He tauākī herenga ōkawa mō te wāhanga ako Pāngarau e pā ana ki te whakaako, te ako, me te aromatawai ki ngā kura arareo katoa.

PUKAPUKA

Pāngarau

Tūārere 2 – Tau 4-6

Pāngarau
Tau 0‑8

Pāngarau
Tūārere 1 – Tau 0‑3

Pāngarau

Tūārere 2 – Tau 4‑6

Pāngarau
Tūārere 3 – Tau 7‑8

Ngā Ihirangi

Pāngarau: Tūārere 2 – Tau 4-6

Whāinga

Kia Mataara

Te Ngako o te Whāinga – Mā te Kaiako

Te Ngako o te Whāinga – Mā te Mokopuna

Te Roanga o te Kōrero

Tau

Taurangi

Ine

Āhuahanga

Tauanga

Tūponotanga

Hei Tautoko i Te Ako

Pāngarau Kuputaka

Mō tēnei rauemi

E wātea ana ngā mōhiotanga o te wāhanga ako Pāngarau tau 0-8 i nāianei.

Tāpirihia ki te kete

Tāpirihia ki te kohinga

Tikiake i te rauemi

Ngā rawa kei tēnei rauemi:

A graphic showing phase two out of five phases

Tūārere 2

Tau 4-6

An image of four happy children playing on the beach

Whenu

hoki ki runga ake

HE TANGATA
tūhura ki te ao

HE URI WHAKAHEKE
ki te whai ao

HE PUNA KŌRERO
o te reo pāngarau

HE ĀKONGA
mauri oho

Toi Mokopuna

He tāwariwari, he aro, he pākiki, he mahi ngātahi, he auaha, he huritao, he kaitūhura whakaata hoki te mokopuna, e ako ana ki te whakamahi tikanga pāngarau me te whakaoti rapanga mō te kura, te whānau, te hapū me te iwi, ā, mō rātou anō te take.

He koi te hinengaro o te mokopuna, rite ana ki ōna mātua tīpuna. Ko ngā whakaaro me te whakamahi pāngarau he mea tuku iho ki a ia, ā, ka tukuna ki ētahi atu.

He māia, he pūkōrero hoki te mokopuna ki te whakamārama me te whakaputa i ōna whakaaroaro me āna tukanga pāngarau ki te reo pāngarau. E ngākaunui ana ia ki te pāngarau me te motuhaketanga o taua reo.

He manawanui, he huritao, he aroturuki te mokopuna ki te panoni i ōna whakaaro me āna mahi, ā, ka tautohu tauira, hononga hoki hei hanga pāngarau me tōna anō ao.

Tohu Ako: Tūārere 2: Tau 4–6

Whāinga

Ka aro te ako a te mokopuna
te taki tūhuratanga pāngarau e hāngai ana ki tōna ao, ka ako rautaki ai hei whakamahinga mōna ki tōna ia ra.

Ka aro te ako a te mokopuna
te whakamahi pāngarau hei taunaki ki te whakaoti rapanga pūāhua o tōna ao hoki.

Ka aro te ako a te mokopuna
te whai māramatanga me te whakamahi i te huhua o ngā kīanga me ngā huatau pāngarau ki te tuku pūrongo mō āna kitenga.

Ka aro te ako a te mokopuna
te whai mārama, te waihanga, me te whakamārama i ngā pānga, ngā tauira, ngā whakatauira, me ngā whakaahuahanga e hāngai pū ana ki ngā tukanga me ngā mātauranga pāngarau.

Whenu

hoki ki runga ake

HE TANGATA
tūhura ki te ao

HE URI WHAKAHEKE
ki te whai ao

HE PUNA KŌRERO
o te reo pāngarau

HE ĀKONGA
mauri oho

Toi Mokopuna

He koi te hinengaro o te mokopuna, rite ana ki ōna mātua tīpuna. Ko ngā whakaaro me te whakamahi pāngarau he mea tuku iho ki a ia, ā, ka tukuna ki ētahi atu.

He manawanui, he huritao, he aroturuki te mokopuna ki te panoni i ōna whakaaro me āna mahi, ā, ka tautohu tauira, hononga hoki hei hanga pāngarau me tōna anō ao.

Tohu Ako: Tūārere 2: Tau 4–6

Kia Mataara

Hei te mutunga o te tau 4 me mōhio te mokopuna ki te:

whakamahi i te mātauranga Māori hei tūāpapa tūhura i ngā toi Māori, ka tiro pāngarau atu ai ki ngā āhua, ki te whakaatatanga, ki te hurihanga me te panonitanga hoki.

Hei te mutunga o te tau 4 me mōhio te mokopuna ki te:

whakamahi pāngarau ki te whakaoti rapanga e whai pānga ana ki tōna ao, ki tōna kāinga, ki tōna hapori.

Hei te mutunga o te tau 4 me mōhio te mokopuna ki te:

whakamahi i te reo pāngarau ki te matapaki i āna mahi
whakamārama i āna rautaki whakaoti meka tāpiri, meka tango, me te whakamārama i te hononga o te whakarea me te whakawehe
matapaki i te tikanga o tētahi rerenga tau.

Hei te mutunga o te tau 4 me mōhio te mokopuna ki te:

pānui, te tuhi, te whakaraupapa, te wāwāhi, me te whakarōpū i ngā tauoti ki te 10,000
whakaoti i ngā rapanga tāpiri, rapanga tango mati-2, mati-3 hoki, mā te whakamahi i ngā rautaki wāwāhi tau
whakautu i ngā meka whakarea me ngā meka whakawehe 3 me te 4
whakamahi i ngā meka tāpiri me ngā meka tango ki te whakaoti rapanga
whakamahi i te hononga o ngā whakarea me ngā whakawehe ki te whakaoti rapanga whakawehe
whakaahua i ngā hautau, me te whai wāhi mai o ngā hautau nui ake i te kotahi, kei te rārangi tau
whakaoti rapanga tāpiri, rapanga tango mā te mōhio ki te pānga o te tohu ōrite
whakaahua ā-hinengaro, te whakapae, te tautohu hoki i te whakaatatanga o te āhua, i te hurihanga o te āhua me te panonitanga o te āhua ahu-2.

Hei te mutunga o te tau 5 me mōhio te mokopuna ki:

whakataurite hautau, ka whakaraupapa ai mā te tūhura i te tikanga o te hautau
whakahuri i ngā hautau, i ngā tau ā-ira me ngā ōrau: h.t., 1—2 = 50% = 0.5
whakaahua ā-hinengaro me te tā raumata mō tētahi mataono
whai māramatanga i te take mō ngā raraunga whai tikanga, ki ngā raraunga whai take e whakautu pātai tūhura ai.

Hei te mutunga o te tau 5 me mōhio te mokopuna ki:

whakamārama he aha pea e rerekē ai ngā raraunga i ētahi horopaki
whakatakoto pātai e hāngai pū ana, e whai take ana ki tana kohinga raraunga ka hua mai i tōna ao, tōna whānau, me tōna hapori anō hoki
tū hei kaitūhura mākoha.

Hei te mutunga o te tau 5 me mōhio te mokopuna ki:

whakawhitiwhiti whakaaro mō ngā hoahoa rerekē, ka matapaki ai i te hoahoa tika
whakawhiti whakaaro me te matapaki he aha pea e rerekē ai ngā raraunga i tētahi horopaki, ka whakatauira ai hei tautoko i ngā whakaaro.

Hei te mutunga o te tau 5 me mōhio te mokopuna ki:

pānui, te tuhi, te whakaraupapa, te wāwāhi, me te whakarōpū i ngā tauoti ki te 100,000
whakaoti i ngā rapanga tāpiri, rapanga tango tauoti, mā te whakamahi i ngā rautaki wāwāhi tau
whakaoti rapanga whakarea mati-2 mā te āhuatanga tohatoha
whakaputa maharatanga i ngā meka whakarea me ngā meka whakawehe, 6, 8, 9
whakaoti whārite mō ngā pāheko katoa mā te whakamahi i te hononga o ngā taha e rua o te tohu ōrite.

Whenu

hoki ki runga ake

HE TANGATA
tūhura ki te ao

HE URI WHAKAHEKE
ki te whai ao

HE PUNA KŌRERO
o te reo pāngarau

HE ĀKONGA
mauri oho

Toi Mokopuna

He koi te hinengaro o te mokopuna, rite ana ki ōna mātua tīpuna. Ko ngā whakaaro me te whakamahi pāngarau he mea tuku iho ki a ia, ā, ka tukuna ki ētahi atu.

He manawanui, he huritao, he aroturuki te mokopuna ki te panoni i ōna whakaaro me āna mahi, ā, ka tautohu tauira, hononga hoki hei hanga pāngarau me tōna anō ao.

