1. Rauemi Reo
  2. He Rauemi Ako
  3. Rapua Ngā Rauemi
  4. Rapua Ngā Rauemi

Rapua Ngā Rauemi

Nau mai ki te kokonga rapu rauemi reo Māori o nzmaths.

Mā tēnei wāhanga o nzmaths e rapu ai koe i ngā rauemi reo Māori o nzmaths e hiahia nā koe.

Tomokia, tonoa rānei kia whai mana koe ki tēnei wāhanga o te pae ipurangi (he utu-kore), kia āhei ai koe ki te pupuri i ō kohinga rauemi hei whakamahere i ō akoranga. Pānuihia te help file hei āwhina i a koe ki te hanga i ō mahere ako (kei roto tēnei pae āwhina i te reo Ingarihi).

Tirohia ngā Rauemi e Hāngai ana ki ngā Whāinga Paetae o te Marautanga

Thanks for visiting NZMaths.
We are preparing to close this site by the end of August 2024. Maths content is still being migrated onto Tāhūrangi, and we will be progressively making enhancements to Tāhūrangi to improve the findability and presentation of content.
 

For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

Ngā Tikanga o Te Tekau

Taumata 1
No strand
Maori Resource
Ka tūhurangia ngā tikanga o te tekau i roto i te tāpiritanga me te tangohanga. Arā, he aha ngā takirua tau ina tāpirihia, ko te 10 te tapeke, ko te hanga hoki i tētahi tekau kia ngāwari ai te whakaoti i te tāpiritanga, te tangohanga rānei.
  • Kia ū marika ngā meka matua mō te tāpiritanga (kaua e nui atu i te 10 te otinga) me ngā tāngohanga e whai pānga ana.  Hei tauira, 3 + 7 = 10, 10 – 7 = 3.  Arā, kia makere noa iho ngā otinga
  • Ki te whakamahi i te rautaki ‘Hangaia he tekau’ hei whakaoti tāpiritanga, tangohanga hoki.

Ōku Hū E Hīkoi Ana

Taumata 1
Te Tauanga
Maori Resource
Ko te wehewehe me te whakarōpū taonga te kaupapa o tēnei kōwae ako. Ka whai wāhi atu hoki ko te tuhi me te whakamāori kauwhata whakaahua

Kia mohio te ākonga ki te:

  • whakarōpū taonga
  • pānui, ki te whakamāori kauwhata whakaahua
  • hanga kauwhata whakaahua (kia ōrite te rahi o ia whakaahua, kia whai ingoa anō te kauwhata me ngā huinga raraunga)
  • whakatakoto pātai hei torotoro
  • whakaputa whakaaro, ki te matapaki i ngā otinga

Te Ōrau

Taumata 4
Te Tau me te Taurangi
Maori Resource
Ko tā te kaupapa nei, he tirotiro i te hononga o te ōrau, te hautau me te . hautanga ā-ira. Ka whakaotia he rapanga e whai wāhi mai ana te whiriwhiri ōrau o tētahi rahinga

Kia mōhio te ākonga:

Te Ōwehenga Me Te Hautau

Taumata 4
No strand
Maori Resource
Ko te kaupapa nei, he tirotiro i te tikanga o tēnei mea te ōwehenga hautau me tōna hononga ki te . Kia rua wiki pea hei whakaoti i ngā mahi o tēnei kōwae ako.
Kia mōhio te ākonga:
  • ki te rerekētanga o te hautau me te ōwehenga me te hononga o tētahi ki tētahi.
  • ki te kimi mai i ngā ōwehenga ōrite.
  • ki te whakaoti rapanga e whai wāhi mai ana te ōwehenga
  • ki te kimi mai i ngā tapao tētahi āhua whakarahi

Ōwehenga Pākoki

Taumata 5
Te Ine me te Āhuahanga
Maori Resource
Ko te kaupapa nei, he tūhura i ngā ōwehenga pākoki e rua nei, te aho (sin) me te whenu (cosine). Ka tirohia ngā ōwehenga o ngā tapa o tētahi tapatoru hāngai, me te whakamahinga o aua ōwehenga hei tātai i tētahi tapa, hei tātai rānei i tētahi o ngā koki.

