Peke atu ki te ihirangi matua

Pāngarau 2026

  • Pāngarau
  • Ngā Tatauranga
  • Ngā Tikanga Ārai
  • Tātaitai

Pāngarau

Pāngarau Whānui - NCEA Taumata 1

Whakaahuatanga o te Hōtaka:

He akoranga tēnei kua hangaia hei whakapakari i te māia ki te pāngarau me te whakaaro pāngarau ki te whakaoti rapanga Pāngarau me ētahi tatauranga, ā, ka hoatu hoki he kōwhiringa ki ngā akoranga tau tuarua o te heke mai.

Ngā Putanga Ako / Ngā Ihirangi:

Ka ako ngā ākonga ki te whakamahi i te huringa uiui tatauranga hei whakahaere me te tūhura i ngā raraunga i roto i ngā horopaki o te ao tūturu. Ka uru atu ki tēnei ko te kohikohi me te whakaatu raraunga, te tātari i ngā raraunga, te whakamārama i ngā kitenga me te whakatau i ngā whakatau mō ngā raruraru e pā ana ki ngā raraunga. Ka whakaatuhia ngā taunakitanga mō tēnei Paerewa hei pūrongo tuhituhi, whakarongo, tirohanga rānei. Ka whai wāhi ngā ākonga ki te tūhura i ngā raruraru o te ao tūturu mā te whakamahi i tētahi horopaki e pārekareka ana ki a rātou.

Ka ako hoki ngā ākonga ki te whakamahi i ngā kaupapa matua o ngā tatau tapatoru hāngai, tae atu ki a Pythagoras me te trigonometry, me te whakakotahi i ēnei me ngā rangahau tau me te ine. Ka ahu mai ēnei rangahau i te whakamahi i ngā ōrau, te GST me te moni, te horahanga, te rōrahi, te kaha me ngā reiti e whakamahia ana i roto i ngā horopaki haere, pūtea, whakahaere huihuinga, hangahanga, waka rānei. Ka ako hoki ngā ākonga ki te whakarato whakamārama mō ngā whakataunga pāngarau katoa e mahia ana e rātou i a rātou e whakahaere ana i ngā rangahau.

Tērā pea ka uru atu hoki ki ēnei whai wāhitanga ako ngā ākonga e ako ana puta noa i ngā marautanga i MBAS.

Ngā Pūkenga me ngā Āheinga:

E hiahiatia ana ngā pūkenga pāngarau i ngā āhuatanga katoa o te ao, he maha ngā wā kāore i te tūmanakohia, he hunga whakaoti rapanga ngā tohunga pāngarau, ā, he pūkenga ēnei e tino hiahiatia ana e ngā kaitukumahi. Ka whiwhi ngā ākonga e uru ana ki te akoranga i te māia ki te whakamahi i ngā pūkenga pāngarau, te whakaoti rapanga me te whakawhitiwhiti kōrero, ā, ka noho rātou ki tētahi wāhi e whakawhanakehia ana, e whakamahia ana hoki ēnei pūkenga.

He hononga pea ki:

BCAT, Hangarau, Akoranga Pakihi, Tūruhi, Hauora me te Mātauranga Hauora.

Tērā pea ka arahi ki:

Ngā Tatauranga L2 me ngā Tikanga Tūponotanga

Ngā Aromatawai:

E rua ngā aromatawai ā-roto i te wāhanga 1, 2, me te wāhanga 3 pea, ka ahu mai ngā aromatawai e rua i te uiuinga me te ako kaupapa, ko tētahi e ahu mai ana i te horopaki tatauranga, ko tētahi e ahu mai ana i te pāngarau whānui, ka arotahi ngā mea e rua ki te whakaoti rapanga i roto i ngā horopaki o te ao tūturu. Ka whai wāhi ngā ākonga ki te noho i tētahi whakamātautau o waho mēnā kua oti i a rātou ngā paerewa ā-roto e rua, ā, e hiahia ana rātou ki te haere tonu ki te Pāngarau i te tau 12.

