Mahere Tukutuku

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Hei Whakarāpopoto

I tēnei kōwae ako ka tūhurangia te whakamahinga o te tukutuku hei tautohu pūwāhi, hei tautohu ara anō hoki.

Achievement Objectives
8. Ka hanga, ka whakamahi mahere māmā: ka whakaatu taunga; ka whakaatu ahunga; ka whakamārama huarahi; ka whakamārama tirohanga.
Te Hononga ki te Marautanga

Taumata 2

Te Ine me te Āhuahanga

Whāinga Paetae 8 (Te Wāhi me te Ahunga):

Ka hanga, ka whakamahi mahere māmā: ka whakaatu taunga; ka whakaatu ahunga; ka whakamārama huarahi; ka whakamārama tirohanga.

Ngā Whāinga Ako

Kia mōhio te ākonga ki:

  • te tautohu pūwāhi ki te tukutuku
  • te whai me te hoatu tohutohu mō te neke i te pūnaha tukutuku
Ngā Tikanga Pāngarau
  • Ko te tukutuku tētahi pūnaha matua e tautohua ai tētahi pūwāhi me tētahi ara neke i tētahi papa.
  • E rua ngā momo tapa i ngā kapa me ngā pou o tētahi papa tukutuku:
    • ko te tapa i ngā kapa me ngā pou kei waenganui i ngā rārangi o te tukutuku
    • ko te tapa i ngā rārangi huapae me ngā rārangi poutū o te tukutuku
Ngā Rauemi
Whārangi Tārua 2

Whārangi Tārua 1

He pepa tukutuku

He Rārangi Kupu
tukutuku grid
huapae horizontal
poutū vertical
kapa row
pou column
ahunga direction
aronga orientation
papa tukutuku plane grid
pūwāhi point (in space)
taunga cordinate
takirua raupapa ordered pair
pūtahi intersect
Hei Raupapa I Ngā Mahi Ako

Hei Raupapa i ngā Mahi Ako

  1. Ko te mahi tuatahi, he arataki i ngā ākonga kia tūhura i te āhua o te tukutuku me te tautohu pūwāhi i te tukutuku.
Ngā tohutohu He tauira whakawhitinga kōrero

Whakarārangihia ētahi tūru e 20 ki ngā kapa e 4 me ngā pou e 5:

Whakanōhia ngā ākonga ki ētahi o ngā tūru. E pai ana mēnā kei te wātea tonu ētahi.

Whakawhitiwhiti kōrero mō ngā kapa me ngā pou.

Titiro ki te rārangi mai o ngā tūru. E hia katoa ngā tūru?

He tauira whakautu: 
  • E 20 nā te mea e 5 ngā tūru kei ngā rārangi e 4. Whakareatia te 5 ki te 4, ka 20. 
  • Tatauria ia rārangi tūru: 5, 10, 15, 20. 
  • Tatauria ia whakarōpūtanga o ngā tūru e 4: 4, 8, 12, 16, 20. 
  • Rearuatia te 5 ka 10. Rearuatia te 10, ka 20.

Haere koutou ki te noho ki ētahi o ngā tūru, ka anga mai ai ki ahau. Whakatūria tō ringaringa mēnā kei te noho koe ki te kapa tuatahi o ngā tūru.

Ko te kapa tūru tuatahi, koirā te rārangi tūru kei mua tonu i ahau.

Ko wai kei te kapa tuarua e noho ana?

E hia katoa ngā kapa o ngā tūru? E 4.

E hia ngā tūru kei ia kapa? E 5.

Ko te rārangi tūru e haere pēnei ana, ka kīia he pou. Ko wai kei te noho ki te pou tuatahi o ngā tūru?

E hia katoa ngā pou? E 5.

E hia ngā tūru kei ia pou? E 4.

Ko wai kei te noho ki te kapa tuatahi me te pou tuatahi?

Ko wai kei te noho ki te kapa tuatoru me te pou tuawhā?

E Hī, kei hea koe e noho ana? Kei tēhea kapa, kei tēhea pou?

Whakawhitiwhiti kōrero mō te takirua raupapa hei tautohu pūwāhi i te tukutuku tūru.

