I tēnei kōwae ako ka tūhurangia te āhua o te rōpinepine i ētahi taparau. He mea pūtake mai tēnei kōwae ako i te kōwae ako reo Ingarihi Fitness.
Taumata 4
Te Ine me te Āhuahanga
Whāinga Paetae 2 (Te Hanga):
Ka tautohu, ka whakamārama i ngā tikanga āhuahanga o ngā rōpū āhua ahu-2 me ngā rōpū āhua ahu-3.
Whāinga Paetae 7 (Te Panoni):
Ka tautohu, ka whakamārama, ka whakamahi i ngā āhuatanga pūmau o ngā panoni.
Kia mōhio te ākonga ki:
- te hanga, me te whakamārama i ngā rōpine-rite-takitahi me ngā rōpine-rite-takimaha
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He rūri
He huinga poro āhuatanga ake
Whārangi Tārua 1
Whārangi Tārua 2
āhua ahu-2 | 2-dimensional shape |
āhua ahu-3 | 3-dimensional shape |
āhuatanga pūmau | invariant property |
āputa | gap |
ine-koki | protractor |
koki huripū | whole angle, full turn (360º) |
koki rārangi | straight line angle (180º) |
koki roto | interior angle |
panoni | transformation |
papariki | tile |
poro āhuatanga ake | attribute blocks/shapes |
putu | degree |
rōpinepine | tessellation |
rōpine-rite-takimaha | semi-regular tessellation |
rōpine-rite-takitahi | regular tessellation |
taparau rite | regular polygon |
tauwehe | factor |
- Ko te mahi tuatahi, he tūhura i ngā koki roto o ngā momo taparau.
- Ko te mahi tuarua, he tūhura i te rōpine-rite-takitahi o ngā momo taparau rite.
- te tapatoru rite:
- te tapatoru waerite:
- te taparara waerite:
- He aha ngā taparau rite ka rōpinepine?
- He aha ngā mea kāore e rōpinepine?
- He aha pea te take e rōpinepine ai ētahi taparau rite, kāore ētahi?
- 3.3.3.3.3.3
- 4.4.4.4
- 6.6.6
- Ko ngā koki roto o aua taparau rite, ka taea te whakawehe pū ki roto i te 360º. Arā:
- Ngā koki roto o te tapatoru rite = 60º, 360 ÷ 60 = 60
- Ngā koki roto o te tapawhā rite = 90º, 360 ÷ 90 = 4
- Ngā koki roto o te tapaono rite = 120º, 360 ÷ 120 = 3
- He ōrite te roa o ngā tapa o ēnei taparau rite katoa.
- Ko te mahi tuatoru, he tūhura i te rōpine-rite-takimaha o ngā momo taparau rite.
Ngā tohutohu | He tauira whakawhitinga kōrero | |||||||||||||||||||||
Aratakina ngā ākonga kia whakarārangi i ngā koki roto o tētahi tapatoru rite, ka whakawhitiwhiti kōrero mō te tapeke o ngā koki roto. |
He aha tēnei momo tapatoru? He tapatoru rite nā te mea he ōrite te roa o ia tapa, he ōrite hoki ia kokonga.
Titiro ki taku mahi. He tīhaehae i ia kokonga, me te whakatakoto kia piritahi. He aha tētahi mea e kitea ana i te takoto o ngā kokonga nei? He rārangi torotika ka hua mai.
E hia putu i te rārangi torotika? Kotahi rau waru tekau putu.