Ko te tapeke whiwhinga e wātea ana he 15, 10 mai i ngā aromatawai ā-roto, ā, 5 mai i ngā aromatawai o waho.

Ka whai wāhi anō hoki ngā ākonga ki te whakaoti i ngā Paerewa Wāhanga Tau mēnā kāore anō kia whiwhi i tēnei whakaritenga matua. Ka taea te whiwhi i ngā whiwhinga 10 e hiahiatia ana mā te noho anō ki te CAA, mā roto rānei i ngā whiwhinga ā-roto 10 e tukuna ana hei wāhanga o tēnei akoranga.

Ngā Tikanga Pāngarau - NCEA Taumata 1

Whakaahuatanga o te Hōtaka:

Ko tēnei akoranga Pāngarau he mea whakarite mā ngā ākonga e pai ana ki te "āraipū" me te hiahia ki te whakapakari i ngā pūkenga whakahaere āraipū, whārite, whakatauira me te whakawhitiwhiti kōrero! Ko tēnei akoranga he mea whakarite mā ngā ākonga e hiahia ana ki te ahu whakamua ki te Tātaitai taumata tuarua.

Ngā Putanga Ako/Ihirangi:

Kua hangaia tēnei akoranga hei wero i ngā ākonga ki te whakawhanake i ngā pūkenga matua o te whakahaere taurangi, he mea tūāpapa mō ngā akoranga tātaitai me te taurangi katoa o ngā tau tuawhā. Ka whakawhanakehia e koe ngā pūkenga whakaaro pai kia taea ai e koe te whakamārama me te māia he aha koe i whakaaro ai he huarahi hei whakamahi hei whakaoti rapanga.

Ka ako ngā ākonga ki te whakamahi i ngā pūkenga Pāngarau Tautoru me te Pāngarau Rārangi i roto i ngā āhuatanga mahi maha, me te whakamārama i ā rātou tikanga whiriwhiri hei whakaoti rapanga Pāngarau. Ka ako hoki ngā ākonga ki te whakamārama i ngā mōhiohio pāngarau me ngā mōhiohio tatauranga mai i ngā momo puna, tae atu ki ngā whakaahua taipitopito, ngā whakaaturanga me ngā tuhinga pāpāho, kātahi ka whakaatu i tētahi pūrongo e hono ana i ā rātou kitenga ki te horopaki o te ao tūturu. Hei whakamutunga, ka mahi ngā ākonga me ētahi ariā pāngarau matatau mai i ngā whenu Pāngarau Tau, Tau me te Āhuahanga tae atu ki te whakahaere pāngarau, te arotautanga, ngā whārite tukutahi, ngā tere huringa, te pāngarau tautoru 3D, ngā tapawhā, ngā horahanga mata me ngā rōrahi me te whakamahi i ēnei hei whakaoti rapanga i roto i ngā horopaki mahi me te whakamārama i ā rātou tikanga.

Ngā Pūkenga me ngā Āheinga:

E hiahiatia ana ngā pūkenga pāngarau i ngā āhuatanga katoa o te ao, he maha ngā wā kāore i te tūmanakohia, he hunga whakaoti rapanga ngā tohunga pāngarau, ā, koinei ngā pūkenga e tino hiahiatia ana e ngā kaitukumahi. Ka whiwhi ngā ākonga e uru ana ki tēnei akoranga i te māia ki te whakamahi i ngā pūkenga Pāngarau, te whakaoti rapanga me te whakawhitiwhiti otinga i roto i tētahi raupapa o ngā kaupae arorau. Ka noho ngā ākonga ki tētahi wāhi e tumanakohia ana, e whakanuia ana hoki te mahi uaua, ā, ka whakawhanakehia, ka whakamahia hoki ngā pūkenga kua whakahuatia ake nei.

