He mea nui i roto i te mahi pāngarau te whakamārama i te huarahi i tae atu ai te tamaiti ki tana whakautu. Mā konei e pakari ai tōna reo me tōna hinengaro whakaaro whaitake. Kei konei ētahi tauira whakamārama mō ngā momo rautaki whakaoti paheko. Ka kīia he rautaki wāwāhi tau ēnei.
In mathematics it is important for children to explain how they achieved an answer to a particular problem. This helps to strengthen their language and mathematical reasoning. This section presents examples of explanations for various number operational strategies. The strategies are called part-whole strategies.
te whakamahi meka mōhio me te tikanga paremata
using known facts and compensation
Hei tauira: 8 + 9 = ?
Hei whakamārama:
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He tino pātata te 8 tāpiri i te 9 ki te 8 tāpiri i te 8. |
8 + 9 ≈ 8 + 8 |
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E mōhio ana ahau ki te rearua o te 8, arā, tāpirihia te 8 me te 8, ka 16. |
8 + 8 = 16 |
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E tika ana kia tāpirihia tētahi '1' atu anō kia rite ki te 8 tāpiri i te 9. |
16 + 1 = 17 |
te wāwāhi uara tū
place value partitioning
Hei tauira: 23 + 36 = ?
Hei whakamārama:
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Ka wāwāhia te 23 ki ōna tekau me ōna tahi. |
23 = 20 + 3 |
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Ka wāwāhia te 36 ki ōna tekau me ōna tahi. |
36 = 30 + 6 |
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Ka tāpirihia ngā rōpū o te tekau me ngā rōpū o te tahi. |
(20 + 30) = 50(3 + 6) = 9 |
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Ka tāpirihia ngā tapeke, arā, te 50 me te 9. |
50 + 9 = 59 |
Hei tauira anō: 36 x 8 = ?
Hei whakamārama:
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Ka wāwāhia te 36 ki ōna tekau me ōna tahi. |
36 = 30 + 6 |
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Ka whakareatia ngā wāhanga e rua o te 36 ki te 8. Arā, ka whakareatia te 30 me te 6 ki te 8. |
30 x 8 = 240 |
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Ka tāpirihia ngā otinga o ngā whakareatanga. |
240 + 48 = 288 |
te tau māmā me te tāpiritanga ōrite
easy numbers and equal addition
Hei tauira: 63 - 37 = ?
Hei whakamārama:
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E pātata ana te 37 ki te 40, ā, he tau māmā te 40. |
37 ≈ 40 |
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Ki te tāpirihia te 3 ki te 37, ka 40. Ko te 40, he tau māmā noa iho te tango. E tika ana kia tāpiri hoki i te 3 ki te 63, kia pūmau tonu te rerekētanga i waenganui i ēnei tau e rua. |
37 + 3 = 40 |
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E 66, tangohia te 40, ka 26. He ōrite tēnei ki te 63, tangohia te 37. |
66 - 40 = 26 |
te tau māmā me te tikanga paremata
easy numbers and compensation
Hei tauira: 54 - 28 = ?
Hei whakamārama:
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E pātata ana te 28 ki te 30, ā, he tau māmā te 30. |
28 ≈ 30 |
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He ngāwari te tango i te 30 mai i te 54. |
54 - 30 = 24 |
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E 2 te rahi kē atu o te tango i te 30, tērā i te tango i te 28, nō reira, me whakahoki anō i taua 2 (arā, me tāpiri te 2). |
24 + 2 = 26 |
te paheko kōaro
inverse operation
Hei tauira: 53 - 26 = ?
Hei whakamārama:
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Ko tētahi tikanga o te tangohanga 53 - 26, he kimi i te tau hei tāpiri ki te 26 kia eke ki te 53. |
53 - 26 = ? |
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Tāpirihia te 4 ki te 26, ka 30. Tāpirihia te 20, ka 50. Tāpirihia kia 3 anō, kātahi ka eke ki te 53. |
26 + (4 + 20 + 3) = 53 |
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Ko te 27 te tapeke o ngā tau i tāpirihia. |
(4 + 20 + 3) = 27 |
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Nō reira, 26 tāpirihia te 27, ka 53. |
26 + 27 = 53 |
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He ōrite ki te tangohanga: 53 tangohia te 26, ka 27. |
53 - 26 = 27 |
te rearua
doubling
Hei tauira: 4 x 14 = ?
Hei whakamārama:
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He rite te 4 x 14 ki te (4 x 7) + (4 x 7), nā te mea ko te 7 te haurua o te 14. |
4 x 14 = (4 x 7) + (4 x 7) |
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E mōhiotia ana te meka whakarea 4 x 7. |
4 x 7 = 28 |
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Nō reira, ka tāpirihia ngā 28 e rua, ka 54. |
4 x 14 |
te tikanga paremata
compensation
Hei tauira: 26 x 3 = ?
Hei whakamārama:
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E pātata ana te 26 ki te 25. He tau māmā te 25. |
26 ≈ 25 |
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E mōhiotia ana te whakareatanga 25 x 3 = 75 (he rite ki te 3 x 25). |
25 x 3 = 75 |
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Kotahi anō te 3 hei tāpiri atu kia rite ki te 26 x 3. |
75 + 3 = 78 |
te whakarea me te wehe hei whakaoti rapanga hautanga
using multiplication and division to solve fraction problems
Hei tauira: 
o te 32 = ?
Hei whakamārama:
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Kimihia te kotahi hauwhā o te 32 i te tuatahi. |
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He rite tēnei ki te whakawehe i te 32 ki te 4. Ko te 8 te otinga. |
32 ÷ 4 = 8 |
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Ko te kotahi hauwhā, he rite ki te 8. Nō reira, ka whakareatia ki te 3, ko te toru hauwhā tērā. |
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o te 32 = ? te rearua me te haurua (te reatoru me te hautoru ...)
doubling and halving
Hei tauira: 18 x 4 = ?
Hei whakamārama:
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E 2 ngā 9 i roto i te 18. |
2 x 9 = 18 |
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Nō reira, e 8 ngā 9 i roto i ngā 18 e whā. Ka hauruatia te 18, ā, ka rearuatia te 4. |
18 x 4 = 9 x 8 |
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He meka whakarea e mōhiotia ana te 9 x 8. |
9 x 8 = 72 |
te paheko kōaro me te wāwāhi uara tū
inverse operation and place value partitioning
Hei tauira: 72 ÷ 4 = ?
Hei whakamārama:
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Ka hurihia hei whakareatanga. |
72 ÷ 4 = ? |
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Ka wāwāhia te 72 ki ētahi tau māmā - ko te 40 me te 32. |
72 = 40 + 32 |
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E mōhiotia ana 10 ngā 4 i roto i te 40. |
4 x 10 = 40 |
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E 32 o te 72 e toe ana. |
72 - 40 = 32 |
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Wehea te 32 ki te 4, ka 8. |
32 ÷ 4 = 8 |
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10 ngā 4 i roto i te 40, e 8 ngā 4 i roto i te 32, nō reira, 18 ngā 4 i roto i te 72 |
10 x 4 = 40 |
