| Te Āhuahanga Taumata 5
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| Ngā Whāinga Paetae
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| Te torotoro āhua, mokowā
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| I roto i ngā horopaki whai tikanga, me mōhio te akonga:
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| 1. ki te whakamahi i ngā ahuatanga koki o ngā rarangi whakarara, ki te whakamarama i aua ture ki roto;
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angle properties; parallel |
| 2. ki te whakahāngai i ngā ture hangarite
me ngā ahuatanga koki o ngā taparau;
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symmetry; polygon |
| 3. ki te whakamahi i te ahuatanga mō
te koki i waenganui i te patapa me te pūtoro, me te āhuatanga
mō te koki porohita weherua;
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tangent; radius
semi-circle |
| 4. ki te hanga koki hāngai , rarangi whakarara, rarangi hāngai , porohita, taparau ngawari, weherua tapatoru, rarangi weherua hāngai , teitei, weherua koki;
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perpendicular
median; mediator; altitude; angle bisector |
| 5. ki te whakamahi i te whakaahua awhata, i te ture a Pythagoras, i tētahi owehenga pakoki rānei e tika ana, kia kitea mai ai te tapa o tētahi tapatoru hāngai kāore i te mohiotia;
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scale drawing; trigonometrical ratio |
| 6. ki te tuhi i ngā hoahoa awhata o ngā mea ahu&;3 i hangaia ki te mataono;
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isometric drawing |
| 7. ki te whakaoti rapanga whaitake, ki te pere, ka taea te whakatauira.
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vector; model |
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Te torotoro hangarite, panoni
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| I roto i ngā horopaki whai tikanga, me mōhio te akonga:
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| 8. ki te ahukahuka i te ritenga o etahi
āhua e rua, ki te kimi i te tau rahi e kitea mai ai tētahi
rahinga kāore i te mōhiotia;
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recognise; scale factor |
| 9. ki te whakahangai i ngā ahuatanga hangarite me ngā ahuatanga koki o ngā taparau hei whakaoti rapanga whaitake;
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symmetry and angle properties |
| 10. ki te whakamahi, ki te whai i ngā pere e whakaahua nekehanga ana;
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vector |
| 11. ki te tautuhi, ki te whakamahi i ngā ahuatanga pūmau o ngā panoni.
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invariant |
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He Tauira Horopaki
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- TE KOWHAIWHAI&;I ahu mai te kowhaiwhai i hea? He aha te tikanga o ngā tauira e kitea ana i roto i te kowhaiwhai?
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- TE āhua O
TE WHARENUI&;Arā, ngā pou, ngā maihi, ngā
amo, te whatitoka, te matapihi, te tāhūhū, te aha, te
aha. He aha te tikanga o ēnei mea?
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- TE MARAE&;Tuhia he mahere awhata o tētahi pa, me te titiro-a-manu.
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| He Tauira Mahi
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| Te torotoro āhua , mokowā
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| Anei etahi tauira mahi e taea ai ngā whainga paetae o tēnei taumata te whakatutuki:
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| 1. Me mōhio te ākonga ki te whakamahi i ngā
āhuatanga koki o ngā rārangi whakarara, ki te whakamārama
i te whakaaro whaitake ki roto;
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- he torotoro i ngā panga i waenganui i ngā koki (taurite,
tauwhiti, tauroto) o ētahi rārangi whakarara
kei te haukotitia ki tētahi atu rārangi.
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corresponding; alternate; co-interior; intersected |
| 2. Me mōhio te akonga ki te whakahangai i ngā ahuatanga hangarite me ngā ahuatanga koki o ngā taparau;
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- he torotoro i ngā ahuatanga o te taparau, tae atu hoki ki te
panga i waenganui i te nui o ōna tapa, ahakoa taparau rite, taparau
hikuwaru rānei (tapatoru, tapawhā, taparima, tapaono),
me te tāpiritanga o ngā koki o roto, o waho.
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irregular
interior and exterior angles |
| 3. Me mōhio te akonga ki te whakamahi i te ahuatanga mō
te koki i waenganui i te patapa me te putoro, me te āhuatanga mō
te koki porohita weherua;
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- he torotoro, he whakahangai i te ture a Pythagorus me te āhuatanga
mō te koki porohita weherua ki ngā mahi o ia rā.
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| 4. Me mōhio te akonga ki te hanga koki hāngai ,
rarangi whakarara, rarangi hāngai , porohita, taparau ngāwari,
weherua tapatoru, rārangi weherua hāngai , teitei, weherua koki;
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- he whetui pepa, he whakamahi taputapu tuhi rānei hei hanga rārangi
whakarara, rārangi hāngai , patapa porohita, weherua
koki, weherua tapatoru, koki rānei , hei kimi punga
porohita;
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tangents to a circle; median
centre |
- he torotoro i ngā panga i waenganui i ngā mahi ahuahanga me ngā mahi toi;
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- he torotoro, he matapaki, he hanga i ngā āhua o roto mai i tona ano ao, arā , ngā :
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i) tauira o roto i ngā kowhaiwhai, taniko, tukutuku, whakairo,
moko, tae atu hoki ki ētahi atu mahi toi a ngai taua, a te Māori;
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ii) porohita, pororapa, torino e kitea mai ana i roto i ngā mahi o ia rangi;
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ellipse; sprial |
iii) hoahoa kua āta tuhia ki te taputapu tuhi (pēnei i ngā
taputapu tuhi a te kaihoahoa whare);
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- he āta torotoro ano i tēnei mea, i te huanui. Hei whakatauira,
me torotoro:
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locus |
i) ngā puwāhi e ōrite ana te tawhiti atu i ētahi
atu puwāhi e rua;
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points |
ii) ngā puwāhi e ōrite ana te tawhiti atu i etahi akitu
e rua, tapa tapatoru rānei .