Ngā Hononga Pea ki:

Ngā mara Hangarau, Ahupūngao, Hangarau Hoahoa Whare, Toi, Whakaahua me te Hoahoa, ngā mara Pūtaiao katoa.

Tērā pea ka arahi ki:

ngā akoranga Pāngarau tuākana katoa.

Ngā Aromatawai:

Ka aromatawaihia tētahi Paerewa Paetae ā-Roto i te wāhanga 1, ka arotahi ki te mātauranga tatauranga. I te wāhanga 2 ka noho mātou i tētahi aromatawai ā-roto tuarua e ahu mai ana i te ine me te whārite. I te wāhanga 3 ka tīmata mātou ki te whakarite mō te Paerewa Paetae e aromatawaihia ana i waho, ka uru atu ki tēnei ko te whakaoti rapanga mā te whakamahi i te Pāngarau mō ngā āhuatanga ariā kua hoatu. Ka tangohia ēnei rapanga mai i ngā momo wāhanga o te marautanga pāngarau i te taumata 6.

Ko te tapeke o ngā whiwhinga e wātea ana he 15, 10 mai i ngā aromatawai ā-roto, ā, 5 mai i ngā aromatawai o waho.

Kāore tēnei akoranga e tuku i te whai wāhitanga ki te whiwhi i te whakaritenga matua mō te Pāngarau. Heoi, ka taea te whakatutuki i ngā whiwhinga 10 e hiahiatia ana mō te whakaritenga matua mō te Pāngarau mēnā e hiahiatia ana mā roto i ngā paerewa aromatawai ā-roto e rua e tukuna ana i roto i tēnei akoranga.

Pāngarau

Pāngarau - NCEA Taumata 2

Whakaahuatanga o te Hōtaka:

He akoranga Tatauranga tēnei, ā, kei roto hoki ētahi pāngarau. Kua hangaia hei hoatu ki ngā ākonga he tirohanga whānui mō te Pāngarau me te Tatauranga i te Taumata 2.

Ngā Putanga Ako / Ngā Ihirangi:

Ka tirohia e ngā ākonga tētahi rangahau whakatairite tatauranga. Kei roto i tēnei ko te kohikohi raraunga, te rangahau, ngā rorohiko, ngā kauwhata tatauranga, me te ako ki te tuhi pūrongo tatauranga. Ka rangahauhia e ngā ākonga te tūponotanga me te tūponotanga, me pēhea te whakamahi i ēnei hei whakaoti rapanga, tuatoru, ka mahi ngā ākonga i ngā āhuatanga o te pāngarau tae atu ki ētahi taupū, ētahi ine taurite me ētahi kauwhata.

Ngā Pūkenga me ngā Āheinga:

Te rangahau, te pānui me te tuhituhi, koinei te kaupapa matua o ngā mahi tatauranga. Te pānga o te tūponotanga me te tūponotanga ki te oranga o ia rā. Ka puta he pūkenga hou hei ako i roto i te arapū me te ine whārite. Te kaha ki te ngana me te ngana anō, te tohe tonu ina kore ngā mea e mahi i tāu e whakaaro ana me mahi!

Ngā Hononga Pea ki:

Hoahoa me te Whakawhitiwhiti Ataata, Toi, Whakaahua, Hoahoa, Hinengaro.

Tērā pea ka arahi ki:

Kāore i te hangaia hei ārahi i ngā akoranga tau tuawhā engari ko ngā Tatauranga me ngā Tohatoha Tūponotanga me/ranei te Pūtaiao Whenua me te Ātea me ngā Tatauranga, Pūtaiao Taiao.

Ngā Aromatawai:

Me whiriwhiri ngā aromatawai ā-roto katoa – me ngā aromatawai ā-waho katoa i te tīmatanga o te wāhanga 3.