Kia mōhio te ākonga ki:

  • ngā tikanga mō te whakaingoa i ngā tapa o tētahi tapatoru hāngai, arā, ko te tāroa, te tapa pātata me te tapa hāngai.
  • te tuhi hoahoa āwhata o te tapatoru hāngai, ka ine ai i te roa o ngā tapa. Mā konei e whakaputa ai i ngā ōwehenga pākoki mō te aho (sin) me te whenu300

Te Paemahana

Taumata 4
Te Ine me te Āhuahanga
Maori Resource
Ka āta tirotiro i te taputapu ine-mahana, me ētahi horopaki e pā ana ki te paemahana. Ka whai wāhi atu ko te tau tōraro, te ōwehenga me te tuhi kauwhata. Ko ētahi wāhanga o tēnei kōwae ako he mea tiki atu i te kōwae ako reo Pākehā Cool Times With Heat.
Kia mōhio te ākonga ki:
  • te whakamahi ine-mahana
  • te tāpae whakaaro ki te take i pērā ai tētahi āhuatanga
  • te whakahaere whakamātau
  • te kimi mai i te huatango o tētahi tau tōraro me tētahi tau tōrunga
  • te tuhi, ki te whakamārama hoki i tētahi kauwhata rārangi

Te Paenga Porowhita

Taumata 4
Te Ine me te Āhuahanga
Maori Resource
Ko tā te kōwae ako nei he tūhura i pānga o te whitianga o tētahi porowhita me tōna paenga. Ka tuhi porowhita, ka ine, ka tātai hoki i te roa o te pūtoro, te whitianga me te paenga.
Kia mōhio te ākonga ki:
  • ngā kupu e hāngai ana ki ngā wāhanga o tētahi porowhita
  • te ine, ki te tātai hoki i te paenga o tētahi porowhita
  • te pānga o te paenga o te porowhita me tōna whitianga

Paheko Panoni

Taumata 4
Te Ine me te Āhuahanga
Maori Resource
I tēnei kōwae ako ka tūhurangia te āhuatanga kōaro o ētahi panoni e rua, te tūmau me te kōaro o ngā panoni. Ka whai wāhi mai hoki te hangarite o ētahi āhua. He mea pūtake mai tēnei kōwae ako i te akoranga kei te pae tukutuku nei: http://illuminations.nctm.org/LessonDetail.aspx?ID=L566

Kia mōhio te ākonga ki:

  • te whakaoti tūhuratanga pāngarau
  • te tūmau me te kōaro o te paheko panoni
  • te āhuatanga kōaro o te paheko panoni

He Pānga Riterite

Taumata 4
Te Tau me te Taurangi
Maori Resource
Ko tā te kōwae ako nei he tūhura i ngā rapanga, pānga riterite, ngā rautaki hei whakaoti i ēnei momo rapanga, me te reo e hāngai ana.

Kia mōhio te ākonga:

  • ki te whakatairite ōwehenga
  • ki te whakaoti rapanga e whai wāhi mai ana te ōwehenga
  • ki ngā rautaki whakarea hei whakaoti rapanga pānga riterite

He Pānga Taurangi

Taumata 4
Te Tau me te Taurangi
Maori Resource
Ko te kaupapa nei, he tirotiro i ngā tauira o roto i te tapatoru a Pascal, me tētahi rautaki hei tātai i te tapeke o ētahi tau piri tata.
Kia mōhio te ākonga ki te:
  • kimi mai i ngā tauira i tētahi raupapatanga tau
  • whakamahi tauira ki te whakaroa i tētahi raupapatanga tau
  • whakamārama i ngā tauira i tētahi raupapatanga tau
  • kimi mai i te huarahi māmā hei tātai i te tapeke o ētahi tau piri tata
  • whakamārama i te huarahi māmā hei300

Papa Pūkeko

Taumata 2
Taumata 3
Te Tau me te Taurangi
Maori Resource
Ko te kaupapa nei, he ako i te whakarea. Ko te Papa Pūkeko tētahi tūtohi tukutuku hei āwhina i te ākonga ki te whakaoti whakarea, hei tirotiro i ētahi rautaki whakarea, pērā i te tatau māwhitiwhiti.

