1. Ka mōhio ki ngā tauoti 0 – 100:

• te whakaingoa i ngā tohutau
• ngā raupapa tatauranga whakamua, whakamuri hoki
• ngā tikanga uara tū:

- te rima me ngā tauhono
- ngā tauhono o te tekau
- te tekau me ngā tauhono
- ngā tau ngahuru
- te maha o ngā tekau me ngā tahi kei roto i tētahi tau
- te rahi me te hanga o tētahi tau

2. Ka mōhio ki ngā hautau māmā, pērā i ngā haurua me ngā hauwhā:

• te tuhi i ngā tohu hautau
• te tikanga o te taurunga me te tauraro o tētahi hautau māmā
• te raupapa hautau māmā
• te whakatauira i te hautau (pērā i te hurihanga 3/2)

ngā raupapa tatauranga whakamua, whakamuri

Hei tauira:
Ka tatau ā-tahi, mawhiti-2, mawhiti-5, mawhiti-10

• 1, 2, 3 ...        68, 67, 66 ...        6, 8, 10, 12 ...        100, 95, 90 ...        70, 60, 50 ...

ngā tikanga uara tū

Hei tauira:
te rima me ngā tauhono

ngā tauhono o te tekau

• 9 + 1 = 10       8 + 2 = 10       7 + 3 = 10 ...

te tekau me ngā tauhono

• 10 + 1 = 11       10 + 2 = 12       10 + 3 = 13 ...

ngā tau ngahuru

• 10, 20, 30 ...

te maha o ngā tekau me ngā tahi kei roto i tētahi tau

• 17 = 10 + 7

• E 4 ngā tekau kei roto i te 43
• 63 ngā tahi kei roto i te 63
• Ko te 30 te tikanga o te 3 i roto i te tau 34

ngā hautau māmā

Hei tauira:
1/2, 2/2, 3/2 ...        1/4, 2/4, 3/4, 4/4, 5/4 ...

te tikanga o te taurunga me te tauraro o tētahi hautau māmā

3. Ka whakaoti rapanga e whai wāhi mai ana te tauoti me te hautau māmā, ka whakamārama hoki i te:

• rautaki tatau
• rautaki whakarōpū
• rautaki tohatoha ōrite

whakaoti rapanga

Hei tauira:

• E 5 ngā māpere a Hona. E 8 atu anō ka wini i a ia. E hia katoa ana māpere ināianei?
• Tokowhā ngā tamariki, e 5 ngā māpere a ia tamaiti. E hia katoa ā rātou māpere?
• E 9 ngā ika i mau i a Pāpā. Ka tohaina ki ngā whānau e toru e noho tata ana. He ōrite te maha o ngā ika i tohaina ki ia whānau. E hia ngā ika mā ia whānau?
• Tokowhā ngā tamariki. Ka whakaritea e Whaea Mihi tētahi haurua āporo mā ia tamaiti. E hia katoa ngā āporo?

rautaki tatau

Hei tauira:

• 5 + 8       Ka tīmata i te 8 (nā te mea koirā te tau nui), ka tatau ake: 9, 10, 11, 12, 13.

• 5 x 4       Ka tatau mawhiti-5: 5, 10, 15, 20

• 1/2 x 4       Ka tatau i ngā haurua:

rautaki whakarōpū

Hei tauira:

• 3 x box = 15        (E hia ngā rōpū o te 3 kei roto i te 15?)

rautaki tohatoha ōrite

Hei tauira:

• 9 ÷ 3       Ka tohaina tētahi ki ia rōpū, ka 3 tēnā. Ka tohaina tētahi anō, ka 6. Ka tohaina tētahi anō, ka 9.

4. Ka hanga, ka whakaroa tauira tāruarua, tauira raupapa hoki.

tauira tāruarua

He pūtaketake tō tēnei momo tauira, ā, ka tāruaruatia te pūtaketake hei whakaputa i te tauira.

Hei tauira:

• 1, 2, 3, 1, 2, 3, 1, 2, 3 ...

Koia nei te pūtaketake o tēnei tauira

tauira raupapa

Hei tauira:

• 32, 34, 36 ...
• 1, 2, 4, 7, 11 ...

1. Ka mōhio ki ngā tauoti 0 – 1 000:

• ngā raupapa tatauranga whakamua, whakamuri hoki
• ngā tikanga uara tū:

- te maha o ngā tahi, ngā tekau, me ngā rau kei roto i tētahi tau
- te rahi me te hanga o tētahi tau

• ngā tikanga o te taurua me te taukehe

2. Ka mōhio ki ngā rearua tae atu ki te 20, me ngā haurua e whai pānga ana
3. Ka mōhio ki ngā hautau, pērā i ngā haurua, ngā hautoru, ngā hauwhā, ngā haurima me ngā hautekau:

• te tuhi i ngā tohu hautau
• te tikanga o te taurunga me te tauraro o tētahi hautau
• te raupapa hautau māmā me ngā hautau e ōrite ana te tauraro

raupapa tatauranga whakamua, whakamuri

Hei tauira:

• 497, 498, 499, 500, 501, 502 ...
• 410, 400, 390 ...
• 435, 535, 635 ...
• 712, 702, 692, 682 ...
• 3, 6, 9, 12 ...
• 7/2, 6/2, 5/2, 4/2 ...

tikanga uara tū

Hei tauira:
te maha o ngā rau, ngā tekau me ngā tahi kei roto i tētahi tau

• E 3 ngā rau kei roto i te 361
• E 36 ngā tekau kei roto i te 361
• E 361 ngā tahi kei roto i te 361
• te rahi me te hanga o te 361

- 361 = 300 + 60 + 1
- 361 = (100 x 3) + (10 x 6) + (1 x 1)

tikanga o te taurua me te taukehe

he taukehe te 589 nā te mea he taukehe te 9

ngā rearua tae atu ki te 20, me ngā haurua e whai pānga ana

• 1 + 1 = 2, 2 + 2 = 4, 3 + 3 = 6 ... 8 + 8 = 16, 9 + 9 = 18, 10 + 10 = 20
• 1/2 o te 20 = 10, 1/2 o te 18 = 9, 1/2 o te 16 = 8 ...

ngā hautau

Hei tauira:
te raupapa hautau māmā me ngā hautau e ōrite ana te tauraro

• 1/5, 1/4, 1/3, 1/2 (te iti ki te rahi)
• 3/5, 4/5, 5/5, 6/5 (te iti ki te rahi)
• 2/5, 2/3 (he iti iho te 2/5 i te haurua, he nui ake te 2/3 i te haurua)

4. Ka whakaoti rapanga e whai wāhi mai ana te tauoti me te hautau, ka whakamārama hoki i te rautaki:

• rautaki tatau
• rautaki whakarōpū
• rautaki tohatoha ōrite
• rautaki wāwāhi tau tāpiripiri māmā

5. Ka mārama ki te whaitakenga o te otinga.

whakaoti rapanga

Hei tauira:

• E 56 ngā māpere a Hona. E 23 ka ngaro i a ia. E hia katoa ana māpere ināianei?
• E $28 te rahi o te pūtea a Hinewai. Ka pau i a ia te toru hauwhā o ana moni ki āna hokohoko. E hia tāra i pau i a ia?
• E hia katoa ngā wiki kei roto i ngā tau e 3?

hautau

ko ngā haurua, ngā hautoru, ngā hauwhā me ngā haurima (iti iho, nui ake hoki i te kotahi)

rautaki wāwāhi tau tāpiripiri

Hei tauira:

• 8 + 7 = 8 + 8 – 1 (te whakamahi tau rearua)
• 34 + 45 = (30 + 40) + (4 + 5) = 70 + 9 = 79 (te wāwāhi uara tū)
• 39 + 14 = 40 + 13 = 53 (te tau māmā me te tikanga paremata)
• 3/4 o te 28 = box          1/2 o te 28 = 14, 1/2 o te 14 = 7. Ko te 7 = 1/4 0 te 28, nō reira, ko te 21 (7 + 7 + 7) = 3/4 o te 28 (te whakahaurua me te tatau māwhitiwhiti)

mārama ki te whaitakenga o te otinga

Hei tauira:
38 + 39 = 87
Kāore e tika ana nā te mea 40 + 40 = 80, nō reira he iti iho i te 80 te otinga.

6. Ka mārama ki te tikanga he maha ngā wāwāhitanga o tētahi tau.
7. Ka hanga, ka whakaroa tauira raupapa, ka whakamārama hoki i te ture mō te whakaroa.

ngā wāwāhitanga o tētahi tau

Hei tauira:
16 = 10 + 6
       = 5 x 3 + 1
       = 8 + 8
       = 4 x 4 ...

te ture mō te whakaroa

Hei tauira:

1. Ka mōhio ki:

• ngā momo raupapa tatauranga tauoti, tau ā-ira hoki
• ngā meka matua mō te tāpiri, te tango, me te whakarea
• te whakaawhiwhi tauoti, tau ā-ira hoki ki te 1, te10, te 100 rānei e pātata ana
• ngā tikanga uara tū o ngā tauoti me ngā tau ā-ira:

- te maha o ngā haurau, ngā hautekau, ngā tahi, ngā tekau, ngā rau me ngā mano kei roto i tētahi tau.
- te rahi me te hanga o tētahi tau

2. Ka mōhio ki ngā hautau (tae atu ki ngā hautau nui ake i te kotahi) me ngā tau ā-ira:

• te raupapa hautau (hautahi), tau ā-ira hoki
• ngā raupapa tatauranga hautau, tau ā-ira hoki (hautekau, haurau)

ngā momo raupapa tatauranga tauoti, tau ā-ira hoki

Hei tauira:

• 22 998, 22 999, 23 000, 23 001 ...
• 50 010, 50 000, 49 990, 49 980 ...
• 4582, 5582, 6582 ...
• 0.8, 0.9, 1.0, 1.1 ...

te whakaawhiwhi

Hei tauira:

• 128.7 → 129 (te tahi e pātata ana)
• 128.7 → 130 (te tekau e pātata ana)
• 128.7 → 100 (te rau e pātata ana)

tikanga uara tū

te maha o ngā haurau, ngā hautekau, ngā tahi, ngā tekau, ngā rau me ngā mano kei roto i tētahi tau
Hei tauira:

• e 3 ngā mano kei roto i te 3752.984
• e 37 ngā rau kei roto i te 3752.984
• e 375 ngā tekau kei roto i te 3752.984
• e 3752 ngā tahi kei roto i te 3752.984
• e 37529 ngā hautekau kei roto i te 3752.984
• e 375298 ngā haurau kei roto i te 3752.984
• e 3752984 ngā haumano kei roto i te 3752.984

ngā hautau

te raupapa hautau (hautahi), tau ā-ira hoki
Hei tauira (te iti ki te rahi):

• 1/10, 1/8, 1/6, 1/5, 1/4, 1/3, 1/2
• 0.75, 0.8, 0.92, 1.04
• 0.001, 0.01. 0.1, 1
• 6.98, 6.99, 7.00, 7.01 ...

