Hei Whakarāpopoto
E hāngai ana tēnei kōwae ako ki te rauemi matihiko nei, ‘Whakaranua’. Ko tā tēnei rauemi matihiko, he āwhina i te ākonga ki te whiriwhiri i te ōrau toharite. E hāngai ana ki te Kaupae 8 o Te Mahere Tau (Te Poutama Tau). Kei tēnei kōwae ako ētahi rapanga hei whakamahi mā te ākonga i te rauemi matihiko ‘Whakaranua’. He āhua ōrite tēnei kōwae ako ki te kōwae ako reo Ingarihi Mix Up 1.
Te Hononga ki te Marautanga
Taumata 4
Te Tau me te Taurangi (Te Mātauranga Tau me ngā Rautaki Tau)
Whāinga Paetae 5:
- rautaki tatau;
- rautaki tāpiripiri;
- rautaki whakarea;
- rautaki pānga riterite māmā.
Ngā Whāinga Ako
Kia mōhio te ākonga ki te:
- whakaahua i roto hinengaro ngā rautaki hei whiriwhiri i te ōrau toharite o ngā mea o roto i ētahi ipu he rerekē te rahi.
Hei Raupapa I Ngā Mahi Ako
Te Hononga ki te Mahere Tau
E tino hono ana tēnei kōwae ako ki te Mahere Tau o Aotearoa (tirohia te kaupapa o Te Poutama Tau i te pae tukutuku o www.meaningfulmaths.nt.edu.au/mmws/nz).
E whakaatu ana te wāhanga rautaki o te mahere tau i ngā momo rautaki ka whakamahia e ngā ākonga ki te whakaoti paheko.
E hāngai ana te mahi o tēnei kōwae ako ki te ākonga o te Kaupae 8 o te Mahere Tau.
I te Kaupae 8, e ako ana te ākonga ki te whakaoti rapanga e whai wāhi mai ana te whakakao mai i ētahi ōwehenga rerekē. Koia rā te kaupapa o te rauemi matihiko ‘Whakaranua’.
Ngā Rauemi Matihiko
Kei tēnei wāhi i te ipurangi te rārangi mai o ngā rauemi matihiko katoa kua tuhia ki te reo Māori: Akoranga Matihiko
Ko ētahi o ngā rauemi matihiko (ngā mea o nzmaths) e wātea ana ki te katoa, mā te pāwhiri noa i te pūtohu. Ko ētahi atu o ngā rauemi matihiko (ngā mea o The Le@rning Federation), me rēhita kē tō kura, kātahi koe ka uru atu ai.
Koia nei te wāhi noho o te rauemi matihiko Whakaranua, e hāngai ana ki tēnei kōwae ako: https://meaningfulmaths.nt.edu.au/mmws/nz/sites/default/files/static/LearningObjects/maori/whakaranua2/index.html
I Mua i te Whakamahinga o te rauemi Whakaranua
Me mātau te ākonga ki ngā tikanga o te ōrau. Ko ngā kōwae ako o nzmaths e whai pānga ana ko ēnei:
ōrau: Te Orau
Whakaranua 1: Whakaranua
Whakaranua (PĒKE): Ka Mahi Tahi te Kaiako me tētahi Rōpū ākonga
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Huakina te rauemi matihiko ‘Whakaranua’, ka whakamārama ai i tōna kaupapa ki te whakaatu tauira hei whiriwhiri i te ōrau toharite o ngā porotiti kei rō pēke, o te wai rānei kei rō ipu.
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Pāwhiria te pūtohu RAPANGA PĒKE, kātahi ka kōwhiri kia rua ngā pēke.
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Whakawhitiwhiti kōrero mō te whārangi tuatahi, kia tino mārama ai ngā ākonga ki ēnei āhuatanga:
- te ōrau o ngā porotiti kahurangi kei ia pēke;
- te tikanga o te pātai.
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Whakawhitiwhiti kōrero mō ngā rautaki hei whiriwhiri i te ōrau toharite:
RAUTAKI 1:
(76% + 60% + 60% + 60%) ÷ 4
= 256% ÷ 4
= 64%
RAUTAKI 2
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Tatauria ngā porotiti: E 25 ngā porotiti kei roto i te pēke iti (19 he kahurangi), e 75 kei roto i te pēke nui (e 45 he kahurangi).
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Nō reira, 100 katoa ngā porotiti, e 64 o ēnei (19 + 45) he kahurangi.
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Nō reira, e 64% te ōrau toharite.
Tuhia te whakautu ki te pouaka, ka pāwhiri ai i te pūtohu TUKUNA.
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Mā te pāwhiri i te pūtohu PŪRERE WHAKARANU e kitea ai te rautaki tuatahi i runga nei hei whiriwhiri i te ōrau toharite.
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Mēnā e hē ana te whakautu, ka puta mai ētahi kōrero hei āwhina kia whiriwhiri anō.
- Mēnā ka hē anō te whakautu, ka tonoa kia whakamahia te PŪRERE WHAKARANU hei āwhina kia whiriwhiri anō i te ōrau toharite.
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Ko tā te PŪRERE WHAKARANU, he whakaatu i ngā porotiti o ngā pēke e rua e whakaranua ana, e tohaina ana kia ōrite te tohatoha o ngā tae ki ia pēke. Whakawhitiwhiti kōrero mō te mahi a te PŪRERE WHAKARANU.
