Ka āta tirohia ngā tauira ka hua mai i ētahi horopaki āhuahanga, pērā i te hononga o te paenga me te horahanga o te tapawhā hāngai. I takea mai tēnei kōwae ako i te kōwae ako reo Ingarihi You Can Count On Squares.
- ka kōwhiri, ka whakamahi i te waeine e hāngai ana mō te roa, te horahanga, te rōrahi (kìtanga), te papatipu (taumaha), te paemahana, te koki me te wā;
- ka whakawhitiwhiti waeine māmā;
- ka whakamahi i ngā inenga tapa ki te whiriwhiri i te paenga me te horahanga o te tapawhā hāngai, me te rōrahi o te poro tapawhā hāngai;
- ka tuhi, ka whakamārama, ka whakamahi hoki i ngā momo wātaka me ngā mahere;
- ka mārama ki te whaitakenga o tētahi inenga.
- whiriwhiri i te paenga me te horahanga o tētahi tapawhā hāngai
- hononga i waenganui i te paenga me te horahanga o tētahi tapawhā hāngai
- whiriwhiri i te horahanga o tētahi tapawhā whakarara
- whakahaere tūhuratanga āhuahanga
TauiraĀhuahangaWT1
TauiraĀhuahangaWT2
TauiraĀhuahangaWT3
he pepa tukutuku
| hononga | relationship |
| horahanga | area |
| mitarau pūrua | square centimetre |
| paenga | perimeter |
| pepa tukutuku | grid paper |
| rahirahi | thin |
| taparara | trapezium |
| tapawhā whakarara | parallelogram |
| tūtohi | table |
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I te tuatahi, ka tūhura ngā ākonga i te paenga o ētahi tapawhā hāngai he rerekē te āhua, engari he ōrite te horahanga.
Ngā Tohutohu He Tauira Kōrero Mā Te Pouako Tūhuratia ngā tapawhā hāngai e taea te tuhi (te hanga rānei), ko te 24 waeine pūrua te horahanga.
Titiro ki te Tauira Āhuahanga WT1 (PDF, 136KB). Kua tuhia ētahi tapawhā hāngai e toru ki te pepa tukutuku. Ko te 1cm te rahi o ngā tukutuku. Tuhia ngā inenga o ngā tapa ki ia tapawhā hāngai.
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He aha te horahanga o ia tapawhā hāngai? Ko te 24 cm2.
Ka taea ētahi atu tapawhā hāngai te tuhi, ko te 24 cm2 te horahanga? Tuhia ngā tapawhā hāngai katoa, ko te 24 cm2 te horahanga.
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Tuhia te roa, te whānui me te horahanga o ngā tapawhā hāngai ki tētahi tūtohi:
te roa
(cm)te whānui
(cm)te horahanga
(cm2)24 1 24 12 2 24 8 ... ... ... ... ... Āta tirotirohia te hononga o te paenga o ngā tapawhā hāngai me te horahanga. Tuhia tētahi atu pou ki te tūtohi, hei whakaatu i te paenga o ngā tapawhā hāngai. Tuhia ngā paenga o ia tapawhā hāngai ki te tūtohi. te roa
(cm)te whānui
(cm)te horahanga
(cm2)te paenga
(cm)24 1 24 50 12 2 24 28 8 3 24 22 6 4 24 20 4 6 24 20 3 8 24 22 2 12 24 28 1 24 24 50 He aha te tauira e kitea mai ana i te tūtohi? He nui ake te paenga o ngā tapawhā hāngai āhua rahirahi nei.
Ka taea te tauira nei te whakaatu ki te kauwhata:
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Me āta tirotiro te tūtohi me te kauwhata, ka whakaaro ai, he pēhea nei te roa o ngā tapa kia iti rawa atu te paenga? Kei waenganui i te 4 me te 6. Mēnā ko te 5 te roa o ngā tapa e rua, ko te 25 cm2 te horahanga, nō reira he iti iho i te 5 te roa o ngā tapa kia iti rawa atu te paenga.
Kia pērā anō te mahi hei kimi i ngā tapawhā hāngai katoa, ko te 36 cm2 te horahanga. - Tuhia te roa o ngā tapa, te horahanga me te paenga o ia tapawhā hāngai ki te tūtohi.
- Whakaaturia te hononga o te roa o tētahi tapa me te paenga o te tapawhā hāngai ki te kauwhata. Whakawhitiwhiti kōrero mō te āhua o te kauwhata.
- Kimihia te roa o ngā tapa mō te tapawhā hāngai he iti rawa atu te paenga.
- Kimihia te roa o ngā tapa mō te tapawhā hāngai he nui rawa atu te paenga.
Kia pērā anō te mahi hei kimi i ngā tapawhā hāngai katoa, ko te 60 cm2 te horahanga. Tuhia te roa o ngā tapa, te horahanga me te paenga o ia tapawhā hāngai ki te tūtohi.
- Tuhia te roa o ngā tapa, te horahanga me te paenga o ia tapawhā hāngai ki te tūtohi.
- Whakaaturia te hononga o te roa o tētahi tapa me te paenga o te tapawhā hāngai ki te kauwhata. Whakawhitiwhiti kōrero mō te āhua o te kauwhata.
- Kimihia te roa o ngā tapa mō te tapawhā hāngai he iti rawa atu te paenga.
- Kimihia te roa o ngā tapa mō te tapawhā hāngai he nui rawa atu te paenga.
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I konei, ka tūhuratia te horahanga o ētahi tapawhā hāngai mēnā ka pūmau te paenga.
Ngā Tohutohu He Tauira Kōrero Mā Te Pouako Tukuna ngā ākonga kia kimi i ngā tapawhā hāngai katoa e taea ana, mēnā ko te 24 te paenga.
