1.º PORTUGAL - ITÁLIA EM GeCla

Transcrição

1.º PORTUGAL - ITÁLIA EM GeCla
ATRACTOR
No âmbito de uma colaboração
entre a Gazeta e o Atractor, este
é um espaço da responsabilidade
do Atractor, relacionado com
conteúdos interactivos do seu
site www.atractor.pt .
Quaisquer reacções ou sugestões
serão bem-vindas para
[email protected]
1.º PORTUGAL - ITÁLIA EM GeCla
Em 2009, o Atractor concluiu o DVD “Simetria – apresentação dinâmica”,
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FDGDSDGUmRRXIULVRHVWiDVVRFLDGRXPFDULPERVyGH-
A
pendente da simetria desse padrão ou friso, que permite
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&RPHFHPRVSRUYHUDOJXQVH[HPSORVFRQVWLWXtGRVSHORVTXDWURWLSRVGHFDULPERVPRVWUDGRVQDÀJXUDXPFRQHURODQGR
DSLQWDUXPDURViFHDXPFLOLQGURDFDULPEDUXPIULVRVyFRP
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3RUTXHVmR~WHLVRVFDULPERV"eTXHSDUDFRQWDURVGLIHUHQWHVWLSRVGHVLPHWULDEDVWDFRQWDUWRGRVRV´ERQVµFDULPERV8PDH[SOLFDomRGHWDOKDGDGRTXHpXP´ERPµFDULPER
Figura 1
H GH FRPR VH SRGHP HQFRQWUDU WRGRV HOHV p WDPEpP DSUH-
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matemáticas importantes a alunos mais interessados.
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Pouco tempo depois de iniciada a difusão do DVD,
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R $WUDFWRU FRPHoRX R GHVHQYROYLPHQWR GH RXWUR PDWHULDO
com este DVD criar um instrumento didático para ser usado
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UHJXODUPHQWHSRUDOXQRVDOJXPDVGDVVXDVVHFo}HVSRGHPVHU
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ATRACTORr1.º Portugal - Itália em GeCla
03
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de uma larga faixa etária e procuraria ser útil no estudo e na
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de uma escola portuguesa com outros de uma escola italiaQD QXP WRUQHLR FRP FRQWRUQRV LQpGLWRV ( IRUDP R VXFHVVR
GRHYHQWRDDGHVmRHRHQWXVLDVPRGRVDOXQRVSDUWLFLSDQWHV
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jHVFROKDGHVWDQRWtFLDFRPRWHPDGDFROXQDGR$WUDFWRUQR
presente número da Gazeta, na esperança de que mais pro-
Figura 2
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análogas com os seus alunos.
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DQWHV GH GDUPRV PDLV DOJXQV GHWDOKHV VREUH R UHIHULGR WRUQHLR 2 *H&OD WHP XP gerador ÀJXUD TXH SHUPLWH FULDU
XP GHVHQKR DEUHYLDWXUD GH IULVRSDGUmRURViFHD DSyV D
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Figura 3
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LFRPRPRWLYRSDUDGHVHQKDUXPIULVRTXHVyDGPLWDWUDQVODo}HVEDVWDHpQHFHVViULRHVFROKHURFDULPERFLOtQGULFRXP
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Figura 4