Ko Mīria kei te noho ki te kapa tuatahi me te pou tuatoru. Ko te tuhinga poto (3,1) hei whakaatu i te wāhi noho o Mīria. He aha ki ō whakaaro te tikanga o te takirua tau (3,1)? Ko te tau tuatahi hei tohu i te pou. Ko te tau tuarua hei tohu i te kapa.

E tū koe mēnā kei te (4,3) koe e noho ana.

E Mara, he aha te takirua tau mō te tūru kei tō taha matau?

E tū koutou e noho ana ki ēnei pūwāhi: (2,1) (2,2) (2,3) (2,4). He aha ētahi kōrero mō koutou?
He tauira whakautu:
Kei te pou tuarua mātou katoa. He rārangi torotika ō mātou tūru. Ko te ‘2’ te tau tuatahi o ā mātou takirua tau katoa.

Tūhurangia te takirua raupapa e hāngai ana ki te pūtahitanga o tētahi pou me tētahi kapa.

E tū te pou tuarua me te kapa tuatoru. Ko wai kei te pūtahitanga, (te haukotinga rānei) o ēnei rārangi e rua nei? Ko Himiona. Ko te (2,3) tana takirua tau. Ko ia kei te pou tuarua me te kapa tuatoru e noho ana.

Hoatu he pepa tukutuku (Whārangi Tārua 1) ki ngā ākonga, ka tono ai kia whakaaturia te rārangitanga mai o ngā tūru, me te tautohu anō i te wāhi noho o ētahi.

Anei tētahi momo pikitia hei whakaatu i te rārangi mai o ngā tūru. Ka kīia tēnei momo pikitia he tukutuku.

Tohua mai ētahi kapa o te tukutuku.

E hia katoa ngā kapa? E 4. He rite ki te rārangitanga mai o ngā tūru.

Tohua mai te pou tuatahi o te tukutuku.

Tohua mai te pūwāhi (2,4).

Tohua te pūwāhi e noho ana a Tamahou. He aha te takirua tau e hāngai ana ki tana wāhi noho?

Whakaaturia te wāhi noho o ētahi tāngata tokotoru.

Tuhia he ripeka (+) ki te pūwāhi (4,2)

Tuhia he porowhita ki te pūwāhi (5,3)

Tirohia te tukutuku tuarua kei te Whārangi Tārua 1, ka whakawhitiwhiti kōrero ai mō te tapa i ngā pou me ngā kapa.

Tukuna he tohutohu kia tuhia he āhua ki ētahi pūwāhi i te tukutuku.

Titiro ki te tukutuku tuarua kei te Whārangi Tārua nei. E hia ngā kapa o te tukutuku? E 6.

Pēhea nei te tapa i ngā kapa o tēnei tukutuku? Ka tīmata i runga. Ko te kapa kei runga, koirā te tuatahi, heke haere ai ki te tuarua, te tuatoru, tae atu ki te tuaono.

E hia ngā pou o te tukutuku? E 8.

Pēhea nei te tapa i ngā pou? Kua tapaina ki ngā pūmatua, e tīmata mai ana i te taha mauī, koirā te ‘A’, ko te pou ‘E’ kei te taha matau o tērā.

Āe rā, he rerekē te āhua o te tapa i ētahi tukutuku. Ko ētahi ka whakamahi i ngā tau anake, ko ētahi ka whakamahi i ngā pū. Ko ētahi ka tauria whakarunga, ko ētahi ka heke whakararo te tauria o ngā kapa.

Tuhia he whetū ki te pūwāhi (E,4) o te tukutuku.

Tuhia he porowhita ki ngā pūwāhi katoa i te pou ‘M’.

  1. Ko te mahi tuarua, he tūhura i te neke, me te tautohu ara neke ki te papa tukutuku.
Ngā tohutohu He tauira whakawhitinga kōrero

Tuhia he tukutuku nui ki te papa tākaro, ki te papa rānei o te akomanga (whakamahia pea he tioka, he tēpa rānei hei whakaatu i ngā rārangi o te tukutuku). Kia 8 mā te 8 te rahi o te tukutuku.

Tuhia he pūmatua hei tapa i ngā pou o te tukutuku, tauria ngā kapa mai i runga ki raro.

