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 3: Tau 7–8

Whāinga

Ka aro te ako a te mokopuna ki
te kōwhiri kaupapa tūhuratanga pāngarau me te whakatau he aha i kōwhiria ai ngā tikanga hei whakaoti rapanga me te aromātai pūāhua hoki.

Ka aro te ako a te mokopuna ki
te whakamahi pāngarau hei whakatutuki i ētahi kaupapa, māna anō, mā te kura, mā te hapori hoki.

Ka aro te ako a te mokopuna ki
te whakamārama i ngā putanga mā te whakamahi i ngā tikanga o te reo e hāngai ana ki ngā whenu pāngarau.

Ka aro te ako a te mokopuna ki
te waihanga me te whakaputa tauira, ‘tauira me te pānga’ e whakamārama ana i te mātauranga pāngarau e whakamahia ana.

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 3: Tau 7–8

Kia Mataara

Hei te mutunga o te tau 7 me mōhio te mokopuna ki te:

tūhura i te ariā o ngā tau ā-ira me ngā huatau hei torohanga o te pūnaha uara tū
tūhura tau tōpū
whakamahi i te tukanga tauanga pakirēhua (rapanga, mahere, raraunga, tātari, otinga) hei tūhura ā-raraunga i te hapori whānui tonu.

Hei te mutunga o te tau 7 me mōhio te mokopuna ki te:

tūhura i ngā horopaki e whai wāhi ana ngā tau tōrunga me ngā tau tōraro: h.t., te pūtea, te paemahana
whai māramatanga: - he whakapapa tō ngā huinga raraunga - he take ka kohi raraunga tangata, raraunga ao tūroa hoki, ka whakamāori ai - mā wai ngā raraunga e whai hua ai taua hunga, he pēhea hoki te kimi rautaki ki te tāwharau i a rātou.
whakaahua i te tūranga, i te ahunga me ngā huarahi mā te whakamahi i te ao tū roa, arā, ngā pūnaha mātauranga Māori, mā te whakamahi rānei i ngā tohu āwhata, ngā tohu kāpehu, me ngā āhuatanga taiao.

Hei te mutunga o te tau 7 me mōhio te mokopuna ki te:

whakamārama i te pūnaha uara tū mō ngā tau ā-ira me ngā tauoti
whakaputa mōhio ki ngā paheko i whakamahia mō ngā tau tōrunga me ngā tau tōraro
whakamahi kupu pāngarau pēnei i ēnei; tau toitū, hiato, tau pūrua.

Hei te mutunga o te tau 7 me mōhio te mokopuna ki te:

whai māramatanga ki ngā whanaungatanga rārangi tau (e whai wāhi ana te hautau me te hautanga ā-ira ki waenga i ngā tau tōpū, ko ngā tau tōraro, ka noho ki te taha mauī o te kore)
āhuatanga o ngā uara tū me tōna hāngai ki ngā tau-ā-ira
whakamahi i te ahunga me te mahere ki te whakatau i te taunga, te ahunga me ngā ara.

Hei te mutunga o te tau 8 me mōhio te mokopuna ki te:

tūhura i te hononga o ngā āhua ahu-2 ki te ahu-3.

Hei te mutunga o te tau 8 me mōhio te mokopuna ki te:

tūhura i ngā tauira Māori e whai pānga ana ki te mātauranga Māori me te tūhura i ngā āhuatanga pāngarau ki aua tauira, āhua hoki.

Hei te mutunga o te tau 8 me mōhio te mokopuna ki te:

whakaahua āhuatanga e whai wāhi ana ngā tau toitū, tau hiato, tau pūrua hoki.
whakamārama me te whai māramatanga ki ngā ture whakawehe o te 2, te 3, te 5, te 9, me te 10
whakamahi i ngā kupu me ngā tohu ki te whakaahua paheko āhuatanga kōaro, te āhuatanga tohatoha, te āhuatanga herekore me te kōaro
tautohu me te whakaputa kōrero mō te āhuatanga ki ngā paheko pāngarau rerekē.

Hei te mutunga o te tau 8 me mōhio te mokopuna ki te:

whai māramatanga ki ngā taurangirangi o ngā tau katoa
whai māramatanga he pāpātanga pūmau tō te tauira rārangi, me te pānga rārangi anō hoki. Ka whakaahuatia hei raupapa takirua, hei tūtohi, hei kauwhata X,Y, hei whārite (ture) rānei
tauira, te ia, te taurangirangi anō hoki ki roto i ngā whakaaturanga raraunga. Mēnā he rerekē te momo whakaaturanga, ka rerekē hoki ngā hua ka puta.

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 3: Tau 7–8

Te Ngako o te Whāinga

Mā te Kaiako

Tau 7
E tautoko ana te mokopuna kia:

waihanga me te whakarite i ngā momo pātai tūhuratanga huhua mō ngā horopaki huhua
whakahaere i tētahi tūhuratanga mā te whakamahi i te tūkanga tauanga pakirēhua
tīpako i te inenga e tika ana ki te ine i te horopaki me te āhuatanga o te wā.

Tau 7
E tautoko ana te mokopuna kia:

whakahono i ngā āhuatanga o tōna ao o ia rā ki ngā ariā pāngarau
tūhura i ngā momo tau me ngā whakamahinga o ērā ki ngā horopaki o ia rā.

Tau 7
E tautoko ana te mokopuna kia:

whakamahi i te reo o ngā tauoti, ngā hautau, me ngā tau tōpū
whakawhiti whakaaro me te whakaputa kōrero mō ngā āhuatanga kōaro, ngā āhuatanga herekore, me ngā āhuatanga tohatoha hoki.