Kia mōhio te ākonga ki:

  • te whakamahi i tētahi tūtohi tukutuku (te Papa Pūkeko) hei rautaki whakaoti whakareatanga
  • te tatau māwhitiwhiti hei rautaki whakaoti whakareatanga.
  • te whakamahi i ngā rōpū o te tekau, i ngā rōpū o te rima rānei hei whakaoti whakareatanga  
  • te whakamahi tau māmā hei300

He Papa Raraunga 1

Taumata 2
Te Tauanga
Maori Resource
Ko te kaupapa nei, he tirotiro i tētahi rautaki mō te kohikohi, mō te wehewehe, mō te whakaari raraunga tauanga. E hāngai ana tēnei kōwae ako ki te taumata tuarua o te marautanga pāngarau. Ko te kōwae ako He Papa Raraunga 2 e hāngai ana ki te taumata tuatoru.

Kia mōhio te ākonga ki te:

  • whakarōpū raraunga
  • tuhi whakaari raraunga e hāngai ana ki te tūhuratanga
  • whakaputa whakaaro whaitake e pā ana ki te kaupapa i tūhurangia, ki te whakaatu whakaari raraunga hoki hei parahau i ngā whakaaro
  • tuhi pātai hei tūhura māna
  • kohikohi raraunga

He Papa Raraunga 2

Taumata 2
Taumata 3
Te Tauanga
Maori Resource
Ko te kaupapa nei, he tirotiro i tētahi rautaki mō te kohikohi, mō te wehewehe, mō te whakaari raraunga tauanga. E hāngai ana tēnei kōwae ako ki te taumata tuatoru o te marautanga pāngarau. Ko te kōwae ako He Papa Raraunga 1 e hāngai ana ki te taumata tuarua.

Kia mōhio te ākonga ki te:

  • kohikohi raraunga
  • whakarōpū raraunga
  • te wehewehe, te whakarite raraunga hei whakautu pātai
  • whakaputa whakaaro whaitake e pā ana ki te pātai i tūhurangia, i runga anō i te āhua o ngā raraunga i kohia.

Papa Whakarea (Kaupae 5)

Taumata 3
Te Tau me te Taurangi
Maori Resource
E hāngai ana tēnei kōwae ako ki te rauemi matihiko nei, te Papa Whakarea. Ko tā te Papa Whakarea, he āwhina i ngā ākonga ki te tūhura i ngā rautaki wāwāhi tau mō te whakarea. I tēnei kōwae ako, ka whakamahia te Papa Whakarea ki te whakarea i tētahi tau mati-2 ki tētahi tau mati-1. E rua atu anō...

Kia mōhio te ākonga ki te:

  • wāwāhi i tētahi tau mati-2 ki ōna tekau me ōna tahi
  • whakamahi i te Papa Whakarea ki te wāwāhi i ngā tau o roto i tētahi whakareatanga tau mati-2 mā te tau mati-1, ki te whakaoti hoki i taua whakareatanga
  • tuhi i tētahi pikitia ki te whakamārama i ngā rautaki wāwāhi tau300

Papa Whakarea (Kaupae 6)