Whakatūria tētahi ākonga ki tētahi wāhi o te tukutuku.

Whakaaturia ētahi kāri hei tohutohu i tana neke haere i te tukutuku.

Kia pērā anō te mahi mō ētahi atu huinga kāri tohutohu.

Rāpata, e tū koe ki te pūwāhi (E,2), ka aro mai ai ki ahau. Anei ngā kāri hei tohutohu i a koe ki te neke haere i te tukutuku.

He aha ki a koe te tikanga o ngā tohutohu? 

  • Ko te whakamua e mea ana kia neke whakamua kotahi te wāhi i te tukutuku. 
  • Ko te whakamuri e mea ana kia neke whakamuri kotahi te wāhi i te tukutuku. 
  • Ko te huri matau e tohutohu ana kia huri koe ki tō taha matau, he hurihanga hauwhā. 
  • Ko te huri mauī e tohutohu ana kia huri koe ki tō taha mauī, he hurihanga hauwhā.

Tēnā, whāia e koe ngā tohutohu nei. Ko hea te pūwāhi whakamutunga o tō haere?

Hoatu he papa tukutuku ki ia ākonga (Whārangi Tārua 2). Tonoa ngā ākonga kia mahi takirua, ko tētahi hei tuku tohutohu mō te neke i te papa tukutuku, ko tētahi hei tuhi i te ara neke a tana hoa.

Anei tētahi papa tukutuku hei tuhi māu i tētahi ara. Tuhia te wāhi tīmatanga me te aronga whakamua. Tuhia hoki ngā tohutohu katoa o te ara. Whakamahia ngā tohutohu e whā nei:
whakamua, whakamuri, huri matau, huri mauī.

Hoatu ō tohutohu ki tō hoa hei whaitanga māna. Māna e tuhi tō ara neke i tana papa tukutuku, māu tāna e tuhi.

  1. Mō te roanga atu o te kōwae ako nei, tukuna ngā ākonga kia tūhura i ēnei āhuatanga o te ara neke i te papa tukutuku: 
    • He aha ngā tohutohu mō te ara poto rawa atu mai i te (E,6) ki te (K,3)? Kotahi anake te ara poto rawa atu, e rua, nui ake rānei? Whakamāramatia mai. 
       
    • Tuhia ngā tohutohu mō tētahi ara mai i te (H,2) ki te (Ng,5), kia 3 ōna huringa matau. 
       
    • Tuhia ngā tohutohu mō tētahi ara mai i te (I,4) ki te (N,8). He aha ngā tohutohu mō te hokinga atu i te (N,8) ki te (I,4), me te takahi anō i te ara tuatahi mai i te (I,4) ki te (N,8)? 
       
    • Tuhia ngā tohutohu mō tētahi ara he tapawhā hāngai te āhua. 
       
    • Ka taea tētahi ara he tapatoru te āhua? Whakamāramatia mai. 
       
    • Ko tētahi tikanga mō te tāpiritanga tau e mea ana, kāore he take o te raupapatanga mai o ngā tauhono, arā, 3 + 4 + 5 = 4 + 5 + 3. He pērā anō te tikanga mō te tohutohu ara neke i te papa tukutuku, kāore rānei? Arā:
      whakamua + huri matau + whakamuri = whakamuri + whakamua + huri matau
      Whakamāramatia mai. 
       
    • Whakaarohia tētahi tohutohu mō te neke tītaha i te papa tukutuku. Hei tauira:
      ✔ mai i te (H,2) ki te (M,5)
      ✔ mai i te (I,7) ki te (N,4)
      Tuhia he tohutohu mō tētahi ara neke i te papa tukutuku e whai wāhi mai ana te neke tītaha. 
       
    • Me āta whakaaro i roto i tō hinengaro ngā tohutohu mō te neke i te papa tukutuku kia rite ki te pūmatua ‘T’. Kaua e titiro ki te papa tukutuku, ka tuhi ai i ngā tohutohu. Kia mutu, whakaaturia tō ara neke ki te papa tukutuku hei whakamātau i ō tohutohu. Kia pērā anō mō ētahi atu pūmatua, pēnei i te E, te F me te H.
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Taumata 2