1. Ka mārama ki ēnei āhuatanga o tētahi mea e taea ana te ine:

• te roa
• te horahanga
• te rōrahi (kītanga)
• te taumaha (papatipu)
• te hurihanga
• te paemahana
• te wā
• te utu

2. Ka mārama ki te tikanga o tēnei mea te ine, arā, ko te whakatairite i te mea e inea ana ki te rahi o tētahi waeine
3. Ka whakamahi taputapu ine aronga kē
4. Ka raupapa, ka whakatairite hoki i ngā inenga
5. Ka tatau waeine māmā
6. Ka mōhio ki te pūmautanga o tētahi inenga

āhuatanga o tētahi mea e taea ana te ine

Hei tauira:

taputapu ine aronga kē

Hei tauira:
mō te roa:

E hia matikara te roa o te rārangi?

mō te horahanga:

E hia papanui te horahanga o te tēpu?

mō te rōrahi:

E hia kapu te rōrahi o te pākete?

ka tatau waeine māmā

Hei tauira:

te pūmautanga o tētahi inenga

Hei tauira:
He ōrite te rōrahi o te haurua kapu wai, ahakoa kei roto taua wai i te kapu, i te pākete rānei.

7. Ka whakarōpū taonga i runga i te āhua o ngā taonga, pērā i te tae, te nui, me te maha o ngā tapa.
8. Ka mōhio ki ngā āhua ahu-2, pērā i te tapatoru, te tapawhā rite, te tapawhā hāngai, te porowhita, te taparima, te tapaono me te tapawaru
9. Ka mōhio ki ngā āhua ahu-3, pērā i te pouaka, te rango me te poi

ka mōhio ki ngā āhua ahu-2

ka mōhio ki ngā āhua ahu-3

10. Ka whai, ka hoatu hoki i ngā tohutohu mō te nekeneke e whai wāhi mai ana:

• te tawhiti
• te ahunga
• te hurihanga (hurihanga 0, 1/4, 1/2, 3/4, 1, 11/4, 11/2 ...).

11. Ka whakamārama i te wāhi noho o tētahi mea

ngā tohutohu mō te nekeneke

Hei tauira:
Hikoi whakamua, kia toru ngā whetoko. Kia hauwhā te huri whakatekaraka ...

Ētahi kupu mō te ahunga e hāngai ana:
whakamua, whakamuri, whakatemauī, whakatematau, whakarunga, whakararo, whakatemaunga, whakatetai, whakatekaraka, kōaro ...

te wāhi noho o tētahi mea

Hei tauira:
Kei tua atu i a Henare a Mārama e tū ana.

Ētahi kupu e hāngai ana:
tua atu, tua mai, kō atu, kō mai, rahaki, taha mauī, taha matau, mua, muri, runga, raro ...

12. Ka tuhi, ka whakamārama i ngā hua o te neke, o te whakaata, o te huri i ngā āhua ahu-2 māmā

ngā hua o te neke, o te whakaata, o te huri i ngā āhua ahu-2 māmā

Hei tauira:
Kua nekea whakatematau te pūtaketake o te tauira:

Kua whakaatangia te pūtaketake o te tauira:

Kua huri hauwhātia whakatekaraka te pūmatua A:

1. Ka hanga, ka whakamahi taputapu, waeine hoki e whaitake ana, ka whakaoti rapanga māmā:

• te roa
• te horahanga
• te rōrahi (kītanga)
• te taumaha (papatipu)
• te koki
• te paemahana
• te wā
• te utu

2. Ka mārama ki te tikanga o tētahi āwhata, arā, he wehewehenga, he tāruaruatanga o tētahi waeine
3. mōhio ki te wāwāhi, ki te tāpiri hoki i ngā inenga
4. Ka mārama ki te rahi o ngā waeine aro whānui māmā
5. Ka mārama ki te whaitakenga o tētahi inenga

whakaoti rapanga

Hei tauira:
Pēhea nei te roa o te rārangi kōpiko me te rārangi roa o te rohe tītere o te papa tākaro poitarawhiti? He aha ngā waeine hei whakamahi?

