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Te Poutama Tau: He Whakaaturanga mā te Kaiako Te Whakaaro Whakarearea 1

Te Poutama Tau: He Whakaaturanga mā te Kaiako Te Whakaaro Whakarearea 1. Ngā whāinga mō tēnei akoranga:. • Kia mōhio ki ngā ngā kupu matua mō te whakarea me te wehe, me te whakamahinga o aua kupu i roto I ngā rerenga kōrero pāngarau.

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Te Poutama Tau: He Whakaaturanga mā te Kaiako Te Whakaaro Whakarearea 1

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  1. Te Poutama Tau: He Whakaaturanga mā te Kaiako Te Whakaaro Whakarearea 1

  2. Ngā whāinga mō tēnei akoranga: • Kia mōhio ki ngā ngā kupu matua mō te whakareame te wehe, me te whakamahinga o aua kupu i roto I ngā rerenga kōrero pāngarau. • Kia mōhio ki ngā āhuatanga tātai o te whakarea me te wehe. Calculationproperties • Kia mārama ki te whakamahinga o ēnei āhuatanga tātai i roto i ngā rautaki matua mō te whakarea me te wehe.

  3. Ngā kupu mō te whakarea me te wehe: Ko te whakarea me te whakarau ngā kupu e rua e whakamahia ana mō te ‘multiply’. Nā te nui o te whakamahinga o te ‘rau’ hei ingoa tau (100, 200 ...), kua riro ko te whakarea’ te kupu e tino whakamahia ana mō tēnei paheko tau(kia kore ai e pōhēhē te ākonga ko tēhea o ngā ‘rau’ e kōrerohia ana). Numberoperation Ko te wehe te kupu e tino whakamahia ana mō te ‘division’.

  4. Ngā kupu mō te whakarea me te wehe: Ehara i te mea he kupu hou ēnei ki tō tātou reo. Kei roto ēnei kupu i te papakupu o Wiremu, he mea whakamahi hoki i roto i ngā tuhituhinga tawhito a ngā mātua tīpuna. Tā Wiremu: rea – multiply, numerous wehe – detach, divide He aha ngā kupu e whakamahia ana i tōu kura? Ko te mea nui pea kia ōrite te kupu a tēnā kaiako a tēnā kaiako i roto i te kura kotahi.

  5. Ngā kupu mō te whakarea me te wehe: Ko tā te whakarea, he tātai i te maha o ngā mea katoa kei roto i ētahi rōpū (huinga).Kia ōrite te maha o ngā mea kei ia rōpū. Hei tauira ... E toru ngā rōpū (huinga). E rua ngā mea kei roto i ia rōpū.

  6. Ngā kupu mō te whakarea me te wehe: E rua ngā tauwehe o tētahi whakareatanga. Factor Ko tētahi hei whakaatu i te maha o ngā mea kei roto i ia rōpū (huinga). Ka kīia tēnei ko te ‘tau e whakareatia ana’ Ko tētahi hei whakaatu i te maha o ngā rōpū (huinga). Ka kīia ko te tau whakarea tēnei. 2 x 3 = 6 otinga tau e whakareatia ana Multipicand tau whakarea Multiplier He tauwehe te rua me te toru o te ono. He aha ngā tauwehe katoa o te 12?

  7. Ngā kupu mō te whakarea me te wehe: Mō te wehe: tau e wehea ana otinga 18 ÷ 6 = 3 Dividend tau whakawehe Divisor

  8. Te whakahua me te whakaahuai te whakareatanga: Expressing, representing E rua ngā whakahuatanga matua mō te whakarea: 1. “Whakareatia te rua ki te toru, ka ono.” (“E rua, whakareatia ki te toru, ka ono”) Me pēhea te whakaahua i tēnei whakareatanga? 2 x 3 = 6 Ko te 2 te rōpū e whakareatia ana. Kia 3 ngā rōpū o te 2.

