 4/2/>1:;3B

.>6/? L./?/ L:3L34/: .41 3 ?3> :34?1> 5A> L1:1 />61 L1:6/J

_J )=/F/ 1 21P3 =1 91:6/ [ ?/ =1 126;F;?1?J Z41 F/H O./ 63?1> =1> L1:/C1> Q1E14 C.01?3 =1> j :34?1>B L:/0.46/ 1= 0:.L3 =3 >;0.;/46/,WO.G 234>/C3> =/ ?1:K14 1

1=0.;/4 O./ O.;/:/ ==/01: 1= 4D5/:3 [TXB WE L1:1 1=0.;/4 O./ O.;/:/ ==/01: 1=

4D5/:3 eTXB WE L1:1 O.;/4 O.;/:/ ==/01: 1= 4D5/:3 jTX W'4 O.G >/ @;C14 E O.G

Q12/4 L1:1 ==/01: 1 2.1=O.;/: 4D5/:3 /4 .4 L:;5/: ;46/463X

#&.'"J,<.#"'- '-8'<KL.<,- 8,&, '+ $#".J#&

M/0.:15/46/ F1:;3> ?/ =3> 1=.543> E1 Q14 6/4;?3 /bL/:;/42;1> 234 36:1> 21=2.=1?3:1>B E1

>/1 L3:O./ =1> .>14 /4 /= >1=I4 ?/ 2=1>/ 3 /4 >. 21>1J (/ 63?1> @3:51> /> 234F/4;/46/O./ /= 0:.L3 /bL=3:/ /= @.42;3415;/463 PA>;23 ?/ =1 21=2.=1?3:1 2353 >/ L:3L34/ /4 /=


$;/46:1> =1> L1:/C1> C./014B L:32.:/ 2;:2.=1: /46:/ /==1> L1:1 1E.?1:=/> /4 21>3 ?/ O./

6/4014 ?;@;2.=61?/> L1:1 3:014;H1:>/ 3 L1:1 235L:/4?/: =1> :/0=1> ?/= C./03J



YL

M; .>6/? =3 234>;?/:1 4/2/>1:;3B L./?/ 1.5/461: 3 ?;>5;4.;: =3> :1403> 4.5G:;23> L1:1

21?1 0:1?3 />23=1:J



Yb

"#$%&' ( ")$'&# *' +, -'-./"0 “Rompecabezas II”1MJ -34567 1M

,8&'"*.9,:'- '-8'&,*#-

)3> 1=.543> 235L34/4 @;0.:1> 1 L1:6;: ?/ 36:1>B .6;=;H14?3 .4 :35L/21P/H1> 0/35G6:;23B

234 =1 @;41=;?1? ?/ ?/>1::3==1: >. L/:2/L2;I4 0/35G6:;21J

#&;,".9,<./" *'+ ;&=8#

g3:5/ /O.;L3> ?/ 6:/> 1 2.16:3 1=.543>B L:32.:14?3 O./ >/14 ?/ ?;>6;463> 0:1?3>J

'46:/0./ 1 21?1 1=.543 .41 Q3C1 ?/ 23=3: 234 /= :35L/21P/H1> ;5L:/>3 NF/: >/>;I4 SSUJ

9:32.:/ /46:/01: Q3C1> ?/ ?;>6;463 23=3: /4 21?1 /O.;L3B 1>K =3> 1=.543> L3?:A4

;46/:215P;1: >.> L;/H1> L1:1 O./ >. :35L/21P/H1> 6/401 ?;>6;463> 23=3:/>J (G .4 6;/5L3

L1:1 O./ 21?1 1=.543 :/23:6/ >. L:3L;3 :35L/21P/H1>\ 1L3E/ 1 =3> 1=.543> O./

:/O.;/:14 1E.?1B L./> >; 43 :/23:614 23::/2615/46/ 6/4?:A4 ?;@;2.=61?/> ?/>L.G> L1:1

1:51: =1> @;0.:1> O./ >/ =/> >3=;2;6/4J

8@>H3 .2 Z41 F/H O./ =3> 1=.543> Q1E14 :/23:61?3 / ;46/:215P;1?3 >.> L;/H1> L1:1 6/4/:

?/ ?;>6;463> 23=3:/>B ?;P.C/ .41 >;=./61 /4 /= L;H1::I4 234 ?3> 3 6:/> L;/H1> ?/=

:35L/21P/H1>B L1:1 O./ =3> 1=.543> =1 :/L:3?.H214 234 >. L:3L;3 :35L/21P/H1> N/>

4/2/>1:;3 ;4?;21:=/> /= 4D5/:3 ?/ L;/H1> O./ 4/2/>;61:A4 L1:1 Q12/:=3UJ Z41 F/H O./ =3>

1=.543> Q1E14 @3:51?3 =1 @;0.:1 >/ P3::1 ?/= L;H1::I4 E >/ ?;P.C1 36:1J

)1 126;F;?1? >/ :/L;6/ ?3> 3 6:/> F/2/>J '4 21?1 321>;I4 L1>1 .4 1=.543 3 1=.541 1

?;P.C1: =1 @3:51 /4 O./ >/ 23=321:34 =1> L;/H1> ?/= :35L/21P/H1> L1:1 @3:51: =1 @;0.:1J

(/P/ Q12/:=3 >3P:/ =1 >;=./61 O./ >/ ?;P.CI L:/F;15/46/J

8@>H3 ..

AW Tomada de la Ficha 56, “El rompecabezas”, del 3$-L'54D :-+$7$&"&'( &$&,-+$-"(D C"+'*,+$-"(D I'5-'5

J5"&4D 1/,*/)+*F+ $/ 4$5,+,&-' ;R>0&,+H AbbWH [:T&,3H



Z@

+Q3:1B 21?1 1=.543 /=1P3:1 >3P:/ .41 Q3C1 P=1421B >;4 O./ =3> ?/5A> =3 F/14B .41 @;0.:1

234 6:/> 3 2.16:3 L;/H1> ?/= :35L/21P/H1>J (/>L.G>B 234 .4 =AL;H 51:21 /= 23463:43 3

>;=./61 ?/ =1 @;0.:1 O./ @3:5I E :/6;:1 =1> L;/H1>J

93: 6.:43> 21?1 5;/5P:3 ?/= /O.;L3 23=321 1= 2/46:3 ?/ =1 5/>1 =1 >;=./61 O./ @3:5I L1:1

O./ =3> ?/5A> =1 @3:5/4 234 =1> L;/H1> 23::/>L34?;/46/>J R.;/4 23=321 =1 >;=./61 ?/P/

?/2;: 1 =3> ?/5A> 2.A461> L;/H1> @3:514 =1 @;0.:1J

a141 /= 1=.543 3 1=.541 O./ 23=3O./ 23::/2615/46/ =1> L;/H1> /4 /= 5/43: 6;/5L3J

)1 126;F;?1? >/ :/L;6/ Q1>61 O./ >/ Q1E14 :/L:3?.2;?3 63?1> =1> @;0.:1> O./ ?;P.C1:34 =3>

5;/5P:3> ?/= /O.;L3J

+= @;41= >/ /46:/01 .4 >3P:/ 1 21?1 1=.543 L1:1 O./ 234>/:F/ =1> L;/H1> ?/ >.

