Te Rōrahi

Thanks for visiting NZMaths.
We are preparing to close this site and currently expect this to be in June 2024
but we are reviewing this timing due to the large volume of content to move and
improvements needed to make it easier to find different types of content on
Tāhūrangi. We will update this message again shortly.

For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

Hei Whakarāpopoto

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
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 wh
Te Hononga ki te Marautanga
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.
Ngā Whāinga Ako
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
Ngā Rauemi

he nūpepa

he ruri

he tēpa whakapiri

Whārangi Mahi 1

he henemita pūtoru

he kāri A4

Poumahi 1

Poumahi 2

Poumahi 3

He Rārangi Kupu

 

henemita pūtoru cubic centimetre
horahanga mata surface area
mita pūtoru cubic metre
raumata net
rōrahi volume
poro-tapawhā hāngai rectangular based prism
Hei Raupapa I Ngā Mahi Ako
  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.

    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.

 

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

 


rōrahi (poro tapatoru) =ptr/2 (p = pūtake, t = teitei, r = roa)

Attachments
Add to plan

Log in or register to create plans from your planning space that include this resource.


Taumata 4