I tēnei kōwae ako ka tūhurangia ētahi rautaki paheko tau e whai wāhi mai ana te whakaaro tūhonohono.
Taumata 3
Te Tau me te Taurangi
Whāinga Paetae 3 (Ngā Rautaki Tau):
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.
Whāinga Paetae 5 (Te Tauira me te Pānga):
Ka mōhio ki ngā wāwāhitanga tāpiripiri o tētahi tau.
Kia mōhio te ākonga ki:
Ko tā te whakaaro tūhonohono, he tautohu, he whakamahi i te pānga o ngā tau kei ia taha o te tohu ōrite o tētahi whārite. He nui ngā hua o te whakaaro tūhonohono, koia hoki hei tūāpapa mō ētahi rautaki tau maha. Hei tauira:
he porotiti
huatango | difference (in a subtraction) |
paremata | compensation |
rautaki paheko tau | operational number strategies |
tāpiritanga ōrite | equal addition |
tau māmā | easy number |
tau mamā me te tikanga paremata | tidy number and compensation |
tauhono | addend |
tūāpapa | foundation |
whakaaro tūhonohono | relational thinking |
whakarea me te whakawehe whai pānga | proportional multiplying and dividing |
Ngā tohutohu | He tauira whakawhitinga kōrero | ||||
Aratakina ngā ākonga kia mārama ki te rautaki nei, te ‘tau māmā me te tikanga paremata’ hei whakaoti tāpiritanga. | Ko te mahi a Huriana hei whakaoti i te tāpiritanga 48 + 17, he huri ki te 50 + 15. Ko tāna, he ōrite ēnei tāpiritanga e rua, ā, he māmā noa iho te whakaoti i te 50 + 15. Whakamāramatia mai tana mahi. He aha i ōrite ai te 48 + 17 me te 50 + 15? Ko tāna, he tango i te 2 i tētahi o ngā tauhono, he tāpiri atu i taua 2 ki tērā o ngā tauhono:
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Kia taunga ngā ākonga ki tēnei rautaki, tukuna rātou kia whakaoti i ētahi atu tāpiritanga mā te whai i tēnei rautaki, me te tuhi pikitia anō hei whakamārama i te rautaki. | Anei ētahi atu tāpiritanga hei whakaoti māu, mā te whai i te rautaki nei a Huriana. Mō ia tāpiritanga tuhia he pikitia hei whakaatu i te rautaki:
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Whakawhānuihia tēnei rautaki hei tūhura i te whakaaro tūhonohono, arā, te pānga o tētahi tauhono ki tētahi. | E ai ki a Huriana, he māmā noa iho te whakatau mēnā e tika ana ēnei whārite tāpiritanga, e hē ana rānei. Ko tāna he whai i tētahi rautaki e āhua ōrite ana ki tana rautaki i mua, kāore ia e whakaoti i ngā tāpiritanga kei ia taha o te tohu ōrite:
Kei te tika te mea tuatahi. Kotahi te rahinga ake o tētahi o ngā tauhono, kotahi te itinga ake o tētahi, nō reira ka noho pūmau tonu te tapeke:
Kei te hē te mea tuarua. Tekau te itinga ake o tētahi o ngā tauhono, tekau mā tahi te rahinga ake o tētahi, nō reira kāore e noho pūmau tonu te tapeke: Kei te tika te mea tuatoru. E 30 te itinga ake o tētahi o ngā tauhono, e 30 te rahinga ake o tētahi, nō reira ka noho pūmau tonu te tapeke: Kei te tika te mea tuawhā. E 210 te itinga ake o tētahi o ngā tauhono, e 210 te rahinga ake o tētahi, nō reira ka noho pūmau tonu te tapeke: |
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Kia taunga ngā ākonga ki tēnei rautaki, arā, kia mārama rātou ki te pānga o tētahi tauhono ki tētahi, tukuna rātou kia whakaoti i ētahi atu tāpiritanga mā te whai i tēnei rautaki, me te tuhi pikitia anō hei whakamārama i te rautaki. | Anei ētahi atu tāpiritanga hei whiriwhiri māu i te tauhono e ngaro ana, mā te whai i te rautaki nei a Huriana. Mō ia tāpiritanga tuhia he pikitia hei whakaatu i te rautaki:
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Hei whakakapi i tēnei akoranga: He aha ētahi tau mō roto i ngā tapawhā me ngā porowhita e tika ai ēnei whārite. E hia ngā otinga rerekē e taea ana? Mō ia tāpiritanga, he aha te hononga o te porowhita me te tapawhā.