Taumata 3
Te Tau me te Taurangi
Maori Resource
E hāngai ana tēnei kōwae ako ki te rauemi matihiko nei, te Papa Whakarea. Ko tā te Papa Whakarea, he āwhina i ngā ākonga ki te tūhura i ngā rautaki wāwāhi tau mō te whakarea. I tēnei kōwae ako, ka whakamahia te Papa Whakarea ki te whakarea i tētahi tau mati-rua ki tētahi tau mati-1. E hāngai ana ki...
Kia mōhio te ākonga ki te:
  • wāwāhi i tētahi tau mati-2 ki ōna tekau me ōna tahi
  • whakamahi i te Papa Whakarea ki te wāwāhi i ngā tau o roto i tētahi whakareatanga tau mati-2 mā te tau mati-1, ki te whakaoti hoki i taua whakareatanga
  • tuhi pikitia ki te whakamārama i ngā rautaki wāwāhi tau hei whak300

Papa Whakarea (Kaupae 7)

Taumata 4
Te Tau me te Taurangi
Maori Resource
E hāngai ana tēnei kōwae ako ki te rauemi matihiko nei, te Papa Whakarea. Ko tā te Papa Whakarea, he āwhina i ngā ākonga ki te tūhura i ngā rautaki wāwāhi tau mō te whakarea. I tēnei kōwae ako, ka whakamahia te Papa Whakarea ki te whakarea i tētahi tau mati-2 ki tētahi tau mati-2, hei whakatauira i...

Kia mōhio te ākonga ki te:

  • whakamahi i te Papa Whakarea ki te wāwāhi i ngā tau o roto i tētahi whakareatanga tau mati-2 mā te tau mati-2, ki te whakaoti hoki i taua whakareatanga;
  • tuhi pikitia ki te whakamārama i ngā rautaki wāwāhi tau hei whakaoti rapanga whakarea (tau mati-2 mā te tau mati-2)300

Pātapa

Taumata 5
Te Ine me te Āhuahanga
Maori Resource
Ko te kaupapa nei, he tūhura i te tikanga o tēnei mea te pātapa , he whakamahi hoki i te pātapa hei whiriwhiri i te roa o ngā tapa me te rahi o ngā koki o tētahi tapatoru hāngai. Kia rua wiki pea te roa o tēnei kōwae ako. I takea mai tēnei kōwae ako i te kōwae ako reo Ingarihi Investigating the Idea...

Kia mōhio te ākonga:

  • ki te whakamahi i ngā tikanga pātapa hei whakaoti rapanga e whai wāhi mai ana te tapatoru hāngai
  • ki te whakaoti whārite pēnei i te tan(θ) = a, mēnā kei waenganui i te 0° me te 360° te koki θ?’
  • ki te rahi o tan(θ) mō ēnei koki: 0°, 45°, 135°, 180°, 225°, 315°, 360°.
  • kāore300
Resource logo

Pēhea Nei Te Tāroaroa

No strand
Maori Resource
Ko tā te kōwae ako nei he tūhura i tēnei mea te ine, he ine i ētahi wāhanga o te tinana, he whakaraupapa inenga, he whakatau tata inenga hoki.

Kia mōhio te ākonga ki te:

  • whakamahi aho hei whakatairite i ngā roa o ētahi wāhanga o tōna Tinana
  • whakatau tata i te roa o ētahi wāhanga o tōna Tinana
  • whakaraupapa inenga

Pēhea Nei Te Tōkeke

Taumata 5
Te Tauanga
Maori Resource
Ko te kaupapa nei, he tirotiro i te tōkeke o ētahi kēmu. Mā te whakamātau, mā te tātai rānei e kitea ai te tōkeke, he pēhea rānei te tōkeke o tētahi kēmu. I takea mai tēnei kōwae ako i te kōwae ako reo Ingarihi Fair Games. Kia rua wiki pea te roa hei whakaoti i ngā mahi katoa o tēnei kōwae ako.
Kia mōhio te ākonga:

Poraka Uara Tū

Taumata 2
Te Tau me te Taurangi
Maori Resource
E hāngai ana tēnei kōwae ako ki te rauemi matihiko nei, te Poraka Uara Tū. Ko tā tēnei rauemi, he āwhina i te ākonga ki te tūhura i te tikanga uara tū o ngā tau mai i te 0 ki te 9,999. Ka whakamahia he poraka uara tū hei whakaahua i ngā tau. E hāngai ana tēnei kōwae ako ki te Kaupae 5 o Te Mahere...

