Kia mōhio te ākonga:
hātepe | algorithm |
hau-tahi | unit fraction |
pakitau | number story |
pou | column |
rāwekeweke | manipulate |
rōrahi | volume |
tāhei | bar, strip |
tau hanumi | mixed number |
tauoti | whole number |
tau taupoki | reciprocal |
tūtohi | table |
whakaputa | derive, produce |
whārite taurangi | algebraic equation |
Ngā tohutohu | He Tauira Kōrero Mā Te Pouako |
Tuhia te rapanga nei ki te papa tuhituhi, ka pānui tahi ai me ngā ākonga.
Kotahi te poro tiakareti a Mareta. E hiahia ana ia kia wehea tana poro tiakareti, kia haurua te rahi o ngā wehenga. E hia ngā wehenga ka hua mai? Aratakina ngā ākonga ki te whiriwhiri i te otinga. |
He aha te whārite e hāngai ana ki te rapanga nei? E wehea ana te kotahi mā te haurua, arā, 1 ÷ ½ = □ He tāhei tēnei hei tohu i te poro tiakareti: He tāhei tēnei hei tohu i te haurua poro tiakareti: Mēnā ka whakatakotoria ngā haurua ki raro i te kotahi, he mārama te kitea, ina wehea te kotahi mā te haurua, ko te rua te otinga. Nō reira, he aha te otinga o te whārite? 1 ÷ ½ = 2 He aha te whakareatanga e hāngai ana? E rua ngā haurua kei roto i te kotahi, arā, ½ x 2 = 1 |
Tukuna ngā ākonga ki te tūhura i ngā rapanga nei. Tonoa rātou ki te:
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Ngā tohutohu | He Tauira Kōrero Mā Te Pouako |
Tuhia te rapanga nei ki te papa tuhituhi, ka pānui tahi ai me ngā ākonga.
E 2 mita te roa o te poro rākau a Hinewai. E hiahia ana ia kia tapahia tana poro rākau, kia hautoru mita te roa o ngā tapahanga. E hia ngā wehenga ka hua mai? Aratakina ngā ākonga ki te whiriwhiri i te otinga. |
He aha te whārite e hāngai ana ki te rapanga nei? E wehea ana te rua mā te hautoru, arā, 2 ÷ ⅓ = □
He tāhei tēnei hei tohu i te poro rākau: Mēnā ka tapahia te poro rākau kia hautoru mita te roa o ngā wehenga, e 6 katoa ngā wehenga ka hua mai: Nō reira, he aha te otinga o te whārite? 2 ÷ ⅓ = 6 He aha te whakareatanga e hāngai ana? E ono ngā hautoru kei roto i te rua, arā, ⅓ x 6 = 2 |
Tukuna ngā ākonga ki te tūhura i ngā rapanga nei. Tonoa rātou ki te:
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Ngā tohutohu | He Tauira Kōrero Mā Te Pouako |
Tuhia te rapanga nei ki te papa tuhituhi, ka pānui tahi ai me ngā ākonga.
E 3 ngā kapu maramara tiakareti a Hone hei tunu keke māna. E ¾ kapu hei tunu i te keke kotahi. E hia ngā keke ka taea e ia te tunu? Aratakina ngā ākonga ki te whiriwhiri i te otinga. |
He aha te whārite e hāngai ana ki te rapanga nei? E wehea ana te toru mā te toru hauwhā, arā, 3 ÷ ¾ = □
E toru ngā kapu maramara tiakareti e whakaaturia ana i tēnei pikitia. Kua wāwāhia ki ngā wehenga ¾ kapu te rōrahi. E 4 katoa ngā ¾ kei roto i te 3: Nō reira, he aha te otinga o te whārite? 3 ÷ ¾ = 4 He aha te whakareatanga e hāngai ana? E whā ngā toru hauwhā kei roto i te toru, arā, ¾ x 4 = 3 |
Tukuna ngā ākonga ki te tūhura i ngā rapanga nei. Tonoa rātou ki te:
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Ngā tohutohu | He Tauira Kōrero Mā Te Pouako |
Tuhia te rapanga nei ki te papa tuhituhi, ka pānui tahi ai me ngā ākonga.
E 2 ngā poro tiakareti a Hone hei wehewehe māna kia ¾ te rahi o ia wehenga. E hia ngā wehenga tiakareti ka hua mai? Aratakina ngā ākonga ki te whiriwhiri i te otinga. |
He aha te whārite e hāngai ana ki te rapanga nei? E wehea ana te rua mā te toru hauwhā, arā, 2 ÷ ¾ = □
E rua ngā poro tiakareti e whakaaturia ana i tēnei pikitia: Kua wāwāhia ki ngā wehenga ¾ te rahi. E 2 ⅔ ngā ¾ kei roto i te 2: Nō reira, he aha te otinga o te whārite? 2 ÷ ¾ = 2 ⅔ He aha te whakareatanga e hāngai ana? E rua me te rua hautoru ngā toru hauwhā kei roto i te rua, arā, ¾ x 2 ⅔ = 2 |
Tukuna ngā ākonga ki te tūhura i ngā rapanga nei. Tonoa rātou ki te:
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Ngā tohutohu | He Tauira Kōrero Mā Te Pouako |
Tuhia te rapanga nei ki te papa tuhituhi, ka pānui tahi ai me ngā ākonga.