Ko te tapeke o ngā whiwhinga e wātea ana he 17, ko te 13 o ēnei i ahu mai i ngā aromatawai ā-roto, ā, ko te 4 i ahu mai i tētahi whakamātautau o waho i te mutunga o te tau.

Ngā Tikanga Tātaitai me te Ārai - NCEA Taumata 2 me te 3

Whakaahuatanga o te Hōtaka:

Ko te arotahi o tēnei akoranga he whakapakari i ngā mōhiotanga taurangi, tauwhāinga me te tātai kauwhata i whiwhihia i te tau 11. Ka whakaurua hoki tētahi kaupapa hou, arā, ko te Tātaitai.

Ngā Huanga Ako/Horopaki:

Ka whanakehia e ngā ākonga he māramatanga hōhonu ake mō ngā tukanga taurangi me te whakamahinga o ēnei hei whakaoti rapanga. Ka whanakehia hoki e koe he māramatanga hōhonu ake mō te Tauritenga me ngā ariā hou me ngā ariā whānui e tūhuratia ana. Ka tirohia e mātou te āhua o te tūhuratanga o ngā ariā Tauritenga uaua i roto i ngā āhuatanga mahi.

Ka whakahaerehia hoki e ngā ākonga ngā whakaaturanga whakairoiro uaua ake, tae atu ki te whakaurunga o ngā pūtoru, ngā hyperbola me ngā mahi. Ka whakaurua hoki te kaupapa hou o te Tātaitai, ka tirohia ngā tere o te huringa o ngā mahi me te whakamahinga o ēnei hei whakaoti rapanga.

Ngā Pūkenga me ngā Āheinga:

He maha ngā ariā hou e whakamōhiotia ana e tēnei akoranga ki ngā ākonga, ā, me u tonu rātou ki te mahi i waho o te akomanga kia mārama ai, kia mau ai hoki ēnei ariā hou.

Ngā Hononga Pea ki:

Ahupūngao, Matū, Hoahoa me te Whakawhitiwhiti Kōrero Ātaata, Toi, Whakaahua, Hoahoa.

Tērā pea ka arahi ki:

Tātaitai L3, Tatauranga L3.

Ngā Huarahi Aromatawai:

Aromatawai ā-roto Ngā paerewa paetae mō te ine whārite me te tuhi kauwhata me ngā whakamātautau ā-waho mō te taupū me te tātaitai. Mēnā ka wātea te wā, ka taea pea te tuku aromatawai ā-roto taumata 3.

Ko te tapeke o ngā whiwhinga e tukuna ana he 16, e 9 nō ngā aromatawai ā-roto, ā, e 7 nō ngā whakamātautau o waho i te mutunga o te tau.

Ngā Tatauranga me ngā Tikanga Tūponotanga - NCEA Taumata 2

Whakaahuatanga o te Hōtaka:

Ko te arotahi o tēnei akoranga he whakawhanake i te whakaaro tatauranga me te mātauranga tatauranga mā te whakakotahi i ngā rangahau a ngā ākonga me te ako ariā i roto i ngā tatauranga me te tūponotanga.

Ngā Huanga Ako/Horopaki:

Ka whakamahia e ngā ākonga ō rātou wā ki te rangahau, ki te kohikohi raraunga, me te whakawhanake i ngā pūkenga tatauranga me te tātari e hiahiatia ana mō te mahi tahi me ngā raraunga ine me ngā raraunga whakamātautau. Ka akiakihia ngā ākonga ki te whakaaro me te whakamahi i ngā take o te ao tūturu/ā-rohe hei pūtake mō ā rātou rangahau tatauranga. Ka whakawhanakehia hoki e koe he māramatanga mō te Tohatoha Tūponotanga Noa, me pēhea tā tātou aromatawai i te mōrearea me te whakamahi i tēnei hei whakaoti rapanga.