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j GHWHUPLQDomR GR VHX WLSR GH VLPHWULD H SRUWDQWR GR FDULPER DVVRFLDGR 6H R ÀFKHLUR GR GHVHQKR TXH VH SUHWHQGH FODVVLÀFDU WLYHU VLGR SURGX]LGR SHOR JHUDGRU GR *H&OD
04
GAZETA DE MATEMÁTICA r171
Figura 5
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'HSRLVXVDQGRRPRWLYRJXDUGDGRSRGHJHUDUFRPRFDULP-
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ERHQFRQWUDGRXPQRYRGHVHQKRTXHWHUiDVSHWRLJXDODRGD
QKHFHUWRGDVDVVLPHWULDVGRGHVHQKRHRSURJUDPDSHUPLWH
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HQFULSWDGDVREUHDVVLPHWULDVH[LVWHQWHV)RLDVVLPREWLGDDLPD-
HOHWHQKDSUHYLDPHQWHHVFROKLGRHPPRGRGHajuda máxima,
JHPTXHHVWiDVHUPRVWUDGDHPIDVHGHFODVVLÀFDomRQDÀJXUD
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TXH FRQVLGHUH LQFRUUHWD QR GH ajuda mínima, pode deixar
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GDÀJXUD1RSRUWDOGR$WUDFWRUHQFRQWUDVHXPDJUDQGHYD-
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da aprendizagem e, após alguma experiência, começar a re-
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GX]LURJUDXGHDMXGD
IRWRJUDÀDVSHORSURFHVVRGHVFULWR
(RTXHDFRQWHFHVHTXLVHUPRVFODVVLÀFDUXPGHVHQKRREWL-
$OpPGRJHUDGRUHGRFODVVLÀFDGRUFXMRVHVTXHPDVGHIXQ-
GRSRUH[HPSORIRWRJUDIDQGRXPDSDUHGHGHD]XOHMRV"2EYLD-
FLRQDPHQWR DFDEDP GH VHU EUHYHPHQWH GHVFULWRV R SURJUDPD
PHQWHQHVWHFDVRRÀFKHLURQmRFRQWpPQHQKXPDLQIRUPDomR
FRPSRUWD
HQFULSWDGDVREUHDVVLPHWULDVHRFODVVLÀFDGRUQmRSRGHDMXGDU
8PDVHFomRTXHSHUPLWHDRXWLOL]DGRUWHVWDUSRUTXDOTXHU
QDVHVFROKDVGRXWLOL]DGRUH[FHWRSDUDH[LJLUFRHUrQFLDQDLQIRU-
RUGHPHVHPTXDOTXHUUHJLVWRYLVDQGRXPDFODVVLÀFDomR
PDomRTXHOKHpWUDQVPLWLGD0DVVHRXWLOL]DGRUQmRPDUFDU
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corretamente qual o tipo de simetria e o correspondente carim-
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ER1XPDVLWXDomRFRPRHVWDXPSURIHVVRUTXHHVWHMDLQWHUHV-
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VDGRHPSHUPLWLUTXHRVVHXVDOXQRVFODVVLÀTXHPFRPDMXGD
DV LVRPHWULDV TXH FRQVHUYDP R GHVHQKR SRGH FRP HVWD
GRSURJUDPDRGHVHQKRGDIRWRJUDÀDSRGHVHPSUHWRUQHDUD
IHUUDPHQWDYHULÀFDUIDFLOPHQWHDYDOLGDGHGDVFRQMHWXUDV
GLÀFXOGDGH EDVWDOKH FODVVLÀFDU FRUUHWDPHQWH R SDGUmR VHP
TXHDVXDLQWXLomROKHVXJHUH
DMXGDJXDUGDURPRWLYRHQFRQWUDGRHWRPDUQRWDGRFDULPER
2. Outra secção que permite a realização de uma competi-
Figura 6
Figura 7
Figura 8
ATRACTORr1.º Portugal - Itália em GeCla
05
Figura 9
Figura 10
omR HQWUH GRLV MRJDGRUHV GXUDQWH D TXDO FDGD XP JHUD
GRLVWLSRVQDIDVHVHJXLQWHFDGDMRJDGRUWHPSRLVDSHQDVGH
XP FRQMXQWR GH GHVHQKRV FRP PRWLYRV j VXD HVFROKDH
GHVFREULUTXDLVRVIULVRVJHUDGRVSHORDGYHUViULRTXH´DGPL-
XWLOL]DQGRGLIHUHQWHVFDULPERVHGHSRLVWHQWDFODVVLÀFDU