Tau 7
E tautoko ana te mokopuna kia:

whakawhiti i waenganui i te huhua o ngā whakaahuahanga pāngarau ahakoa ōkawa, ōpaki rānei
waihanga i ngā tauira ahu-2, ahu-3 hoki
whakatauira i ngā kauwhata taurangi, kauwhata tauanga hoki.

Tau 8
E tautoko ana te mokopuna kia:

tūhura tauira i ngā tau tōpū
tautohu i ngā āhuatanga kōaro, āhuatanga herekore, āhuatanga tohatoha hoki
whai māramatanga ki ngā pānga me ngā tauira rārangi
huri i te maha o ngā inenga ngahuru.

Tau 8
E tautoko ana te mokopuna kia:

whai māramatanga he tohu tō ngā taurangirangi; hei tauira, ko te ‘t’ e tohu ana i te wā, ki reira tātou whakamahi ai i te waihanga whārite mō te nekehanga, mō te panonitanga rānei o ētahi horopaki
whai māramatanga ki te pānga o te rahinga rawa ka hokona me te moni whiwhi ka rite ki tētahi hononga i te ao pakihi
whai māramatanga ki te whakaahuahanga ahu-rua, ahu-3 hoki ki tōna marae.

Tau 8
E tautoko ana te mokopuna kia:

ako i ngā kupu ahunga mokowā, kia 8 ngā wehenga, me ngā tohu kāpehu Māori
waihanga me te pānui i te huhua o ngā kauwhata, ngā tūtohi, me ngā wātaka
whakaatu, me te whakawhiti putanga mō āna tūhuratanga mā te whakamahi i ngā pūtakenga reo huhua.

Tau 8
E tautoko ana te mokopuna kia:

mārama ki ngā momo hautau me te whakaahuahanga o ēnei momo tau
mārama ki te whakaahuahanga tāpiri, tango, whakarea, whakawehe hoki mō ngā momo hautau
whakaahua ki te whakaatu i ngā whakaaturanga raraunga
whakamahi i ngā whakaahuahanga ahunga mokowā.

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 3: Tau 7–8

Te Ngako o te Whāinga

Mā te Mokopuna

Kei te ako au ki te:

whakatakoto pātai tūhura, te whakapae me te whakatau tāpae kawatau mō tōku rohe, hapori hoki
whakatakoto pātai tūhura mō ngā pūāhua tūponotanga me ngā tūponotanga kāore e ōrite ana ngā putanga.

Kei te ako au ki te:

wāhi e taea ai te whakamahi tauoti me ngā hautau
horopaki e taea ai te whakamahi ngā tau tōrunga me ngā tau tōraro
tikanga matatika mō te kohikohi, te tātari, me te whakatakoto putanga raraunga
whakatau tata i te inenga o ngā taonga o ia rā me te matapaki tirohanga e pā ana ki te kōrero tika o tērā inenga, te aha rānei
whakatakoto paerewa inenga mō ētahi taonga tūturu o tēnei ao tūroa.

Kei te ako au ki te:

āhukahuka, te pānui, te tuhi, te whakaatu, te whakataurite, te raupapa, me te takahuri i ngā hautau, ngā tau ā-ira, me ngā ōrau
whakamahi kupu, tohu hoki ki te whakaahua me te whakaatu i ngā āhuatanga paheko, arā, āhuatanga kōaro, āhuatanga herekore, āhuatanga tohatoha, kōaro me te tūmau
pānui tika i ngā wā-ringa, wāmati hoki, me te whakamāori tika i ngā āwhata
pānui, te whakamāori, me te whakamahi wātaka, tūtohi hoki ki te whakaatu atu i ngā pārongo inenga
tātari raraunga me te whakawhiti putanga ki roto i ngā horopaki
whakamahi tika i ngā waeine ngahuru mō te roanga, te horahanga, te rōrahi, te kītanga, te papatipu, te paemahana, te putunga raraunga, te wā, me te koki
whakahua kupu me ngā tau ki te whakamāori tika i ngā āwhata
whakamahi tūmau pērā i te ‘ōrite’, ‘tairite’, ‘whakarara’, ‘hāngai’ ki te tautohu āhuatanga, ki te tautohu hoki i ngā āhua pēnei i te ‘tapawhā’, ‘tapatoru’, ‘porowhita’, aha atu ki te whakarōpū āhua.

Kei te ako au ki te:

whakaahuahanga tauoti me ngā tau ā-ira ki te pū ngahuru
pānga i waenganui i ngā momo hautau rerekē
whakaahuahanga me te hono i ngā pānga rārangi mā te whakamahi tūtohi, whārite, kauwhata XY hoki
whakaahua ā-hinengaro me te tuhi raumata poro e mau ana i tētahi motuhanga pūmau. Me whakamahi he tirohanga mahere ki te whakaahua ā-hinengaro, me hanga hoki i ngā āhua ahu-3
pānga i waenganui i ngā inenga mō ngā āhua āhuahanga me ngā āhuatanga o ērā āhua
pānga i waenganui i ngā āhua ahu-2 me ngā āhua ahu-3
whakamahi whakaahuahanga raraunga hei whakaahua i ngā putanga ka kitea.

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 3: Tau 7–8

Te Roanga o te Kōrero

Te Āhua o te Mokopuna
E ngahau ana tā te mokopuna whakamahi i ngā tūhuratanga ki te whai māramatanga mō ngā huatau me ngā ariā pāngarau, ngā pūāhua, ngā pātai tūhura me ngā rapanga mā te whakamahi mōhiotanga pāngarau ki ngā wāhi e whai take ana.

E taea ana e te mokopuna te arohaehae te pāngarau ka whakamahia, te whakamahi ngā taputapu me te reo pāngarau ki te arohaehae pūāhua me ngā putanga e pā ana ki ngā rapanga e whai take ana ki tōna ao.

