| Te Ine, Tuanaki Taumata 8
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| Ngā Whāinga Paetae
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| Te whakatau tata, te ine
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| I roto i ngā horopaki whai tikanga, me mōhio te ākonga :
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| 1. ki te tātai i te pānga tapeke o te whakatau tata i te rahinga o tētahi mea, te whakatau tika ai;
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cumulative effect |
| 2. ki te kimi mai i te nui o te kotiti ka puta ake i te whakataunga tata i roto i tētahi horopaki tūturu , ka whakaahua ai i tōna takenga mai;
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uncertainty
source |
| 3. ki te whakamaori, ki te kimi mai i ngā hātepe e oti ai ētahi mahi whaitake, ētahi tātaitanga hoki.
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algorithm
calculation |
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Te whakapakari orotau ki ngā āhuatanga papatanga, āhuatanga whiti
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| I roto i ngā horopaki whai tikanga, me mōhio te ākonga :
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| 4. ki te kimi mai i ngā aputa o roto i tētahi pānga , ka kimi ai i te tepe (mehemea rāhe tepe);
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discontinuity; limit |
| 5. ki te whiriwhiri, ki te whakahangai i ngā ture pārōnaki tika ki ngā wāhi tika;
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differentiation |
| 6. ki te tautuhi i ngā wāhi e ōwehe ana te papatanga whiti ki te uara o te pānga , ki te whakamahi hoki i te pānga pūtanga i ngā wāhi e hangai ana;
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proportional
exponential |
| 7. ki te mahi mai i tētahi tauira wharite pārōnaki e pā ana ki tētahi pūāhua tūturu , pūāhua
whakatau ke rānei , ā, ki te whakamaori, ki te kimi otinga
e pā ana ki taua āhuatanga .
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differential equation model; situation
simulated |
| 8. ki te whakamahi i ngā tikanga ine pēnei i te ture kimi pāwhaitua , i te ture a Simpson, i te ture taparara hoki, hei kimi mai i te horahanga;
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integration
trapezium rule |
| 9. ki te whakamahi i ngā rautaki ine e tika ana mō te rorahi;
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strategy |
| 10. ki te whakamahi i ētahi tikanga kimi pāwhaitua hei whakaoti rapanga tūturu , rapanga whakatau hoki.
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simulated problems |
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He Tauira Horopaki
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- NGA IWI MAORI&;Kimihia, ki ngā tikanga wharite pārōnaki , te papatanga taupū o te nui haere o te taupori Maori.
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exponential rate
population |
- TE MAHI HANGI&;Kimihia, ki ngā tikanga tuanaki, te papatanga o te matao haere o te hangi.
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calculus |
| He Tauira Mahi
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| Te whakatau tata, te ine
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| Anei ētahi tauira mahi e taea ai ngā whainga paetae o tēnei taumata te whakatutuki:
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| 1. Me mōhio te ākonga ki te tātai i te pānga tapeke o te whakatau tata i te rahinga o tētahi mea, te whakatau tika ai;
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| 2. Me mōhio te ākonga ki te kimi mai i te nui o te kotiti ka puta ake i te whakataunga tata i roto i tētahi horopaki tūturu , ka whakaahua ai i tōna takenga mai;
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- he hōpara i ngā kotiti ka puta ake i ngā pūāhua whaitake e whai wāhi mai ana te ine me te tātaitanga .
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| 3. Me mōhio te ākonga ki te whakamaori, ki te kimi mai i ngā hātepe e oti ai ētahi mahi whaitake, ētahi tātaitanga hoki;
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- he hanga, he whakamahi hātepe mō roto i ngā tātaitanga , pēnei i te whakahoki, i te tapeke, i te whiriwhiri kaupapa.
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| Te whakapakari orotau ki ngā āhuatanga papatanga, āhuatanga whiti
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| Anei ētahi tauira mahi e taea ai ngā whainga paetae o tēnei taumata te whakatutuki:
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| 4. Me mōhio te ākonga ki te kimi mai i ngā aputa o roto i tētahi pānga , ka kimi ai i te tepe (mehemea rāhe tepe);
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- he hōpara ariā e pā ana ki ngā raraunga aputa kore me te tepe o te pānga .
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| 5. Me mōhio te ākonga ki te whiriwhiri, ki te whakahangai i ngā ture pārōnaki tika ki ngā wāhi tika;
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- he tuhi pārōnaki kia pēnei te āhua :
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- he kimi pārōnaki tapeke, whakarau, whakawehe, pānga hiato (ki te ture mekameka), ka kimi ai i te pārōnaki tuarua, tuaaha ke rānei ;
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- he kimi mai i ngā pārōnaki o ngā pānga pakoki, pānga taupū kōaro , pānga taupū .
