Papa Whakarea (Kaupae 6)

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Hei Whakarāpopoto
E hāngai ana tēnei kōwae ako ki te rauemi matihiko nei, te Papa Whakarea. Ko tā te Papa Whakarea, he āwhina i ngā ākonga ki te tūhura i ngā rautaki wāwāhi tau mō te whakarea. I tēnei kōwae ako, ka whakamahia te Papa Whakarea ki te whakarea i tētahi tau mati-rua ki tētahi tau mati-1. E hāngai ana ki te Kaupae 6 o te Mahere Tau (Te Poutama Tau), arā, ka whakamahi te ākonga i ngā meka whakarea mōhio me ētahi rautaki ā-hinengaro ki te whakaoti whakareatanga. E rua atu anō ētahi atu kōwae ako e pā ana ki te akoranga matihiko nei, te Papa Whakarea, ko tētahi e aro ana ki te whakarea tau mati-rua māmā ki tētahi tau mati-tahi, ko tētahi e aro ana ki te whakarea i tētahi tau matirua ki tētahi (Kaupae 7).
Achievement Objectives
3. Ka kōwhiri, ka whakamārama i te rautaki e tino whaihua ana hei whakaoti rapanga e whai wāhi mai ana te tauoti, te hautau, te tau ā-ira me te ōrau: rautaki tatau; rautaki whakarōpū; rautaki tohatoha ōrite; rautaki tāpiripiri; rautaki whakarea māmā.
Te Hononga ki te Marautanga
Taumata 3
Te Tau me te Taurangi (Te Mātauranga Tau me ngā Rautaki Tau)
Whāinga Paetae 3:
Ka kōwhiri, ka whakamārama i te rautaki e tino whaihua ana hei
whakaoti rapanga e whai wāhi mai ana te tauoti, te hautau, te tau ā-ira me te ōrau:
  • rautaki tatau;
  • rautaki whakarōpū;
  • rautaki tohatoha ōrite;
  • rautaki tāpiripiri;
  • rautaki whakarea māmā.
Ngā Whāinga Ako
Kia mōhio te ākonga ki te:
  • wāwāhi i tētahi tau mati-2 ki ōna tekau me ōna tahi
  • whakamahi i te Papa Whakarea ki te wāwāhi i ngā tau o roto i tētahi whakareatanga tau mati-2 mā te tau mati-1, ki te whakaoti hoki i taua whakareatanga
  • tuhi pikitia ki te whakamārama i ngā rautaki wāwāhi tau hei whakaoti rapanga whakarea (tau mati-2 mā te tau mati-1)
Ngā Tikanga Pāngarau

E tino hono ana tēnei kōwae ako ki te Mahere Tau o Aotearoa (tirohia te kaupapa o Te Poutama Tau i te pae tukutuku o nzmaths.co.nz).

E whakaatu ana te wāhanga rautaki o te mahere tau i ngā momo rautaki ka whakamahia e ngā ākonga ki te whakaoti paheko.

E hāngai ana te mahi o tēnei kōwae ako ki te Kaupae 6 o te Mahere Tau. I tēnei kaupae, e mōhio ana te ākonga ki ngā meka whakarea matua, me ētahi rautaki wāwāhi tau hei whiriwhiri i te otinga o tētahi whakareatanga.

I tēnei kōwae ako, ka whakamahia te Papa Whakarea ki te whakarea i tētahi tau mati-2 ki tētahi tau mati-1. Ka wāwāhia te tau mati-2 ki ōna tekau me ōna tahi, kātahi ka whakareatia ngā wāhanga e rua ki te tau mati-1. Hei tauira: 63 x 4 = (60 x 4) + (3 x 4)

He Rārangi Kupu

 

tāneke
slider
tāpiri taruarua
repeated addition
skip counting
rauemi matihiko
digital resource
paheko tau
number operation
wāwāhi
partition
Hei Raupapa I Ngā Mahi Ako

E ono ngā rauemi matihiko pāngarau kua tuhia ki te reo Māori. Koia nei ngā whakamārama:

 