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vertices |
| 5. Me mōhio te ākonga ki te whakamahi i te hoahoa
āwhata, i te ture a Pythagoras, i tētahi ōwehenga pakoki
rānei e tika ana, kia kitea mai ai te tapa o tētahi tapatoru hāngai
kāore i te mōhiotia;
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- he hanga tauira mama o ngā mea ahu-3 e āta kitea atu ai ngā
koki hāngai o roto.
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| 6. Me mōhio te akonga ki te tuhi i ngā hoahoa āwhata
o ngā mea ahu&;3 i hangaia ki te mataono;
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- he tuhi mea ahu-3 ki te pepa āwhata, pepa tukutuku rānei .
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| Te torotoro hangarite, panoni
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| Anei etahi tauira mahi e taea ai ngā whainga paetae o tēnei taumata te whakatutuki:
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| 7. Me mōhio te akonga ki te ahukahuka i te ritenga o ētahi
āhua e rua, ki te kimi i te tau rahi e kitea mai ai tētahi
rahinga kāore i te mohiotia;
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scale factor |
- he kimi mai i te tau rahi o etahi mea ahu-2, ahu-3 rānei e āhua
rite ana, ka kimi ai i ētahi inenga kāore i te mōhiotia;
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- he whakanui, he whakaiti āhua māmā (ahu-2, ahu-3 rānei
) mehemea kei te mōhiotia te punga o te whakarahinga
me te tau rahi (he tau topu rānei , he hautanga rānei
), ka torotoro ai i te panga atu o te tau rahi ki te roa, te horahanga,
me te rorahi.
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centre; enlargement; integral |
| 8. Me mōhio te akonga ki te whakamahi, ki te whai i ngā pere e whakaahua nekehanga ana.
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vectors
translations |
| 9. Me mōhio te akonga ki te tautuhi, ki te whakamahi i ngā ahuatanga pūmau o ngā panoni;
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- he torotoro i te whakamahia i te hurihanga i roto i ngā horopaki whaitake;
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- he torotoro i ngā whakamarama reo pāngarau mō ngā
panoni (tae atu hoki ki ngā pere e whakaahua nekehanga ana);
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- he tautuhi i ngā ahuatanga pūmau , āhuatanga huri o tētahi
āhua kua meatia ki te panoni (ko ngā panoni aronga whānui
noa iho);
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standard |
- he torotoro i ngā panoni o ngā āhua kua tuhia ki te pepa tukutuku
tapawhā-kore.
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non-square grids |
| He Tauira Aro Matawai
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| He tauira noa enei hei āwhina i te kaiwhakaako:
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- He tuhi panui whakamarama i te hanga o te "tapawhā hāngai
koura" me ngā āhua e arā ake ana e puta ai ai
ngā torino ā-nuku.
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golden rectangle
spirals found in nature |
Mā tēnei tauira ka mōhio te kaiwhakaako e pēhea ana te matatau o ngā akonga ki te:
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- He tuhi poro he hikuwaru te pūtake , hei whakatauira, ko tētahi poro he "L" te āhua o te pūtake .
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prism |
Mā tēnei tauira ka mōhio te kaiwhakaako e pēhea ana te matatau o ngā akonga ki te:
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- He hoahoa tauwhainga kopapa e whai wahi mai ana he pere.
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board game |
Mā tēnei tauira ka mōhio te kaiwhakaako e pēhea ana te matatau o ngā akonga ki te:
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- He hoahoa raumata mō tētahi pouaka e rite ana ki te koeko
tapatoru te āhua hei pupuri i i tētahi taonga he porohita
te āhua , mehemea e mōhiotia ana te rahi o taua taonga. (Otira
me pa te porohita ki ngā taha o te pouaka.) Kia oti mai te raumata
te ata hoahoa, me huri hei pouaka.
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net; triangular-based pyramid |
Mā tēnei tauira ka mōhio te kaiwhakaako e pēhea ana te matatau o ngā akonga ki te:
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- He tuhi pūrongo e pā ana ki te whakamahia o tētahi
inenga whaitake e whai wāhi mai ana ētahi āhua ōrite
. Hei whakatauira, ko te rapanga e whakaahuatia ana i raro nei:
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Mā tēnei tauira ka mōhio te kaiwhakaako e pēhea ana te matatau o ngā akonga ki te:
| Ahua 5/8 |
Ahua 5/9 |
TP6 |
TP5 |
Inenga 5/2 |
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- He whakamātautau tapaetanga kōrero . Hei whakatauira,
me torotoro e te ākonga te tika, te he rānei o te tapaetanga
kōrero e whai ake nei, ka parahau ai i tāna i whakatau
ai, "Kāore e taea tētahi porohita te tuhi, ko te pae
e pā atu ana ki ngā akitu katoa o te tapatoru e pēnei
ana te roa o ngā tapa: 3, 4, 5."
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conjecture
justify |
Mā tēnei tauira ka mōhio te kaiwhakaako e pēhea
ana te matatau o ngā ākonga ki te:
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