Kia mōhio te ākonga ki:

  • te maha o ngā tahi, ngā tekau, ngā rau me ngā mano kei roto i tētahi tau, tae noa atu ki te 9,999.

Ripanga

Taumata 4
Te Tauanga
Maori Resource
Ko te kaupapa nei, he tirotiro i te whakamahinga o te Excel, te pūmanawa rorohiko matua mō tēnei mea te ripanga.
Kia mōhio te ākonga ki te:
  • hanga i tētahi ripanga i te pūmanawa rorohiko Excel
  • whakamahi whārite hei whakatutuki tātaitanga i tētahi ripanga kua hangaia ki te pūmanawa rorohiko Excel
  • whakaputa i ngā momo kauwhata i tētahi ripanga kua hangaia ki te pūmanawa rorohiko Excel
  • whiriwhiri300

Ripanga Kapa Haka

Taumata 2
Te Tauanga
Maori Resource
I tēnei kōwae ako ka tirohia ngā māka ka riro i ngā kapa haka i tētahi whakataetae. Ka whakamahia tētahi hōtaka ripanga rorohiko pērā i te Excel hei pupuri i ngā māka o ngā kaiwhakawā, hei tātai i ngā tauanga pērā i te toharite, hei whakaputa kauwhata anō hoki.

Kia mōhio te ākonga ki te:

  • whakamahi i tētahi hōtaka ripanga rorohiko pērā i te Excel hei pupuri raraunga, hei tātai toharite, hei whakaputa kauwhata hoki;
  • tikanga o tēnei mea te toharite;
  • tātai i te toharite;
  • whakaputa whakaaro mō te hora o tētahi huinga raraunga, ōna mōwaho, tōna300

Rōpinepine Taparau

Taumata 4
No strand
Maori Resource
I tēnei kōwae ako ka tūhurangia te āhua o te rōpinepine i ētahi taparau. He mea pūtake mai tēnei kōwae ako i te kōwae ako reo Ingarihi Fitness.

Kia mōhio te ākonga ki:

  • te hanga, me te whakamārama i ngā rōpine-rite-takitahi me ngā rōpine-rite-takimaha

Te Rōrahi

Taumata 4
Te Ine me te Āhuahanga
Maori Resource
Ko te kaupapa nei, he tirotiro i te tikanga o te rōrahi , he tātai i te rōrahi o te poro-tapawhā hāngai, he tirotiro hoki i te hononga o te rōrahi me te horahanga papa.
Kia mōhio te ākonga:
  • he aha te rōrahi me te horahanga papa o tētahi pouaka, me pēhea hoki e inea ai
  • ki te rahi o te mm3, te cm3, me te m3, me te hononga o tētahi ki tētahi.
  • ki te tātai i te rōrahi o tētahi poro-tapawhā hāngai
  • ki te hoahoa raumata hei hanga i tētahi poro-tapawhā hāngai

Tāhei Hautau

Taumata 4
Te Tau me te Taurangi
Maori Resource
E hāngai ana tēnei kōwae ako ki te rauemi matihiko nei, te Tāhei Hautau. Ko tā te Tāhei Hautau, he āwhina i ngā ākonga ki te whiriwhiri i te hautanga o tētahi tauoti. Ka whai wāhi mai ngā hautau mai i te kore ki te tahi, me ngā hautau mai i te tahi ki te rua.
 Kia mōhio te ākonga ki te:
  • whakaahua i roto hinengaro ngā rautaki hei whiriwhiri i te hautau o tētahi tauoti mēnā he tauoti te otinga;
  • whiriwhiri i te hautau o tētahi tauoti (mēnā he tauoti te otinga) me te whai wāhi mai o ngā hautau nui ake i te kotahi.