:35L/21P/H1> E L./?1 C.01: /4 21>1B >; 1>K =3 ?/>/1J

*'-,&&#++# *' +, -'-./"

SJ $;/46:1> =3> 1=.543> :/23:614 /= :35L/21P/H1>B 1L:3F/2Q/ /= 535/463 L1:1 O./B

4./F15/46/B ;?/46;@;O./4 =1> @;0.:1> O./ =3 235L34/4 L=146/14?3 =1> >;0.;/46/>

L:/0.461>, W<.A461> L;/H1> 6;/4/ /= :35L/21P/H1>XB WO.G @;0.:1> :/23432/4XB

W2.A463> 6:;A40.=3> Q1EXB W2.A463> 2.1?:1?3> Q1EXB W2I53 >/ ==151 =1 @;0.:1 O./

43 /> 6:;A40.=3 4; 2.1?:1?3X

[J )=/F/ 1 21P3 =1 91:6/ 7 2353 >/ L:3L34/ EB L3>6/:;3:5/46/B 2.14?3 =3> 1=.543>

/>6G4 ?/>1::3==14?3 =1 91:6/ 77B .>6/? L./?/ Q12/: .41 P:/F/ L1.>1 L1:1 L:/0.461:

1= 0:.L3, W'4 O.G >/ @;C14 L1:1 L3?/: ;?/46;@;21: =1> L;/H1> O./ 235L34/4 .41

@;0.:1XB WR.G =/ :/235/4?1:K14 1 1=0.;/4 O./ L3: L:;5/:1 F/H F1 1 1:51: .41

@;0.:1 1 L1:6;: ?/ >. >;=./61X

#&.'"J,<.#"'- '-8'<KL.<,- 8,&, '+ $#".J#&

M; .>6/? =3 234>;?/:1 4/2/>1:;3B 1.5/46/ /= 4D5/:3 ?/ L;/H1> 234 O./ >/ @3:514 =1>

>;=./61>B 61463 =1> O./ .>6/? Q1:A /4 /= L;H1::I4 2353 =1> O./ =3> 1=.543> 32.L1:A4 L1:1

>.> L:3L;3> ?;>/`3>J



ZA

"#$%&' ( " $'&# *' +, -'-. "0 “Calculadora descompuesta” J

-34567 1T

,8&'"*.9,:'- '-8'&,*#-

)3> 1=.543> ?/>235L34/4 4D5/:3> /4 2/46/41>B ?/2/41> E .4;?1?/>B 5/?;146/ .4

C./03 234 =1 21=2.=1?3:1B 234 =1 @;41=;?1? ?/ Q12/: .>3 ?/ .41 ?/ =1> L:3L;/?1?/> ?/

4./>6:3 >;>6/51 ?/ 4.5/:12;I4, /= 10:.L15;/463 ?/2;51=J

#&;,".9,<./" *'+ ;&=8#

8@>H3 12 '46:/0./ 1 21?1 1=.543 .41 21=2.=1?3:1 E />2:;P1B E1 >/1 /4 /= L;H1::I4 3 /4

.41 Q3C1B .4 4D5/:3 /46:/ [T E eTB L3: /C/5L=3B [hJ 'bL=;O./ =1> :/0=1> ?/= C./03,

1U “Se trata de escribir /4 =1 21=2.=1?3:1 /= 4D5/:3 [hB L/:3 F153> 1 ;510;41: O./ =1

21=2.=1?3:1 />6A ?/>235L./>61B >I=3 L3?/53> .>1: =1> >;0.;/46/> 6/2=1>, 1R UR ^R

_2 NZ43B 2/:3B 5A>B ;0.1=UJ '46342/>B .>14?3 >I=3 />1> 6/2=1>B 3!+ 5.&.+ 01.

1+6.(.+ 3$ #.&.+'6.#B ?/P/:A4 3P6/4/: 1= @;41= /= 4D5/:3 [hJ '= L:;5/: 1=.543 3

1=.541 ?/= 0:.L3 O./ =30:/ 3P6/4/:=3 E O./ Q1E1 :/>L/61?3 =1> :/0=1>, gana”.