Whakawhitiwhiti kōrero mō te hononga o te paenga me te horahanga o ngā tapawhā hāngai.
Titiro ki te Tauira Āhuahanga WT2 (PDF, 136KB). Kua tuhia ētahi tapawhā hāngai. Mēnā ko te 1 cm te rahi o ngā tukutuku, he aha te paenga o ngā tapawhā hāngai nei? Ko te 24 cm.
Tuhia ētahi atu tapawhā hāngai, ko te 24 cm te paenga.
Whakaaturia te roa o ngā tapa, te paenga me te horahanga o ngā tapawhā hāngai ki tētahi tūtohi:
te roa (cm) te whānui (cm) te paenga (cm) te horahanga (cm2) 11 1 24 11 10 2 24 20 9 3 24 27 8 ... Ko tēhea te tapawhā hāngai he nui rawa atu te horahanga? Ko te tapawhā rite, arā, ko te 6 cm te roa o ia tapa.
He aha te tauira e kitea mai ana? He iti ake te horahanga o ngā tapawhā hāngai āhua rahirahi nei. Ka pātata haere te āhua o te tapawhā hāngai ki te tapawhā rite, ka nui haere te horahanga.
Whakaaturia tēnei tauira ki te kauwhata rārangi:
Kia pērā anō te mahi hei kimi i ngā tapawhā hāngai katoa, ko te 16 cm te paenga.
- Tuhia te roa o ngā tapa, te paenga me te horahanga o ia tapawhā hāngai ki te tūtohi.
- Whakaaturia te hononga o te roa o tētahi tapa me te paenga o te tapawhā hāngai ki te kauwhata. Whakawhitiwhiti kōrero mō te āhua o te kauwhata.
- Kimihia te roa o ngā tapa mō te tapawhā hāngai he iti rawa atu te horahanga.
- Kimihia te roa o ngā tapa mō te tapawhā hāngai he nui rawa atu te horahanga.
Kia pērā anō te mahi hei kimi i ngā tapawhā hāngai katoa, ko te 12 cm te paenga.
- Tuhia te roa o ngā tapa, te paenga me te horahanga o ia tapawhā hāngai ki te tūtohi.
- Whakaaturia te hononga o te roa o tētahi tapa me te paenga o te tapawhā hāngai ki te kauwhata. Whakawhitiwhiti kōrero mō te āhua o te kauwhata.
- Kimihia te roa o ngā tapa mō te tapawhā hāngai he iti rawa atu te horahanga.
- Kimihia te roa o ngā tapa mō te tapawhā hāngai he nui rawa atu te horahanga.
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Ko te mahi tuatoru, he tūhura i te horahanga o tētahi tapawhā whakarara.
Ngā Tohutohu He Tauira Kōrero Mā Te Pouako Whakamahia he ngaku pepa māro (he rākau rānei) me ētahi pine hei hanga i tētahi tapawhā hāngai:
Tukuna ngā ākonga kia tūhura i te horahanga o tētahi tapawhā whakarara.
Anei tētahi tapawhā hāngai. Me pēhea te tātai i te horahanga o te tapawhā hāngai? Inea te roa me te whānui, ka whakarea ai. Mēnā ka panaia tētahi o ngā kokonga, ka tītaha te tapawhā hāngai. Ka kīia he tapawhā whakarara.
He aha ki tōu whakaaro i kīia ai he tapawhā whakarara? Nā te mea he whakarara te tapa mauī me te tapa matau, he whakarara hoki te tapa raro me te tapa runga.
Ko ngā pere iti nei hei whakaatu i ngā tapa whakarara:
Titiro ki ngā tapawhā e toru nei. He ōrite te roa o ngā tapa o tēnā me tēnā o ngā tapawhā.
tapawhā hāngai
tapawhā whakarara āhua māmā te tītaha
tapawhā whakarara tino tītaha
Ki tāu titiro, he ōrite te horahanga o ēnei tapawhā katoa? Kāore pea. Ahakoa he ōrite te roa o ngā tapa o tēnā me tēnā, ki tā te karu titiro, he iti ake te horahanga o te mea tino tītaha.
Whakawhitiwhiti kōrero mō te tātai i te horahanga o tētahi tapawhā whakarara. Tuhia tētahi tapawhā whakarara ki te pepa tukutuku. Tuhia he rārangi hei wāwāhi i te tapawhā whakarara ki ētahi tapatoru e rua kei ngā pito, me tētahi tapawhā hāngai kei waenganui:
Tapahia tētahi o ngā tapatoru o te tapawhā whakarara, ka whakatakoto ai ki te taha o tērā atu o ngā tapatoru.
He aha te āhua kua hua mai? He tapawhā hāngai.
Me pēhea te tātai i te horahanga o taua tapawhā hāngai? Whakareatia te roa ki te whānui. Arā, whakareatia te 9 ki te 4, ka 36 mitarau pūrua te horahanga (36 cm2).
He ōrite tēnā ki te horahanga o te tapawhā whakarara i te tīmatanga. Āe, he ōrite nā te mea kāore i tangohia i tāpirihia rānei tētahi wāhanga o te tapawhā whakarara, ko te hunuku noa iho i te tapatoru i tētahi pito kia noho tahi me te tapatoru i tērā o ngā pito.
Hoatu te Tauira Āhuahanga WT3 (PDF, 129KB) hei whakaoti mā ngā ākonga. Whakawhitiwhiti kōrero mō te whiriwhiringa poto hei tātai i te horahanga o ngā tapawhā whakarara. Arā, ko te whakamahi i te ture tātai: H = p x t (H = horahanga, p = pūtake, t = teitei) 
He Whakawhānui:
Tūhuratia te horahanga o tētahi taparara:
Tūhuratia te horahanga o ētahi o ngā āhua o ngā pū:
