Te Whakaari Raraunga

The Ministry is migrating nzmaths content to Tāhurangi.           
Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz). 
When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024. 
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For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

Hei Whakarāpopoto

Ka tirohia te kauwhata rautō me te kauwhata tāhei.  Kia rua pea ngā rā mahi ki ia momo kauwhata, ā, kia kotahi te rā hei aromatawai, hei whakakapi i ngā mahi.

Te Hononga ki te Marautanga

Taumata 3

Te Tauanga (Te Tūhuratanga Tauanga)
Whāinga Paetae 1:
Ka whai i ngā tikanga mō te tūhuratanga tauanga e whai wāhi mai ana
  • ka whakatakoto pātai;
  • ka kohikohi raraunga;
  • ka wehewehe raraunga;
  • ka hanga whakaari raraunga e whaitake ana;
  • ka whakaputa kōrero hei whakautu i te pātai i tūhuratia;
  • ka mārama ki ngā tikanga matatika e hāngai ana.
 
Whāinga Paetae 2:
Ka tautohu i ngā tauira me ngā ia e kitea mai ana i roto i tētahi huinga raraunga, i waenganui rānei i ētahi huinga raraunga.
 
Whāinga Paetae 3:
Ka arotake i te whaihua o ngā momo whakaari raraunga rerekē hei whakaatu i ngā hua o tētahi tūhuratanga tauanga.
Ngā Whāinga Ako

 

Kia mōhio te ākonga:
  • ki te pānui, ki te whakamāori, ki te tuhi i te kauwhata tāhei me te kauwhata rautō
  • ngā tikanga o te āwhata o tētahi kauwhata
  • ki te tuhi kōrero mō ngā āhuatanga e whakaaturia ana ki tētahi kauwhata
  • ki te momo kauwhata e tika ana mō tētahi kaupapa
Ngā Rauemi

Whārangi Mahi 1

Whārangi Mahi 2

Whārangi Mahi 3

He Rārangi Kupu

 

āwhata

scale

kauwhata rautō

stem and leaf graph

tūtohi

table (of data)

poutū

vertical

tapeke

total, score

whakaari raraunga

data display

raraunga

data

kauwhata tāhei

strip graph

kauwhata tāhei hiato

composite strip graph, stacked bar graph

tuaka

axis

raraunga tau

number data

tuari

distribution

rāpoi

cluster

mōwaho

outlier

auau

frequency

Hei Raupapa I Ngā Mahi Ako
  1. Ko te mahi tuatahi he tirotiro, he matapaki, he whakamārama i te kauwhata rautō.

     

    Te mahi a te pouako

    He tauira kōrero mā te pouako

    Whakaaturia tētahi huinga raraunga tau, ka whakawhiti kōrero ai mō ngā momo whakaari i aua raraunga.

    Anei ētahi tauira:

    Koia nei ngā tapeke o ētahi tāngata tekau i hua mai i tētahi whakataetae hahau pōro:

    {78, 74, 62, 68, 76, 78, 83, 92, 79, 75}

    He tauira atu anō:

    Koia nēi ngā oma i riro i a Hakopa i roto i ana kēmu kirikiti i te roanga atu o tētahi raumati:

    {70, 45, 21, 4, 0, 8, 18, 89, 101, 82, 32, 2, 52, 41, 9, 2, 76}

     

    Tekau ngā tangata tākaro hahau pōro.  Koia nei ngā tapeke i riro i a rātou i tētahi whakataetae.  Me pēhea e whakaatu ai i ēnei tapeke.

     

    Ko ngā momo whakautu tērā pea ka hua mai:

    • Whakaaturia ki te kauwhata pou.  Tuhia ngā ingoa o ngā tāngata me tētahi pou hei whakaatu i te tapeke o tēnā me tēnā.
    • Whakaaturia ki tētahi tūtohi.  Arā, ka tuhia te ingoa o te tangata me tāna tapeke i te taha.

     

    Whakamāramahia ngā tikanga o te kauwhata rautō hei whakaatu i tētahi huinga raraunga tau.  Whakaaturia ngā wāhanga o te kauwhata rautō ki te papatuhituhi.

     

     

    Ko te kauwhata rautō tētahi momo kauwhata.  Mehemea he tau anake ngā raraunga, koinei tētahi kauwhata pai.

    E rua ngā wāhanga o te kauwhata rautō, ko te tō me te rau.  Ko te tō, he rite ki te tuara.  He poutū te tuhi i te tō.

    Ka tuhia tētahi wāhanga o ngā tau ki roto i te tō o te kauwhata.  Hei tauira, ko ngā oma i riro i a Hākopa i ana kēmu kirikiti.  Ka tuhia ngā ‘tekau’ o ana oma ki te tō.

    Mai i te 0 ki te 101 te maha o ana oma, nō reira ka tuhia ngā tekau mai i te 0 ki te 10 ki te tō o te kauwhata.

    Ko te ‘rau’ te wāhanga tuarua o te kauwhata.  Ka whakaaturia tēnei wāhanga o te kauwhata ki te taha o te tō.  Ko te rau hei whakaatu i tētahi atu wāhanga o ngā tau. 

     

     

    Whakawhitiwhiti kōrero mō ngā āhuatanga e kitea ana i te kauwhata rautō.

    Ki te taha o te ‘0’ o te tō (arā, he kore ngā tekau), ka tuhia te 0, 2, 2, 8, 9 (he piko ki waenganui).  Koinei te raupapa o ngā oma mai i te 0 ki te 9.

    Ki te taha o te ‘1’ o te tō (arā, kotahi te tekau), ka tuhia te 8 anake.  Ko te 18 anake te tapeke i waenganui i te 10 me te 19.  Ko te 10 o te tō me te 8 o te rau hei tohu i te 18.

    Ki te taha o te 2, ka tuhia he ‘1’, nā te mea ko te 21 anake te tapeke i waenganui i te 20 me te 29.

    Kia pērā te tuhi haere i ngā ‘tahi’ ki te taha o ngā ‘tekau’

    Koinei te whakamutunga o te kauwhata.

    He tauira whakautu:

    • He mārama te kitea atu o te tapeke iti rawa (te 0) me te tapeke nui rawa (te 101). 
    • E toru ngā whakarōpūtanga o ngā tapeke – tētahi rōpū kei raro i te 21, arā, ngā tapeke iti.  Ko tētahi rōpū kei waenganui, arā, ngā tapeke mai i te 32 ki te 52, ā ko tētahi rōpū ko ngā tapeke teitei (nui ake i te 70).
    • He maha ake ngā tapeke iti i ngā tapeke waenganui, tapeke nui rānei.

     

     

    Hoatu te Whārangi Mahi 1 hei whakaoti mā ngā ākonga.  He pai pea te mahi takirua.

  2. Ko te mahi tuarua he tirotiro, he matapaki, he whakamārama i te kauwhata tāhei.

     

    Te mahi a te pouako

    He tauira kōrero mā te pouako

     

    Whakaaturia te kauwhata tāhei nei ka whakawhitiwhiti kōrero ai mō ngā āhuatanga e kitea mai ana.

    He kauwhata tāhei tēnei.  Ko te tāhei, koia tētahi tapawhā hāngai, he roa, he tūpuhi te āhua.  Ki tō titiro, he aha te kaupapa e whakaaturia ana?

    Ko te tokomaha o ngā tamariki i ahu mai ai i tēnā Kōhanga Reo i tēnā Kōhanga Reo.

    Ko tēhea te Kōhanga Reo i ahu mai ai te nuinga o ngā tamariki?

    Ko te Kōhanga Reo o Te Oranga.

    He aha tātou i mōhio ai?