Te Āhua o te Mokopuna
E whanake ana tā te mokopuna arohaehae i āna mahi pāngarau ki tōna ao o ia rā, me tōna āhei ki te tīpako i ngā ritenga me ngā rerenga kētanga o te ao Māori me te ao pāngarau.

E mōhio ana te mokopuna ki te whai take o te pāngarau hei whakatutuki i ōna hiahia mō tōna anamata.

E whakaaro ana te mokopuna ki ngā take o te takiwā, o te ao whānui hoki, me te pānga o tōna māramatanga pāngarau ki te panoni me te hāpai ake i ngā āhuatanga e whai hua ai mō te takiwā me te ao whānui.

Te Āhua o te Mokopuna
E ui ana te mokopuna i ngā pātai whai kiko, arotahi, hāngai hoki, e pā ana ki tōna anō ao.

E āhei ana te mokopuna ki te whakamahi i te reo pāngarau whānui ki te whakawhiti whakaaro mō āna tūhuratanga pāngarau me ngā putanga.

E taea ana e te mokopuna te matapaki āna tūhuratanga me ngā putanga hei mema o ētahi hapori pāngarau, (mōhio ia ki te mahi ngātahi i tōna ngākau whakaute ki ētahi atu ki reira matapaki ai, tautohe ai hoki i te painga o āna putanga pāngarau ki te minenga).

Ka whakamahi te mokopuna i te reo pāngarau ki te aromātai me te huritao i te ao hurihuri, ka mutu, i te pāngarau ka whakamahia e rātou (h.t., ko te kauwhata i tīpakohia, te kauwhata pai rawa atu hei whakaatu i ngā putanga o tāna tūhuratanga).

E mārama ana te mokopuna ki te whakahuri i tōna reo pāngarau ina whakawhiti whakaaro ai ia ki ngā rōpū tāngata kanorau, ki ngā pūāhua rerekē hoki.

Te Āhua o te Mokopuna
Kua kite te mokopuna ko tā te pāngarau he āhukahuka i ngā tūmomo tauira rerekē, he whakaahua āhuatanga, he kite i a ia ki ngā wāhi katoa, ka mutu, he whai whakaaro ki ngā āheinga me ngā ahunga kē atu o ētahi mea.

E mārama ana te mokopuna me pēhea te whakamahi i ngā whakaaro arorau pāngarau me ngā whakatau whānui kia mārama ai ngā pūāhua, ā, hei whakaoti rapanga hoki.

E taea ana e te mokopuna te whakaahua tikanga ahurea pāngarau kei kō atu i te ahurea me ngā tikanga Māori, mā konā whakamahia ai aua tūāhua i waho i te akomanga.

Ka whai hononga te mokopuna puta noa i ngā wāhanga o te pāngarau, me ētahi atu wāhanga ako hoki.

E tipu ana te māia o te mokopuna ki te whakamahi tāiringa kōrero, ki te kimi hāpono hoki.

Ngā tini mata o te tuakiri
Ko ngā tūhuratanga pāngarau ka tautoko i te mokopuna ki te aro ki ngā mahi a ētahi atu, ki te whakaoti āhuatanga, ki te aronga a ētahi atu tāngata, ā, e whai mātauranga ana kia pēhea āna mahi e whai pānga ai, e tautoko ai i a ia ki te mahi takitahi, mahi ngātahi hoki. E ngākau auaha ana te mokopuna ki āna mahi pāngarau.

Ngā tini mata o te tuakiri
E mārama ana te mokopuna ki te ahurea pāngarau e mau ana ki tōna ake reo me āna ake tikanga, ahakoa te rerekē o tērā ki tōna ake ahurea, ā, e pai ana tana whai whakaaro ki aua whakaaro ahurea rerekē i te wā kotahi. E mōhio ana ia e kore e rerekē tōna mana āhua ake, ahakoa e puta pea ai he hapa pāngarau.

Ngā tini mata o te tuakiri
I te nuinga o te wā, e māia ana te mokopuna ki te whakawhiti whakaaro e pā ana ki ōna huatau pāngarau me āna putanga; ina e whai wāhi ana ki ngā āheinga matapaki, whakawhiti kōrero ki ngā minenga whānui tonu.

Ngā tini mata o te tuakiri
E whai pānga ana te mokopuna ki ngā mātauranga pāngarau mō te mahi pāngarau te take, me ngā tukanga o te whakamahi pāngarau i tōna ao o ia rā.

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 3: Tau 7–8
Te Roanga o te Kōrero

Tau

Ngā Tini Mata o te Ako

Kei te ako te mokopuna ki te:

whakaoti i ngā rapanga whakarea, whakawehe hoki mō ngā tauoti, hautau, tau ā-ira, ōrau ki te whānuitanga o ngā rautaki mō ngā momo rapanga me ngā momo tau
whakaoti i ngā rapanga tau mati-2, tau mati-3, mā te whakamahi whakamahi rautaki wāwāhi uara tū, tikanga paremata rānei mehemea he tata ki te tau māmā.

Ko ngā rautaki matua hei whakamahi mā te mokopuna, ko te:

whakaoti rapanga whakarea māmā me ngā rapanga hautanga māmā mā te whakamahi i ngā meka matua
whakaputa otinga ki ngā rapanga whakareatanga, whakawehenga, ā, mā te whakamahi i ngā meka matua me ngā rautaki ā-hinengaro
whakamahi rautaki wāwāhi uara tū, tau māmā me te tikanga paremata, tāpiritanga ōrite me te pāheko kōaro
kimi hautanga o tētahi rahinga mā te toharite
whakaoti rapanga mā te hanga tekau, te tau māmā me te tikanga paremata, te wāwahi uara tū me ngā meka e mōhiotia ana (ngā rearua).

