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Eines TIC per al professorat de matemtiques Mdul 2: Nombres, mesures i polinomis Mdul 3: Resoluci de problemes Mdul 4: Geometria plana i de l'espai Mdul 5: Funcions i anlisi matemtica Mdul 6: Combinatria, probabilitat, estadstica, matemtica comercial i fractals  B  Cada mdul ( Prctiques: 3 de 4  Exercicis: 3 de 4     :;     Dsma_m6_p4   Traducci automtica de la taula de continguts Traducci automtica de les notes del mestre/a (Nivell: 6 primria a 4t ESO) Traducci automtica de la 1a lli (Per qu els fractals?) Activitats sobre el floc de neu de Koch Dibuixar el floc de neu en paper engraellat Utilitzar un applet Java per veure el dibuix del floc de neu Un fenomen fascinant: permetre infinit I qu passa amb l'rea? " Z" Z  % D  H:m 4 Dsma_m6_p4   .Traducci automtica de la taula de continguts*/"  /5 Dsma_m6_p4   P2. Traducci automtica de les notes del mestre/a (Nivell: 6 primria a 4t ESO)&Q : Q6 Dsma_m6_p4   >3. Traducci automtica de la 1a lli (Per qu els fractals?)D?Z    ?#$'Aquest activitat ...@Continguts curriculars: pautes, ordenaci de fraccions, rees, permetres, semblances, mesures i potncies. Metodologia: els alumnes treballaran les propietats dels fractals utilitzant recursos en lnia. Les llions estan dissenyades perqu els alumnes treballin independentment o amb l'ajuda del professor o professora.AZAA Connexions: Relaciona les matemtiques amb l'art, l'escriptura, la histria i les professions. Relaciona l'aritmtica i la geometria. Z | R&/0    ,-0789=><  ` ̙33` ` ff3333f` 333MMM` f` f` 3>?" dd@,|?" dd@   " @ ` n?" dd@   @@``PR    @ ` ` p>> h`(    6تg  P g  c+Haga clic para cambiar el estilo de ttulo ,,3  0g   g  kHaga clic para modificar el estilo de texto del patrn Segundo nivel Tercer nivel Cuarto nivel Quinto nivel7   l  0g  `` g  `*  0$g  `  g  b*  0g  `  g  b*H  0޽h ? ̙33 *Diseo predeterminado' 0 @7(    0jx  P   x  T*   0,px     x  V* d  c $ ?  x 3  0Lkx   0 x  kHaga clic para modificar el estilo de texto del patrn Segundo nivel Tercer nivel Cuarto nivel Quinto nivel7   l  6vx  _P  x  T*   6}x  _  x  V* H  0޽h ? 3380___PPT10."pz 0x(  x  c $\=x  x  x  c $>x G  x    0I t*David Obrador Sala: 26 de novembre de 2005+(2+ +d  s <A logomigfH  0޽h ? ̙33___PPT10i.>K+D=' = @B + ` r(   x  S (A DSMAd| d 0  S ,H  ,Z  g  T Portada DSMA ( H  0޽h ? ̙33___PPT10i." +D=' = @B +  p((  (T ( C ,Atitolcurszr ( S  P  /  v ( 0lx "t  Proporcionar informaci al professorat de matemtiques (ESO i batxillerat) sobre els recursos que ofereixen Internet i les (TIC), i que donen suport a la tasca docent.  4 H ( 0޽h ? ̙33___PPT10i."f+D=' = @B +{  um,(  ,T , C ,Atitolcursz , S x  <$D 0 x  r , S Шx   x  Q , 0x "`I7U,$D 0 Gcurs per a usuaris de recursos TIC, no per a creadors de recursos TIC. 8H 2  HH , 0޽h ? ̙33___PPT10."f+vrD"' = @B D' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,^%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,^%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,1%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,1Y%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*,Y%(D' =%(D' =%(D8' =A@BB BB0B%(D' =1:Bvisible*o3>+B#style.visibility<*,%(D' =-g6B fade*<3<*,+8+0+,  +l  YQ <0 (  <T < C ,Atitolcursz <  BĽx  "`q<$D 0 x  5 < 0U "`a OCurs de 6 mduls i projecte final 45 hores 6 hores per mdul 9 hores projecteP 2P@ "  < lA$estructura_moduls<$D 0  l  <,$@  0  < s 4A mapa"`V ,d 0  < s 4A mmap"`d *d 0l F   <F  ,$D  0 < s 4A mapa"`WF   4d 0 < s 4A mmap"`F e  2d 0r < S  wN    RB < s *Dj 6jH < 0޽h ? 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̙33___PPT10i."f+D=' = @B + @ T(  TT T C ,Atitolcursz T ^Amapa_m4_m6 F q T q T c .A mapa"`dq   d 0 T c .A mmap"`qr  d 0  T S po   R Mapa m4-m6   H T 0޽h ? ̙33___PPT10i."f+D=' = @B +m |0P(  P P fA 02_fractals  x  P S $A1"`  d 0 P S $A2"`  d 0 P S $A3"`  d 0 P S $A4"`  d 0\ P C &A batct"`] P S $A1"`<]  d 0 P S $A2"`N]  d 0\ P C &A batcs"`   P S $A1"`9   d 0 P S $A2"`J   d 0X P C "Aeso"`; P S x P  x  P currculum  H P 0޽h ? ̙33___PPT10i."f+D=' = @B +  PXD(  X X fA 02_fractals  ,  X <L , J! ,$D 0 Hem recollit algunes adreces on es poden trobar recursos interessants per a la docncia de les matemtiques a secundria, i els hem classificat en els documents segents: Webs de departaments de matemtiques de centres Webs personals de professors i professores2]\</*d 0d 0 X S \ , P  ,  WWebs centres i profes&H X 0޽h ? ̙33___PPT10."f+ksD~' = @B