Tohu Ako: Tūārere 2: Tau 4–6

Te Ngako o te Whāinga

Mā te Kaiako

Tau 4
E tautoko ana te mokopuna kia:

whai wāhi ki ngā ngohe huhua e mārama ai te mokopuna ki te tikanga o te tohu ōrite
whakamahi rauemi, pikitia, kōrero paki hoki e mārama ai te mokopuna ki te pūtake o ia wāhanga o te hautau
whakamahi rauemi, pikitia, kōrero paki hoki e mārama ai te mokopuna ki te hononga o te hautau, te tau ā-ira me te ōrau
tūhura i ngā tini āhua ahu-3 me ōna rau mata
whai wheako hei kaitātari.

Tau 4
E tautoko ana te mokopuna kia:

whakahono i ngā whakaaroaro pāngarau ki ō rātou ao o ia rā
whai hononga ki roto i ngā huatau me ngā ariā pāngarau, hei tauira, i ngā inenga ka whakamahi tau.

Tau 4
E tautoko ana te mokopuna kia:

matapaki, kia tā, kia hanga, kia whakatauira hoki i te hanganga o ngā tauoti
matapaki, kia tā, kia hanga, kia whakatauira hoki i te hanganga o ngā hautau, ngā tau ā-ira me ngā ōrau.

Tau 4
E tautoko ana te mokopuna kia:

whai māramatanga ki te pūnaha uara tū me te whakarōpū i ngā tau: h.t., tau kiato, tau roha
whai māramatanga ki tēnei mea te whakarea, tōna pūtake me tana mahi (whakamahi tauira, hoahoa, rauemi hoki).

Tau 5
E tautoko ana te mokopuna kia:

whakamahi tika i te tohu ōrite i āna tūhuratanga
whai māramatanga ki te tikanga o ia wāhanga o te hautau e pai ai tā rātou whakamahi mō ngā mahi tūhura.

Tau 5
E tautoko ana te mokopuna kia:

kite mēnā rānei e whai pānga ana te pāngarau ki tō rātou ao
whai wāhi atu ki te whakamahi pāngarau e taunga ana ki ngā tikanga Māori.

Tau 5
E tautoko ana te mokopuna kia:

mōhio ki te tuku pātai pāngarau e whai hua ana
matapaki i ngā tāiringa pāngarau hei whakawhānui ake i ngā whakaaro mō tētahi pūāhua.

Tau 5
E tautoko ana te mokopuna kia:

tū hei mokopuna whakaaroaro whakarea.

Tau 6
E tautoko ana te mokopuna kia:

tūhura i ētahi kaupapa pāngarau, kaupapa hapori whai tikanga rānei e whai hua ai mōna, mō tōna whānau me tōna kura.

Tau 6
E tautoko ana te mokopuna kia:

kōtui i ngā ariā o ētahi atu wāhanga ako, ngā horopaki ahurea, ngā mātauranga wetereo, me ngā horopaki hītori hoki.

Tau 6
E tautoko ana te mokopuna kia:

matapaki i ngā whakataunga whānui mō ngā ariā pāngarau me ngā pānga i whai wāhi ai rātou ki te whakatau tata, ki te whakatau hāpono hoki.

Tau 6
E tautoko ana te mokopuna kia:

āhukahuka ko te whakarea te pāheko ki te kimi i te horahanga me te rōrahi o tētahi āhua.

Whenu

hoki ki runga ake

HE TANGATA
tūhura ki te ao

HE URI WHAKAHEKE
ki te whai ao

HE PUNA KŌRERO
o te reo pāngarau

HE ĀKONGA
mauri oho

Toi Mokopuna

He koi te hinengaro o te mokopuna, rite ana ki ōna mātua tīpuna. Ko ngā whakaaro me te whakamahi pāngarau he mea tuku iho ki a ia, ā, ka tukuna ki ētahi atu.

He manawanui, he huritao, he aroturuki te mokopuna ki te panoni i ōna whakaaro me āna mahi, ā, ka tautohu tauira, hononga hoki hei hanga pāngarau me tōna anō ao.

Tohu Ako: Tūārere 2: Tau 4–6

Te Ngako o te Whāinga

Mā te Mokopuna

Kei te ako au ki te:

whakamahi tika i te tohu ōrite i āna tūhuratanga
tikanga o ia wāhanga o te hautau e pai ai tāku whakamahi mō ngā mahi tūhura
tūhura i ētahi kaupapa pāngarau, kaupapa hapori whai tikanga rānei e hua ai mōku, mō tōku whānau me tōku kura.

Kei te ako au ki te:

kite mēnā e whai pānga ana te pāngarau ki tōku anō ao
whakamahi pāngarau e taunga ana ki ngā tikanga Māori
kōtui i ngā ariā pāngarau ki ngā wāhanga ako, ngā horopaki ahurea, ngā mātauranga wetereo, me ngā horopaki hītori hoki.

Kei te ako au ki te:

tuku pātai pāngarau e whai hua ai
matapaki i ngā tāiringa pāngarau hei whakawhānui ake i ngā whakaaro mō tētahi pūāhua
matapaki i ngā whakataunga whānui mō ngā ariā pāngarau me ngā pānga i whai wāhi ai au ki te whakatau tata, ki te whakatau hāpono hoki.

Kei te ako au ki te:

whakaaroaro whakarea
mōhio ko te whakarea te pāheko ki te kimi i te horahanga o tētahi āhua.

Whenu

hoki ki runga ake

HE TANGATA
tūhura ki te ao

HE URI WHAKAHEKE
ki te whai ao

HE PUNA KŌRERO
o te reo pāngarau

HE ĀKONGA
mauri oho

Toi Mokopuna

He koi te hinengaro o te mokopuna, rite ana ki ōna mātua tīpuna. Ko ngā whakaaro me te whakamahi pāngarau he mea tuku iho ki a ia, ā, ka tukuna ki ētahi atu.

He manawanui, he huritao, he aroturuki te mokopuna ki te panoni i ōna whakaaro me āna mahi, ā, ka tautohu tauira, hononga hoki hei hanga pāngarau me tōna anō ao.

Tohu Ako: Tūārere 2: Tau 4–6

Te Roanga o te Kōrero

Te Āhua o te Mokopuna

Ka mahi ngātahi te kaiako me te mokopuna ki te tuku pātai mō ngā wheako o ia rā me ngā wheako pāngarau, kia kounga ai ngā pātai.

Ka mahi ngātahi te mokopuna me ōna hoa ako ki te kaiako, ki te whakamahere tūhuratanga pāngarau, i tōna whanake me ngā wheako huhua ka ako takitahi ai te mokopuna.

Ka manawanui te mokopuna, ka ngana hoki ki te whakatutuki i āna mahi. E mōhio ana ia, he akoranga kei roto i ana hapa. Pai noa ana tana tīmata anō, pai noa ana hoki tana panoni i āna tūhuratanga mēnā rānei he take kia panoni.

Ka mahi ngātahi, ka mahi takitahi hoki te mokopuna, me tāna mōhio ki te whakawhiti whakaaro. He mōhio hoki nōnā, ko te whakamahi i ngā kohinga kōrero hei tikanga mahi ā-hapori pāngarau.

Te Āhua o te Mokopuna

Ka toro atu te mokopuna ki ngā tini āheinga e kite ai rātou i te whakamahinga o te pāngarau i tōnā anō ao o ia rā.

Ka whakamārama te mokopuna i ngā ōritenga me ngā rerekētanga o te ao Māori i me te ao pāngarau, ā, ka mahea tāna whakamahi i ngā ao e rua, kāore e rangirua ana.

Ka āhukahuka te mokopuna i te whaitake o te pāngarau ki tōna ao, me ōna hiahia mō tōna anō anamata.

Te Āhua o te Mokopuna

E ngākaunui ana te mokopuna ki te whakaputa huatau pāngarau me tōna whakawhanake i ōna mōhio ki te whakaputa kōrero mō ngā ariā pāngarau e whai wāhi ana ngā tauira, ngā kupu me ngā tohu whakaahuahanga.

Nā te tūmomo tūhuratanga e marutuna ake ai tō rātou whakaputa kōrero mō ngā huatau pāngarau. Ka whakamahi rauemi, tauira, whakaahuahanga, me ngā pikitia ki te whakapūaki i ā rātou whakaaro pāngarau.

Mā te reo matatini o te pāngarau e āhei ai te mokopuna ki te whakamārama āhuatanga, pāpono, me ngā rapanga e ngana ana ki te whakaoti. I te whakatauiratanga o ngā reo matatini o te pāngarau, ka tipu ake te puna o te reo pāngarau, ngā tauira, ngā whakaahuahanga, ngā ariā me ngā whakamāramatanga a te mokopuna.

Te Āhua o te Mokopuna

E whai māramatanga ana te mokopuna ki ngā huatau pāngarau ki tō rātou ia te rā, ā, e whai hua ana te pāngarau ki te rātou.

