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:
- te whakaaro tūhonohono hei tūāpapa mō ētahi rautaki paheko tau, pērā i te ‘tau mamā me te tikanga paremata’ mō te tāpiritanga, te ‘tāpiritanga ōrite’ mō te tangohanga, me te ‘whakarea me te whakawehe whai pānga’ mō te whakarea.
- te whakaatu rautaki tau ki te rauemi, ki te pikitia hoki.
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:
- 6 + 7 = 6 + 6 + 1
Ka tūhonoa te 7 i te taha mauī me te 6 + 1 i te taha matau. - 28 + 17 = 30 + 15
Ka tūhonoa te 28 i te taha mauī me te 30 i te taha matau, ka tūhonoa hoki ko te 17 i te taha mauī me te 15 i te taha matau. Ina ka tāpiria te 2 ki tētahi tauhono, ka tangohia te 2 i tētahi kia noho pūmau tonu te tapeke o te tāpiritanga. - 3 x 14 = 6 x 7
Ka tūhonoa te 3 i te taha mauī me te 6 i te taha matau, ka tūhonoa hoki ko te 14 i te taha mauī me te 7 i te taha matau. Ina ka whakareatia tētahi tau ki te 2, ka whakawehea tētahi ki te 2, kia noho ōrite tonu te otinga o te whakareatanga.
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 |
- Ko te mahi tuatahi, he tūhura i te whakaaro tūhonohono kei roto i ētahi rautaki whakaoti tāpiritanga.
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:
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: 39 + 18 67 + 24 397 + 65 58 + 227 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: 58 + 36 = 57 + 37 58 + 36 = 48 + 47 146 + 35 = 116 + 65 475 + 326 = 265 + 536 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:
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: 
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.
- Kia pērā anō i te mahi tuatahi hei arataki i ngā ākonga ki tēnei rautaki tūhonohono mō te tangohanga. Arā, mēnā ka tāpiria tētahi tau ki ngā tau e rua o te tangohanga, ka noho pūmau tonu te huatango. Ka kīia tēnei rautaki te ‘tāpiritanga ōrite. Hei tauira:
- He pērā anō te mahi i konei hei tūhura i te whakaaro tūhonohono kei roto i ngā rautaki whakaoti whakareatanga.
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:
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: 38 x 5 39 x 5 26 x 4 6.5 x 20 27 x 3 28 x 50 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: 6 x 8 = 3 x 16 20 x 4.5 = 10 x 9 24 x 30 = 8 x 90 23 x 4 = 46 x 8 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:
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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:
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: 
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?