Te Poutama Tau:He Whakaaturanga mā te Kaiako

Te Whakaaro Tūhonohono

Te Tohu Ōrite=

He aha te tikanga o te tohu ōrite ‘=‘?

• Whakawhitiwhiti kōrero me tētahi hoa, ka tuhi ai i tētahi whakamārama poto

He tauira whakamārama:

• He ōrite te tapeke ki ia taha o te tohu ‘=‘.

Te Tohu Ōrite=

• He tokomaha ngā ākonga e pōhēhē ana ko te ‘=‘ hei tohu mō te otinga, te whakautu rānei.

• He tokomaha ngā ākonga ka tuhi i te 12, i te 17 rānei hei whakaoti i tēnei whārite:

• 8 + 4 = + 5

Te Tohu Ōrite=

• Ka whakamahia te tohu ‘=‘ hei tūhonohono i ngā tau, kia kitea ai te pānga o tētahi ki tētahi.

• Hei tauira: 7 + 3 = 10 7 x 6 = 7 x 5 + 7 7 + 3 + 24 = 10 + 24 5a – 24 = 81

5a – 24 + 24 = 81 + 24

5a = 105

a = 21

Whakaaro Tūhonohono

• Āta whakaarohia tēnei whārite:

7 – = 6 – 4 • Āta whakaarohia ngā rautaki e rua nei:

1) 6 – 4 = 2, nō reira 7 - = 2, nō reira = 5

2)

• Whakamāramatia ēnei rautaki e rua

relational thinking

Whakaaro Tūhonohono

• Rautaki 1: Ka tātaihia ia taha, ānō nei kāore e tūhonotia ana

Rautaki 2: Ka kitea, ka whakamahia te hononga o ngā tau i ia

taha o te tohu ‘=‘ Arā, te hononga o te 6 ki te 7 (6 + 1 = 7), me pērā

anō te hononga o te 4 ki te

(4 + 1 = )

Whakaaro Tūhonohono

• Ko tēhea te rautaki e tino whaihua ana hei whakaoti i tēnei whārite? 278 – = 276 – 134

Whakaaro Tūhonohono

• Ko tēhea te rautaki e tino whaihua ana i tēnei whārite? 175 + 534 = + 535

Whakamāramatia tēnei rautaki.

Whakaaro Tūhonohono

• 175 + 534 = + 535• He ōrite te rahi o ia taha o te tohu ‘=‘.• Ka tuhia he tāhei hei tohu i ia taha. Kia ōrite te rahi o ia

tāhei nā te mea he ōrite te tapeke o ia taha o te tohu ‘=‘.

• Ka wehea te tāhei o runga hei whakaatu i ngā wāhanga e rua o te taha mauī o te whārite (ko te 175 me te 534).

• Ka wehea hoki te tāhei raro hei whakaatu i ngā wāhanga e rua o te taha matau (ko te me te 535).

• Kotahi te rahinga ake o te 535, tērā i te 534.• Nō reira kia kotahi te itinga iho o te , i te 175, kia ōrite

tonu te rahi o ngā tāhei.

Whakaaro Tūhonohono

• Ka kīia tēnei ko te ‘whakaaro tūhonohono’

• Arā, ka tūhonotia ngā tau i ia taha o te tohu ōrite (=)

relational thinking

Whakaaro Tūhonohono

• He mea nui te whakaaro tūhonohono i ētahi o ngā rautaki tau huhua.

• Whakamāramatia te whakaaro tūhonohono e noho ana ki muri i ngā rautaki tau nei: 6 + 7 = 6 + 6 + 1 (te tau rearua) 3 x 16 = 6 x 8 (te rearua me te haurua) 3 x 16 = 3 x 8 x 2 (te wāwāhi whakarea)

doublesdoubling and halving

multiplicative partitioning

Whakaaro Tūhonohono

6 + 7 = 6 + 6 + 1

E tūhono ana i te 7 ki te 6 + 1

• E mōhio ana te ākonga ki te 6 + 6 (tau rearua)• He māmā te tāpiri i te 1

Whakaaro Tūhonohono

3 x 16 = 6 x 8

• E tūhono ana i ngā taha o tētahi tapawhā hāngai.

• Ka rearuatia tētahi taha, ka hauruatia tētahi, engari ka pūmau tonu te horahanga

Whakaaro Tūhonohono

3 x 16 = 6 x 8

• Kāore e mōhio ana te ākonga ki te 3 x 16, engari e mōhio ana ki te 6 x 8.

Whakaaro Tūhonohono

3 x 16 = 3 x 8 x 2

E tūhono ana i te 16 ki te 8 x 2

E mōhio ana te ākonga ki te 3 x 8 me te 24 x 2

Whakaaro Tūhonohono

• Whakamāramatia te whakaaro tūhonohono i tēnei whārite. Tuhia he pikitia: 674 – 389 = 664 – 379

10 te itinga iho o te 664 i te 674 Nō reira e tika ana kia 10 te itinga iho o te 379 i te 389, kia ōrite

te tapeke o ia taha o te tohu =

Whakaaro Tūhonohono

• Whakamāramatia te whakaaro tūhonohono i tēnei whārite. Tuhia he pikitia: 73 + 56 = 71 + 58

E 2 te itinga iho o te 71 i te 73. Nō reira e tika ana kia 2 te rahinga ake o te 58 i te 56, kia ōrite

te tapeke o ia taha o te tohu =

Whakaaro Tūhonohono

• Whakamāramatia te whakaaro tūhonohono i tēnei whārite. Tuhia he pikitia: 84 x 5 = 42 x 10

Ka rearuatia tētahi taha o te tapawhā hāngai, ka hauruatia tētahi.

He māmā te whakaoti i te 42 x 10

84

510

42

Whakaaro Tūhonohono

• Whakamāramatia te whakaaro tūhonohono i tēnei whārite. Tuhia he pikitia: 56 ÷ 14 = 28 ÷ 7

Hauruatia te 56, ka 28 Me haurua anō te 14, kia ōrite tonu te tapeke o ia taha o te tohu

=.

Te Whakaaro Tūhonohono:Hei whakarāpopoto

• He mea nui te whakaaro tūhonohono i ētahi o ngā rautaki tau huhua.

• Nō reira e tino whaihua ana kia mārama te ākonga ki tēnei āhua o te whakaaro pāngarau.

• He ōrite te tapeke ki ia taha o te tohu ‘=‘.