Ngā Pūkenga me ngā Āheinga:

  • Kimihia, pānuihia hoki ngā tuhinga ipurangi me ētahi atu pūrongo rangahau mō te take, mō ia kaupapa rānei o āu rangahau, kia mōhio ai koe ki tāu e pūrongo ana!
  • Te whakamahinga o te hangarau NZgrapher me pēhea te whakamārama i ngā kauwhata tatauranga rerekē me ngā tatauranga matua.
  • Whakawhanakehia ngā taumata teitei ake o te pūkenga tuhituhi, te pūkenga tatauranga, me te hiahia ki te tuhituhi maha mā te whakamahi i te reo ōkawa.
  • Te tohutoro i ngā puna rangahau mā te whakamahi i te pūnaha tohutoro APA kua whakamanahia e te Whare Wānanga.
  • Te whakatika me te arotake me te whakaute i ngā pūrongo/ngā kōrero a ētahi atu.
  • Te kaha ki te pātai i ngā tau, te arotake arohaehae i ngā mea kāore pea i te mōhiotia!

Ngā Hononga Pea ki:

Ngā Pūtaiao Pāpori tae atu ki te Tūruhi, Ngā Pūtaiao Tinana me te Taiao, te Hauora me te Kai Totika, te Hinengaro, me te Ahumahi.

Tērā pea ka arahi ki:

Ngā ara mātauranga tuatoru i roto i ngā kaupapa e hiahia ana ki ngā Tatauranga; Ngā Mahi Tauhokohoko, Ngā Pūtaiao me te Ahumahi. L3 Tatauranga me ngā Tohatoha Tūponotanga.

Ngā Huarahi Aromatawai:

Ko ngā aromatawai ā-roto ka uru atu ki te rangahau mahi me te tuhi i ngā pūrongo tatauranga takitahi, i ngā whakaaturanga rānei e whakaatu ana i ō kitenga, me te whai wāhitanga aromatawai ā-waho mō ngā tikanga tūponotanga.

Ko te tapeke o ngā whiwhinga e tukuna ana he 15, 11 nō ngā aromatawai ā-roto, ā, e 4 nō ngā whakamātautau o waho i te mutunga o te tau.

Pāngarau

Tātaitai - NCEA Taumata 3

Whakaahuatanga o te Hōtaka:

Kua hangaia tēnei akoranga mā ngā ākonga e aroha ana ki ngā mea katoa o te pāngarau, me/ranei e hiahia ana ki te ako i te Hoahoa Whare, te Hangarau, te Matū, te Ahupūngao, te Rorohiko rānei i te taumata tuatoru.

Ngā Putanga Ako / Ngā Ihirangi:

  • Whakawhanakehia ngā kaupapa matua o te ine whārite me te whakamahinga o ngā mahi whārite whārite hei whakatauira i ngā āhuatanga o te ao.
  • He nui ake ngā ture rerekētanga.
  • Te whakawhanuitanga nui o ngā tere huringa me te whakamahi i te tere huringa mai i ētahi atu tere huringa.
  • Engari… i roto i ngā āhuatanga maha ka mōhio koe ki te tere o te huringa o ngā mea, ā, me mōhio koe ki te tīmatanga. Nō reira ka whakauru tātou.
  • Kia ngahau koe ki te hoahoa me te mahi i ngā wāhi i raro me i waenganui i ngā pihi, arā, te Whakauru.

Ngā Pūkenga me ngā Āheinga:

  • Te aro atu ki te whakaaturanga tonu me te tere o ngā whakaaro hou.
  • Te āhei ki te whakaaro – 'he aha ngā mea kua mahia e tātou i mua, ā, tera pea ka whai hua ki konei?'
  • He manawanui ki te whakamātau i ngā ariā taurangi rerekē hei whakaoti rapanga.
  • Te mahi tahi, te rite ki te whakaaroaro me/te whakamārama i ō whakaaro/ara ki te kimi i tētahi otinga.
  • Ngā pātai whakaharatau, me ētahi atu pātai anō hoki.

