# Te Paenga Porowhita

Hei Whakarāpopoto

Ko tā te kōwae ako nei he tūhura i pānga o te whitianga o tētahi porowhita me tōna paenga. Ka tuhi porowhita, ka ine, ka tātai hoki i te roa o te pūtoro, te whitianga me te paenga.

Achievement Objectives
2. Ka tautohu, ka whakamārama i ngā tikanga āhuahanga o ngā rōpū āhua ahu-2 me ngā rōpū āhua ahu-3.
Te Hononga ki te Marautanga
Taumata 4
Te Ine me te Āhuahanga (Te Hanga)
Whāinga Paetae 2:
Ka tautohu, ka whakamārama i ngā tikanga āhuahanga o ngā rōpū āhua ahu-2 me ngā rōpū āhua ahu-3.
Ngā Whāinga Ako
Kia mōhio te ākonga ki:
• ngā kupu e hāngai ana ki ngā wāhanga o tētahi porowhita
• te ine, ki te tātai hoki i te paenga o tētahi porowhita
• te pānga o te paenga o te porowhita me tōna whitianga
Ngā Rauemi

he aho

he tioka

he tātaitai

he ruri

Wharangi Mahi 1

He Rārangi Kupu

 paenga porowhita circumference pūtoro radius whitianga diameter
Hei Raupapa I Ngā Mahi Ako
1. Ko te mahi tuatahi, he tuhi porowhita ki te papa tākaro, he tautuhi i te pūtoro, te whitianga me te paenga o te porowhita, he paku tūhura i te pānga o te whitanga me te paenga.

 Ngā tohutohu He Tauira Kōrero Mā Te Pouako Haere ki waho me ngā ākonga ki te papa tākaro poitarawhiti. Tonoa rātou ki te mahi takirua ki te tuhi porowhita ki te papa. Hoatu he aho, he tioka hei mahi mā rātou. Ko tā kōrua mahi ko tō hoa, he tuhi porowhita ki te papa. He tioka, he aho noa iho hei mahi mā koutou. Tonoa ngā ākonga ki te waitohu i te pokapū o te porowhita, te whitianga, te pūtoro, me te paenga. Haere tētahi o kōrua ki te tū i te pokapū o te porowhita. Ko tētahi o kōrua me hīkoi i te paenga o te porowhita. Tohua mai te pūtoro me te whitianga o te porowhita. E hia ngā pūtoro o te porowhita? He mutunga kore. Ko ngā rārangi katoa e tīmata ana i te pokapū, e toro atu ana ki te paenga. E hia ngā whitianga o te porowhita ka taea te tuhi? He mutunga kore anō. Ko ngā rārangi katoa mai i tētahi taha ki tētahi mā roto tonu i te pokapū o te porowhita. E hia ngā paenga o te porowhita? Kotahi anake. Whakawhitiwhiti kōrero mō te takenga mai o ngā ingoa nei, te pūtoro me te whitianga. He aha i whakamahia ai te kupu pūtoro mō tēnei wāhanga o te porowhita? Nā te mea, ka tīmata i te pokapū o te porowhita, ka toro atu i reira kia tae atu ki te paenga o te porowhita. Koia i kī ia ai ko te pūtoro. Pēhea te kupu whitianga? Ko te tikanga o te whitianga e mea ana ka whakawhitia te porowhita mai i tētahi taha ki tētahi, engari me haere mā te pokapū tonu o te porowhita. Tonoa ngā tokorua ki te āta whiriwhiri me pēhea e ine ai i te pūtoro, te whitianga me te paenga o te porowhita. Ko tā kōrua mahi ināianei, he ine i te roa o te pūtoro, te whitianga me te paenga o te porowhita. Kāore e whakamahia he ruri. Mā kōrua ko tō hoa e āta whiriwhiri me pēhea te ine. Tuhia ngā inenga ki tētahi pepa. Hei tauira: Ka whakamahia he wāhanga tīnana pērā i te matikara, te tapuwae rānei. Ka whakamahia he poro aho. Ka whakamahia he rākau aihikirīmi.
1. Ko te mahi tuarua, he tirotiro i te pānga o te whitianga me te pūtoro, te whitianga me te paenga, te pūtoro me te paenga. Kia rua rangi pea te roa o tēnei mahi.