Ngā tini mata o te tuakiri

Ka whai whakaaro te mokopuna ki ngā āhuatanga mahi a ētahi atu, ngā uinga a ētahi atu me te whai hononga i waenga i a rātou anō, i a rātou e mahi ngātahi ana, e mahi takitahi ana hoki. He auaha te mokopuna pāngarau.

Ngā tini mata o te tuakiri

E mārama ana te mokopuna he reo anō, he tikanga anō tō te ahurea pāngarau e rerekē ana i ō rātou anō ahurea. E ngana ana te mokopuna ki te whakamahi tika i ngā pūkenga whakaaroaro o ngā pūnaha e rua.

Ngā tini mata o te tuakiri

E māia ana te mokopuna ki te whakaputa i ōna whakaaroaro me āna kitenga pāngarau i ngā pūāhua huhua.

Ngā tini mata o te tuakiri

Ka taea e te mokopuna te whai pānga ki te pāngarau me tō rātou mōhio ki te whakamahi ki roto i tōna anō ao.

Whenu

hoki ki runga ake

HE TANGATA
tūhura ki te ao

HE URI WHAKAHEKE
ki te whai ao

HE PUNA KŌRERO
o te reo pāngarau

HE ĀKONGA
mauri oho

Toi Mokopuna

He koi te hinengaro o te mokopuna, rite ana ki ōna mātua tīpuna. Ko ngā whakaaro me te whakamahi pāngarau he mea tuku iho ki a ia, ā, ka tukuna ki ētahi atu.

He manawanui, he huritao, he aroturuki hoki te mokopuna ki te panoni i ōna whakaaro me āna mahi, ā, ka tautohu tauira, hononga hoki hei hanga pāngarau me tōna anō ao.

Tohu Ako: Tūārere 2: Tau 4–6
Te Roanga o te Kōrero

Tau

Ngā Tini Mata o te Ako

Kei te ako te mokopuna ki te:

whakaoti rapanga tāpiri, rapanga tango mā te whakamahi i ngā rautaki wāwāhi tau
whakaoti rapanga whakarea, rapanga whakawehe tau mati-2, mati-3 hoki mā te whakamahi rautaki wāwāhi tau
whiriwhiri i te hautau waetahi o tētahi huinga, ō tētahi āhua mā te toharites.

Ko ngā rautaki matua mā te mokopuna:

whakamahi i ngā meka mōhio me ngā rautaki ā-hinengaro ki te whakaoti rapanga mati-1
whakamahi i ngā meka e mōhiotia ana hei whakaoti rapanga whakarea māmā me ngā rapanga hautanga māmā
whakaoti rapanga tāpiri, rapanga tango mā te whakamahi i ngā rautaki; rearua, huri hei tau māmā, wāwāhi uara tū, tau māmā me
te tikanga paremata, tāpiritanga ōrite, paheko kōaro
whakaoti rapanga whakarea, rapanga whakawehe mā te whakamahi i ngā rautaki; tāpiri tāruarua, te wāwahi uara tū, te tau māmā
me te tikanga paremata me te rearua haurua
kimi hautanga o tētahi rahinga mā te tohatoha.

Ngā Tini Mata o te Mātauranga

Te Hanga o Ngā Tau

Tau 4
Kei te ako te mokopuna ki te:

Tau 5
Kei te ako te mokopuna ki te:

Tau 6
Kei te ako te mokopuna ki te:

tatau whakamua, whakamuri ki te 1,000
tautohu, te pānui, te tuhi, te whakatairite me te whakaraupapa tau ki te 10,000
taurea o te 25, te 50 me te 100.

tautohu, te panui, te tuhi, te whakatairite me te whakaraupapa i ngā tau ki te 100,000.

tautohu, te panui, te tuhi, te whakatairite me te whakaraupapa i ngā tau ki te 1,000,000.

Te Whakarōpu/Te Uara Tū

tautohu i te tikanga o ngā mati i te uara tū o ngā tau ki te 10,000.

āhukahuka i te tikanga o ngā mati i te uara tū o ngā tau ki te 100,000.

āhukahuka i te tikanga o ngā mati i te uara tū o ngā tau ki te 1,000,000.

whakaputa i te maha o ngā 10, o ngā 100, o ngā 1,000 kei roto i tētahi tau mati-4.

whakaputa i te maha o ngā 10, o ngā 100, o ngā 1,000, o ngā 10,000 kei roto i tētahi tau mati-5.

whakaputa i te maha o ngā 10, o ngā 100, o ngā 1,000, o ngā 10,000 kei roto i tētahi tau mati-6.

Ngā Meka Matua

whakaputa maharatanga meka whakarea, meka whakawehe 4, 6, 9, me ngā 10
whakarea ki te 10, ki te 100, ki te 1,000:
h.t., 10 × 100 = 1,000 32 × 100 = 3,200.

whakaputa maharatanga meka whakarea, i ngā meka whakawehe ki te 10 × 10
whakaputa maharatanga ki ture whakawehe mō ngā whakarea 2, 3, 5, 9 me ngā 10.

whakaputa maharatanga meka whakarea, i ngā meka whakawehe ki te 10 × 10.

Ngā Paheko

whakamahi whakaāwhiwhi me te whakatau tata
whakaāwhiwhi tauoti ki te 10, 100 me te 1000 pātata
whakaāwhiwhi i ngā hautekau ki te tauoti pātata.

whakamahi whakaāwhiwhi me te whakatau tata
whakaāwhiwhi tau oti ki te pū 10 e pātata: h.t., whakaāwhiwhi 4560 ki te pū 10 pūrua (arā × 100) ka 4600
whakaāwhiwhi i ngā hautekau me ngā haurau ki te tauoti pātata.

whakamahi whakaāwhiwhi me te whakatau tata
whakaāwhiwhi tau oti ki te pū 10 e pātata ana
whakaāwhiwhi ki te tauoti pātata, ki te tau-a-ira kotahi mati whai ira.

tāpiri me te tango tau mati-2, tau mati-3 hoki.

tāpiri me te tango tau ki te 10,000.

tāpiri me te tango tauoti.

whakarea tau mati-1, mati-2 ki te tau matitahi:
h.t., 5 × 46, 8 × 7.

whakarea tau mati-3 ki ngā tau mati-1 tau mati-2 hoki:
h.t., 6 × 248, 37 × 84

whakarea tauoti matimaha:
h.t., 54 × 112.

whakawehe tauoti ki ngā tau mati-1 kāore he toenga:
h.t., 65 ÷ 5.

whakawehe tauoti ki ngā tau mati-1 kia whiwhi toenga:
h.t., 22 ÷ 5 = 4 toenga 2.

whakawehe tauoti ki ngā tau mati-1, kia whiwhi toenga:
h.t., 35 ÷ 6, 4154 ÷ 8.

Ngā Tau Whakahau

āhukahuka te pānui, te tuhi me te waihanga hautekau hei hautau, hei hautanga ā-ira hoki.

āhukahuka te pānui, te tuhi me te waihanga i ngā hautekau, i ngā haurau hei hautau, hei hautanga ā-ira hoki.

āhukahuka te pānui, te tuhi me te waihanga hautau, hautanga ā-mati (kia rua mati ā-ira), ōrau hoki.

whakatairite me te whakaraupapa i ngā hautau hautekau, i ngā hautanga ā-ira hautekau hoki.
huri i te hautanga ā-ira hei hautau.

whakatairite me te whakaraupapa i ngā hautau hautekau, i ngā hautau haurau, i ngā hautanga ā-ira hautekau, i ngā hautanga ā-ira haurau hoki
huri i te hautanga ā-ira hei hautau.

whakatairite me te raupapa i ngā hautau, hautanga ā-mati (kia rua mati ā-ira), ōrau hoki
huri i te hautanga ā-ira, te ōrau hoki hei hautau.

waihanga hautanga ā-ira mā te whakawehe i ngā tauoti 0-9, ki te 10.

waihanga hautanga ā-ira, tauoti hoki mā te whakawehe ki te 10, ki te 100 rānei.

waihanga hautanga ā-ira, tauoti hoki mā te whakarea, mā te whakawehe hoki ki te 10, ki te 100 rānei.

whiriwhiri i te hautau waetahi o tētahi rahinga mā te toharite.

whiriwhiri i te hautau waetahi o tētahi rahinga mā te whakamahi whakareatanga.

whiriwhiri i te hautau, i te ōrau hoki o tētahi rahinga:
h.t., 30% o te 50, 3—8 o te 48.

tāpiri, ki te tango rānei i ngā hautau, e ōrite ana ngā tauraro, kia 1 te otinga:
h.t., 3—8 + 3—8 + 2—8 = 8—8 = 1.

tāpiri, ki te tango rānei i ngā hautau, e ōrite ana ngā tauraro.

tāpiri, ki te tango rānei i ngā hautau, e ōrite ana, e whai pānga rānei ngā tauraro:
h.t., 1—4 + 1—8.