PU '= 1=.543 3 1=.541 O./ >/1 /= L:;5/:3 /4 3P6/4/: /= 4D5/:3B ?/P/:A /bL=;21: 1=

0:.L3 O.G Q;H3 L1:1 3P6/4/: /= 4D5/:3 [hJ +E.?/ 1 />/ 1=.543 3 1=.541 L1:1

O./ :/0;>6:/ >.> L:32/?;5;/463> /4 /= L;H1::I4B ?/ 61= 514/:1 O./ 63?3> L./?14

/46/4?/:=3>J '= 0:.L3 F1=3:1:A >; /@/26;F15/46/ >/ :/>L/61:34 =1> :/0=1> N>I=3 .>1:

=1> 6/2=1> ;4?;21?1>U\ >; 43 /> 1>KB /46342/> 5./>6:1 >. L:32/?;5;/463 O.;/4 Q1E1

6/:5;41?3 /4 >/0.4?3 =.01:J

8@>H3 N2 #:014;2/ 1= 0:.L3 /4 L1:/C1>B L:/@/:/46/5/46/ O./ >/14 1=.543> ?/= 5;>53

grado escolar, y explique las reglas del juego: “AhoraB 1= ;46/:;3: ?/ 21?1 L1:/C1B .43 ?/

.>6/?/> F1 1 L:3L34/: .4 4D5/:3 N=3 />2:;P/4 /4 .41 Q3C1U E 21?1 O.;/4B 234 >.21=2.=1?3:1B 6:161:A ?/ 3P6/4/: />/ 4D5/:3 .>14?3 >I=3 =1> 6/2=1> 1R UR ^R _2 R.;/4

AY Adaptación de “1-03 ,3' 5'3( 9 ,/*3(”, en Gálvez, G; Navarro, S; Riveros, M; Zanocco, P. (1994)

:=5'.&$'.&4 *"+'*,+$-"( -4. -"%-<%"&45"D [&'&()/*&3 $/ 4$5,+,&-' $/ VO&0/H



Z"

3P6/401 L:;5/:3 /= 4D5/:3 E =3 Q1E1 Q/2Q3 :/>L/614?3 =1> :/0=1>B 0141 />1 L1:6;?1\ L1:1

/==3 ?/P/:A4 53>6:1:=/ 1 >. 235L1`/:3 3 235L1`/:1 2I53 3P6.F;/:34 /= 4D5/:3J '4 =1

>;0.;/46/ L1:6;?1 /= O./ L:3L34/ /= 4D5/:3 /> /= 36:3 235L1`/:3 3 235L1`/:1J 814 1

C.01: c L1:6;?1> /4 6361=B /= 0141?3: 3 0141?3:1 ?/@;4;6;F3 >/:A O.;/4 014/ /= 51E3:

número de partidas”.

'>2:;P1 /4 /= L;H1::I4 3 /4 .4 21:6/= =3> :1403> 4.5G:;23> 234 =3> O./ =1> L1:/C1> L./?/4

C.01:B >/0D4 >. 0:1?3 />23=1:,

f 9:;5/: 0:1?3, 9./?/4 /=/0;: 4D5/:3> /46:/ /= [T E /= STTJ

f M/0.4?3 0:1?3, 9./?/4 /=/0;: 4D5/:3> /46:/ /= dT E /= dTTJ

f */:2/: 0:1?3, 9./?/4 /=/0;: 4D5/:3> /46:/ /= STT E /= dTTT

*'-,&&#++# *' +, -'-./"

SJ +46/> ?/ O./ =3> 1=.543> ==/F/4 1 21P3 =1 91:6/ SB L/:5;61 O./ /bL=3:/4

=;P:/5/46/ /= @.42;3415;/463 ?/ =1 21=2.=1?3:1J 91:1 1L3E1: />1 /bL=3:12;I4B

.>6/? L./?/ L/?;:=/> O./ 1F/:;0l/4 234 O.G 6/2=1 >/ /42;/4?/B 234 2.A= >/ 1L101J

9./?/ L/?;:=/> 615P;G4 O./ L:/>;34/4 F1:;1> 6/2=1> ?/ 4D5/:3> L1:1 F/: Q1>61

2.A461> 2;@:1> L./?/4 F/:>/ /4 =1 L1461==1 N/4 =1 51E3:K1 ?/ =1> 21=2.=1?3:1>

235.4/> 1L1:/2/4 Q1>61 j 2;@:1>UJ 9:/0.46/, WO.G L1>1 >; 6/2=/14 5A> ?/ 32Q3

2;@:1>X N1L1:/2/ .na letra E, que indica “Error”).