Te Rauemi Matihiko Te Whakamārama
Tāhei Tau Punarua Mēnā e mōhio ana te tamaiti ki ngā tau tāpiri o tētahi tau, he māmā ake tana whakaoti paheko tau. Ko tēnei akoranga matihiko hei whakapakari i a ia ki tēnei āhuatanga o te tau.
Tāhei Tāpiripiri Hei whakaako, hei whakapakari i te tamaiti ki ngā momo rautaki whakaoti tāpiritanga i rō hinengaro.
Tāhei Tangotango Hei whakaako, hei whakapakari i te tamaiti ki ngā momo rautaki whakaoti tangohanga i rō hinengaro.
Tāhei Huatango Ka tirohia tētahi rautaki matua mō te whakaoti tangohanga, arā, ko te huri i taua tangohanga hei tāpiritanga. Mā konei e māmā ai te kimi i te huatango (te rerekētanga) o ētahi tau e rua.
Tūtohi Tukutuku E aro ana tēnei o ngā akoranga matihiko ki te tikanga o tēnei mea te whakareatanga, me te hononga ki te tāpiri tāruarua. Hei āwhina i te tamaiti e tīmata ana ki te ako i te whakareatanga.
Papa Whakarea Mā te wāwāhi i ngā tau o roto i tētahi whakareatanga, e māmā ake ai te whakaoti i rō hinengaro. He rauemi tēnei hei āwhina i te tamaiti ki te whakaoti whakareatanga.

Haere ki tēnei wāhi i te ipurangi ki te tiki atu i ēnei rauemi matihiko:
http://www.tki.org.nz/r/digistore/register_e.php

E 5 ngā akoranga matihiko i te huinga akoranga matihiko 'Papa Whakarea'. Kotahi anake ka whakamahia i roto i tēnei kōwae ako, arā, ko tēnei: 'Papa Whakarea: Hangaia āu ake whakareatanga'

He Hononga ki Rauemi Kē

Tirohia te Pukapuka Tuaono o Te Poutama Tau.

Ka Mahi Tahi te Pouako me tētahi Rōpū Ākonga ki te Whakamahi i te Tāhei Tāpiripiri

  1. Whakamāramatia te tikanga o te rerenga 'wāwāhi tau' (he pai pea te whakatairite ki te rerenga 'wāwāhi tahā'). Arā, ngā whakarōpūtanga e taea ana mō tētahi tau. Whakatauiratia ki tētahi tau māmā. Anei ētahi wāwāhitanga e taea ana mō te 8:
    • 5 + 3 = 8
    • 4 + 4 = 8
    • 2 + 2 + 2 + 2 = 8
    • 6 + 2 = 8
    • 2 x 4 = 8 ...
  2. Whakamāramatia te mahi a te Papa Whakarea ki te wāwāhi i ngā tau o roto i tētahi whakareatanga, hei whakamāmā i te whakareatanga.
  3. Huakina te Papa Whakarea, ka pāwhiri ai i te pūtohu 'Hangaia āu ake whakareatanga'. Whakaurua tētahi whakareatanga. Hei tauira, ko te 73 x 8. Pāwhiria te pūtohu 'Whiriwhiria te otinga'

    diagram.

  4. Whakaaturia te mahi a te tāneke o runga ki te wāwāhi i te 73 ki te 50 me te 23. E rua ngā whakareatanga māmā ka puta mai. Pātai atu:
    • Kua ahatia te 73? (Kua wāwāhia ki ētahi wāhanga e rua, te 50 me te 23.)
    • He aha i pēnā ai te wāwāhi? (Hei whakamāmā i te whakareatanga.)