ka mārama ki te tikanga o tētahi āwhata

Hei tauira:

ka mōhio ki te wāwāhi, ki te tāpiri hoki i ngā inenga

Hei tauira:
Mēnā e 30 mita te roa o tētahi papa tākaro, ki hea te rārangi hei whakaatu i te haurua me ngā rohe hauwhā o te papa tākaro.

ka mārama ki te rahi o ngā waeine aro whānui māmā

Hei tauira: mō te roa: mita (m), mitamano (mm), mitarau (cm), manomita (km)

mō te rōrahi: rita (l) ritamano (ml)

mō te taumaha: karamu (g), karamumano (kg)
mō te koki: ngā hurihanga hautau
mō te wā: te hākona, te meneti, te rā, te marama me te tau
mō te paemahana: te tākiri (°)

ka mārama ki te whaitakenga o tētahi inenga

Hei tauira:
Mēnā ka kīia ko te 1.7 cm te tāroaroa o tētahi tangata, kua mōhio te ākonga kāore e whaitake ana tēnei inenga nā te mea he tino poto rawa atu. E tika kē ana ko te 1.7 m tōna tāroaroa.

6. Ka whakarōpū taonga i runga i te āhuahanga o aua taonga, ka whakamārama hoki i ngā rōpū
7. Ka tautohu, ka whakamārama i ngā āhua ahu-2 me ngā āhua ahu-3 e kitea mai ana i te taiao, i te hanga o ngā whare me ngā taonga o ia rā

te āhuahanga

Hei tauira:

• E whai koki hāngai ana ngā āhua nei:

• Kāore ēnei āhua i te whai koki hāngai:

• Ētahi atu whakarōputanga (hei tauira):
  te maha o ngā tapa, te maha o ngā kokonga, mēnā he torotika, he kōpiko rānei ngā tapa, te āhua o ngā koki, he papatahi (āhua ahu-2), he āhua ahu-3 rānei.

ngā āhua ahu-2 me ngā āhua ahu-3 e kitea mai ana i te taiao, i te hanga o ngā whare me ngā taonga o ia rā.

Hei tauira:

8. Ka hanga, ka whakamahi mahere māmā:
   • ka whakaatu taunga
   • ka whakaatu ahunga
   • ka whakamārama huarahi
   • ka whakamārama tirohanga
9. Ka whakamārama taunga, ahunga hoki o ngā wāhi matua o te kura, te tāone me te rohe

ka whakaatu taunga

Hei tauira:

Kei te taihauāuru o Te Ika a Māui a Taranaki.
Kei te tairāwhiti o Te Ika a Māui a Tūranga-nui-a-Kiwa.
Kei te puku o Te Ika a Māui te moana o Taupō-nui-a-Tia.
Kei te raki o te moana o Taupō-nui-a-Tia te tāone o Taupō.
Kei te tonga o te moana o Taupō-nui-a-Tia te tāone o Tūrangi.

ka whakaatu ahunga

Hei tauira:
Ka piki ake au i taku maunga i a Hiwiroa, ka titiro whakateraki. Ki tua atu i te ngahere o Paparahi ko te kāinga o Kahuora.

ka whakamārama huarahi

Hei tauira: Atu i te marae, hīkoi whakaterāwhiti, ka huri whakatemauī i te kokonga tuatahi. Huri mauī anō i te kokonga tuarua. Kei tēnei huarahi te whare o Rongopai, nama 42.

ka whakamārama tirohanga

Hei tauira:
Ko te āhua o te maunga: te tirohanga mai i tai, mai i uta, mai i te raki ...

ka whakamārama taunga, ahunga hoki o ngā wāhi matua o te kura, te tāone me te rohe.

Hei tauira:
Kei te rāwhiti o te taone te pae maunga e tū mai ana.
Atu i taku whare, ka haere whakatetonga ki te kura.

10. Ka neke, ka whakaata, ka huri, ka whakarahi i ngā āhua ahu-2, ka tuhi, ka whakamārama hoki i ēnei panoni

Ka neke, ka whakaata, ka huri, ka whakarahi i ngā āhua ahu-2, ka tuhi, ka whakamārama hoki i ēnei panoni.

Hei tauira:
Kua whakarahia te tapawhā hāngai mā te rearua:

• Ehara tēnei i te whakarahinga nā te mea he rerekē te āhua o ngā tapawhā hāngai e rua:

1. Ka whakaoti rapanga whaitake e whai wāhi mai ana:

• te roa
• te horahanga
• te rōrahi (kītanga)
• te taumaha (papatipu)
• te koki
• te paemahana
• te wā
• te utu

2. Ka whakamahi i ngā momo āwhata maha e whakaatu ana i ngā waeine tauoti me ngā waeine hautau
3. Ka whiriwhiri i te horahanga o ngā tapawhā hāngai kua hangaia ki te tukutuku tapawhā rite
4. Ka whiriwhiri i te rōrahi o ngā poro-tapawhā hāngai kua hangaia ki te mataono rite
5. Ka mārama ki te rahi o ngā waeine aro whānui
6. Ka mārama ki te whaitakenga o tētahi inenga

rapanga whaitake

Hei tauira:
E hia ngā tapawhā hāngai rerekē ka taea te hanga, kia 24 cm te roa o te paenga?
Whakatairitea te horahanga o ēnei tapawhā hāngai.

te horahanga o ngā tapawhā hāngai kua hangaia ki te tukutuku tapawhā rite

Hei tauira:

te rōrahi o ngā poro-tapawhā hāngai kua hangaia ki te mataono rite

Hei tauira:

Ka mārama ki te rahi o ngā waeine aro whānui

Hei tauira:
te horahanga: mita pūrua(m2), mitarau pūrua(cm2), heketea (ha)
te rōrahi: mitarau pūtoru (cm3), mita pūtoru (m3)
te koki: te tākiri (°), te koki hāngai

7. Ka whakamārama i te āhuahanga o ngā āhua ahu-2 me ngā āhua ahu-3
8. Ka tuhi hoahoa, ka hanga tauira hei whakaatu taonga
9. Ka tūhura i ngā raumata e hangaia ai he āhua ahu-3 māmā

te āhuahanga o ngā āhua ahu-2 me ngā āhua ahu-3

Hei tauira:

• e rua ngā tapa ōrite o te tapatoru waerite
• e rua ngā koki ōrite o te tapatoru waerite
• kotahi te rārangi hangarite

ka tuhi hoahoa

Hei tauira:

• Ko te mahere papa o tētahi whare

ka tūhura i ngā raumata

Hei tauira:

• Ko te raumata hei hanga pouaka

10. Ka hanga, ka whakamahi pūnaha ki te:

• whakaatu taunga
• whakaatu ahunga
• whakamārama huarahi

11. Ka whakamahi i ngā tōpito matua ki te whakamārama taunga, ahunga hoki

Ka hanga, ka whakamahi pūnaha ki te whakaatu taunga, whakaatu ahunga, whakamārama huarahi

Hei tauira:

• Kei te takiwā o te taunga (3,7) te marae e tū ana.
• Kei (11,6) a Motutoka.
• Kei te tonga o Awaiti te marae, kei te raki ko Pukeiti.

ngā tōpito matua

Hei tauira:

• raki, rāwhiti mā raki, rāwhiti, rāwhiti mā tonga, tonga ...

12. Ka whakamārama i ngā panoni (whakaata, hurihanga, nekehanga, whakarahinga rānei), e hua ai tētahi mātātuhi, mai i tōna mātāoroko

Ka whakamārama i ngā panoni (whakaata, hurihanga, nekehanga, whakarahinga rānei), e hua ai tētahi mātātuhi, mai i tōna mātāoroko

Hei tauira:

• Tuatahi, kua whakaatangia te tapatoru waerite (ko te pūtake o te tapatoru te rārangi whakaata). Tuarua, kua whakaitia, (ko te 1/2 te taurahi, ko te akitu 'A' te pū o te whakarahi):

1. Ka whakaoti rapanga whaitake:

• ka kōwhiri, ka whakamahi i te waeine e hāngai ana mō te roa, te horahanga, te rōrahi (kītanga), te papatipu (taumaha), te paemahana, te koki me te wā
• ka whakawhitiwhiti waeine māmā
• ka whakamahi i ngā inenga tapa ki te whiriwhiri i te paenga me te horahanga o te tapawhā hāngai, me te rōrahi o te poro-tapawhā hāngai
• ka tuhi, ka whakamārama, ka whakamahi hoki i ngā momo wātaka me ngā mahere
• ka mārama ki te whaitakenga o tētahi inenga

rapanga whaitake

Hei tauira:

• 17 hāora te tōmua atu o te taima i Aotearoa i te taima i Washington. Ka wehe mai a Roimata i Washington i te 2130 hāora i te 1 o Poutū-te-rangi, ki te hoki mai ki Aotearoa. 18 hāora te roa o te haerenga mā runga waka rererangi. He aha te taima ka tau mai tana waka ki Tāmaki-makau-rau?
• He aha te pānga o te whitianga o tētahi porowhita me tōna paenga?

ka whakawhitiwhiti waeine

Hei tauira:
te roa: 1km = 1000 m = 100,000 cm = 1,000,000 mm
       1 mm = 0.1 cm = 0.001 m

te taumaha (papatipu): 1kg = 1,000g
              1t = 1,000kg

te rōrahi (kītanga): 1L = 1,000ml
           1ml = 1cm³
           1m³ = 1,000,000cm³

te rōrahi (kītanga): 1m² = 10,000cm²
           1ha = 10,00m²
           1km² = 100ha

2. Ka tautohu, ka whakamārama i ngā tikanga āhuahanga o ngā rōpū āhua ahu-2 me ngā rōpū āhua ahu-3
3. Ka tūhono i te āhua ahu-3 me tōna hoahoa ahu-2
4. Ka tuhi raumata hei hanga matarau

ngā tikanga āhuahanga

Hei tauira:

• He momo poro katoa ēnei āhua ahu-3. He rerekē te āhua o te pūtake o ngā poro, engari he tapawhā hāngai te āhua o ērā atu o ngā mata. Mā te whakarea i te horahanga o te pūtake ki te teitei o te poro e tātaihia ai te rōrahi.

Ka tūhono i te āhua ahu-3 me tōna hoahoa ahu-2

Hei tauira:

• Koia nei te āhua o ngā mata o tētahi āhua ahu-3 e ai ki tā te karu titiro:

• Koia nei te hanga o taua āhua ahu-3:

5. Ka whakaatu, ka whakamārama, ka whakamahi i te wāhi noho (taunga) o tētahi mea, me te ahunga:

• ngā tōpito
• ngā koki o te kāpehu
• ngā āhuatanga o te taiao
• te tukutuku (takirua raupapa)
• te mahere

ngā tōpito me ngā koki o te kāpehu

Hei tauira:

Ko te 46º 25' ki te tonga te ahopae e noho nei a Te Waihopai.
Ko te 168º 21' ki te rāwhiti te ahopou e noho nei a Te Waihopai.

6. Ka tautohu, ka whakamārama, ka whakamahi i te hangarite o tētahi āhua ahu-2, āhua ahu-3
7. Ka tautohu, ka whakamārama, ka whakamahi i ngā āhuatanga pūmau o ngā panoni

Ka tautohu, ka whakamārama, ka whakamahi i te hangarite o tētahi āhua ahu-2

Hei tauira:

• E 3 ngā rārangi hangarite o te tapatoru rite, kotahi noa iho tō te tapatoru waerite.
• Ko te 3 te hangarite hurihanga o te tapatoru rite, kotahi noa iho tō te tapatoru waerite
• Nō reira ko te 6 te hangarite tapeke o te tapatoru rite, ko te 2 tō te tapatoru waerite

Ka tautuohu, ka whakamārama, ka whakamahi i ngā āhuatanga pūmau o ngā panoni

Hei tauira:

• He ōrite te koki 'A' me 'E' nā te mea he whakarahinga tētahi tapatoru o tētahi, ā, ko te koki tētahi āhuatanga pūmau o te whakarahinga.