E rua me te haurua rita (2 ½ l) te rōrahi o te wai ārani, ka wehea ki ētahi ipu ¾ rita te kītanga. E hia ngā ipu ka taea te whakakī? Aratakina ngā ākonga ki te whiriwhiri i te otinga. |
He aha te whārite e hāngai ana ki te rapanga nei? E wehea ana te rua me te haurua mā te toru hauwhā, arā, 2 ½ ÷ ¾ = □
He tāhei tēnei e tohu ana i te 2 ½ rita wai ārani: Kua wehea te 2 ½ ki ētahi ipu e toru hauwhā rita (¾) te rōrahi. E 3 ⅓ ngā ipu ka taea te whakakī: Nō reira, he aha te otinga o te whārite? 2 ½ ÷ ¾ = 3 ⅓ He aha te whakareatanga e hāngai ana? E toru me te kotahi hautoru ngā toru hauwhā kei roto i te rua me te haurua, arā, ¾ x 3 ⅓ = 2 ½ |
Tukuna ngā ākonga ki te tūhura i ngā rapanga nei. Tonoa rātou ki te:
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Ngā tohutohu | He Tauira Kōrero Mā Te Pouako | |||||||||||||||||||||||||||||||||||||||
E hoki ki te tirotiro i ētahi o ngā wehenga kua oti i tēnei kōwae ako, me te whakaatu anō i te hatepe hei whakawehe i tētahi tau mā tētahi hautau. | Koia nei tētahi o ngā wehenga i oti i a tātou, me te pikitia e hāngai ana: 2 ÷ ⅓ = 6
Ka taea ngā tauoti o te whārite te huri hei hautau:
Ināianei, ka hurihia te wehenga hei whakareatanga, ā, ka huri taupoki i te hautau tuarua o te whārite. Ka puta tētahi tauira, arā, ka tika tonu te whakareatanga:
E kitea ana te tika o te whakareatanga. |
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Kia pērā anō te huri i ētahi atu o ngā wehenga kua oti i tēnei kōwae ako. Kua oti ētahi o ngā whārite i raro nei hei tauira:
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Āta tirohia te tauira e puta ake ana i ngā whārite, ka whakawhitiwhiti kōrero mō te ture hei whakaoti wehenga. | I te pou tuatoru o te tūtohi, i hurihia ngā wehenga hei whakareatanga, ā, i huri taupoki anō hoki te hautau tuarua o te whārite. He tika katoa ngā whakareatanga i te pou tuatoru nei? Āe, kei te tika katoa.
Nō reira, kua kitea he huarahi hei whakaoti wehenga. Arā, hurihia te wehenga hei whakareatanga, me te huri taupoki anō i te hautau tuarua o te whārite. Hei tauira:
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Hoatu ētahi atu rapanga wehe hei whakaoti mā ngā ākonga. Tonoa hoki rātou ki te tuhi pakitau e hāngai ana ki te whārite. Hei tauira:
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Ngā tohutohu | He Tauira Kōrero Mā Te Pouako |
Āta whakamārama i te whakaputanga o te ture mō te whakawehe hautau.
Me āta whakamārama ia hīkoi: Mēnā ka ōrite te rāwekeweke i ia taha o te tohu ‘=’, ka tika tonu te whārite. Hei tauira: |
Anei tētahi wehenga hautau, hei tirotiro mā tātou:
3/4 ÷ 5/6 = □ Ka rāwekeweke haere tātou i te whārite nei, kia kitea he aha e tika ai te ture nei mō te whakawehe hautau: Tuatahi, ka hurihia te wehenga hei whakareatanga: 5/6 x □ = 3/4 Tuarua, ka whakareatia ia taha o te whārite ki te 6/5. Ko te 6/5 te tau taupoki o te 5/6: 6/5 x 5/6 x □ = 3/4 x 6/5 Ko te take i whakareatia te 5/6 ki te 6/5, kia huri i te tau whakarea i te pouaka ki te tahi. Arā: 30/30 x □ = 3/4 x 6/5 He ōrite te 30/30 ki te 1, nō reira: □ = 3/4 x 6/5 Kia tīkina atu te whārite wehe i te tīmatanga: 3/4 ÷ 5/6 = □ Nō reira: 3/4 ÷ 5/6 = 3/4 x 6/5 |
Tukuna ngā ākonga ki te whai i tēnei rāwekeweketanga mō ētahi atu whārite wehenga hautau.
Whakawhitiwhiti kōrero mō te tika o te ture, ahakoa he aha te whārite wehenga hautau. |
Kia pērā anō tō rāwekeweke i ngā whārite wehenga nei:
2/3 ÷ 1/2 = □ 5/3 ÷ 3/4 = □ Ahakoa te whārite, e kite ana tātou i te tika o te ture mō te whakawehe hautau, arā: |
Hei Whakawhānui:
Tirohia te rāwekeweketanga o te wehenga hautau taurangi nei:
a/h ÷ e/k
hei whakaputa i te ture hei whārite taurangi:
a/h ÷ e/k = a/h x e/k
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/wehenga-hautau at 9:59pm on the 26th February 2024