Nō reira e hia te tapeke o ngā koki roto o te tapatoru rite? Ko te 180 º |
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Tukuna ngā ākonga kia tūhura mēnā ko te 180º te tapeke o ngā koki roto o ngā tapatoru katoa, ahakoa te āhua o aua tapatoru. |
Mā koutou e tuhi ētahi tapatoru, kia rerekē te āhua o tēnā me tēnā. Tapahia, ka tīhaehae i ngā kokonga. Whakatakotoria ngā kokonga o ia tapatoru kia kitea ai mēnā he rārangi torotika ka hua mai. He aha te whakakitenga? Ahakoa te āhua o te tapatoru, he rārangi torotika ka hua mai. Nō reira ko te 180º te tapeke o ngā koki roto o ngā momo tapatoru katoa. |
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Tonoa ngā ākonga kia tūhura i te tapeke o ngā koki roto o ngā momo tapawhā. |
Ko tā koutou mahi ināianei, he tūhura i te tapeke o ngā koki roto o ngā momo tapawhā rerekē. Mā koutou e tuhi ētahi tapawhā, kia rerekē te āhua o tēnā me tēnā. Tapahia, ka tīhaehae i ngā kokonga. Whakatakotoria kia piritahi ngā kokonga o ia tapawhā. He aha te whakakitenga? Ahakoa te āhua o te tapawhā, he koki huripū ka hua mai. Nō reira ko te 360º te tapeke o ngā koki roto o ngā momo tapawhā katoa.
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Aratakina ngā ākonga kia tūhura i te tapeke o ngā koki o tētahi taparima. |
Titiro ki tēnei āhua. He tapawhā. E hia te tapeke o ōna koki roto? Ko te 360º.
Mēnā ka tāpirihia tētahi tapatoru ki tētahi o ngā tapa, he aha te āhua ka hua mai? He taparima.
Nō reira, ki ō whakaaro, e hia putu te tapeke o ngā koki roto o tētahi taparima? E 360º te tapawhā, kātahi ka tāpiria te 180º o te tapatoru, nō reira ko te 540º pea. Me pēhea te whakamātau i tēnei whakaaro. Mā te tuhi i tētahi taparima, me te whakamahi ine-koki hei ine i ngā koki roto katoa, kātahi ka tāpiria. |
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Kia pērā anō te arataki i ngā ākonga kia tūhura i te tapeke o ngā koki roto o ētahi atu taparau. Ka whakaaturia ki tētahi tūtohi. |
Mēnā ka tāpiria tētahi anō tapatoru ki tētahi tapa o te taparima, he aha te āhua ka hua mai? He tapaono. Nō reira e hia te tapeke o ngā koki roto o tētahi tapaono? Ko te 540º o te taparima, tāpiria te 180º o te tapatoru, ko te 720º tērā. Tuhia te tapeke o ngā koki roto o ngā taparau ki tētahi tūtohi:
He aha te tauira e kitea ana i te tūtohi? Mo ia pikinga i te maha o ngā tapa, ka tāpiria te 180º. |
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Tonoa ngā ākonga kia tātai i te rahi o ia koki roto o tēnā momo taparau rite o tēnā momo taparau rite. |
Mēnā he tapatoru rite te tapatoru, me pēhea te tātai i te rahi o ia koki roto? 180º te tapeke o ngā koki, ā, he ōrite te rahi o ia koki. Nō reira me whakawehe te 180º ki te 3, ka 60º. Tātaihia te rahi o ngā koki roto o ia momo taparau rite, ka tuhi atu ai ki te tūtohi.
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Tonoa ngā ākonga kia tuhi i ētahi o ngā taparau rite. |
Ko tā koutou mahi, he tuhi i ētahi o ngā taparau rite. He aha ngā taputapu hei mahi māu? He ine-koki me he rūri. Me tīmata ki tētahi tapa, ka inea ngā koki ki ia pito o taua tapa. Hei tauira (mō tētahi wāhanga o te tapawaru rite): |
Hoatu he huinga poro āhuatanga ake ki ia takirua ākonga. Whakamāramatia te tikanga o tēnei mea te rōpinepine. Tonoa ngā ākonga kia tūhura i ngā momo poro, kia kitea ai mēnā ka rōpinepine, kāore rānei e rōpinepine. |