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Ina pāwhiria te pūtohu I MUA I MURI, e tino kitea ai te tikanga o te ōrau toharite, arā, ko te wāhi kei waenganui i ngā ōrau e rua.
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Pāwhiria te pūtohu RAPANGA HOU, ka mahi anō ai i tētahi tauira.
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Kia taunga ngā ākonga ki te whiriwhiri i te ōrau toharite o ētahi pēke e rua, me kōwhiri kia whā ngā pēke. Whakawhitiwhiti kōrero mō ngā rautaki e hāngai ana mēnā e whā ngā pēke.
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Kia taunga ngā ākonga ki te whiriwhiri ōrau toharite, tukuna rātou kia mahi wehe kē i ētahi atu tauira.
Whakaranua (IPU): Ka Mahi Tahi te Kaiako me tētahi Rōpū ākonga
- Pāwhiria te pūtohu RAPANGA IPU, kātahi ka kōwhiri kia rua ngā ipu.
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Whakawhitiwhiti kōrero mō te whārangi tuatahi, kia tino mārama ai ngā ākonga ki ēnei āhuatanga:
- te ōrau kī o te wai kei ia ipu;
- te tikanga o te pātai.
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Whakawhitiwhiti kōrero mō ngā rautaki hei whiriwhiri i te ōrau toharite.
RAUTAKI 1
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E tika ana kia ōrite te rahi o ngā ipu, e tika ai te tātai i te toharite.
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Nō reira me whakawehe te ipu nui mā te toru, kātahi ka ōrite ki te rahi o te pēke iti.
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Ināianei, kotahi te ipu e 56% te kī, e toru ngā ipu e 40% te kī. Nō reira, hei tātai i te toharite:
(56% + 40% + 40% + 40%) ÷ 4
= 176% ÷ 4
= 44%
RAUTAKI 2
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Tangohia te 6% o te wai i te ipu A, ka
tāpiri atu ai ki te ipu B. He ōrite te 6% o te ipu A ki te 2% o te ipu B, na te mea e toru te
whakareatanga ake o te ipu B i te ipu A.
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Nō reira, e 50% te kī o te ipu A ināianei, e 42% te kī o te ipu B.
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Me
tango te 6% anō o te wai i te ipu A, ka heke ki te 44% te kī. Tāpirihia atu ki te ipu B, ā, ka piki ake ki te 44% te kī.
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Ināianei, e 44% te kī o ngā ipu katoa.
Tuhia te whakautu ki te pouaka, ka pāwhiri ai i te pūtohu TUKUNA.
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Mā te pāwhiri i te pūtohu PŪRERE WHAKARANU e kitea ai tētahi rautaki hei whiriwhiri i te ōrau toharite.
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Mēnā e hē ana te whakautu, ka puta mai ētahi kōrero hei āwhina kia whiriwhiri anō.
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Mēnā ka hē anō te whakautu, ka tonoa kia whakamahia te PŪRERE WHAKARANU hei āwhina kia whiriwhiri anō i te ōrau toharite.
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Ko tā te PŪRERE WHAKARANU, he whakaatu i te wai o ngā ipu e rua e whakaranua ana, e tohaina ana, kia ōrite te kī o te wai ki ia ipu. Whakawhitiwhiti kōrero mō te mahi a te PŪRERE WHAKARANU.
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Ina pāwhiria te pūtohu I MUA I MURI, e tino kitea ai te tikanga o te ōrau toharite, arā, ko te wāhi kei waenganui i ngā ōrau e rua.
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Pāwhiria te pūtohu RAPANGA HOU, ka mahi anō ai i tētahi tauira.
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Kia taunga ngā ākonga ki te whiriwhiri i te ōrau toharite o ētahi ipu e rua, me kōwhiri kia whā ngā ipu. Whakawhitiwhiti kōrero mō ngā rautaki e hāngai ana mēnā e whā ngā ipu.
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Kia taunga ngā ākonga ki te whiriwhiri ōrau toharite, tukuna rātou kia mahi wehe kē i ētahi atu rapanga.
Ka Mahi Takitahi, Takirua rānei ngā ākonga
Kia taunga rā anō ngā ākonga ki te whakamahi i te rauemi rorohiko nei, me te whiriwhiri ōrau toharite, tukuna rātou kia mahi wehe kē, takitahi, takirua rānei. Tonoa rātou kia tuhituhi i ētahi o ngā rapanga ka oti i a rātou, ā, ka whakamārama ai i te rautaki hei whakaoti.
He Mahi Whakawhānui
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Tonoa ngā ākonga ki te whakaoti rapanga e whai wāhi mai ana te toharite. Hei tauira:
- Whiriwhiria te toharite o ngā pakeke (tau) o ngā tāngata i tō whānau.
- Whiriwhiria te tāroaroa toharite o ngā tāngata i tō whānau.
- Whiriwhiria toharite o te wā mātakitaki pouaka whakaata ia pō o ngā ākonga i tō akomanga.
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Tonoa ngā ākonga ki te whakamahi rauemi (pērā i te porotiti) hei whakamārama i te rautaki whakaoti i tētahi rapanga toharite.