  9. Te whakahua me te whakaahuai te whakareatanga: Expressing, representing 2. “E rua ngā rōpū (huinga) o te toru, ka ono.” (“E rua ngā toru, ka ono”) Me pēhea te whakaahua i tēnei whakareatanga? 2 x 3 = 6 Ko te 3 te rōpū e whakareatia ana. Kia 2 ngā rōpū o te 3.

  10. Te whakahua me te whakaahuai te whakareatanga: Expressing, representing The usual convention (in English) is that 4 x 8 refers to four sets of eight, not eight sets of four. There is absolutely no reason to be rigid about this convention. The important thing is that students can tell you what each factor in their equation represents. (Van de Walle, 2007. p154) Kua riro ko tēnei hei tikanga matua mō te whakarea i roto i te reo Māori: “Whakareatia te rua ki te toru, ka ono.” 2 x 3 = 6

  11. Te whakahua me te whakaahuai te whakareatanga: Expressing, representing Engari, kia mōhio hoki te ākonga, kei te tika hoki tēnei: “E rua ngā rōpū (huinga) o te toru, ka ono.” (“E rua ngā toru, ka ono”) 2 x 3 = 6

  12. Te whakahua i te rerenga whakareatanga: Expressing E whai ake nei ētahi o ngā whakahuatanga rerenga kōrero mō te whakarea e rangona ana i roto i ō tātou kura. Whakawhitiwhiti kōrero mō te tika, te hapa, te mārama rānei o ēnei rerenga kōrero. He aha ngā rerenga kōrero mō te whakarea e rangona ana, e whakamahia ana i roto i tōu kura?

  13. Te whakahua i te rerenga whakareatanga: Expressing 5 x 3 = 15  Rima whakarea toru rite tekau mā rima.  Whakarea te rima me te toru, ka tekau mā rima.  Whakareatia te rima mā te toru, ka tekau mā rima.  Rima toru ka tekau mā rima.  E rima ngā toru ka tekau mā rima.  Whakareatia te rima ki te toru, ka eke ki te tekau mā rima.  Whakareatia te rima ki te toru ka rite ki te tekau mā rima.  E rima ngā rōpū toru ka tekau mā rima.  E rima ngā huinga o te toru, ka tekau mā rima.

  14. Te Whakaaro Tāpiripirime te Whakaaro Whakarearea: Additive thinking, Multiplicativethinking Whakaarohia te rapanga nei: Ka pau i te whānau Horomona te $96, hei hoko hāngi. E $8 te utu mō ia tākaikai hāngi. E hia ngā tākaikai hāngi i hokona e rātou?

  15. Te Whakaaro Tāpiripirime te Whakaaro Whakarearea: Additive thinking, Multiplicativethinking Anei ngā rautaki a ētahi ākonga tokorua: • Ka tangotango haere au i te $8 i te $96. E hia ngā tangohanga o te $8 kia pau katoa te $96? 96 - 8 = 88 88 - 8 = 80 80 - 8 = 72 Manahi

  16. Te Whakaaro Tāpiripirime te Whakaaro Whakarearea: Additive thinking, Multiplicativethinking • Tekau ngā $8, ka $80. $16 atu anō kia eke ki te $96. Nō reira ... 8 x 10 = 80 Whakawhitiwhiti kōrero mō ngā rautaki e rua.  Ko wai te mea e whakaaro tāpiripiri ana?  Ko wai te mea e whakaaro whakarearea ana?  Ko tēhea te rautaki e tino whaihua ana mō tēnei rapanga? He aha ai? 80 + 16 = 96 nō reira… Awhina

  17. Ngā Āhuatanga Tātaimō te Whakarea: Calculation properties • E toru ngā āhuatanga tātai matua mō te whakarea: •  āhuatanga tātai kōaro • āhuatanga tātai tohatoha • āhuatanga tātai herekore Commutative property Distributive property Associative property He mea whakamahi ēnei āhuatanga tātai i roto i ngā rautaki whakarea. Multiplicative strategies Mēnā he mārama te ākonga ki ēnei āhuatanga tātai mō te whakarea, he māmā anō tana tūhura i ngā rautaki hei whakaoti whakareatanga.

  18. Ngā Āhuatanga Tātaimō te Whakarea: Calculation properties Kāore he take kia mōhio te ākonga ki ngā kupu nei (āhuatanga tātai kōaro, āhuatanga tātai tohatoha, āhuatanga tātai herekore), engari ... Kia mōhio ia ngā tikanga o ēnei āhuatanga tātai. Kia āta tūhura tātou i ēnei āhuatanga tātai ...

  19. Te Āhuatanga Tātai Kōaroo te Whakareatanga: Commutativeproperty Kāore he take o te raupapa mai o ngā tauwehe o tētahi whakareatanga ki te otinga o taua whakareatanga. Factor Whakamārama atu ki tō hoa he aha e ōrite ai te otinga o te 4 x 5 me te 5 x 4.

  20. Te Āhuatanga Tātai Kōaroo te Whakareatanga: Commutativeproperty He ōrite te otinga o te 4 x 5 me te 5 x 4. Anei te kapa kotahi o te 4 Anei ngā kapa e 5 o te 4. Hei whakaahua tēnei i te 4 x 5. Representation 4 5

  21. Te Āhuatanga Tātai Kōaroo te Whakareatanga: Commutativeproperty Hurihia te mahere tukutuku, he ōrite tonu te maha o ngā pūkeko, kāore i tāpirihia tētahi i tangohia tētahi rānei. 5 4 Ināianei e 4 ngā kapa o te 5. Hei whakaahua tēnei i te 5 x 4. He ōrite te otinga o te 4 x 5 me te 5 x 4.

  22. Te Āhuatanga Tātai Kōaroo te Whakareatanga: Commutativeproperty He ōrite te otinga o te 4 x 5 me te 5 x 4. Hei whakaahua anō: Representation E 5 ngā rourou. E 4 ngā āporo kei ia rourou. Hei whakaahua tēnei i te 4 x 5. Tohaina ngā āporo o tētahi o ngā rourou ki ērā atu o ngā rourou. Ināianei, e 4 ngā rourou, e 5 ngā āporo kei ia rourou. Hei whakaahua tēnei i te 5 x 4.

  23. Te Āhuatanga Tātai Kōaroo te Whakareatanga: Commutativeproperty Kāore i tāpirihia tētahi āporo, kāore i tangohia tētahi rānei. Nō reira he ōrite te otinga o te 4 x 5 me te 5 x 4.

  24. Te Āhuatanga Tātai Kōaroo te Whakareatanga: Commutativeproperty Mēnā e mārama ana te ākonga ki te āhuatanga tātai kōaro o te whakarea, kāore he raruraru ki a ia te whakaoti i ngā whakareatanga pēnei i ēnei ... 3 x 100 . . .

  25. Te Āhuatanga Tātai Kōaroo te Whakareatanga: Commutativeproperty Ka huri kōarohia te whakareatanga: 100 x 3 He māmā ake te whakaoti i te 100 x 3, tērā i te whakaoti i te 3 x 100.

  26. Te Āhuatanga Tātai Kōaroo te Whakareatanga: Commutativeproperty Hei tauira anō: 3 x 99 =  99 x 3 = (huri kōaro) Reverse order (100 x 3) = 300 (tau māmā) Easy number 300 – 3 = 297 (tikanga paremata) Compensation Hei tauira anō: 5 x 398 =  398 x 5 = (huri kōaro) Reverse order 400 x 5 = 2,000 (tau māmā) Easy number 2,000 – 10 = 1990 (tikanga paremata) Compensation

  27. Te Āhuatanga Tātai Kōaroo te Whakareatanga: Commutativeproperty Whakaarohia tēnei rapanga: E 78 katoa ngā ākonga o te kura i mau mai i te $4 hei utu i te pahi kawe i a rātou ki te konohete kapa haka.

  28. Te Āhuatanga Tātai Kōaroo te Whakareatanga: Commutativeproperty Whakaarohia ngā rautaki a ngā ākonga tokorua nei. Ko tēhea e mārama ana ki te āhuatanga tātai kōaro o te whakarea? He māmā ake te tātai i te $78 x 4 Whakareatia te $4 ki te 78 ... . . . Awhina Manahi

  29. Te Āhuatanga Tātai Kōaro: Commutativeproperty He aha te otinga o te 4 ÷ 2? He aha te otinga o te 2 ÷ 4? E whai ana te wehe i te āhuatanga kōaro, kāore rānei? Tuhia he pikitia, ka whakamāramatia atu ki tō hoa.

  30. Te Āhuatanga Tātai Tohatoha o te Whakarea: Distributiveproperty Whakaarohia tēnei rapanga: E $5 te utu mō te pukapuka kotahi. E 36 ngā pukapuka i hokona e Whaea Mihi.E hia katoa te utu? E whakareatia ana te $5 ki te 36. Arā te whārite $5 x 36 =  Ka huri kōarohia: 36 x 5 = 

  31. Te Āhuatanga Tātai Tohatoha o te Whakarea: Distributiveproperty Whakaarohia tēnei rautaki hei whakaoti i tēnei whakareatanga: 36 30 x 5 = 150 6 x 5 = 30 5 Tuhia tēnei rautaki hei whārite. Equation 36 x 5 = (30 x 5) + (6 x 5) = 150 + 30 = 180

  32. Te Āhuatanga Tātai Tohatoha o te Whakarea: Distributiveproperty I whakamahia te āhuatanga tātai tohatoha o te whakarea i roto i tēnei rautaki. I wāwāhia te 36 ki ētahi wāhanga māmā (te 30 me te 6). 30 6 5

  33. Te Āhuatanga Tātai Tohatoha o te Whakarea: Distributiveproperty Kātahi ka tohainate whakareatanga ki te 5 (x 5) ki ngā wāhanga e rua, arā, te 30 me te 6. Distributed 30 6 30 x 5 = 150 6 x 5 = 30 5

  34. Te Āhuatanga Tātai Tohatoha o te Whakarea: Distributiveproperty Anei tētahi anō tauira o te āhuatanga tātai tohatoha o te whakarea: 8 x 7 = 8 x 4 + 8 x 3 Ko tēhea o ngā tauwehe i wāwāhia? Factor

  35. Te Āhuatanga Tātai Tohatoha o te Whakarea: Distributiveproperty Hei tauira anō: Ko tēhea o ngā tauwehe i wāwāhia i konei? Tuhia te whāritee hāngai ana. Equation

  36. Te Āhuatanga Tātai Herekore o te Whakarea: Associativeproperty Kia hoki tātou ki te rapanga nei: E $5 te utu mō te pukapuka kotahi. E 36 ngā pukapuka i hokona e Whaea Mihi. E hia katoa te utu? E whakareatia ana te $5 ki te 36. Arā te whārite $5 x 36 =  Ka huri kōarohia: 36 x 5 = 

  37. Te Āhuatanga Tātai Herekore o te Whakarea: Associativeproperty Whakaarohia tēnei rautaki hei whakaoti i tēnei whakareatanga: 18 36 5 10 36 x 5 = 18 x 10 (te haurua me te rearua) = 180 Doublingand halving

  38. Te Āhuatanga Tātai Herekore o te Whakarea: Associativeproperty He mea whakamahi te āhuatanga tātai herekore o te whakarea i roto i tēnei rautaki. Tirohia, whakaarohia ... 36 x 5 =  = (18 x 2) x 5 (i wāwāhia te 36 kia rua ngā 18) Partition = 18 x (2 x 5) kāore he take o te raupapa mai o ngā tauwehe – (he ‘herekore’ te tātai) Factor = 18 x 10 = 180

  39. Te Āhuatanga Tātai Herekore o te Whakarea: Associativeproperty He tauira anō tēnei o te āhuatanga tātai herekore o te whakarea. Whakaarohia tēnei rapanga: E hia ngā mataono rite paku hei hanga i tēnei āhua: Cube

  40. Te Āhuatanga Tātai Herekore o te Whakarea: Associativeproperty E toru ngā raupapatanga o te whakarea hei whakaoti i tēnei rapanga: 1. (3 x 5) x 4 E 4 ngā paparangao te 3 x 5. Layer

  41. Te Āhuatanga Tātai Herekore o te Whakarea: Associativeproperty 2. (4 x 3) x 5 E 5 ngā paparanga o te 4 x 3. 3. (4 x 5) x 3 E 3 ngā paparanga o te 4 x 5.

  42. Te Tikanga Paheko Kōaro: Inverseoperation Ko tētahi atu āhuatanga matua o te whakarea me te wehe, ko te tikanga paheko kōaro. Ko te wehe te kōaro o te whakarea. Hei tauira ... 2 x 5 = 10 Huri kōarotia: 10 ÷ 5 = 2

  43. Te Tikanga Paheko Kōaro: Inverseoperation Ko te whakarea te kōaro o te wehe.Hei tauira ... 8 ÷ 4 = 2 Huri kōarotia: 2 x 4 = 8 Tuhia ētahi atu tauira o te tikanga paheko kōaro o te whakarea me te wehe. Whakamāramatia atu ki tō hoa.

  44. Te tikanga paheko kōaroo te whakarea me te wehe: Inverseoperation He tino rautaki te ‘huri kōaro’ hei whakaoti whakareatanga, hei whakaoti wehenga rānei. Whakaarohia tēnei rapanga: E 70 ngā āporo i wehea ki ētahi pēke 14, kia ōrite te maha o ngā āporo ki ia pēke. E hia ngā āporo ki tēnā, ki tēnā o ngā pēke? • Wehea te 70 ki te 14. • 70 ÷ 14 = ??? • Aue, kei hea taku tātaitai? Manahi

  45. Te tikanga paheko kōaroo te whakarea me te wehe: Inverseoperation • Wehea te 70 ki te 14. • 70 ÷ 14 =  • Ka hurihia kōarohia hei whakareatanga • 14 x  = 70 • Whakareatia te 14 ki te aha, ka 70? • Whakareatia te 14 ki te 10, ka 140, nō reira… Awhina

  46. Whakaarohia tēnei rapanga me te rautaki a tēnei ākonga: E 280 ngā pou a tētahi kaimahi pāmu. E 8 ngā pou hei hanga i te iari kotahi. E hia ngā iari ka taea e ia te hanga? Yard

  47. Whakaarohia tēnei rapanga me te rautaki a tēnei ākonga: Wehea te 280 ki te 8. 280 ÷ 8 =  He rite tēnā ki te whakareatanga 8 x = 280 8 x 30 = 240 E 40 atu anō kia eke ki te 280 8 x 5 = 40 Hui katoa, e 35 ngā 8 kia eke ki te 280. He aha ngā āhuatanga tātai o te whakarea e whakamahia ana e tēnei ākonga? Multiplicative properties

  48. Whakaarohia tēnei rapanga me te rautaki a tēnei ākonga: E 8 ngā kapa whutupōro kei roto i te whakataetae. E 22 ngā kaitākaro o ia kapa. E hia katoa ngā kaitākaro i tēnei whakataetae? 22 x 8 =  22 x 2 = 44 44 x 2 = 88 88 x 2 = 176 He aha ngā āhuatanga tātai o te whakarea e whakamahia ana e tēnei ākonga? Multiplicative properties

  49. Hei whakakapi ... Kāore he take kia mōhio te ākonga ki ngā kupu nei: • āhuatanga tātai kōaro • āhuatanga tātai tohatoha • āhuatanga tātai herekore Commutative properties Distributive properties Associative properties Engari ... Kia matatau ia ki te whakamahi i ēnei āhuatanga tātai o te whakarea i roto i ā rātou rautaki whakaoti rapanga.

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