tāpiri me te tango tau ā-ira, kia kotahi te mati ā-ira.

tāpiri me te tango tau ā-ira, kia rua ngā mati ā-ira.

tāpiri me te tango tau oti me ngā tau-a- ira kia rua mati ā-ira.

tautohu, ki te whakatairite, ki te whakaraupapa hoki i ngā hautau ōrite me ngā tauraro 2, 4 me te 8; 3 me te 6; 5 me te 10.

tautohu, ki te whakatairite ki te whakaraupapa hoki i ngā hautau me ngā tauraro 2, 3, 4, 5, 6, 8, 10, 12, 100
tautohu i ngā hautau e whai pānga ana tētahi ki tētahi
whakarūnā hautau.

tautohu, ki te whakatairite ki te whakaraupapa hoki i ngā hautau me ngā tauraro 2, 3, 4, 5, 6, 8, 10, 12, 100
tautohu i ngā hautau e whai pānga ana tētahi ki tētahi
whakaruna hautau.

huri i ngā hautau hanumi me ngā tau hanumi, mō ngā tauraro pātahi 2, 3, 4, 5, 6, me te 10.

huri i ngā hautau nui ake i te kotahi hei tau hanumi, mō ngā hautau, me ngā tauraro pātahi ki te 10.

huri i ngā hautau nui ake i te kotahi hei tau hanumi.

kimi i te hautanga o tētahi tauoti, he tauoti te whakautu mā te whakamahi i ngā meka whakarea, me ngā meka whakawehe:
h.t., 1—4 of 40.

kimi i te hautanga o tētahi tauoti, he tauoti te whakautu, mā te whakamahi i ngā meka whakarea, me ngā meka whakawehe:
h.t., 2—3 of 24.

kimi i te hautanga, i te ōrau rānei o tētahi tauoti, he tauoti te whakautu:
h.t., 30% of $150.

Mātau Ahumoni

whakatau tata me te tātai i te tapeke utu me ngā wāwāhinga moni.

whakatau tata i te utu, i te wāwāhinga moni hoki, ki te tāra pātata, ki te 10 tāra pātata rānei.

tātai i te hekenga ōrau, o te 10%, o te 25%, o te 50% rānei, o tētahi rahinga tāra:
h.t., 10% o $180.

Ngā Tini Mata o Te Reo o Tau

E mōhio ana ki ngā kupu nei:

whakatau tata
whakaāwhiwhi
tapeke
hautanga nui atu i te kotahi
tau whakarūnā
hautanga
hautanga ā-ira.

ōrau
hautekau
haurau
haumano
tauwehe pātahi
taurea pātahi
tau pūrua
wāwāhinga moni.

ekenga ōrau
tau hanumi
tau māmā
tāpiri ōrite
paheko kōaro
taupū
tau pūrua.

Whenu

hoki ki runga ake

HE TANGATA
tūhura ki te ao

HE URI WHAKAHEKE
ki te whai ao

HE PUNA KŌRERO
o te reo pāngarau

HE ĀKONGA
mauri oho

Toi Mokopuna

He koi te hinengaro o te mokopuna, rite ana ki ōna mātua tīpuna. Ko ngā whakaaro me te whakamahi pāngarau he mea tuku iho ki a ia, ā, ka tukuna ki ētahi atu.

He manawanui, he huritao, he aroturuki hoki te mokopuna ki te panoni i ōna whakaaro me āna mahi, ā, ka tautohu tauira, hononga hoki hei hanga pāngarau me tōna anō ao.

Tohu Ako: Tūārere 2: Tau 4–6
Te Roanga o te Kōrero

Taurangi

Ngā Tini Mata o te Ako

Kei te ako te mokopuna ki te:

whakoti rapanga mā te whakamahi i te tāpiri tāruarua ki te rapu hoki i ngā wahanga o tētahi tauira
ko te ture nō tētahi tauira e whakamahia ana ki te whakaoti rapanga.

Ngā Tini Mata o te Mātauranga

Tau 4
Kei te ako te mokopuna ki te:

Tau 5
Kei te ako te mokopuna ki te:

Tau 6
Kei te ako te mokopuna ki te:

whakaahua, te waihanga me te whakapae tauira raupapa, tauira tau hoki mā te whakamahi rautaki e whai wāhi mai ana te taurangi, te tāpiri tāruarua, te tangohanga me te whakarea māmā.

whakaahua, te waihanga, te mahi tonu, me te whakapae tauira raupapa, tauira tau hoki mā te whakamahi i ngā ture e tika ana, e wāhi mai ai te taurangi, te tāpiri tāruarua, te tangohanga me te whakarea māmā
whakamahi hoahoa, tūtohi, kauwhata me ngā whārite ki te whakaoti rapanga pānga rārangi.

whakamahi tūtohi, kauwhata XY, me ngā hoahoa hei tautohu pānga rārangi
whakarite i tētahi ture a-kupu hei tautuhi i te pāpātanga o te whiti o ngā huānga, ngā taurangi rānei o tētahi tauira, whakamahia taua ture ki te whakamahi matapae.

tūhura i ngā āhuatanga herekore tāpiri me ngā āhuatanga herekore whakarea.

tūhura he aha i kore ai te āhuatanga herekore me te āhuatanga kōaro e tika ana mō ngā tangohanga me ngā whakawehenga.

whakamahi i ngā āhuatanga kōaro, āhuatanga herekore hoki mō ngā pāheko e tika ana.

whakaoti rapanga whakarea, rapanga whakawehe mā te whakamahi i te pāheko kōaro.

whakaoti rapanga whakarea, rapanga whakawehe mā te whakamahi i te pāheko kōaro.

whakaoti rapanga whakarea, rapanga whakawehe mā te whakamahi i te pāheko kōaro.

tūhura i ngā āhuatanga tohatoha o te whakarea i ngā tauhono, hei tauira, kimihia te:
7 × 8 ki te 7 × (5 + 3) = (7 × 5) + (7 × 3)
(whakaoti rapanga whakarea mā te wāwāhi tauwehe).

tūhura i ngā āhuatanga tohatoha o te whakarea i ngā tauhono me ngā tautango:
h.t., 6 × 18 ki te 6 × (20 − 2)
whakaoti rapanga whakarea mā te whakamahi i te rautaki tau māmā me te tikanga paremata.

whakamahi i ngā āhuatanga tohatoha, ngā āhuatanga pāheko kōaro me ngā āhuatanga herekore.

Ngā Whārite me ngā Pānga

tuhi me te whakaoti whārite pono, whārite parau rānei, whārite whānui hoki e whai wāhi mai ana te whakarea me te whakawehe, he whakamahi i tōna mōhiotanga ki te tohu ōrite:
h.t., 5 × __ = 20, __ ÷ 3 = 6.

tuhi me te whakaoti whārite pono, whārite parau rānei, whārite whānui hoki e whai wāhi mai ana ngā pāheko e whā:
h.t., 674 + 56 − k = 671.

tuhi me te whakaoti whārite pono, whārite parau rānei, whārite whānui hoki e whai wāhi mai ana pāheko e whā, e whai wāhi mai ana hoki i te rite, i te tōrite rānei:
h.t., 4 × 5 < 3 × 5 + 3 (p/h).

tautohu i te pānga i te tipu o tētahi tauira, me ngā āhuatanga rerekē, whakamāramahia te ture e whakaahua ana o ngā tauira, ka whakamahi ai i te ture ki te kimi huānga anō o tētahi tauira.

tautohu i te pānga i te tipu o tētahi tauira, me ngā āhuatanga rerekē, tuhia te ture e whakaahua ana o ngā tauira, ka whakamahi ai i te ture ki te kimi huānga anō o tētahi tauira.

whakamahi tūtohi, kauwhata XY, me ngā hoahoa ki te tautohu pānga kei roto i te tauira rārangi. Tuhia he ture e tautohu ana i te maha pūmau o ngā panonitanga i waenga i ngā huānga piri tata, ngā ture o te tauira, ā, ka whakamahi i te ture hei whakaputa whakapae.

Ngā Tini Mata o Te Reo o Taurangi

E mōhio ana ki ngā kupu nei:

pānga
wāwāhi
tūtohi
hoahoa pere
paparau
kauwhata whakaahua
rārangi tau
anga pirepire.

Ngā rerenga kōrero me ngā tohu hei whakamārama i te ture o tētahi tauira tau, o tētahi pānga māmā rānei. Hei tauira:

He tāpiri i te 3 te tipu o tēnei tauira raupapa (+3): 2, 5, 8, 11 ...
Ka whakareatia te roa o tētahi tapa ki te 4 hei tātai i te paenga tapawhā rite (tapa × 4 = paenga).

tohu tōrite nei me ngā tikanga e hāngai ana:
- pūmau
- wāwāhi
- tauwehe/taurea
- rite/tōrite.