Ko tā tātou mahi, he tūhura i tēnei mea te rōpinepine. Ākene pea he kupu hou te rōpinepine. Ko tōna tikanga mai rā anō, ko te whakanoho i ētahi mea kia piritata. Ko tōna tikanga pāngarau, ko te whakanoho i ētahi āhua (pēnei i ngā poro nei) kia piri, engari kaua tētahi e noho ki runga i tētahi, kia kaua hoki e kitea he āputa ki waenganui. Ko te mea māmā, ko te tapawhā rite. He rōpinepine ka puta i te whakanoho i ētahi tapawhā rite kia piri tahi: Tūhurangia ngā poro katoa. He aha ngā poro e hua mai ai he rōpinepine mēnā ka whakanoho kia piritahi? Tuhia he pikitia o ia rōpinepine ki te pepa inerite. Hei tauira: |
Whakaahuangia te Whārangi Tārua 1, ka tapahia ai i ngā taparau rite. Hoatu ki ia takirua ākonga. Tonoa rātou kia tūhura i te rōpinepine o ngā taparau rite: |
Anei ētahi taparau rite. Ka mahi takirua koutou ki te tūhura i te rōpinepine o ēnei taparau rite. Mēnā ka rōpinepine tētahi taparau rite, ka kīia tērā he rōpine-rite-takitahi. He aha ngā taparau rite e hua mai ai he rōpine-rite-takitahi? Ko te tapatoru rite, te tapawhā rite me te tapaono rite. Ka tapaina ēnei rōpinepine: He aha ki ō whakaaro te tikanga o ēnei tapanga? Ko te 3.3.3.3.3.3 e tohu ana e ono ngā tapatoru rite huri noa i ia kokonga. Ko te 4.4.4.4 e tohu ana e whā ngā tapawhā rite huri noa i ia kokonga. Ko te 6.6.6 e tohu ana e toru ngā tapaono rite huri noa i ia kokonga. He aha ki ō whakaaro te take e rōpinepine ai te tapatoru rite, te tapawhā rite me te tapaono rite, kāore ētahi atu? E rua ngā take: |
Ngā tohutohu | He tauira whakawhitinga kōrero |
Aratakina ngā ākonga kia tūhura i te rōpine-rite-takimaha. |
Arā anō ētahi rōpinepine ka puta i te whakamahinga o ētahi taparau rite e rua. Titiro ki te tūtohi e whakaatu ana i ngā koki roto o ngā momo taparau rite. Ki tō whakaaro, he aha ētahi taparau rite e rua e hua mai ai he rōpinepine? Kia rua ngā tapawhā rite, kia toru ngā tapatoru rite. Hui katoa ngā koki roto, ka 360º. Arā, 90 + 90 + 60 + 60 + 60 = 360. Tuhia he pikitia o te rōpinepine o ētahi tapawhā rite e rua me ētahi tapatoru rite e toru. Me pēhea te whakanoho kia piritahi kia hua mai ai he rōpinepine? Koia nei tētahi. Ko te 4.3.3.4.3 hei tapanga poto mō tēnei rōpinepine, nā te mea koia te raupapa o te whakanoho i ia kokonga – huri whakatekaraka i ia pū, he tapawhā rite, he tapatoru rite, he tapatoru rite, he tapawhā rite, he tapatoru rite. Koia anō tētahi. Ko te 4.4.3.3.3 hei tapanga poto mō tēnei rōpinepine, nā te mea koia te raupapa o te whakanoho i ia kokonga – huri whakatekaraka i ia pū, he tapawhā rite, he tapawhā rite, he tapatoru rite, he tapatoru rite, he tapatoru rite.
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Hoatu ngā taparau rite (Whārangi Tārua 1), ka tono ai i ngā ākonga kia tūhura i ngā rōpine-rite-takimaha. Koia nei ngā rōpinepine e taea ana (Kei te Whārangi Tārua 2 ēnei rōpinepine e whakaaturia ana):
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Anei ētahi taparau rite hei tūhura māu i ngā rōpinepine katoa e taea ana. Tuhia ngā rōpinepine ki te pepa, me te tapanga poto ki raro iho. |
Hei Whakawhānui
Tukuna ngā ākonga kia tūhura i ētahi atu āhua e hua mai ai he rōpinepine. Hei tauira ēnei:
Kei ngā pae tukutuku nei ētahi atu tauira:
http://www.tessellations.org/eschergallery1thumbs.htm
http://www.google.co.nz/images?hl=en&q=examples+of+tessellations&um=1&ie=UTF-8&source=univ&ei=gGHsS8PbH5Hg7APe4pGPBg&sa=X&oi=image_result_group&ct=title&resnum=4&ved=0CDcQsAQwAw