  5. Tuhia te otinga o ngā whakareatanga ki ngā pouaka. Tirohia ngā otinga o ēnei whakareatanga ka puta ki raro i te Papa Whakarea. Arā 73 x 8 = (50 x 8) + (23 x 8) = 400 + 184 = 584. Pātai atu:
    • He aha i puta ai te 400 me te 184? (Ko te 400 te otinga o te whakareatanga 50 x 8. Ko te 184 te otinga o te whakareatanga 23 x 8)
  6. Tuhia te otinga o te whakareatanga ki te pouaka.
  7. Pāwhiria te pūtohu 'E Hoki', ka tūhura ai i ētahi atu wāwāhitanga mō te 73 x 8, pērā i te 70 x 8 me te 3 x 8. Whakawhitiwhiti kōrero mō te wāwāhitanga māmā.
  8. Whakaaturia te mahi a te tāneke i te taha mauī o te Papa Whakarea. Tūhuratia te mahi a tēnei tāneke ki te wāwāhi i te 23 me te whaihua o tēnei ki te whakaoti i te whakareatanga.
  9. Whakaaturia te mahi a te tāneke i te taha matau o te Papa Whakarea. Tūhuratia te mahi a tēnei tāneke ki te kukume i te 8 ki te 10, me te whaihua o tēnei ki te whakaoti i te whakareatanga. Pātai atu:
    • Ki te kukume i tēnei tāneke, ka ahatia te 8? (Ka kumea ake ki te 10)
    • He aha ngā whakareatanga e rua ināianei? (Ko te 73 x 10 me te 73 x 2)
    • He aha te take ka tangohia te otinga o te 73 x 2 i te otinga o te 73 x 10? (Nā te mea, koirā te rahinga kē atu o te whakareatanga. E 2 te kumetanga ake o te 8 ki te 10, nō reira me tango atu taua wāhanga o te Papa Whakarea.)
    • Whakaaturia te mahi a te tāneke o raro. Tūhuratia te mahi a tēnei tāneke ki te kukume i te 73 ki te 80, me te whaihua o tēnei ki te whakaoti i te whakareatanga. Pātai atu:
      • Ki te kukume i tēnei tāneke, ka ahatia te 73? (Ka kumea ake ki te 80)
      • He aha ngā whakareatanga e rua ināianei? (Ko te 80 x 8 me te 7 x 8)
      • He aha te take ka tangohia te otinga o te 7 x 8 i te otinga o te 80 x 8? (Nā te mea, koirā te rahinga kē atu o te whakareatanga. E 7 te kumetanga ake o te 73 ki te 80, nō reira me tango atu taua wāhanga o te Papa Whakarea.)
    • Whakamahia te Papa Whakarea ki te whakaoti i ētahi atu whakareatanga. Tonoa mā ngā ākonga e whakaaro ngā wāwāhitanga e tino whaihua ana.
    • Tuhia te rapanga nei ki te papa tuhituhi, ka pānui tahi ai me ngā ākonga. Tuhia he pikitia o ngā papariki
      • Kei te whakatakoto a Manawanui i ētahi papariki ki te papa o tōna ruma horoi. He tapawhā hāngai te āhua o te papa, 32 ngā papariki ki tētahi tapa, e 9 ki tētahi. E hia katoa ngā papariki?

      grid.

    • Whakaurua te whakareatanga 32 x 9 ki te Papa Whakarea. Whakawhitiwhiti kōrero mō ngā wāwāhitanga hei whakamāmā i te whakareatanga (arā pea:

      32 x 9 = (30 x 9) + (2 x 9).
      32 x 9 = (32 x 10) – (32 x 1)

    • Whakaotia te whakareatanga ki te Papa Whakarea.
    • Tuhia he pikitia hei whakaatu i te wāwāhitanga o te whakareatanga.
    • Kia pērā anō te mahi mō ētahi tau atu whakareatanga. Hei tauira:
      • Kei te whakatakoto a Manawanui i ētahi papariki ki te papa o tōna kīhini. He tapawhā hāngai te āhua o te papa. 27 ngā papariki ki tētahi tapa, e 7 ki tētahi. E hia katoa ngā papariki?
      • Kei te whakatakoto a Manawanui i ētahi papariki ki te papa o tōna kīhini. He tapawhā hāngai te āhua o te papa. 58 ngā papariki ki tētahi tapa, e 8 ki tētahi. E hia katoa ngā papariki?
      • Kei te whakatakoto a Manawanui i ētahi papariki ki te papa o tōna kīhini. He tapawhā hāngai te āhua o te papa. 84 ngā papariki ki tētahi tapa, e 6 ki tētahi. E hia katoa ngā papariki?