Whenu

hoki ki runga ake

HE TANGATA
tūhura ki te ao

HE URI WHAKAHEKE
ki te whai ao

HE PUNA KŌRERO
o te reo pāngarau

HE ĀKONGA
mauri oho

Toi Mokopuna

He koi te hinengaro o te mokopuna, rite ana ki ōna mātua tīpuna. Ko ngā whakaaro me te whakamahi pāngarau he mea tuku iho ki a ia, ā, ka tukuna ki ētahi atu.

He manawanui, he huritao, he aroturuki hoki te mokopuna ki te panoni i ōna whakaaro me āna mahi, ā, ka tautohu tauira, hononga hoki hei hanga pāngarau me tōna anō ao.

Tohu Ako: Tūārere 2: Tau 4–6
Te Roanga o te Kōrero

Ine

Ngā Tini Mata o te Ako

Kei te ako te mokopuna:

ki te whakapae me te whakamahi i ngā waeine ngahuru; pēra i ngā mitarau, mita, rita, kirokaramu hei ine i tētahi āhuatanga
i te tikanga o te āwhata
te wāwāhi i tētahi waeine, ki te ine hoki i tētahi haurua waeine
ki te ine i te roa, te kītanga, te rōrahi me te taumaha mā tētahi taputapu ine whaitake
ki te pānui āwhata, ka mōhio hoki ki ngā ingoa me ngā tohu waeine (mm, cm, m, km, g, kg, ml, l)
te whakamahi paearu inenga ki te whakatau tata
i te tikanga o te tūtohi tukutuku hei āwhina i a rātou ki te tātai horahanga me te rōrahi.

Ngā Tini Mata o te Mātauranga

Te Ine

Tau 4
Kei te ako te mokopuna ki te:

Tau 5
Kei te ako te mokopuna ki te:

Tau 6
Kei te ako te mokopuna ki te:

waihanga paearu inenga ki te whakatau tata me te ine i te roa, te paenga, te taumaha, te kītanga, me te roa mā te whakamahi i ngā tohu ine tika.

whakatau tata me te ine i te roa, te horahanga, te taumaha, te kītanga, me te roa mā te whakamahi i ngā tohu ine tika, he kohinga ine rānei.

whakatau tata me te ine i te roa, te rōrahi, te taumaha, te kītanga,m me te roa mā te whakamahi i ngā tohu ine tika, he kohinga ine rānei.

whakamahi i ngā waeine me ngā taputapu e tika ana ki te ine i te roa, te papatipu, te kītanga me te wā.

whakamahi i ngā waeine me ngā taputapu e tika ana mō te mahi e inea ana.

tīpako me te whakamahi i ngā waeine me ngā taputapu e tika ana mō te mahi e inea ana.

whakamahi i te pūnaha ngahuru ki te tūhura i te hononga o ngā waeine.

tūhura i te hononga o ngā waeine mā te whakamahi i te pūnaha ngahuru pū-tekau mō ngā rahinga, e whai wāhi ana ngā hautau,ngā hautanga ā-ira, ngā koeko-tapawhā me ngā poro-tapawhā hoki.

huri waeine mō te roa, te papatipu, te kītanga, me te tautohu waeine, ka whakamahi ai i ngā hautanga ā-ira ki te whakaatu i tētahi wāhanga o te inenga.

ine koki mā te ine ā-putu hei ine paearu.
- 90°, 180° 360°.

whakamārama i tētahi koki mā te whakamahi i te koki tāhapa, te koki te hāngai, te koki hāpūpū, te koki rārangi, te koki rāwaho ki nga putu; 90°, 180°, me te 360°.

whakaahua ā-hinengaro i ngā nekehanga ā-koki (ki te 360°), ka ine, ka tuhi ai i ngā koki ki te putu e pātata ana.

whai māramatanga ki ngā momo āwhata inenga me ngā waeine hautanga ā-ira.

whakatau tata ka ine ai i ngā horahanga me ngā rōrahi māmā.

Te Paenga, te Horahanga me te Rōrahi

whakatau tata me te tātai i te:
- paenga o ngā taparau mā te whakamahi waeine ngahuru
- horahanga o tētahi āhua kua kapi ki ngā tapawhā, ki ngā tapawhā haurua rānei
- rōrahi o ngā āhua kua whakakiia ki te porowhā mā te whakamahi i nga paparanga.

whakatau tata me te tātai i te:
- paenga o ngā taparau,
- horahanga o tētahi āhua kua kapi ki ngā tapawhā, ki tētahi wāhanga rānei o te tapawhā
- rōrahi o ngā poro tapawhā .

whakaahua ā-hinengaro, ki te whakatau tata, ki te tātai hoki i te horahanga o ngā tapawhā hāngai me te rōrahi o ngā poro-tapawhā hāngai mā te whakamahi whakareatanga.

Te Wā

pānui i te wā ki te 5-miniti e pātata ana
ko ngā kupu ka whakamahia:
- hipa i te/mai i te
- ki te.

whakamārama i te hononga o ngā rā, ngā wiki, ngā marama me ngā tau
whakaoti rapanga mō te wā e whai wāhi mai ana ngā reo tohu wā; ‘ata’ me te ‘ahiahi’.

huri i te wā-12 me te wā-24
whakaoti rapanga mō te wā.

Ngā Tini Mata o Te Reo o Ine

E mōhio ana ki ngā kupu nei:

koki
koki hāngai
hautanga koki hāngai.

Ngā waeine o ia rā

mitamano
mitarau
mita
kiromita
karamu
kirokaramu.

Tohu reo wā

hipa i te/mai i te
ki te.

Ka tuhi kauwhata pou hei whakatairite inenga.

rahinga āwhiwhi (o tētahi koki)
hautanga ā-ira
waeine
pū tekau
poro tapawhā hāngai
tauoti
ahu
koki hāpūpū
koki torotika
koki tāhapa
koki hāngai
koki whakaata
putu
paenga
horahanga
rōrahi
taparau (rite)
ata
pō.

mō ngā waeine horahanga (m², cm², ha)
me te waeine rōrahi nei, te cm³
putu
huri.

Whenu

hoki ki runga ake

HE TANGATA
tūhura ki te ao

HE URI WHAKAHEKE
ki te whai ao

HE PUNA KŌRERO
o te reo pāngarau

HE ĀKONGA
mauri oho

Toi Mokopuna

He koi te hinengaro o te mokopuna, rite ana ki ōna mātua tīpuna. Ko ngā whakaaro me te whakamahi pāngarau he mea tuku iho ki a ia, ā, ka tukuna ki ētahi atu.

He manawanui, he huritao, he aroturuki hoki te mokopuna ki te panoni i ōna whakaaro me āna mahi, ā, ka tautohu tauira, hononga hoki hei hanga pāngarau me tōna anō ao.

Tohu Ako: Tūārere 2: Tau 4–6
Te Roanga o te Kōrero

Āhuahanga

Ngā Tini Mata o te Ako

Kei te ako te mokopuna ki te:

whakarōpū, te tautohu, te whakaahua, me te whakatairite hoki i ngā āhua ahu-2 me ngā ahu-3
tautohu i te whakaatatanga, te nekehanga, te hurihanga o tētahi āhua māmā, ki te tautohu hoki i ngā āhuatanga pūmau, āhuatanga rerekē rānei
tuhi hoahoa me te hanga tauira o ngā āhua ahu-2, āhua ahu-3 hoki
tautohu ahunga matua, ki te whakamārama taunga ki tētahi mahere, ki te whakaatu ahunga, taunga hoki ki tētahi mahere
whai tohutohu me te tuku tohutohu hoki ahunga tiriti.

Ngā Tini Mata o te Mātauranga

Ngā Hanga

Tau 4
Kei te ako te mokopuna ki te:

Tau 5
Kei te ako te mokopuna ki te:

Tau 6
Kei te ako te mokopuna ki te:

tautohu, te whakarōpū, me te whakaahua i nga taparau, pēnei i te tapatoru me te tapawhā, mā te whakamahi i te hanga o te āhua, te rārangi me te hangarite hurihanga hoki o te āhua.

tautohu, te whakarōpū, me te whakamārama i te hanga mā te:
- whakaingoa taparau rite me ngā taparau kore rite mā te whakamahi i nga tapa, ngā akitu, me nga koki
- poro mā te whakamahi i te hauroki o te āhua, ngā tapa, ngā mata, me ngā koki.

whakarōpū, te tautohu me te whakamārama i ngā ōritenga me ngā rerekētanga i waenganui i ngā:
- āhua ahu-2 o ngā momo tapatoru, o ngā poro me ngā koeko.

whakataurite me te whakarōpū i nga koki e rite ana, e iti ake ana, e nui ake ana rānei i te koki hāngai, i tētahi āhua ahu-2.

tautohu me te whakamārama i nga rārangi whakarara, ngā rārangi poutū me ngā tapa o ngā taparau.

tautohu me te whakamārama i nga koki roto o te tapatoru me te tapawhā.

tā raumata mō ngā āhua ahu-toru māmā
tā mahere o te kāinga.

tā i ngā āhua ahu-3 ki tōna raumata
tā mahere o te kura.

whakaatu i ngā āhua ahu-3 hei ahu-2:
h.t., tā raumata me ngā tā inerite
tā mahere mō te haere ki te kura.