    Ko te rahi o ia wāhanga o te tāhei e tohu ana i te tokomaha o ngā tamariki.  Mēnā he roa te wāhanga koia e tohu ana he tokomaha.  mēnā he paku noa te wāhanga o te tāhei, koia e tohu ana he tokoiti.  Ko te wāhanga mō Te Oranga, koira te wāhanga roa rawa, nō reira te tokomaha o ngā tamariki.

     

    Whakaaturia te kauwhata tāhei whai āwhata, ka whakawhiti kōrero ai mō te āwhata.

    Anei anō te kauwhata tāhei e whakaatu ana i ngā Kōhanga Reo i ahu mai ai ngā tamariki.  Kua tuhia ētahi tohu ki te āwhata.  He aha pea te tikanga o ngā tohu?

    Koia e whakaatu ana i te tokomaha o ngā tamariki.  Akene pea ko ia tohu he rite ki te tamaiti kotahi.

    Nō reira, tokohia i ahu mai ai i te Kōhanga Reo o Puawai?

    Tokorua.

    Mehemea e rite ana ia tohu ki ētahi tamariki tokorua, tokohia mai i te Kōhanga Reo o Te Uru Karaka?

    Tekau, nā te mea e rima ngā tohu e rite ana ki te wāhanga o te tāhei mō Te Uru Karaka.

    Tokohia katoa ngā tamariki o tēnei akomanga (mēnā e rite ana ia tohu ki ētahi tamariki tokorua)?

    E 24, nā te mea 12 ngā tohu i te roanga atu o te tāhei.

     

    Whakaaturia ngā raraunga me te kaupapa tauanga nei:

    I tukuna te pātai ki ngā tamariki o tētahi akomanga, he aha tā rātou tino kai?   Koinei ngā whakahokinga mai:

    te kai

    te tokomaha

    kaimoana

    4

    hāngi

    7

    kōhua

    3

    Makitānara

    2

    huamata

    8

     

    Whakamāramahia me pēhea e whakaatu ai ēnei raraunga ki te kauwhata tāhei. 

     

     

     

     

     

     

     

     

     

    Titiro ki tēnei kaupapa.  I pātaihia ngā tamariki o tētahi akomanga, he aha tā rātou tino kai?   Ka tuhia ngā whakahokinga ki tētahi tūtohi.  Me pēhea te whakaatu i tēnei kaupapa ki te kauwhata tāhei?

    Anei te tauira whakamārama:

    Ko te mea tuatahi, he āta whakaaro ki te roa o te tāhei.  E 24 katoa ngā tamariki hei whakaatu ki te tāhei (koira te tapeke o te tokomaha mō ia momo kai).  He roa rawa te tāhei mēnā ka hoatu te mitarau (henemita) kotahi mō ia tamaiti).  He pai kē te mitarau haurua, nō reira kia 12cm te roa o te tāhei.

     

    Ko te mea tuarua, he tuhi i te tāhei (kia 12cm te roa), kātahi ka whakaatu ai i ia wāhanga.  Tokowhā e pai ana ki te kaimoana, nō reira kia 2cm te roa o tērā wāhanga o te tāhei.

     

    Tuatoru, ka karangia, ka kaurukutia rānei ia wāhanga, ā, ka tuhia te tohu hei whakaatu i te tikanga o ia kara, o ia momo kauruku rānei.

     

    Ko te mea whakamutunga, he tapa i te kauwhata kia mōhiotia ai he aha te kaupapa.

     

     

    Hoatu te Whārangi Mahi 2 hei whakaoti mā ngā ākonga.  He pai pea te mahi takirua.

     

  3. Hei whakaoti i tēnei kaupapa, hei mahi aromatawai rānei, tukuna ngā ākonga ki te mahi i te Whārangi Mahi 3.  Ko ētahi o ngā mahi, he āta whakaaro ki te momo whakaari raraunga e tika ana, he tuhi hoki i te kauwhata.  Ko tētahi, he whakahaere tūhuratanga kohikohi raraunga, he whakaatu i aua raraunga ki te kauwhata, he tuhi kōrero mō te kaupapa o te tūhuratanga.
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