1. Ka whakaoti rapanga whaitake:

• ka kōwhiri, ka whakamahi i ngā waeine, ngā taputapu me ngā āwhata e hāngai ana mō te roa, te horahanga, te rōrahi (kītanga), te papatipu (taumaha), te paemahana, te koki me te wā
• ka whakawhitiwhiti waeine

2. Ka whakaputa, ka whakamahi hoki i ngā ture hei tātai i te paenga me te horahanga o tētahi taparau
3. Ka whakaputa, ka whakamahi hoki i ngā ture hei tātai i te rōrahi o tētahi poro
4. Ka mārama ki te whaitakenga o tētahi inenga

rapanga whaitake

Hei tauira:

• Raupapahia ēnei, mai i te tere ki te pōturi:
• te hīkoi a Himiona i te 8 km i te hāora
• te kauhoe a Rāmeka i te 400 m i te 6 meneti
• tō tere ki te eke pahikara mō te 20 m.

Ka whakaputa, ka whakamahi hoki i ngā ture hei tātai i te paenga me te horahanga o tētahi taparau.

Hei tauira:
He tapatoru waerite:

He tapawhā whakarara:

5. Ka whakaputa, ka whakamahi i ngā tikanga koki o rārangi pūtahi, te rārangi whakarara me te taparau
6. Ka whakamahi taputapu ki te waihanga taparau māmā
7. Ka tuhi raumata tōtika hei hanga matarau māmā
8. Ka tuhi i ngā momo hoahoa hei whakaatu āhua ahu-3
9. Ka whakamahi ōwehenga pākoki me te ture a Pythagoras ki te whakaoti rapanga e whai wāhi mai ana te tapatoru hāngai

te rārangi pūtahi

Hei tauira:
E pūtahi ana te rārangi AE me te rārangi IO.

• Hui katoa ngā koki, e 360º te tapeke: a + e + i + o = 180
• 180º te tapeke o ngā koki e noho ana ki te rārangi torotika: a + e = 180, e + i = 180, i + o = 180, o + a = 180
• He ōrite ngā koki tauaro: a = i, e = o

te rārangi whakarara

Hei tauira:
He whakarara ngā rārangi AE me IO. Haere tonu ai ēnei rārangi engari kore rawa e pātahi. He rārangi whakawhiti te HK.

• E tohua ana he koki taurite. He ōrite te rahi o ngā koki taurite.

• E tohua ana he koki tauwhiti. He ōrite te rahi o ngā koki tauwhiti.

• E tohua ana he koki tauroto. Ko te 180º te tapeke o ngā koki tauroto.

ngā momo hoahoa hei whakaatu āhua ahu-3

Hei tauira:

• He hoahoa inerite tēnei

ka whakamahi ōwehenga pākoki

Hei tauira:

• Hei tātai i te tawhiti whakateraki o te haerenga o tētahi waka, mēnā kua oti te 4.5 km i te ahunga 040º

te ture a Pythagoras

Hei tauira:

• Hei tātai i te tāroa o tētahi tapatoru hāngai:

10. Ka waihanga, ka whakamārama huanui māmā
11. Ka tuhi, ka whakamārama taunga, rārangi hoki ki tētahi papa tukutuku, mā te whakamahi i:

• ngā momo āwhata
• ngā tōpito
• ngā inenga koki o te kāpehu
• ngā momo mahere

Ka waihanga, ka whakamārama huanui

Hei tauira:

• He porowhita te huanui o te poi.

• He rārangi whakarara takirua te huanui o ngā pūwāhi katoa e ōrite ana te tawhiti mai i tētahi rārangi

Ka tuhi, ka whakamārama taunga, rārangi hoki ki tētahi papa tukutuku, mā te whakamahi i ngā momo āwhata, ngā tōpito, ngā inenga koki o te kāpehu, me ngā momo mahere

Hei tauira:
Mā te āta tirotiro i tētahi mahere whenua o Te Ika a Māui, ka whiriwhiri i te:

• tawhiti o tētahi haerenga (mā te whakamahi āwhata)
• te ahunga mai i tētahi taone ki tētahi (mā te whakamahi ine-koki me ngā tōpito matua)
• taunga o tētahi taone (mā te whakamahi i te tukutuku o te mahere)

12. Ka tautuhi, ka whakamahi, ka whakamārama i ngā momo panoni me ngā āhuatanga pūmau.

tautohu, ka whakamahi, ka whakamārama i ngā momo panoni me ngā āhuatanga pūmau.

Hei tauira:

• He tautohu, he whakamārama i ngā whakaatanga, ngā hurihanga me ngā nekehanga o roto i te tauira nei.