Te Tūnga me te Ahunga

whakamahi i ngā tukutuku, ngā takirua raupapa, ngā pito matua o te kāpehu, me ngā mahere māmā hei whakaatu, hei whakamārama hoki i te ara me te tūwāhi
whai māramatanga ki te ture taunga (X, Y) ki runga i tētahi mahere tukutuku.

whakamahi i ngā takirua raupapa, i te hurihanga, i ngā pito matua o te kāpehu ki te whakamārama tūwāhi, ki te tuku ahunga
pānui, ki te tuhi i ngā taunga.

whai tohutohu me te tuku tohutohu mā te mōhio i te reo ahunga; ngā pito katoa o te kāpehu, te karaka, putu
whakamahi pūwāhi ki te tautohu rohenga me ngā taunga ki runga mahere; whakamāori me te whakaahua huarahi, te tautohu i ngā huringa haurua, hauwhā me te tawhiti.

Ngā Panoni

tautohu i te panonitanga, i te whakaatatanga, i te hurihanga, i te nekehanga āhua ahu-2 o tētahi mahi toi Māori.

whakarahi i tētahi āhua ahu-2 o tētahi mahi toi Māori; kia nui ake, kia iti iho rānei
whakamahi tikanga o te mātāoroko me te mātātuhi
whiriwhiri i te taurahi mō te whakarahi
whiriwhiri i te pū huringa me te pū whakarahi..

whakaahua ā-hinengaro, te tuhi, te whakamārama i ngā āhua ahu-2 me ngā rōpinepine kei roto i ngā kōwhaiwhai, i ngā tukutuku, me ēra atu tauira, ka tautohu ai mēnā rānei he hurihanga, he whakaatahanga, he nekehanga
whakaingoa i ngā āhuatanga pūmau kāore e panonitia.

Ngā Tini Mata o Te Reo o Āhuahanga

E mōhio ana ki ngā kupu nei:

poro
poro tapawhā
poro tapatoru
mataono rite
koeko
koeko tapawhā
koeko tapatoru
tihi
ahu-2
ahu-3
tūwāhi
pūwāhi
pūtake.

Pito matua o te kāpehu

uru
raki
tonga
rāwhiti.

raumata
mātāoroko
panonitanga
hurihanga
nekehanga
whakarahi
pū hurihanga
pū whakarahi
taunga.

ōrite
ōrite te rahi
ōrite te āhua
rōpinepine
whakatekaraka
kōaro whakatekaraka
uru-mā-tonga
uru-mā-raki
rāwhiti-mā-tonga
rāwhiti-mā-raki.

Whenu

hoki ki runga ake

HE TANGATA
tūhura ki te ao

HE URI WHAKAHEKE
ki te whai ao

HE PUNA KŌRERO
o te reo pāngarau

HE ĀKONGA
mauri oho

Toi Mokopuna

He koi te hinengaro o te mokopuna, rite ana ki ōna mātua tīpuna. Ko ngā whakaaro me te whakamahi pāngarau he mea tuku iho ki a ia, ā, ka tukuna ki ētahi atu.

He manawanui, he huritao, he aroturuki hoki te mokopuna ki te panoni i ōna whakaaro me āna mahi, ā, ka tautohu tauira, hononga hoki hei hanga pāngarau me tōna anō ao.

Tohu Ako: Tūārere 2: Tau 4–6
Te Roanga o te Kōrero

Tauanga

Ngā Tini Mata o te Ako

Kei te ako te mokopuna ki te:

whakahaere tūhuratanga tauanga
whakarite i ngā momo pātai whakarāpopoto
kohi, te whakarōpū me te whakaatu hoki i ngā raraunga hei whakautu pātai
whakaputa kīanga mō tā rātou i tūhura ai
kohikohi me te whakaatu i ngā raraunga tatau hei raraunga motumotu, hei raraunga motukore
whakaputa kōrero mō tā rātau i kite ai e hāngai ana ki tētahi horopaki.

Ngā Tini Mata o te Mātauranga

Tau 4
Kei te ako te mokopuna ki te:

Tau 5
Kei te ako te mokopuna ki te:

Tau 6
Kei te ako te mokopuna ki te:

whakahaere tūhuratanga tauanga amio:
- ka kohi, ka wehewehe, ka whakaatu i ngā raraunga whakarōpū matatini, ngā raraunga tauoti, me ngā raraunga houanga māmā hei whakautu pātai
- ka tautohu tauira, ka hono hoki ki tētahi horopaki, ki roto, ki waenga hoki i ngā huinga raraunga
- ka whakawhiti putanga mā ngā whakaari raraunga.

whakahaere tūhuratanga tauanga amio:
- ka kohi, ka wehewehe, ka whakaatu i ngā raraunga whakarōpū matatini, ngā raraunga tauoti, me ngā raraunga houanga māmā hei whakautu pātai
- ka tautohu tauira, ka hono hoki ki tētahi horopaki, ki roto, ki waenga hoki i ngā huinga raraunga
- ka whakawhiti putanga mā ngā whakaari raraunga.

whakahaere tūhuratanga tauanga amio:
- ka kohi, ka wehewehe, ka whakaatu i ngā raraunga whakarōpū matatini, ngā raraunga tauoti, me ngā raraunga houanga māmā hei whakautu pātai
- ka tautohu tauira, ka hono hoki ki tētahi horopaki, ki roto, ki waenga hoki i ngā huinga raraunga
- ka whakawhiti putanga mā ngā whakaari raraunga.

Te Whakarite Rapanga

tūhura pūāhua whakarāpopoto me ngā pūāhua whakatairite ki ngā raraunga whakarōpū me ngā raraunga motumotu mā te whakamahi i ngā raraunga matatini (kia rua nui ake rānei ngā taurangirangi):
- tautohu i ngā taurangirangi e inehia ana
- whakarite pātai whakarāpopoto, pātai whakatairite hoki kia whakautua e te raraunga
- whakaputa whakapaenga, tāpaetanga rānei mō ngā putanga kawatau.

tūhura pūāhua whakarāpopoto me ngā pūāhua whakatairite ki ngā raraunga whakarōpū me ngā raraunga motumotu mā te:
- tautohu i ngā taurangirangi e inehia ana
- whakarite pātai whakarāpopoto, pātai tūhura hoki ka whakautua e te raraunga
- whakapae me te whakatakoto tāpae kōrero rānei mō ngā raraunga ka puta mai.

tūhura pūāhua whakarāpopoto me ngā pūāhua whakatairite me ngā pūāhua raraunga houanga mā te:
- tautohu i ngā taurangirangi e inehia ana
- whakarite pātai tūhura ka whakautua e te raraunga
- whakapae, ki te tāpae rānei i ngā kitenga kawatau.

Whakamahere

whakamahere ki te kohi raraunga hei taunaki i te pātai tūhura:
- whiriwhiri i te rōpū e rangahautia ana
- whiriwhiri i ngā taurangirangi e kohia ana
- whai whakaaro mō ngā ritenga matatika i te wā o te kohi raraunga.

whakamahere ki te kohi raraunga hei taunaki i te pātai tūhura:
- whiriwhiri i te rōpū e rangahautia ana
- whiriwhiri i ngā taurangirangi e kohia ana
- whai whakaaro mō ngā ritenga matatika i te wā o te kohi raraunga; kirimuna i te kaiurupare.

whakamahere ki te kohi raraunga hei taunaki i te pātai tūhura:
- tautohu i ngā kaiurupare
- tautohu i ngā taurangirangi e kohia ana
- tautohu i tā te kaituhura pūtake ki te kohi i ngā raraunga.

Te Kohi Raraunga

tautohu i ngā taurangirangi e taea ana te ine
whakamahi i ngā rautaki huhua ki te kohi raraunga matarua, raraunga matatini, raraunga houanga hoki
whakamahi i ngā rautaki kohi raraunga huhua ki te whakarāpopoto, ki te kohi raraunga whakarōpū hoki.

tautohu i ngā taurangirangi me te whakarite mahere e whakamahi ai ngā tirohanga tauanga
kohi raraunga e hāngai ana ki te pātai
whakamahi i ngā rautaki huhua ki whakarāpopoto, ki te whakarōpū me te whakatairite raraunga
whakatau me pēhea e pupuri me te tiaki i ngā raraunga.

tautohu i ngā taurangirangi e taea ana te ine
whakamahi i ngā rautaki kohi raraunga huhua ki te whakarāpopoto, ki te whakarōpū me te whakatairite i ngā raraunga matāmua, i ngā raraunga mātāmuri rānei
whakatau me pēhea te pupuri me te tiaki i ngā raraunga.

