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Te Rōrahi

Submitted by Frances Neill on Sun, 08/30/2009 - 21:17
in
Purpose: 

Ko te kaupapa nei, he tirotiro i te tikanga o te rōrahi, he tātai i te rōrahi o te poro-tapawhā hāngai, he tirotiro hoki i te hononga o te rōrahi me te horahanga papa.

Achievement Objectives:

Maori AOs: 
Taumata 4
Te Ine me te Āhuahanga (Te Ine)
Whāinga Paetae 1:
Ka whakaoti rapanga whaitake:
  • 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.
Specific Learning Outcomes: 
Kia mōhio te ākonga:
  • he aha te rōrahi me te horahanga papa o tētahi pouaka, me pēhea hoki e inea ai
  • ki te rahi o te mm3, te cm3, me te m3, me te hononga o tētahi ki tētahi.
  • ki te tātai i te rōrahi o tētahi poro-tapawhā hāngai
  • ki te hoahoa raumata hei hanga i tētahi poro-tapawhā hāngai
Required Resource Materials: 
he kāri A4
he henemita pūtoru
he tēpa whakapiri
he nūpepa
he ruri
Whārangi Mahi 1
Poumahi 1
Poumahi 2
Poumahi 3
Key Vocabulary: 

henemita pūtoru cubic centimeter
horahanga mata surface area
mita pūtoru cubic metre
raumata net
rōrahi volume
poro-tapawhā hāngai rectangular based prism

Activity: 
  1. Ko te mahi tuatahi, he tirotiro i te rerekē o te ine i te horahanga tērā i te ine i te rōrahi.
    Te mahi a te pouako He tauira kōrero mā te pouako
    Whakaaturia tētahi pouaka (pērā i tētahi pouaka hū), me tētahi kāri 1 cm2.
    Whakawhitiwhiti kōrero mō te ine i te horahanga o ngā papa o te pouaka.    		 He henemita pūrua tēnei. He tapawhā rite te āhua, kotahi henemita mā te kotahi henemita.
    He aha te āhuatanga o te pouaka e taea ana te ine mā te whakamahi i te henemita pūrua? Ko te rahi o ngā mata (papa) o te pouaka, pērā i te taupoki.
    3d box.
    Ko te kupu mō tēnā āhuatanga, ko te horahanga. Ka whakamahia he henemita pūrua hei ine i te horahanga o tētahi o ngā papa o te pouaka. Ko te tohu ko te cm2.
    He aha ngā rautaki hei ine i te maha o ngā henemita pūrua ka taea ki te taupoki o te pouaka?
    1. Whakatakotoria he henemita pūrua ki te taupoki o te pouaka. Tatauria te maha o ngā henemita pūrua ka taea te whakatakoto.
    2. Inea te roa me te whānui o te taupoki o te pouaka. Whakareatia.
    Hoatu he mahi e kite ai koe mēnā kua mau i te ākonga te rautaki hei tātai horahanga. Whiriwhiria te horahanga o ngā mata katoa o te pouaka.
    Whakawhitiwhiti kōrero mō te ine i te rōrahi o te pouaka.
    Whakaaturia tētahi henemita pūtoru (matono rite, 1 cm x 1 cm x 1 cm)    		 Pēhea te rahi o roto i te pouaka? Ka taea te henemita pūrua te whakamahi hei ine i te rahi o roto? Kāore, nā te mea he papatahi te henemita pūrua, engari he whaitua kei roto i te pouaka. He whānui, he roa tō te āhua papatahi, engari he whānui, he roa, he teitei tō te pouaka.
    Nō reira he aha hei ine i te rahi o roto i te pouaka? Ko te mataono rite.
    He mataono rite tēnei, kotahi henemita te roa o ia tapa. Ka kīia he henemita pūtoru. Anei te tohu: 1 cm3.
    Ko te mahi, he āta tirotiro e hia ngā henemita pūtoru ka taea ki roto i te pouaka. Kātahi koe ka mōhio ki te rahi o roto i te pouaka. Ko te kupu mō tēnā ko te rōrahi o te pouaka. He whakapotonga o te ‘rahi o roto’.
    He aha ngā rautaki hei ine i te maha o ngā henemita pūtoru ka taea ki roto i te pouaka?
    1. Whakatakotoria he henemita pūtoru ki roto i te pouaka. Tatauria e hia ngā henemita pūtoru ka taea te kuhu ki roto.
    2. Inea te roa, te whānui me te teitei o te pouaka. Whakareatia.
    Hoatu te Whārangi Mahi 1 (PDF, 117KB)hei whakaoti mā ngā ākonga.

     

  2. Mō te roanga atu o te wiki ka huri haere ngā ākonga ki ngā poumahi e toru e whai ake nei.

Poumahi 1(PDF, 118KB)
Poumahi 2 (PDF, 87KB)
Poumahi 3 (PDF, 87KB)

Hei Whakawhānui:

Tirohia te hononga o te rōrahi me te kītanga (Arā, 1 000 cm3 = 1 rita)
Tirohia te rōrahi o ētahi atu āhua ahu-3, pērā i te rango, te poro-tapatoru rānei.

cylinder.

rōrahi (rango) = πp2t (r = pūtoro, t = teitei)

   3d triangle.

rōrahi (poro tapatoru) = equation. ptr (p = pūtake, t = teitei, r = roa)

AttachmentSize
TeRorahiWM1.pdf116.74 KB
TeRorahiPomahi1.pdf118.16 KB
TeRorahiPomahi2.pdf87.22 KB
TeRorahiPomahi3.pdf86.91 KB

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