[J )=/F/ 1 21P3 =1 91:6/ S ?/ =1 126;F;?1?J '= L:3LI>;63 ?/ />1 L1:6/ /> O./ =3>

1=.543> 235L:/4?14 =1> :/0=1> ?/= C./03 E O./ =30:/4 6/4/: 1= 5/43> .41

/>6:16/0;1 ;4;2;1=, L/:2161:>/ O./ 234 =1> 6/2=1> S E T L./?/4 @3:51: =3> 4D5/:3>

STB STTB STTTB /62G6/:1\ E O./ 234 =1 6/2=1 m L./?/4 ;: 1?;2;3414?3 />1>

2146;?1?/> L1:1 3P6/4/: /= 4D5/:3 ?/>/1?3\ 1>;5;>53B >.514?3 F1:;1> F/2/> /= S

L./?/4 3P6/4/: =1> .4;?1?/> ?/>/1?1>J

_J )=/F/ 1 21P3 =1 91:6/ [ ?/ =1 126;F;?1?J Z41 F/H O./ /4 21?1 L1:/C1 Q1E1 .4

0141?3:B L:/0.46/ 1= 0:.L3 =3 >;0.;/46/, WO.G 234>/C3> =/ ?1:K14 1 1=0.;/4 O./O.;/:/ 3P6/4/: /= 4D5/:3 hdXB WE L1:1 1=0.;/4 O./ O.;/:/ 3P6/4/: /= 4D5/:3 _eSXB

WE L1:1 O.;/4 O.;/:/ 3P6/4/: /= 4D5/:3 S[TSX W'4 O.G >/ @;C14 E O.G Q12/4 L1:1

3P6/4/: :AL;?15/46/ 2.1=O.;/: 4D5/:3X



#&.'"J,<.#"'- '-8'<KL.<,- 8,&, '+ $#".J#&

M/0.:15/46/ F1:;3> ?/ =3> 1=.543> E1 Q14 6/4;?3 /bL/:;/42;1> 234 36:1> 21=2.=1?3:1>B E1

>/1 L3:O./ =1> .>14 /4 /= >1=I4 ?/ 2=1>/ 3 /4 >. 21>1J (/ 63?1> @3:51> /> 234F/4;/46/

O./ /= 0:.L3 /bL=3:/ /= @.42;3415;/463 PA>;23 ?/ =1 21=2.=1?3:1 2353 >/ L:3L34/ /4 /=


$;/46:1> =1> L1:/C1> C./014B L:32.:/ 2;:2.=1: /46:/ /==1> L1:1 1E.?1:=/> /4 21>3 ?/ O./

6/4014 ?;@;2.=61?/> L1:1 3:014;H1:>/ 3 L1:1 235L:/4?/: =1> :/0=1> ?/= C./03J +LIE/=3>

L1:1 O./ /bL=;O./4 2I53 3P6.F;/:34 /= 4D5/:3B L./> /> L3>;P=/ O./ 1=0.43> ?/ /==3>

6/4014 ?;@;2.=61?/> L1:1 :/234>6:.;: >. L:32/?;5;/463J

M; .>6/? =3 234>;?/:1 4/2/>1:;3B L./?/ 1.5/461: 3 ?;>5;4.;: =3> :1403> 4.5G:;23> L1:1

21?1 0:1?3 />23=1:J

juegaconmate ci prim

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