Te Tatari me Te Whakatau

waihanga me te whakamārama whakaari raraunga mō te whakarāpototanga me te whakatairitenga o ngā tūhura;
- mā te whakaingoa i ngā wāhanga o te pikitia
- e whai take ana te whakaari raraunga ki te momo raraunga.

waihanga me te whakamārama i ngā whakaari raraunga mō ngā tūhura whakarāpopoto, tūhura whakatairite hoki;
- whakaingoa i ngā wāhanga o te whakaari
- kei te whai take te whakaari ki te momo raraunga
- tautohu i ngā taurangirangi

waihanga me te whakamārama i ngā whakaari rerekē;
- whakaingoa i ngā wāhanga o te whakaari
- kei te tika te whakaari e ai momo raraunga
- tautohu i ngā taurangirangi
- whakamarāma i ngā āhua, i ngā tauira me ngā ia o roto i te horopaki e whai wāhi ana ngā taurangirangi me ngā rōpū e arohia ana.

whakautu pātai;
- whiriwhirihia ngā rerenga whakaahua e tika ana ki te whakautu i te pātai, ka huritao ai i ngā kitenga me te whakatairite i ngā whakapae, i ngā tāpaetanga rānei nō te timatanga o te tūhura..

whakautu i te pātai tūhura;
- whakatairite i ngā kitenga me ngā whakapae, i ngā tāpaetanga rānei
- whakatairite i ngā kitenga me ō rātou mōhiotanga ki te ao..

whakautu i te pātai tūhura;
- whakatairite i ngā kitenga me ngā whakapae, i ngā tāpaetanga rānei
- whakatairite i ngā kitenga me ō rātou mōhiotanga ki te ao..

whakaahua rauranga mā te whakamahi kauwhata ira, kauwhata pou, tūtohi auau, kauwhata houanga
whakahono i ngā whakataunga me ngā ataata raraunga ki te whakautu pātai tūhura
tūhura pūāhua me te tuku pātai ka taea te whakautu
whai māramatanga ki ngā raraunga motumotu, raraunga motukore hoki.

whakaahua rauranga mā te whakamahi kauwhata ira, kauwhata pou, tūtohi auau, kauwhata houanga
whakahono i ngā whakataunga me ngā ataata raraunga ki te whakautu pātai tūhura
tūhura pūāhua me te tuku pātai ka taea te whakautu
whai māramatanga ki ngā raraunga motumotu, raraunga motukore hoki.

whakaahua rauranga mā te whakamahi kauwhata ira, kauwhata pou, tūtohi auau, kauwhata houanga
whakahono i ngā whakataunga me ngā ataata raraunga ki te whakautu pātai tūhura
tūhura pūāhua me te tuku pātai ka taea te whakautu
whai māramatanga ki ngā raraunga motumotu, raraunga motukore hoki..

Ngā Tini Mata o Te Reo o Tauanga

E mōhio ana ki ngā kupu nei:

kauwhata ira
kauwhata pou
tuaka pae
tuaka pou
raraunga.

kauwhata rārangi
āhuatanga kōhure
ripanga
pou
kapa.

kauwhata pou hiato
kauwhata rautō
mōwaho
manei
rāpoi.

Whenu

hoki ki runga ake

HE TANGATA
tūhura ki te ao

HE URI WHAKAHEKE
ki te whai ao

HE PUNA KŌRERO
o te reo pāngarau

HE ĀKONGA
mauri oho

Toi Mokopuna

He koi te hinengaro o te mokopuna, rite ana ki ōna mātua tīpuna. Ko ngā whakaaro me te whakamahi pāngarau he mea tuku iho ki a ia, ā, ka tukuna ki ētahi atu.

He manawanui, he huritao, he aroturuki hoki te mokopuna ki te panoni i ōna whakaaro me āna mahi, ā, ka tautohu tauira, hononga hoki hei hanga pāngarau me tōna anō ao.

Tohu Ako: Tūārere 2: Tau 4–6
Te Roanga o te Kōrero

Tūponotanga

Ngā Tini Mata o te Ako

Kei te ako te mokopuna ki te:

whakamārama kei te hē, kei te tika rānei ngā kīanga mō te āhua o te whakaaturanga raraunga
whakapae me te whakamātau i ngā putanga katoa o tētahi pūāhua tūponotanga whai take me te whakamārama he aha i pērā ai.

Ngā Tini Mata o te Mātauranga

Tau 4
Kei te ako te mokopuna ki te:

Tau 5
Kei te ako te mokopuna ki te:

Tau 6
Kei te ako te mokopuna ki te:

tūhura i ngā pūāhua māmā e hāngai ana ki ngā tūponotanga mā te whakatairite i ngā otinga o ngā tauira me te whakaputa i ō rātou whakaaro mō ngā putanga.

tūhura i ngā pūāhua māmā e hāngai ana ki ngā tūponotanga mā te whakatairite i ngā otinga o ngā tauira me te whakaputa i ō rātou whakaaro mō ngā putanga.

tūhura i ngā pūāhua māmā e hāngai ana ki ngā tūponotanga mā te whakatairite i ngā otinga o ngā tauira me te whakaputa i ō rātou whakaaro mō ngā putanga.

tomo ki ngā pūāhua tūhura tuponotanga mā te:
- tuku pātai tūhura ka whakapae ai i te putanga
- tautohu i ngā putanga o ngā pātai tūponotanga me te waihanga whakaari raraunga mō ngā auau o ngā putanga
- whakaahua i te āhua o ngā whakaari raraunga
- tautohu i te tūponotanga hei hautanga me te whakautu i te pātai tūponotanga.

tomo ki ngā pūāhua tūhura tuponotanga mā te:
- tuku pātai tūhura ka whakapae ai i te putanga
- tautohu i ngā putanga o ngā pātai tūponotanga me te waihanga whakaari mō ngā auau o ngā putanga
- whakaahua i te āhua o ngā whakaari raraunga
- tautohu i te tūponotanga hei hautanga, hei rārangi hautanga me te hoahoa rākau
- whakautu i te pātai tūponotanga

tomo ki ngā pūāhua tūhura tuponotanga mā te:
- tuku pātai tūhura ka whakapae ai i te putanga
- tautohu i ngā putanga o ngā pātai tūponotanga, ka waihanga whakaari o ngā auau o ngā putanga
- whakaahua i te āhua o ngā whakaari raraunga
- tautohu i te tūponotanga hei hautanga, hei rārangi hautanga me te hoahoa rākau
- tautohu mēnā he pāpono whakawhirinaki, he pāpono wehe kē, he pāpono aukati rānei
- whakautu i te pātai tūponotanga.

tohutau, whakamārama hoki i ngā hapa o ngā whakaaturanga raraunga o ngā hōpara tauranga o tangata kē
tohutau mehemea ka nui ake te tūponotanga mā te tuhi nahanaha i ngā putanga o tētahi whakamātau tūpono.

tohutau, whakamārama hoki i ngā hapa o ngā whakaaturanga raraunga o ngā hōpara tauranga o tangata kē
tohutau mehemea ka nui ake te tūponotanga mā te tuhi nahanaha i ngā putanga o tētahi whakamātau tūpono.

tohutau, whakamārama hoki i ngā hapa o ngā whakaaturanga raraunga o ngā hōpara tauranga o tangata kē
tohutau mehemea ka nui ake te tūponotanga mā te tuhi nahanaha i ngā putanga o tētahi whakamātau tūpono.

tūhura i ngā pāpono māmā
whakapuaki i te tūponotanga hei hautau māmā i waenganui i te kore me te tahi.

whakamahi i te reo whakaniko hei whakaahua i te tūponotanga.

whakatau mēnā he tōkeke, he haukume rānei tētahi pāpono
whakapuaki i te tūponotanga hei ōrau.

Ngā Tini Mata o Te Reo o te Tūponotanga

E mōhio ana ki ngā kupu nei:

E mōhio ana ki te whakaatu i ngā putanga o tētahi whakamātau tūponotanga ki tētahi whakaari raraunga, pērā i te:

kauwhata pou
kauwhata ira
kauwhata whakaahua
āwhata
pāpono.

E mōhio ana ki ngā kupu nei:

āwhata
pāpono.

matapōkere
whakapae
putuaga
pāpono wehe kē
pāpono whakawhirinaki.

hoahoa rākau
pāpono
raupapa.

Hei Tautoko i Te Ako

hoki ki runga ake

Tikanga Whakaako

Kia taea ai te katoa te ako:

Me whai wāhi ngā mokopuna tau 0-8 katoa, ki te ako Pāngarau mō te kotahi hāora ia rā. Ka hua pea mai te kotahi hāora nei i ngā akoranga motuhake, i te kōtui kaupapa ako, ki ētahi atu wāhanga ako rānei o te marautanga.