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| 6. Me mōhio te ākonga ki te tautuhi i ngā wāhi e ōwehe ana te papatanga whiti ki teuara o te pānga , ki te whakamahi hoki i te pānga pūtanga i ngā wāhi e hangai ana;
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- he whakaoti rapanga tūturu , whakatau rānei e whai wāhi mai ana te papatanga whiti taurangi, tae atu hoki ki te whakamahia o ngā pānga pūtanga , taupū kōaro rānei .
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| 7. Me mōhio te ākonga ki te mahi mai i tētahi
tauira wharite pārōnaki e pā ana ki tētahi pūāhua tūturu
, pūāhua whakatau ke rānei , ā, ki te whakamaori, ki
te kimi otinga e pā ana ki taua āhuatanga ;
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- he hōpara i ngā tikanga kimi pārōnaki , pāwhaitua , tae atu ki te whakamahia o te wharite kimi pārōnaki hei whakaoti rapanga tūturu , whakatau rānei ;
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- he whakaoti wharite kimi pārōnaki ki ngā tikanga e tika ana, pēnei i te wehe taurangi, i te tikanga tau rānei ;
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- he whakaatu pāwhaitua hei tepe o tētahi tapeke, he whakaatu hoki i te pānga i waenganui i te kimi pāwhaitua me te kimi pārōnaki kōaro .
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| 8. Me mōhio te ākonga ki te whakamahi i ngā tikanga ine pēnei i te ture kimi pāwhaitua , i te ture a Simpson, i te ture taparara hoki, hei kimi mai i te horahanga;
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| 9. Me mōhio te ākonga ki te whakamahi i ngā rautaki ine e tika ana mō te rorahi;
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- he torotoro i ngā pūāhua tapeke whaitake, tae atu hoki ki te horahanga o raro anau me te rorahi hurihanga, me te whakamahi anō i ngā tikanga tau, tau-kore, tataitai, rorohiko rānei .
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| 10. Me mōhio te ākonga ki te whakamahi i ētahi tikanga kimi pāwhaitua hei whakaoti rapanga tūturu , rapanga whakatau hoki;
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| He Tauira Aro Matawai
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| He tauira noa enei hei awhina i te kaiwhakaako:
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- He hōpara i ngā aputa e pēnei ana te āhua : ka kimi ai i ngā tepe o aua aputa, mehemea rāhe tepe.he whakatakoto kōrero whānui ki ngā tepe o ngā aputa o roto i ngā pānga hautanga.
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Mā tēnei tauira ka mōhio te kaiwhakaako e pēhea ana te matatau o ngā ākonga ki te:
| Inenga 8/4 |
WA-5 |
Taurangi 8 |
Taurangi 7 |
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- Ka mahi-a-ropu ngā ākonga ki te hōpara , ki whakatakoto pūrongo ki ngā rapanga whaitake e whai wāhi mai ana ngā āhuatanga papatanga whiti. Hei whakatauira, ko te tipu o tētahi kahikatea mehemea ko te kaha o te tipu (ara, te papatanga o te whiti), he ōwehe nga no te rahi o te wai e ahei atu ana te rakau.
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Mā tēnei tauira ka mōhio te kaiwhakaako e pēhea ana te matatau o ngā ākonga ki te:
| Taurangi 8 |
WR-3 |
WA-6 |
Taurangi 8 |
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- He whakamahi tikanga tau hei whakatau tata i te uara o te
 i waenganui i te 1 me ētahi atu uara, ka whakamahi ai i tēnei hei whakaatu i te tika o ngā tapaetanga kōrero pēnei i tēnei e whai ake nei: ko te tapeke o te horahanga i waenganui i te 1 me te 2, me te 1 me te 3, he rite ki te horahanga i waenganui i te 1 me te 6.
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Mā tēnei tauira ka mōhio te kaiwhakaako e pēhea ana te matatau o ngā ākonga ki te:
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- He hōpara , he whakatakoto pūrongo e whakaahua ana i te hoahoa me te hanga o tētahi wharenui. Me āta whai whakaaro ki ngā inenga, ki ngā papanga me ngā taputapu e hiahiatia ana, me te roa o te wa ka pau i ngā kaihanga whare ki tēnei mahi.
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Mā tēnei tauira ka mōhio te kaiwhakaako e pēhea ana te matatau o ngā ākonga ki te:
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