D9' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*X%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*X%(+  ld d(  dT d C ,Atitolcursz d 0L, < M,$D 0 Un exemple concret de prctica i que ens conduir a la Experincia a l aula que vull mostrar: geometria fractal Del DSMA, prctica 4 del mdul 6: Fractals a una experincia a l aula: geometria fractal>p 2[(2t& (  d `A 01_fractals\$D 06 d 0 ,   d S  ,   ,  pCap a exp_aula &H d 0޽h ? ̙33  ___PPT10 ."f+<*ΕD ' = @B DX ' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*dp%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =%(D' =%(D+' =4@BB BB%(D' =1:Bvisible*o3>+B#style.visibility<*d%(D' =-g6B fade*<3<*d+7  NF(    fA 02_fractals  , H  0޽h ? ̙33___PPT10i."f+D=' = @B +  @ (  P  0`., 73 k <http://math.rice.edu/~lanius/frac L'autora s Cynthia Lanius= 2=L! :d 0!  `A 02_fractals  ,   c 4A m6p4im1T< ?d 0  S 4, XA  ,  ~Cynthia Lanius 4H  0޽h ? ̙33___PPT10i."f+D=' = @B +   KC(  r  S L=, `  ,    S C, /fO<$D 0 ,  "  @  fA 02_fractals  ,   0Q, < \ _A la prctica del DSMA fem: 2 H  0޽h ? ̙33:2___PPT10."f+ D' = @B D' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*/%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*/}%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*}%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*M%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*Mv%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*v%(+  0m(  0~ 0 s *x P  ,   0 s *g   x  "  @ 0 fA 02_fractals  x  0 ^A m6p4im2  x  0 0,`, < \ _A la prctica del DSMA fem: 2 H 0 0޽h ? 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La major part de la geometria estudiada a secundria va ser organitzada per Euclides 300 anys abans de Crist. En canvi, els fractals es van descobrir al segle XX i sn objecte d'investigaci pels matemtics actuals. Els podem entendre: A diferencia de molts temes de matemtiques, per als quals fan falta anys d'estudi per poder-los entendre, hi ha molts aspectes dels fractals que els alumnes poden entendre. Els objectes naturals sovint tenen estructura fractal: Arbres, nvols, lnies costaneres... sn modelitzats i descrits molt millor pels fractals que no pas pels objectes geomtrics clssics com triangles, quadrats... Hi ha conceptes realment sorprenents relacionats amb els fractals: Si mesureu la lnia de la costa utilitzant mapes a una escala cada cop ms reduda, veureu que la mesura obtinguda va variant i cada cop s ms gran... Els cientfics utilitzen els fractals per resoldre problemes de la vida real. nOZV  H 0, < \ _A la prctica del DSMA fem: 2 H H 0޽h ? ̙33 ~ ___PPT10^ ."f+|3D2 ' = @B D ' = @BA?%,( < +O%,( < +D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*H%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*H\%(D4' =%(D' =%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*H\%(+U ldp(    fA 02_fractals  x \  c 4Am6p4im5 8  S Ԡ, z*l  x  ]El floquet de neu de Koch   0, Z z _A la prctica del DSMA fem: 2    0@,  fc PH@___PPT9" h4. Activitats sobre el floc de neu de Koch Dibuixar el floc de neu en paper engraellat Utilitzar un applet Java per veure el dibuix del floc de neu Un fenomen fascinant: permetre infinit I qu passa amb l'rea? 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Fuentes usadasPlantilla de diseoTtulos de diapositivaT  8@ _PID_HLINKSA Vhttp://jasper.xtec.net:7451/cdweb/dades/actu/actual_matform/materials/tdsma/index.htm../DSMA/DSMA/mapa.htm../DSMA/DSMA/mapa.htm../DSMA/DSMA/mapa.htm../DSMA/DSMA/mapa.htm265,8,Mapa m1-m3265,8,Mapa m1-m3266,9,Mapa m4-m6266,9,Mapa m4-m6!../DSMA/DSMA/dsmam6/dsmam6p4.htm"http://math.rice.edu/~lanius/frac"http://math.rice.edu/~lanius/frac1http://math.rice.edu/~lanius/frac/koch/koch.html ../koch.exe../imatges/triangle.gifXhttp://jasper.xtec.net:7451/cdweb/dades/actu/actual_matform/materials/tdsma/fitxa01.htmXhttp://jasper.xtec.net:7451/cdweb/dades/actu/actual_matform/materials/tdsma/fitxa02.htm"../DSMA/DSMA/curriculums/eso1.htm"../DSMA/DSMA/curriculums/eso2.htm"../DSMA/DSMA/curriculums/eso3.htm"../DSMA/DSMA/curriculums/eso4.htm$../DSMA/DSMA/curriculums/batct1.htm$../DSMA/DSMA/curriculums/batct2.htm$../DSMA/DSMA/curriculums/batcs1.htm$../DSMA/DSMA/curriculums/batcs2.htm%_$0 j David ObradorDavid Obrador  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnoprstuvwxyz{|}~     !"#$%&'()*+,-./012346789:;<>?@ABCDKRoot EntrydO)PicturesCurrent User=SummaryInformation( TPowerPoint Document(qH0DocumentSummaryInformation85