WHPXPDUHÁH[mRKRUL]RQWDOµRTXHpYLVXDOPHQWHPXLWRIiFLO
RVGHVHQKRVJHUDGRVSHORVHXDGYHUViULRQRÀQDORSUR-
YHUÀJXUD8PDYH]IDPLOLDUL]DGRFRPRIXQFLRQDPHQWR
JUDPDSURGX]XPUHODWyULRTXHLQGLFDTXDLVDVFODVVLÀFD-
GRSURJUDPDDHVWHQtYHOPDLVHOHPHQWDUpSRVVtYHORMRJDGRU
o}HVFRUUHWDVHTXDLVDVLQFRUUHWDVDSRQWDQGRSDUDFDGD
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uma das incorretas, o primeiro erro cometido. O progra-
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2*H&ODWHPSUHVHQWHPHQWHLQVWUXo}HVHPTXDWUROtQJXDV
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LQJOrVLWDOLDQRHHVSDQKRODOpPGRSRUWXJXrVHR$WUDFWRU
GH GLÀFXOGDGH 8PD YH] IHLWDV DV HVFROKDV R SURJUDPD
WHPFRQKHFLPHQWRGHTXHIRLXWLOL]DGRFRPVXFHVVRHPDXODV
JHUHDSURJUHVVmRGRMRJRDWpjVXDFRQFOXVmR8PDYHU-
HP3RUWXJDOHHP,WiOLD(IRLSUHFLVDPHQWHGHXPDSURIHVVRUD
VmRSUySULDSDUDRVPDLVMRYHQV²R*H&ODPLQLÀJXUD
LWDOLDQD TXH VXUJLX HP DEULO GHVWH DQR D SULPHLUD SURSRVWD
²QHPVHTXHUSHUPLWHRSWDUSHORVQtYHLVPDLVDYDQoDGRV
SDUDDRUJDQL]DomRGHXPDFRPSHWLomRFRPR*H&ODYLD,Q-
DOpPGLVVRWHPXPDDSUHVHQWDomRHXPFRQMXQWRGHPR-
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WLYRVIHLWRVDSHQVDUHPIDL[DVHWiULDVPDLVEDL[DV
e de uma forma por ele inteiramente controlada. O Atractor
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9HMDPRV XP H[HPSOR H[WUHPR DGDSWDGR D DOXQRV GR ž
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Atractor, alguns dos quais usam regularmente o programa
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FRPRVVHXVDOXQRV&KHJRXDVHUHQFDUDGDDSDUWLFLSDomRGH
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QDIDVHHPTXHWHPGHJHUDUXPGHVHQKRGLVS}HGHDSHQDV
ORJtVWLFRV QD HVFROD OLJDGRV WDPEpP DR IDFWR GH Mi VH HVWDU
GXDV RSo}HV RX XP IULVR Vy FRP WUDQVODo}HV ÀJXUD RX
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quase in extremisSRUXPDSURIHVVRUDTXHHVFROKHXXPJUXSR
06
GAZETA DE MATEMÁTICA r171
Figura 11
WFigura 12
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HQRUPH HQWXVLDVPR SHOD LQLFLDWLYD (P SRXFR PDLV GH XPD
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apenas atestam a participação dos alunos.
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Figura 13
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organizadores…
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REFERÊNCIAS
DSRLRTXHOKHIRLVROLFLWDGRFRPRHVWDUiSDUDLQLFLDWLYDVDQi-
>@http://www.atractor.pt/publicacoes/entrada2.htm
ORJDVTXHYHQKDPDVHUWRPDGDVQRIXWXURHQYROYHQGRXPD
>@ http://www.atractor.pt/mat/GeCla
RXPDLVHVFRODVDQtYHOQDFLRQDORXLQWHUQDFLRQDO
>@http://www.atractor.pt/mat/GeCla/im4.html
ATRACTORr1.º Portugal - Itália em GeCla
07

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