 Ngā tohutohu He Tauira Kōrero Mā Te Pouako Tonoa ngā ākonga ki te tuhi i ā rātou inenga ki tētahi tūtohi i te papa tuhituhi. Haere mai ki te tuhi i ngā inenga mō tā kōrua porowhita me tō hoa ki te tūtohi nei i te papa tuhituhi. Āta tirohia ngā inenga, ka whakawhitiwhiti kōrero ai mō ngā pānga e kitea mai ana. Kia titiro tātou ki ngā inenga mō ngā pūtoro me ngā whitianga. He aha tētahi āhuatanga e kitea mai ana? Whakareatia te pūtoro ki te 2, ka eke ki te inenga o te whitianga. Hauruatia rānei te whitianga, ka hua ko te pūtoro. Ka tika. Ka kīia ko te pānga tēnā o te whitianga me te pūtoro. He haurua tētahi i tētahi. He rearua tētahi i tētahi. Titiro ki te porowhita nei. E rua ngā pūtoro, he ōrite ki te whitianga. Pēhea te pānga o te whitianga me te paenga? Āta tirohia ngā inenga katoa mō te whitianga me te paenga o ngā porowhita. Whakareatia te whitianga ki te 3, ka pātata atu ki te inenga o te paenga. Wehea rānei te paenga ki te 3, ka pātata atu ki te whitianga. Pēhea te pānga o te pūtoro me te paenga? Āta tirohia ngā inenga katoa mō te pūtoro me te paenga o ngā porowhita. Whakareatia te pūtoro ki te 6, ka pātata atu ki te inenga o te paenga. Wehea rānei te paenga ki te 6, ka pātata atu ki te whitianga Me haere tonu te tūhura i te pānga o te whitianga me te paenga o tētahi pūtoro. Kohia mai he rango, ka āta ine ai i ngā paenga me ngā whitianga. Anei ētahi rango. He porowhita te āhua o te pūtake o ngā rango. He rerekē te rahi o tēnā me tēnā o ngā rango. Whakamahia he aho hei ine i te paenga o ngā rango. Inea te roa o ngā aho ki te ruri, ka tuhi ai ki te tūtohi. Inea te whitianga o ngā rango, ka tuhi ai ki te tūtohi. Āta tirohia ngā inenga. He aha te pānga o te paenga me te whitianga.E pātata ana ki te 3 te whakareatanga ake o te paenga, tērā i te whitianga. Arā, whakareatia te whitianga ki te 3, ka rite ki te paenga. Whakamahia he tātaitai, ka wehe ai i te paenga ki te whitianga. Tuhia ki te tūtohi. He aha tētahi āhuatanga e kitea mai ana? Mō ia porowhita he paku nui ake i te 3 te wehenga o te paenga ki te whitianga. Arā, wehea te paenga ki te whitianga, ka paku nui ake i te 3. Whakamāramatia te tau e kīia ana ko pae (π). Ko tētahi tikanga e pā ana ki te porowhita, ahakoa te rahi o te porowhita, te iti rānei, mēnā ka whakareatia te whitianga ki tētahi tau, ka hua ko te rahi o te paenga. He paku nui ake i te 3 taua tau. Ka k?ia taua tau, ko ‘pae’. Ko tōna tohu, ko te π. Tirohia ā koutou tātaitai, ka kimi ai i te pūtohu mō pae. Pēhia taua pūtohu ka puta te tau ki te mata o te tātaitai. Anei te tau: 3.1415927. E hia ngā mati ā-ira? E whitu. Te tikanga, he mutunga kore ngā mati ā-ira o te pae (π). Ka haere tonu mō ake tonu atu. Engari mō ia porowhita, ahakoa te rahi, te iti rānei, ina wehea te paenga ki te whitianga, ka hua ko te tau nei, te pae (π). Mēnā ka whakareatia te whitianga ki te pae (π), ka hua ko te paenga o te porowhita. Titiro anō ki te tūtohi. He aha i rerekē ai ngā tau i puta i te whakawehenga o te paenga ki te whitianga? Nā te kore i tōtika rawa atu ngā inenga o te whitianga me te paenga o ngā porowhita. Hoatu he tātaitanga hei whakaoti mā ngā ākonga. He tauira kei ngā tūtohi nei. E pai ana kia whakatau tata i te tuatahi, kātahi ka whakamahi i te tātaitai. Whakaotia te tūtohi nei. Tuhia tō whakatau tata i te tuatahi, kātahi ka whakamahi i te tātaitai me te pūtohu mō pae (π).
1. Ko te mahi tuatoru, he whakamahi i te pānga o te whitianga me te paenga o tētahi porowhita (arā te tau ‘pae (π) ki te whakaoti rapanga. He pai te tono i ngā ākonga ki te tuhi pikitia hei whakaata i te rapanga, ki te whakamārama hoki i te rautaki i whakamahia. Kei Wharangi Mahi 1 (PDF, 112KB) ētahi rapanga hei tauira.

### Hei Whakawhānui.

Tūhuratia te pānga o te whitianga o tētahi porowhita rāroto o tētahi tapawhā rite me te tapa o te tapawhā rite.
Tūhuratia te pānga o te whitianga o tētahi porowhita rāwaho o tētahi tapawhā rite me te tapa o te tapawhā rite.

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