Ngā Tini Mata o te Mātauranga

Te Hanga o ngā Tau

Tau 7
Kei te ako te mokopuna ki te:

Tau 8
Kei te ako te mokopuna ki te:

tautohu, te pānui, te tuhi, te whakatairite me te raupapa tauoti ki ngā pū o te 10:
ht; 10,000 = 10⁴.

tautohu, te pānui, te tuhi, te whakatairite me te raupapa tauoti me ngā tau-a-ira ki ngā pū o te 10:
h.t., 0.01 =1—100 = 10⁻².

kimi i te tauwehe pātahi nui rawa o ngā tau e rua ki te 100
kimi i te taurea e pātahi iti rawa o ngā tau ki te 10
whakamahi taupū hei tuhi whakareatanga tāruarua me te tautohu pūtakerua ki te 100.

whakamahi i ngā tauwehe toitū ki te whakaahua i tētahi tau kia kite i te tauwehe pātahi nui rawa o ngā tau e rua
tautohu tau tōitū, ngā tau hiatō ki te 100, me ngā pūtakerua ki 125.

Ngā Paheko

Kei te ako te mokopuna ki te:

whakaāwhiwhi me te whakatau tata ki te whakapae me te āta tiro ki te tikanga o ngā tātai
whakaāwhiwhi tauoti ki ngā taurea kua tautohua e pātata ana, ki ngā pū-10 rānei e pātata ana
whakaāwhiwhi i ngā tau-ā-ira ki te hautekau, haurau, tauoti rānei e pātata ana
whakarea tauoti.

whakaāwhiwhi me te whakatau tata ki te āta tiro ki te te tikanga o ngā tātai.

whakawehe tauoti ki tauwehe mati-1, mati-2 rānei:
h.t., 327 ÷ 5 = 65.4 or 65 2—5.

whakawehe tauoti:
h.t., 327 ÷ 15 = 21.8 or 21 4—5.

whakaraupapa, te whakatairite, te tāpiri, me te tango tau tōpū mā te whakamahi taputapu, h.t., tātaitai.

whakaraupapa, te whakatairite, te tāpiri, me te tango tau tōpū.

Ngā Tau Whakahau

Kei te ako te mokopuna ki te:

tautohu, te pānui, te tuhi, te whakaahua hautanga, tau-a-ira (kia 3 ngā mati ā-ira ) me ngā ōrau.

tautohu, te pānui, te tuhi, te whakaahua hautanga, tau-a-ira me ngā ōrau.

whakatairite, te raupapa me te huri i ngā hautau, tau-a-ira (kia 3 ngā mati ā-ira) me ngā ōrau.

whakatairite, te raupapa me te huri i ngā hautau, tau-a-ira me ngā ōrau.

whakarea me te whakawehe tau ki ngā pū-10.

whakarea me te whakawehe tau ki ngā pū-10.

kimi hautau ōrite, te whakarūnā hautanga me te huri hautanga nui atu i te kotahi hei tau hanumi, tau hanumi hei hautanga nui atu i te kotahi rānei.

kimi hautau ōrite, te whakarūnā hautanga me te huri hautanga nui atu i te kotahi hei tau hanumi, tau hanumi hei hautanga nui atu i te kotahi rānei.

whakarea hautanga me ngā ngā tau-a-ira ki ngā tauoti me te kimi ōrau o tētahi tauoti.

whakarea hautanga me ngā ngā tau-a-ira ki ngā tauoti me te kimi ōrau o tētahi tauoti.

kimi i te rahinga mena e mōhio ana ki te hautanga māmā, te tau ā-ira rānei o te rahinga:
h.t., 25% o te rahinga, ko te $100, nō reira, he aha te rahinga?

kimi i te rahinga mena e mōhio ana ki te hautanga, te tau ā-ira rānei o te rahinga:
h.t., 75% o te rahinga, ko te $45, nō reira, he aha te rahinga?

tāpiri me te tango hautanga, rerekē ana te tauraro ki ngā hautekau:
h.t., 3—4 + 1—3.

tāpiri me te tango hautanga he rerekē te tauraro mā te whakamahi hautau ōrite.

whakamahi whakaaro pānga riterite ki te tūhura i te pānga o ngā rahinga:
h.t., e 3 pōro whero ki ngā pōro kikorangi e 7. E hia katoa ngā pōro mehemea 18 ngā pōro whero?

whakamahi whakaaro pānga riterite ki te toha rahinga rerekē:
h.t., ka tohatoha i ngā kāri 100. Mō ia kāri ka riro i ahau, ka riro i a koe e 3. E hia ngā kāri o tēnā, o tēnā o tāua?

Mātau Ahumoni

Kei te ako te mokopuna ki te:

tātai utu me te wāwāhinga moni ahakoa te rahinga o te moni.

waihanga me te whakatairite mahere ahumoni ā-wiki, ā-marama, ā-tau:
h.t., te penapena pūtea, ngā mahere utu waea pūkoro, ngā mahere pūtea me ngā hoko harangote.

tātai i te whakahekenga ōrau mō ngā rahinga tāra:
h.t., te 35% o te $180?

tātai whakahekenga ōrau.

Ngā Tini Mata o Te Reo o Tau

E mōhio ana ki ngā kupu nei:

wāwāhinga moni
mati ā-ira
tauwehe pātahi nui rawa
taurea pātahi iti rawa
ōwehenga
pānga riterite
tau tōrunga
tōraro
tau māmā
tikanga paremata
whakarūnā
whakahekenga ōrau
hautanga nui ake i te kōtahi
tau hanumi
huri
whakaāwhiwhi
taupū
pūtakerua.

mahere pūtea
mahere ahumoni
pānga riterite
tauwehe pātahi nui rawa
taurea pātahi iti rawa
tau māmā
tau toitū
tikanga paremata
whakarūnā
hoko harangote
whakahekenga ōrau
pū-10
taupū
pūtakerua
hautau māmā
tau tōpū
tau toitū
tau hiato
tauraro.

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 3: Tau 7–8
Te Roanga o te Kōrero

Taurangi

Ngā Tini Mata o te Ako

Kei te ako te mokopuna ki te:

whakaoti rapanga e hāngai ana ki ngā tauira raupapa mā te whakamahi i ngā whakaaturanga maha pērā i ngā tūtohi, ngā kauwhata,
ngā ture hoki.

Ngā Tini Mata o te Mātauranga

Te Whakawhānui Āhuatanga Tau

Tau 7
Kei te ako te mokopuna ki te:

Tau 8
Kei te ako te mokopuna ki te:

tūhura whakareatanga kōaro (te tau me te tau huripoki) ki ngā tau whakarea.

tūhura tāpiritanga kōaro hei tāpiri me te tango taurunga me ngā tau tōraro (tau takirua me ngā tauaro):
h.t., −6 + 8 = −6 + 6 + 2.

whakamahi āhuatanga kōaro, herekore, tūmau, kōaro hoki ki ngā kīanga tae rā anō ki ngā tau tōraro.

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

tautohu me te whakaahua ngā āhuatanga o ngā tau toitū me ngā tau hiato me te tūhurua i ētahi atu ture whakawehetanga.

Whārite me te Hononga

Kei te ako te mokopuna ki te:

whakaahua me te whakamahi āhuatanga kōaro, herekore, tohatoha,
h.t., O × _ = _ × O.

whakarūnā rautaki taurangi e whai wāhi ana ki ngā tapeke, ngā otinga, ngā rerekētanga me te whakawhānui hoki i ngā kīanga ki te āhuatanga tohatoha:
h.t., 2 (x + 3) + 1 = 2x + 6 + 1 = 2x + 7.

kimi uara o tētahi kīanga, tētahi whārite rānei kua hoatu i ngā uara o ngā taurangirangi:
h.t., tātaihia w + 12 mehemea w = 4.

kimi uara o tētahi kīanga, tētahi whārite rānei kua hoatu i ngā uara o ngā taurangirangi.

tautohu i te pāpātanga o te whiti me te uara o tētahi tauira rārangi, tuhi ai i te whārite hei taurangi me ngā tohu taurangi hei tuhi i te ture, ā, whakamahia te ture ki te whakapae.

whakatau mēnā he tōtika te tauira, ā, mehemea āe, tuhia te whārite mō te tauira, ka whakamahi ai te whārite.

whakaatu i ngā pūāhua, i ngā pakitau rānei mā te whakamahi i te whārite, ngā tūtohi me ngā kauwhata XY.

whakaatu i ngā pūāhua, i ngā pakitau rānei mā te whakamahi i te whārite, ngā tūtohi me ngā kauwhata XY.

whai māramanga ki te pānga o tētahi taurangirangi ki te panoni i tētahi atu taurangirangi.

tautohu i te tikanga o tuaka pou, te tuaka pae, me ngā huinga takirua raupapa ki te whakaahua i te pānga o ngā taurangirangi ki te kauwhata
tautohu i te pikitanga o te kauwhata rārangi hei whakaatu i te pānga kei waenganui i ngā taurangirangi.

Whakaaro Pāhekoheko

Kei te ako te mokopuna ki te:

waihanga, te whakamātau, te whakahou hoki i ngā hātepe e whai wāhi ana tētahi raupapatanga hātepe me tētahi whakataunga: h.t., whakamātau mena rānei e taea ana te whakawehe i ētahi tau ki te 2, 3, 4, 5, 9, 10.

waihanga, te whakamātau, te whakahou hoki i ngā hātepe ki te tautohu, te whakamāori, te whakamārama hoki i ngā tauira: h.t., whakarōpū tau hei tau toitū, hei tau tapatoru rānei.

Ngā Tini Mata o Te Reo o Taurangi

E mōhio ana ki ngā kupu nei:

taurangi
whārite
huinga takirua raupapa
kauwhata rārangi
tūtohi
tuaka pae
tuaka pou
whakamāori
whakahou.

pānga rārangi torotika
pānga rārangi kōpiko
tuaka pae
tuaka pou
taurangirangi
hātepe
rautaki taurangi
whakamāori
whakahou.

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 3: Tau 7–8
Te Roanga o te Kōrero

Ine

Ngā Tini Mata o te Ako

Kei te ako te mokopuna ki te:

whakamahi i ngā taputapu me ngā tātai māmā hei ine paenga, ine horahanga, ine rōrahi, ine moni me te ine wā
whakarea me te whakawehe, waeine ngahuru whai pānga ki te 10.

Ngā Tini Mata o te Mātauranga

Tau 7
Kei te ako te mokopuna ki te:

Tau 8
Kei te ako te mokopuna ki te:

whakatau tata, ka ine i te roa, te rōrahi, te kītanga, te papatipu, te paemahana, te raraunga pūrokiroki, te wā, me ngā koki mā te whakamahi waeine e whai take ana.

whakatau tata, kātahi ka ine i te roa, te rōrahi, te kītanga, te papatipu, te paemahana, te raraunga pūrokiroki, te wā, me ngā koki mā te whakamahi waeine e whai take ana.

kōwhiri me te whakamahi waeine e tika ana (h.t., mita (m), karamu (g), rita(l)) mō te pūnaha ngahuru me te whakamahi hoki i te kuhi (h.t., mitarau (cm), manokaramu (kg), ritamano(ml)) hei whakaatu i te rahi o ngā waeine.

kōwhiri me te whakamahi waeine e tika ana mō te pūnaha ngahuru me te whakamahi hoki ngā kuhi hei whakaatu i te rahi o ngā waeine.

huri i ngā waeine o te roa, te papatipu me te kītanga mā te whakamahi i ngā tauoti me ngā tau ā-ira ki te whakaatu i tētahi huinga:
h.t., 724 g = 0.724 kg.

huri i waenga i ngā waeine, me ngā waeine pūrua hoki.

kimi i te tere mai i te tawhiti me te wā.

kimi i te tawhiti mai i te tere me te wā, i te wā rānei mai i te tawhiti me te tere.

Te Paenga, Te Horahanga, Te Rōrahi

Kei te ako te mokopuna ki te:

tātai i te paenga me te horahanga o ngā āhua pūhui kua hangā ki te tapatoru me te tapawhā hāngai.
tautohu he ōwehenga auau te pānga o te paenga me te whitianga, te pūtoro rānei:
h.t., 1 g = 1 ml = 1 cm³.

tātai i te rōrahi o ngā poro tapatoru me ngā momo poro kua hangā ki ngā poro tapawhā hāngai.

Te Wā

Kei te ako te mokopuna ki te:

pānui, te whakamāori me te whakamahi wātaka me ngā tūtohi e whakaatu ana i ngā whakamahukitanga ine.

pānui, te whakamāori me te whakamahi wātaka me ngā tūtohi e whakaatu ana i ngā whakamahukitanga ine.

huri ki waenga i ngā waeine o te wā me te whakaoti rapanga wā e whai wāhi ana te hautanga o te wā.

e mōhio ana ki te tuhi me te whakaatu wā-24.

Ngā Tini Mata o Te Reo o Ine

E mōhio ana ki ngā kupu nei:

inenga pāpātanga (h.t., i te km/h me te utu/kg)
paenga
horahanga
rōrahi horahanga
tapawhā hāngai
kuhi (affix)
mita (m)
karamu (g)
rita (l)
mitarau (cm)
manokaramu (kg)
ritamano (ml).

wā24-hāora
poro
poro tapatoru
tawhiti
tere
waeine
waeine pūrua
pūnaha
kuhi
roa
rahi
rōrahi
kītanga
papatipu
paemahana
raraunga pūrokiroki.

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 3: Tau 7–8
Te Roanga o te Kōrero

Āhuahanga

Ngā Tini Mata o te Ako

Kei te ako te mokopuna ki te:

whakaingoa, te whakaahua, te tuhi hoahoa raumata mō ngā āhua ahu-3
tā me te tuhi tukutuku, ngā takirua raupapa me ngā mahere māmā hoki hei whakaatu taunga
whakaatu panoni ki runga i te tukutuku
whai māramatanga ki ngā āhuatanga o ngā momo poro rerekē, ki te hoahoa i ngā momo poro me ngā hoahoa koeko raumata
whakaahua i te taunga, te tuku ahunga mā te whakamahi i te pū tukutuku me ngā tohu matua o te kapehu
hanga me te whakamārama i te hua o te panonitanga o te tauira.

Ngā Tini Mata o te Mātauranga

Ngā Hanga

Tau 7
Kei te ako te mokopuna ki te:

Tau 8
Kei te ako te mokopuna ki te:

whakarōpū hanga e ai ki tōna āhuatanga, me te whakaingoa i ngā rōpū hanga motuhake.

whakaahua tapatoru, tapawhā me ērā atu taparau e ai ki te hanga o ngā tapa, ngā hauroki me ngā āhuatanga koki.

tautohu, me te whakaahua koki kei tētahi pūwāhi, ngā koki kei te rārango tōtika, me ngā koki tauaro poutū.

kimi koki ki ngā pūāhua e whai koki ana kei tētahi pūwāhi, ngā koki ki te rārangi tōtika, ngā koki tauaro poutū, ngā koki whakaroto o ngā tapatoru me ngā taparau.

Te Whakaaro Mokowā

Kei te ako te mokopuna ki te:

whakaahua ā-hinengaro, te waihanga, te tuhi mahere mō ngā poro 3D ki nga hanga poro, ā-rorohiko, a pepa tukutuku; tirohanga mai i mua, mai i muri, mai i runga, mai i raro, mai i te taha matau, mai i te taha mauī.

whakaahua a-hinengaro me te tuhi raumata mō ngā poro e whiwhi wāhanga whakawhiti.

whakarerekē i te rahi o tētahi āhua ki tētahi tauoti, ki tētahi hautanga waetahi iti ake i te kotahi rānei hei panoni hanga ahu-2 me ngā hanga hiato
whakamahi i ngā āhua Toi Māori:
h.t., kōwhaiwhai hei waihanga tauira panoni.

āhukahuka i ngā āhuatanga pūmau o ngā hanga ahu-2 me te ahu-3 ki ngā panoni rerekē
whakarahi me te whakaiti hanga ki te taurahi
mōhio ki te pānga kei waenga i te taurahi, te horahanga me te rōrahi
whakahono pānonitanga:
h.t., te nekehanga me te whakaatatanga
whakamahi i ngā āhua Toi Māori pērā i te kōwhaiwhai hei waihanga tauira panoni.

Te Tūnga me te Ahunga

Kei te ako te mokopuna ki te:

whakamāori me te whakawhiti kōrero mō ngā tūnga me ngā ahunga o ngā taunga, ine koki, me ngā ahunga matua e 8 o te kāpehu:
h.t., 45° = rāwhiti mā raki.

whakamahi mahere āwhata, ahunga kapehu, tawhiti ka huri ai ki te whakamāori me te whakawhiti kōrero mō ngā tūnga, ngā ahunga me ngā tukutuku tūnga tohutoro.

tuku tohutohu mā ngā putu. Kei 0° te raki, ka haere whakatekaraka ngā putu. E 360° te katoa o ngā putu. Kei 90° te rāwhiti, kei 270° te uru. Ka whakamahi i ngā pito ō te kāpehu e te kaiwhakatere ki te urungi i ngā waka.

tikanga o te ara kāpehu e whakahaere nei i tētahi mea, te wāhi e arotia ana rānei. Ko te koki te inenga o ngā putu e ahu ana ki tētahi pūwāhi. Ka whai whakatekaraka ngā putu mai i te rārangi raki.