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Ngā tohutohu | He tauira whakawhitinga kōrero | ||||||
Aratakina ngā ākonga kia mārama ki te rautaki nei, te ‘whakarea me te whakawehe whai pānga’ hei whakaoti whakareatanga. | Ko te mahi a Huriwai hei whakaoti i te whakareatanga 14 x 5, he huri ki te 7 x 10. Ko tāna, he ōrite te otinga o ēnei whakareatanga e rua, ā, he māmā noa iho te whakaoti i te 7 x 10. Whakamāramatia mai tana mahi. He aha i ōrite ai te 14 x 5 me te 7 x 10? Ko tāna, he whakahaurua i tētahi o ngā tau whakarea, he whakarearua i tētahi:
Anei te pikitia hei whakatauira: |
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Kia taunga ngā ākonga ki tēnei rautaki, tukuna rātou kia whakaoti i ētahi atu whakareatanga mā te whai i tēnei rautaki, me te tuhi pikitia anō hei whakamārama i te rautaki. | Anei ētahi atu whakareatanga hei whakaoti māu, mā te whai i te rautaki nei a Huriwai. Mō ia whakareatanga tuhia he pikitia hei whakaatu i te rautaki:
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Whakawhānuihia tēnei rautaki hei tūhura i te whakaaro tūhonohono, arā, te pānga o tētahi tau whakarea ki tētahi. | E ai ki a Huriwai, he māmā noa iho te whakatau mēnā e tika ana ēnei whārite whakareatanga, e hē ana rānei. Ko tāna he whai i tētahi rautaki e āhua ōrite ana ki tana rautaki i mua, kāore ia e whakaoti i ngā whakareatanga kei ia taha o te tohu ōrite:
Kei te tika te mea tuatahi. He mea whakawehe te 6 ki te 2, he whakarea i te 8 ki te 2, nō reira ka noho pūmau tonu te otinga: Kei te tika te mea tuarua. He mea whakawehe te 20 ki te 2, he whakarea i te 4.5 ki te 2, nō reira ka noho pūmau tonu te otinga: Kei te tika te mea tuatoru. He mea whakawehe te 24 ki te 3, he whakarea i te 30 ki te 3, nō reira ka noho pūmau tonu te otinga: Kei te hē te mea tuawhā. He mea whakarea te 23 me te 4 ki te 2, nō reira ka tino rahi kē atu te otinga: |
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Kia taunga ngā ākonga ki tēnei rautaki, arā, kia mārama rātou ki te pānga o tētahi tau whakarea ki tētahi, tukuna rātou kia whakaoti i ētahi atu whakareatanga mā te whai i tēnei rautaki, me te tuhi pikitia anō hei whakamārama i te rautaki. | Anei ētahi atu whakareatanga hei whiriwhiri māu i te tau whakarea e ngaro ana, mā te whai i te rautaki nei a Huriwai. Mō ia whakareatanga, tuhia he pikitia hei whakaatu i te rautaki: |
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Hei whakakapi i tēnei akoranga: He aha ētahi tau mō roto i ngā tapawhā me ngā porowhita e tika ai ēnei whārite. E hia ngā otinga rerekē e taea ana? Mō ia whakareatanga, he aha te hononga o te porowhita me te tapawhā? |
Printed from https://nzmaths.co.nz/resource/te-whakaaro-tuhonohono at 3:17pm on the 1st July 2024