Te whakamahere me te whakaako mā te:

whakarite wheako ki te whakaoti rapanga
whakamahi pānga kupu (h.t., ngā kupu e mōhiotia ana, ngā huatau pāngarau kua ākona kētia, ngā hoahoa me ngā rauemi)
urutau mahi (h.t., tīmata ki ngā tau e mōhiotia ana, nāwai rā, ka whanake ake)
tuku pātai hei ārahi i ō rātou whakaaro me te whakatītina i ngā hononga
whakawhāiti i te mātauranga kia iti iho ngā wāhanga hei ako
whakatakoto whakaaro mā te whakamahi whakaaturanga me ngā rauemi
āta ako horipū, whakatauira, ka whakaū ai
whakarerekē i te horopaki ki tētahi e mōhiotia ana e ngā mokopuna.

Te tautoko ākonga ki ngā tīrewa:

whakarite akoranga kiritahi o ngā rautaki whāiti e whanake ai te mokopuna
te whakapātaritari me te tuku pātai ki te whakahono i te mokopuna ki ngā akoranga o mua
te ui atu ki te mokopuna ki te pānui anō me te whakapuaki anō i te rapanga ki ā rātou ake kupu
ako ki te aroturuki i āna mahi, ka tuku pātai e whai māramatanga ai ia
te whakamahi whakaaturanga me ngā rauemi hei honohono ki ngā huatau pāngarau (h.t., te whakamahi poro, ngā porotiti me ngā anga tekau)
te whakamātau whakaahuatanga anō mei kore tētahi e tau ki te mokopuna
te whakatītina i te mokopuna ki te mahi ā-tinana (h.t, te hikoi ki runga i tētahi rārangi tau)
te akiaki i te mokopuna ki te tuhi pikitia o te whakaaro, o te rapanga pāngarau rānei
te akiaki i te mokopuna ki te ako hautau hou mā te whakamahi i āna mōhiotanga ki ngā huatau kua akona kētia
te āwhina i te mokopuna ki te whai hononga ki ngā kupu e mōhiotia ana mā te whakatairanga me te whakapiri ki te pātū o te wāhi ako
te ako ngātahi, te ako arahanga rānei ki te whai hātepe mō te whakaoti mahi.

Te whakarōpū mokopuna:

me whakamahi i te rautaki whakarōpū mokopuna i runga anō i te kaupapa o te akoranga pāngarau, o te hiahia ako hoki kaua e mau roa i ngā ākonga ki aua rōpū
ka taea te whakarōpū mokopuna ki ngā whakaritenga rerekē i te akoranga kotahi (h.t., ka mahi tahi te katoa i te tuatahi, ka wehe ai ki ngā rōpū rerekē hei tūhura pūāhua pāngarau).

Ngā rautaki whakaako: He tauira noa

Whenu

HE TANGATA
tūhura ki te ao

HE URI WHAKAHEKE
ki te whai ao

HE PUNA KŌRERO
o te reo pāngarau

HE ĀKONGA
mauri oho

Toi Mokopuna

He koi te hinengaro o te mokopuna, rite ana ki ōna mātua tīpuna. Ko ngā whakaaro me te whakamahi pāngarau he mea tuku iho ki a ia, ā, ka tukuna ki ētahi atu.

He manawanui, he huritao, he aroturuki te mokopuna ki te panoni i ōna whakaaro me āna mahi, ā, ka tautohu tauira, hononga hoki hei hanga pāngarau me tōna anō ao.

Tohu Ako: Tūārere 2: Tau 4–6

Whakarite wā kia taea ai ngā ākonga te whakahāngai mātauranga pāngarau

Ka ako ngā mokopuna mā te mahi, te kōrero, te tuhi me te waihanga.
Me whakamahere he wā mō nga mokopuna ki te whakaū i ngā mea i ākona e rātou mā te mahi anō i te tukanga, te mahi rānei i whakaatuhia e te kaiako, ka neke ai i ngā pūāhua e mōhiotia ki ngā pūāhua hou.
Kia kaha ki te whakarite akoranga kia taea ai e te mokopuna te whakaoti rapanga mā te whakamahi tikanga whakaaroaro.
Me whakatauira ngā rapanga mā te whakamahi rauemi, e hono ana ki ngā whakaahuahanga. Tautokohia ngā mokopuna ki te whakaopti rapanga mās te tautohu i ngā kupu matua, i ngā tūmahi me ngā paheko.
Me whakarite tūmahi mō ngā horopaki e mōhiotia ana e te mokopuna; ht, Tekau mā rua tamariki, he ngeru ā rātou. Tokowhitu tamariki, he kurī ā rātou. E hia katoa ngā mōkai?

Whakaakohia, tonohia ngā mokopuna ki te pupuri i ngā taunaki ā rātou akoranga

Tautokona ngā mokopuna ki te tuhi, te arotake, te hono, me te whakahiato whakaaro e tika ana.
Ka ui atu ki ngā mokopuna ki te whakaputa i ō rātou whakakaaro mā te whakamārama, te whakaahua, ā-kupu, ā-tohu, ā-pikitia, ā-tauira me ā rātou mahinga rānei.
Whakamaherehia ngā wā maha i te wiki mō ia mokopuna ki te ako te reo pāngarau mā te waihanga whakaaturanga tūtohi, he tūtohi taunga, te whakaingoa me te tuhi ki roto i ā rātau pukapuka, rorohiko, pūrere matihiko.
Tautokona ngā mokopuna ki te whakarite i ō rātau whakaaro. Ka taea e ngā mokopuna te tuhi kupu, te whakaoti rapanga, te whakarāpopototanga me te huritao mō ō rātau akoranga pāngarau, tēnā pea hei kupu, hei tohu pāngarau me te whānuitanga o ngā whakaaturanga.
Tautokona ngā mokopuna mā te rautaki ako “Whakapuaki Whakaaro” ki te whakaahua tau, āhua rānei ki te hanga, ki te tā rānei ā rātou urupare. Hei tauira. E whakaaro ana ahau ki tētahi āhua ahu-2, e whā ōna tapa, e rua o aua tapa he poto, e rua he roa. Tāngia, whakaingoatia hoki ngā wāhanga e ai ki tāu e whakaaro ana.

hoki ki runga ake

Pāngarau Kuputaka

A
ahu 3	3-dimensional
ahu-2	2-dimensional
āhuatanga pūmau	invariant property
aromātai	to evaluate
aroturuki	monitor
H
hātepe	steps; algorithm
hononga	relationship
hōpara	explore
horopaki	context
huritao	reflect upon
K
kīanga	phrase; expression
kīanga taurangi	algebraic expression
kitenga	finding
kōwhiringa	option; choice
M
māramatanga	understanding
matike	arise
O
otinga	outcome; effect
P
pākiki	curious
pānga rārangi	linear relationship
panoni	transformation; change
pāpātanga	rate
pāpono	event
parahau	justify
pūāhua	situation (like context)
pūhui	compound
pūkenga	skill
pūnaha	system
pūtahitanga	institution
pūtake	purpose
putanga, putanga iho	outcome
R
rahinga	quantity
rārangi whakarara	parallel lines
raraunga houanga	time series data
raraunga matarua	bi-variate data
raraunga motumotu	discrete data
raraunga whakarōpū	category data
raumata	net (of a solid shape)
rautaki	strategy
rawa	natural resources; resource; materials
T
takahuri	amend; alter; change
takirua raupapa	ordered pair
tāpaetanga kōrero	assertion
tāpua	significant
taputapu	tool; instrument
tau hiato	complex number
tau toitū	prime number
tau tōpū	integer
tauira raupapa	sequential pattern
tauira tāruarua	repeating pattern
taunaki (-tanga)	evidence
taupori	population
taupū	exponent
taurangi	variable; algebra
taurea	multiple
taurite	equilibrium
tautohe(tia)	contested
tautohu	identify
tauwehe	factor
tāwariwari	flexible
tipu	plant
tirohanga	perspective
tō	pull
tohu	symbol
toitū	lasting; sustainable
torotoro	explore
tūāhua	description of a person or thing
tuakiri	identity
tūāpapa	foundation; basis
tūārere	phase
tuhi	record
tūhuratanga tauanga	statistical investigation
tukutuku	grid
U
uara	value
urutau	adapt
W
wahapū	articulate
waihanga	shape; devise; create
wāwāhi	partition
whai wāhi (ki) …	participate; have opportunity
whakaahua	describe
whakaahuahanga	representation
whakaari raraunga	data display
whakaata	reflect
whakaawhiwhi	round (a number)
whakamahi	use; apply
whakamātau tika	fair test
whakaoti rapanga	problem-solving
whakatakoto	outline; propose
whakataurite	compare; contrast
whakatinana	implement
whakatutuki (matea tangata)	meet (peoples’ needs)
whakauru	engage; insert; include
whakaute	respectful
wheako	experience