Ngā Tini Mata o Te Reo o Āhuahanga

E mōhio ana ki ngā kupu nei:

taurahi
tauiti
ōwehenga
koki whakaroto
koki tauroto
āwhata
tirohanga (mai i) runga
tirohanga (mai i) mua
tirohanga (mai i te) matau
tirohanga (mai i te) mauī
panoni
hanga hiato
tūnga
ahunga
koki tauaro poutū
ā-rorohiko
putu.

koki tāhapa
koki hāpūpū
koki rārangi
koki huripū
koki rāwaho
koki whakahāngai
koki whakarārangi
koki whakahuripū
koki tauaro
koki whakaroto
koki tauroto
koki taurite
koki tauwhiti
tāroa
wāhanga whakawhiti
whakaatatanga
nekehanga
whakarahi
whakaiti
taurahi
tauiti
horahanga
rōrahi
raumata
koki tauaro poutū.

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 3: Tau 7–8
Te Roanga o te Kōrero

Tauanga

Ngā Tini Mata o te Ako

Kei te ako te mokopuna ki te:

whakarite i ngā pātai whakatairite e hāngai ana ki ngā raraunga matarua, ngā raraunga matatini, ngā raraunga houanga hoki
waihanga me te whakamāori kauwhata rārangi, kauwhata pouhere, kauwhata pou hiato
whakarite i ngā pātai tūhura mō ngā pāpori whānui
kohikohi me te whakaatu i ngā raraunga tatau mā te whakamahi whakaari raraunga ki te kimi tauira i roto, i waenga, kei tua hoki o ngā raraunga, ka tautohu i ngā āhuatanga rerekē
āhukahuka mēnā rānei me whakapai i ngā raraunga me te matapaki i te pūtake o ngā rerekētanga o ngā raraunga
matapaki i ngā kitenga mā te whakamahi i ngā whakaari tika e hāngai ana ki tētahi horopaki.

Ngā Tini Mata o te Mātauranga

Te Whakarite Rapanga

Tau 7
Kei te ako te mokopuna ki te:

Tau 8
Kei te ako te mokopuna ki te:

tūhura, te whakarāpopoto me te whakataurite mokowā me te pānga o ngā pūāhua mō ngā raraunga whakarōpū mā te whakamahi raraunga matatini;
- whakarite pātai tūhura mō ngā take ā-hapori
- whakapae, tāpae rānei i ngā kitenga.

tūhura, te whakarāpopoto me te whakataurite mokowā me te pānga o ngā pūāhua mō ngā raraunga whakarōpū mā te whakamahi raraunga matatini;
- whakarite pātai tūhura mō ngā take ā-hapori
- whakapae, tāpae rānei i ngā kitenga.

Te Whakamahere

Kei te ako te mokopuna ki te:

whakamahere me pēhea te kohi me te kimi raraunga ki te whakautu pātai tūhura me te:
- whakatau, te tautohu rānei i ngā taurangirangi e hiahiatia ana
- whakamahere me pēhea te kohi raraunga mō ia taurangirangi (h.t., me pēhea te ine i ngā taurangirangi), te kimi rānei i pēhea i kohia ai
- tautohu i te rōpū e arohia ana, tautohua rānei i a wai te raraunga
- aro ki ngā tikanga matatika o te kohi raraunga mā te whakarite pātai mō te āhua o ngā raraunga, te āhua o ngā tikanga kohi raraunga anō hoki
- tautohu i ngā taurangirangi me te whakarite mahere e whakamahi ai ōngā tirohanga tauanga.

whakamahere me pēhea te kohi me te kimi raraunga ki te whakautu pātai tūhura me te:
- whakatau, te tautohu rānei i ngā taurangirangi e hiahiatia ana
- whakamahere me pēhea te kohi raraunga mō ia taurangirangi (h.t., me pēhea te ine i ngā taurangirangi), te kimi rānei i pēhea i kohia ai
- tautohu i te rōpū e arohia ana, tautohu rānei i a wai te raraunga
- aro ki ngā tikanga matatika o te kohi raraunga mā te whakarite pātai mō te āhua o ngā raraunga, te āhua o ngā tikanga kohi raraunga anō hoki
- whakatau i ngā taurangi hei ine me ngā waeine e hāngai ana
- whakatau me pēhea te ine taurangi.

Te Kohi Raraunga

Kei te ako te mokopuna ki te:

kohi raraunga me te:
- kimi hapa ka whakatika ai, mena he hapa
- whakarite i te papakupu raraunga hei āwhina i ētahi ki te whai māramatanga ki ngā whakamahukitanga whai tikanga mō tētahi horopaki.

kimi raraunga kua kohia kētia e tētahi tangata, tētahi kamupene, te aha rānei me te whakamārama i ngā taurangirangi ki ngā papakupu raraunga.

