# Rautaki Paheko

## Operational Strategies

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.

# te whakamahi meka mōhio me te tikanga paremata

### using known facts and compensation

Hei tauira: 8 + 9 = ?

Hei whakamārama:

 He tino pātata te 8 tāpiri i te 9 ki te 8 tāpiri i te 8. 8 + 9 ≈ 8 + 8 E mōhio ana ahau ki te rearua o te 8, arā, tāpirihia te 8 me te 8, ka 16. 8 + 8 = 16 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:

 Ka wāwāhia te 23 ki ōna tekau me ōna tahi. 23 = 20 + 3 Ka wāwāhia te 36 ki ōna tekau me ōna tahi. 36 = 30 + 6 Ka tāpirihia ngā rōpū o te tekau me ngā rōpū o te tahi. (20 + 30) = 50(3 + 6) = 9 Ka tāpirihia ngā tapeke, arā, te 50 me te 9. 50 + 9 = 59

Hei tauira anō: 36 x 8 = ?

Hei whakamārama:

 Ka wāwāhia te 36 ki ōna tekau me ōna tahi. 36 = 30 + 6 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 6 x 8 = 48 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:

 E pātata ana te 37 ki te 40, ā, he tau māmā te 40. 37 ≈ 40 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 63 + 3 = 66 63 - 37 = 66 - 40 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:

 E pātata ana te 28 ki te 30, ā, he tau māmā te 30. 28 ≈ 30 He ngāwari te tango i te 30 mai i te 54. 54 - 30 = 24 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:

 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 = ? 26 + ? = 53 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 Ko te 27 te tapeke o ngā tau i tāpirihia. (4 + 20 + 3) = 27 Nō reira, 26 tāpirihia te 27, ka 53. 26 + 27 = 53 He ōrite ki te tangohanga: 53 tangohia te 26, ka 27. 53 - 26 = 27

# te rearua

### doubling

Hei tauira: 4 x 14 = ?

Hei whakamārama:

 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) E mōhiotia ana te meka whakarea 4 x 7. 4 x 7 = 28 Nō reira, ka tāpirihia ngā 28 e rua, ka 54. 4 x 14 = (4 x 7) + (4 x 7) = 28 + 28 = 56

# te tikanga paremata

### compensation

Hei tauira: 26 x 3 = ?

Hei whakamārama:

 E pātata ana te 26 ki te 25. He tau māmā te 25. 26 ≈ 25 E mōhiotia ana te whakareatanga 25 x 3 = 75 (he rite ki te 3 x 25). 25 x 3 = 75 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:

 Kimihia te kotahi hauwhā o te 32 i te tuatahi. o te 32 = ? He rite tēnei ki te whakawehe i te 32 ki te 4. Ko te 8 te otinga. 32 ÷ 4 = 8 Ko te kotahi hauwhā, he rite ki te 8. Nō reira, ka whakareatia ki te 3, ko te toru hauwhā tērā. o te 32 = 8 o te 32 = 3 x 8 = 24

# te rearua me te haurua (te reatoru me te hautoru ...)

### doubling and halving

Hei tauira: 18 x 4 = ?

Hei whakamārama:

 E 2 ngā 9 i roto i te 18. 2 x 9 = 18 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 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:

 Ka hurihia hei whakareatanga. 72 ÷ 4 = ? 4 x ? = 72 Ka wāwāhia te 72 ki ētahi tau māmā - ko te 40 me te 32. 72 = 40 + 32 E mōhiotia ana 10 ngā 4 i roto i te 40. 4 x 10 = 40 E 32 o te 72 e toe ana. 72 - 40 = 32 Wehea te 32 ki te 4, ka 8. 32 ÷ 4 = 8 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 8 x 4 = 32 18 x 4 = 72 72 ÷ 4 = 18