He hononga pea ki:

Tatauranga – te kimi i te tere o te huringa, Ahupūngao, Matū.

Tērā pea ka arahi ki:

Ngā whakaritenga whakauru aunoa mō ngā akoranga Hangarau Whare Wānanga, Hoahoa Whare, Pāngarau, Rorohiko, Ahupūngao, Matū. Te whiwhi i te Pāngarau kua whakaaetia e te UE hei tētahi o ō kaupapa e 3 kua whakaaetia e te Whare Wānanga.

Ngā Huarahi Aromatawai:

Aromatawai ā-roto tuhituhi/matihiko me ētahi atu aromatawai nui e rua o waho.

Ko te tapeke o ngā whiwhinga e tukuna ana he 16, e 4 i ahu mai i ngā aromatawai ā-roto, ā, e 12 i ahu mai i ngā whakamātautau ā-roto i te mutunga o te tau.

Tatauranga me te Tūponotanga - NCEA Taumata 3

Whakaahuatanga o te Hōtaka:

Ko te arotahi o tēnei akoranga he hōhonu ake i te whakaaro tatauranga me te mātauranga tatauranga mā te whakakotahi i ngā rangahau a ngā ākonga me te ako ariā me ngā rangahau whakawhiti-marautanga whiriwhiri i roto i te Koiora, i ētahi atu wāhanga ako rānei.

Ngā Putanga Ako / Ngā Ihirangi:

E taunakihia ana tēnei akoranga mā ngā ākonga e hiahia ana ki te rangahau me te titiro ki ngā raraunga mō ngā take matua o te ao i ēnei rā. Mā te kohikohi raraunga e pā ana ki ngā whakamātautau, ki ngā rangahau rānei i roto i te Koiora, te Pūtaiao Taiao, te Mātauranga Tinana, te Hinengaro, me ētahi atu kaupapa rānei, ka taea te hono i ā rātou tatauranga ki ēnei atu wāhanga ako.

Ngā Pūkenga me ngā Āheinga:

  • Te whakaaturanga o tētahi pūrongo tatauranga ōkawa, tuhinga rānei.
  • Te kimi me te pānui i ngā tuhinga ipurangi me ētahi atu pūrongo rangahau e pā ana ki te take, ki te kaupapa rānei o ia rangahau.
  • Te whakamahi i te hangarau NZgrapher me te whakamārama i ngā kauwhata tatauranga rerekē me ngā tatauranga matua.
  • He taumata teitei o te pūkenga tuhituhi, te pūkenga tatauranga, me te hiahia ki te tuhituhi.
  • Te whakahua tika i ngā puna rangahau.
  • Te whakatikatika me te arotake whakaute i ngā pūrongo a ētahi atu.
  • Te kaha ki te pātai i ngā tau, te arotake arohaehae i ngā mea kāore pea i te mōhiotia!

He hononga pea ki:

Ngā Pūtaiao Pāpori tae atu ki te Tūruhi, Ngā Pūtaiao Tinana me te Taiao, te Hauora me te Kai Totika, me te Hinengaro.

Tērā pea ka arahi ki:

Ngā ara mātauranga tuatoru i roto i ngā kaupapa e hiahia ana ki ngā Tatauranga; Ngā Mahi Tauhokohoko, Pūtaiao me te Ahumahi. Pāngarau kua whakaaetia e te UE.

Ngā Huarahi Aromatawai: Me rangahau ngā aromatawai ā-roto, me whakaatu hoki ngā kitenga tatauranga i roto i tētahi pūrongo ōkawa/puoro whakaatu/wānanga wānanga/kauwhau me ētahi atu. Ko te aromatawai ā-waho e pā ana ki ngā tohatoha tūponotanga.

Ko te tapeke o ngā whiwhinga e tukuna ana he 16, 12 nō ngā aromatawai ā-roto, ā, e 4 nō tētahi whakamātautau i te mutunga o te tau.

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