Ka Mahi Takitahi, Takirua rānei ngā Ākonga me te Papa Whakarea

Koia nei ētahi horopaki me ētahi rapanga hei whakaoti mā ngā ākonga mā te whakamahi i te Papa Whakarea. Kia kotahi, kia rua rānei ngā ākonga ki ia rorohiko.

  • Te Utu ā-Hāora

E $8 te utu ā-hāora a Matewai. Ka mahi ia mō te 34 hāora. He aha te tapeke o tana utu?
Mēnā e $9 te utu ā-hāora, ka mahi ia mō te 57 hāora?
Mēnā e $7 te utu ā-hāora, ka mahi ia mō te 62 hāora?
Mēnā e $8 te utu ā-hāora, ka mahi ia mō te 39 hāora?

  • He Nohoanga i te Whare Pikitia

E 8 ngā rārangi nohoanga i te whare pikitia, 54 ngā nohoanga ki ia rārangi. E hia katoa ngā nohoanga?
Mēnā e 9 ngā nohoanga, 36 ngā nohoanga o ia rārangi?
Mēnā e 8 ngā nohoanga, 48 ngā nohoanga o ia rārangi?
Mēnā e 7 ngā nohoanga, 35 ngā nohoanga o ia rārangi?

  • He Tūnga Motukā

E 7 ngā rārangi tūnga motukā, 43 ngā tūnga ki ia rārangi. E hia katoa ngā tūnga motukā?
Mēnā e 6 ngā rārangi, 68 ngā tūnga ki ia rārangi?
Mēnā e 7 ngā rārangi, 83 ngā tūnga ki ia rārangi?
Mēnā e 9 ngā rārangi, 92 ngā tūnga ki ia rārangi?

Mō ia rapanga, tonoa ngā ākonga ki te tuhi i tētahi pikitia hei whakaatu i te whakamahinga o te Papa Whakarea ki te whakaoti i te rapanga.

Tukuna he wā mā ia ākonga e whakaatu tana pikitia, me te whakamārama i tana whakamahinga i te Papa Whakarea. Koia nei he pātai hei ārahi i ngā ākonga:
 

  • I pēhea tō whakamahi i te Papa Whakarea?
  • Whakamāramatia mai tō whakamahi i te Papa Whakarea ki te whakaoti i te rapanga.
  • Whakamāramatia mai tō wāwāhi i ngā tau?
  • He aha i pērā ai tō wāwāhi i ngā tau?
  • Me pēhea te whakaatu i tō mahi ki te pikitia?
  • Ko tēhea te wāwāhitanga tino māmā?

Ka Mahi Takitahi, Takirōpū rānei ngā Ākonga me ētahi atu Mahi e Whai Pānga ana

Hoatu ētahi atu rapanga hei whakaoti mā ngā ākonga, engari kāore rātou e whakamahi i te Papa Whakarea. Ka tuhi pikitia rātou ki te whakaatu i te wāwāhitanga o ngā tau hei whakamāmā i te whakareatanga.

Tonoa ngā ākonga ki te tuhi pakitau mō ētahi whakareatanga, hei whakaoti mā tētahi hoa, mā tētahi rōpū rānei.

Me haere tonu te whakawhitiwhiti kōrero mō te wāwāhitanga e tino whaihua ana.

Koia nei ētahi atu mahi e tino hono ana ki te Papa Whakarea:
 

  • Tirohia te pae tukutuku
    (Rauemi Tārua):
    • Rauemi Tārua 6-2 (Kāri Meka Whakareatanga Matua)
    • Rauemi Tārua 6-3 (Meka Whakareatanga – Kia Hiwa)
    • Rauemi Tārua 6-4 (Whakareatanga Pī Takahuri)
    • Rauemi Tārua 6-6 (Rārangi Whakareatanga)
    • Ngā ngohe i te Pukapuka Tuaono o Te Poutama Tau
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Taumata 3