Te Tātari me te Whakatau

Kei te ako te mokopuna ki te:

waihanga me te whakaahua i ngā whakaaturanga mō te whakarāpopoto, whakatairite, pānga, tūhura houanga me te kōtui horopaki me ōna āhuatanga
whakahono me te matapaki i te horopaki hei whakautu i te pātai tūhuratanga ki ngā taunaki o te tātari
whakatairite kitenga, ngā whakapaenga tuatahi, ngā tāpaetanga rānei, ki ngā mātauranga o te ao i tēnei wā nei
matapaki i ngā kitenga o te horopaki hei whakautu i te pātai tūhura mā te whakamahi i ngā taunakitanga o te tātari.

waihanga me te whakaahua i ngā whakaaturanga mō te whakarāpopoto, whakatairite, pānga, tūhura houanga mā te whakamahi i ngā whakaaturanga huhua me te kōtui horopaki me ngā tirohanga rerekē o ōna āhuatanga
tūhonohono, te whakawhiti kōrero mō te horopaki hei whakautu i te pātai tūhuratanga ki ngā taunaki o te tātari
whakatairite kitenga, ngā whakapaenga tuatahi, ngā tāpaetanga rānei, ki ngā mātauranga o te ao i tēnei wā nei
matapaki i ngā kitenga o te horopaki hei whakautu i te pātai tūhura mā te whakamahi i ngā taunakitanga o te tātari me ngā tapae kōrero tūtahi.

Ngā Tini Mata o Te Reo o Tauanga

E mōhio ana ki ngā kupu nei:

tau toha ōrite
tau waenga
tau tānui
inenga whānui
tuari
tāpaetanga kōrero
taunaki
taupori
tīpako
matapōkere.

E mōhio ana ki te whakamahi i te kauwhata pou whakaapaapa me te kauwhara pouhere ki te whakaari raraunga.

tōtika
haukume
tikanga
matatika
kauwhata pouhere
raraunga motukore.

E mōhio ana ki te whakaari raraunga mā te whakamahi i tētahi kauwhata pouhere.

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 3: Tau 7–8
Te Roanga o te Kōrero

Tūponotanga

Ngā Tini Mata o te Ako

Kei te ako te mokopuna ki te:

tautohu me te whakamārama i ngā hapa kei roto i ngā kīanga me ngā tūhura tauanga o ētahi atu
tautohu he nui ake rānei, he iti iho rānei, te putanga o tētahi pāpono mā te tuhi nahanaha i ngā whakamātau tūponotanga.

Ngā Tini Mata o te Mātauranga

Tau 7
Kei te ako te mokopuna ki te:

Tau 8
Kei te ako te mokopuna ki te:

whakamahere me te whakahaere whakamātau tūponotanga mō ngā pūāhua tūpono me te whakahaere i te maha o nga whakamātau mā te whakamahi hangarau:
- whakatakoto pātai tūhura
- tautohu, ka whakapae ai i ngā putanga mō ngā pātai kua whakatakotoria
- whakatau i te maha o ngā whakamātau me ngā momo hangarau ka whakamahia me te tikanga tuhi o ngā putanga
- kohi me te tuhi raraunga
- waihanga whakaaturanga raraunga ki te tuku i ngā putanga o ngā whakamātau tūponotanga me ngā putanga kei hua o ngā tauira tūponotanga tātai
- whakaahua i ngā whakaaturanga
- kimi i ngā whakataunga tūponotanga mō ngā putanga rerekē
- whakapae putanga tātai me te tūponotanga herekore mō ngā pūāhua kāore ōna tauira tātai
- tautohu i nga ōritenga me ngā rerekētanga i waenga i ngā kitenga me ngā kitenga a ētahi atu
- arohaehae i ngā putanga e hiahiatia ana
- tautohu i ngā ōritenga me ngā rerekētanga kei waenga i ngā kitenga mai i ngā whakamātau tūponotanga me ngā ariā tūponotanga e hāngai ana.

whakamahere me te whakahaere whakamātautau tūpono mō ngā pūāhua tūpono tae atu ki te whakahaere i te maha o nga whakamātautau ki te whakamahi hangarau mā te:
- whakatakoto pātai tūhura
- tautohu, ka whakapae i ngā putanga mō ngā pātai kua whakatakotoria
- whakatau i te maha o ngā whakamātau, ngā momo hangarau ka whakamahia me te tikanga tuhi o ngā putanga
- kohi me te tuhi raraunga
- waihanga whakaaturanga raraunga ki te tuku i ngā putanga i ngā whakamātau tūponotanga me ngā whakataunga mō ngā tātai tūponotanga e hāngai ana.
- whakaahua i ngā whakaaturanga
- kimi i ngā whakataunga tūponotanga mō ngā putanga rerekē
- whakapae putanga tātai me te tūponotanga herekore mō ngā pūāhua kāore ōna tauira tātai
- tautohu i nga ōritenga me nga rerekētanga i waenga i ngā kitenga me ngā kitenga a ētahi atu
- arohaehae i ngā putanga e hiahiatia ana.
- tautohu i ngā ōritenga me ngā rerekētanga kei waenga i ngā kitenga mai i ngā whakamātau tūponotanga me ngā ariā tūponotanga e hāngai ana.

Te Arohaehae Whakaaro Tūponotanga

Kei te ako te mokopuna ki te:

whakaae, whakahē rānei ki ngā whakatau a ētahi atu mā te tuku tūpātai mō ā rātau whakamātau tūpono.

whakaae, whakahē rānei i nga whakatau a ētahi atu mā te ruku hōhonu ake ki ngā whakaaro pāngarau hei tūpātai, hei whakamārama hoki i ngā whakamātau tūpono.

āhukahuka i ngā kerēme, ngā pōhēhē rānei e pā ana ki ngā pūāhua tūponotanga.

Ngā Tini Mata o Te Reo o te Tūponotanga

E mōhio ana ki ngā kupu nei:

taurangitanga
tuari
haukume
tōkeke
putanga tātai
tauira tātau
putanga
whakamātau tūponotanga
whakamātau.

pūāhua
tūponotanga
pāpono
whakamātau
whakaaturanga raraunga
whakamātau tūponotanga
ariā tūponotanga.

Hei Tautoko i Te Ako

hoki ki runga ake

Tikanga Whakaako

Kia taea ai e 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
hakamahi 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 3: Tau 7–8

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 whakaaro 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 i 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 rānei.
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 i 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 wahanga 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