3. 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:

• rautaki tatau
• rautaki whakarōpū
• rautaki tohatoha ōrite
• rautaki tāpiripiri
• rautaki whakarea māmā

4. Ka mārama ki te whaitakenga o te otinga.

whakaoti rapanga

Hei tauira:

• E 4.6 mita te roa o tētahi o ngā papa rākau i hokona e Pētera, e 2.95 te roa o tētahi. E hia mita te tapeke o te roa o ēnei papa rākau e rua?
• E 7 ngā kete, e 38 ngā rīwai kei ia kete. E hia katoa ngā rīwai?
• E 5.2 rita wai ārani, ka ringihia atu ki ētahi pātara e 4, kia ōrite te rōrahi o ia pātara. E hia rita ki ia pātara?

hautau

ko ngā haurua, ngā hautoru, ngā hauwhā, ngā haurima, ngā hautekau, ngā haurau me ngā haumano, ko ngā hautau tau ā-ira (kia 3 ngā mati ā-ira), ko ngā ōrau māmā, pērā i te 50%, te 25%, te 75%, te 150% ...

rautaki tāpiripiri

Hei tauira:

• 53 – 26 = box → 26 + box = 53 (te huri kōaro)
• 63 – 29 = 64 – 30 (te tāpiritanga ōrite)

rautaki whakarea māmā

Hei tauira:

• 4.6 + 2.95 = 4.6 + 3 – 0.05 = 7.6 – 0.05 = 7.55 (te tau māmā me te tikanga paremata)
• 38 x 7 = (30 x 7) + (8 x 7) = 210 + 56 = 266 (te wāwāhi uara tū)
• 5.2 ÷ 4 = (4 ÷ 4) + (1.2 ÷ 4) = 1 + 0.3 = 1.3 (te wāwāhi uara tū)

mārama ki te whaitakenga o te otinga

Hei tauira:
26 ÷ 4 = 6 1/2
Kāore e whaitake ana tēnei otinga mēnā e 26 ngā tāngata e wehea ana ki ētahi rōpū e whā. He pai kē atu te ‘6 tāngata ki ia rōpū, tokorua e toe mai ana’. E whaitake ana mēnā e 26 km te roa o tētahi omaoma, ā, ka wehea ki ētahi kaioma tokowhā – ko te 6 1/2 km hei whakaoti mā ia tangata.

5. Ka mōhio ki ngā wāwāhitanga tāpiripiri o tētahi tau
6. Ka whakamahi rautaki tāpiripiri ki te whiriwhiri i tētahi tau o roto i tētahi tauira tau
7. Ka whakamahi rautaki āhuahanga ki te whiriwhiri i tētahi āhua o roto i tētahi tauira āhua
8. Ka whakamahi rautaki taurangi māmā ki te whiriwhiri i tētahi huānga o roto i tētahi tauira raupapa

rautaki āhuahanga

Hei tauira:

E hia katoa ngā pūkeko mēnā e 7 ki ia taha o tētahi tapawhā rite?

rautaki taurangi māmā

Hei tauira:
Whakareatia te maha o ngā pūkeko ki ia taha ki te 4, ka tango ai i te 4.

1. Ka mōhio ki:

• ngā meka whakawehe matua
• te whakaawhiwhi tauoti, tau ā-ira hoki

2. Ka mōhio ki ngā tikanga o:

• te tau tōraro me te tau tōrunga
• te tau toitū
• te ōwehenga
• te uara tū o ngā tau ā-ira:

- te maha o ngā haumano, ngā haurau, ngā hautekau, ngā tahi, ngā rau me ngā mano kei roto i tētahi tau ā-ira (tae atu kia 3 ngā mati ā-ira)

3. Ka mōhio ki te kimi mai i ngā taurea me ngā tauwehe o tētahi tau
4. Ka mōhio ki ngā hautau, ngā tau ā-ira, ngā ōrau me ngā ōwehenga māmā:

• ngā huringa hautanga: hautau ↔ tau ā-ira ↔ ōrau
• ngā raupapa tatauranga tau ā-ira (haumano, haurau, hautekau)
• te raupapa hautau, tau ā-ira, ōrau hoki
• te whiriwhiri hautau ōrite

te whakaawhiwhi tauoti, tau ā-ira

Hei tauira:
tauoti, tau ā-ira

• 3.85 → 3.9 (ki te hautekau (0.1) e pātata ana)
• 4.005 → 4.01 (ki te haurau (0.01) e pātata ana)

te tau tōraro me te tau tōrunga

Hei tauira:

• He iti ake ngā tau tōraro i te 0. He nui ake ngā tau tōrunga i te 0.
• He mutunga kore te haere o ngā tau tōraro, he mutunga kore hoki te haere o ngā tau tōrunga.
• He iti ake te -9 i te -8.
• He nui ake te -8 i te -9.
• He ōrite te tango i tētahi tau tōraro ki te tāpiri i te tau tōrunga e hāngai ana: (4 - -3 = 4 + +3 = 7).
• Ina whakareatia (whakawehea rānei) ētahi tau tōraro e rua, he tau tōrunga te otinga: (-4 x -3 = +12)
• Ina whakareatia (whakawehea rānei) tētahi tau tōrunga me tētahi tau tōraro, he tau tōraro te otinga: (-4 x +3 = -12)

te tau toitū

Hei tauira:

• E rua anake ngā tauwehe o tētahi tau toitū – ko taua tau me te kotahi: (7 ÷ 1 = 7, 7 ÷ 7 = 1)
• Ko ngā tau toitū kei raro i te 20: {2, 3, 5, 7, 11, 13, 17, 19}
• Ka whakamahia te hoahoa rākau hei whakaatu i ngā tauwehe toitū o tētahi tau:

te ōwehenga

Hei tauira:

• Ko te 9:12 te ōwehenga o ngā tama ki ngā kōtiro o tētahi akomanga. Arā, tokoiwa ngā tama, 12 ngā kōtiro.
• He ōrite ngā ōwehenga nei: 9:12 = 3:4 = 6:8 = 12:16 = 15:20 ...
• Ko te 2:5 te ōwehenga o ngā tapatoru ki ngā tapawhā:

• He tapatoru te 2/7 o te huinga āhua i runga nei.

te kimi mai i ngā taurea me ngā tauwehe o tētahi tau

Hei tauira:

• Koia nei ngā taurea o te 0.4: {0.4, 0.8, 1.2, 1.6, 2.0 ...}
• Koia nei ngā tauwehe o te 16: {1, 2, 4, 8, 16}

ngā huringa hautanga: hautau ↔ tau ā-ira ↔ ōrau

Hei tauira:

• 1/4 = 0.25 = 25%
• 3 2/5 = 3.4 = 340%

te whiriwhiri hautau ōrite

Hei tauira:

• 1/4 = 2/8 = 3/12 = 4/16 = 25/100 ....

5. 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, te ōrau, te ōwehenga, te tau tōpū me te taupū māmā:

• rautaki tatau
• rautaki tāpiripiri
• rautaki whakarea
• rautaki pānga riterite māmā

6. Ka mārama ki te whaitakenga o te otinga o tētahi rapanga.

whakaoti rapanga

Hei tauira:

• $16 te tuhene o te pūtea pēke a Horiana. Ka whakaurua he moni, ā, ka piki ake tana pūtea ki te $15.50. E hia te moni i whakaurua?
• E 43 o ngā tītere 50 a Roimata i ū. 17 ngā tītere a Hana o roto i ana tītere 20. Ko wai o rāua te ringa tītere tino pai?
• E 9 cm te roa o ngā tapa o tētahi mataono rite. E hia te rōrahi o te mataono rite?

te ōwehenga

Ko te ōwehenga, he whakatairite i te rahi o ētahi mea e rua. Hei tauira:

• Ko te 1:4 (kotahi te ki whā) te ōwehenga o te wai ārani me te wai māori hei whakaranu i tētahi inu. Arā, mō ia kotahi rita wai ārani, ka whakaranua te whā rita wai māori.

rautaki tāpiripiri

Hei tauira:

• -16 + box = +15.5 → 16 + 15.5 → 16 + 16 – 0.5 = 31.5 (te huri kōaro, te rearua me te tikanga paremata)

• 3/4 + 5/8 = (3/4 + 2/8) + 3/8 = 1 3/8 (te wāwāhi hautau)

rautaki whakarea

9 x 9 x 9 = 81 x 9 = (80 x 9) + 9 = 720 + 9 = 729 (wāwāhi uara tū)

24 x 6 = (25 x 6) – 6 = 150 – 6 = 144 (te tau māmā me te tikanga paremata)

rautaki pānga riterite māmā

• 5/6 o te 24 = (1/6 o te 24) x 5 = 4 x 5 = 20 (te wāwāhi hautau)
• Ko tēhea te hautau nui ake, ko te 43/50, ko te 17/20 rānei?

• 43/50 = 86/100, 17/20 = 85/100, nō reira he nui ake te 43/50 i te 17/20 (te hautau ōrite)

7. Ka mōhio ki ngā momo wāwāhitanga whakarea o tētahi tau
8. Ka whakaatu pānga rārangi:

• mā te whārite whai taurangi (ka whakaoti hoki i te whārite)
• mā te ture
• mā te kauwhata

Ka whakaatu pānga rārangi

Hei tauira:
E $2.50 te utu mō te tono i tētahi tēkehi, tāpiri atu ko te $2 mō ia kiromita. Me pēhea te tātai i te utu mō tētahi haerenga?

te whārite whai taurangi

U = 2k + 2.5 (U = utu, k = kiromita)

te ture

Whakareatia te $2 ki te maha o ngā kiromita, ka tāpiri ai i te $2.50

te kauwhata

1. Ka mōhio ki ngā tikanga o te taupū me te tānga ngahuru.

te taupū

Hei tauira:

• 32 = 3 x 3 = 9, 33 = 3 x 3 x 3 = 27, 34 = 3 x 3 x 3 x 3 = 81 ...
• 101 = 10, 102 = 100, 103 = 1,000, 104 = 10,000 ...
• 161/2 = √16 = 4
• ngā tau pūrua ki te 100: {1, 4, 9, 16, 25, 36, 49, 64, 81, 100}
• ngā tau pūtoru ki te 100: {1, 8, 27, 64}
• te taupū o tētahi tau tōraro:

-22 = 4
-23 = -8
-24 = 16

• 32 x 34 = 32+4 = 36
• 58 ÷ 54 = 58-4 = 54

te tānga ngahuru

Hei tauira:

• 361 = 3.61 x 102
• te tawhiti o Papatūānuku i a Tama-nui-te-rā = 150 000 000 km = 1.5 x 108
• te pūtoro o tētahi ngota hauwai = 0.000 000 000 106 m = 1.06 x 10-10 m

2. Ka kōwhiri, ka whakamārama i te rautaki e tino whaihua ana hei whakaoti rapanga e whai wāhi mai ana te tau tōpū, te hautau, te tau ā-ira, te ōrau, te ōwehenga, te pāpātanga, me te taupū:

• rautaki tatau
• rautaki tāpiripiri
• rautaki whakarea
• rautaki pānga riterite

3. Ka whiriwhiri tauwehe pātahi, taurea pātahi hoki
4. Ka mārama ki te whaitakenga o te otinga o tētahi rapanga.

whakaoti rapanga

Hei tauira:

• Ko tēhea o ēnei tohutaka he tino kaha te hā o te ārani:

- Kia 3 ngā kapu wai māori ki ia kapu wai ārani
- Kia 5 ngā kapu wai māori ki ia rua kapa wai ārani
- Kia 9 ngā kapu wai māori ki ia whā kapu wai ārani

• E $261.20 te tuhene o te pūtea pēke a tētahi rōpū. Ka wehea ōritehia te tuhene nei hei utu mā ngā tāngata tokowhā o te rōpū. E hia te moni hei utu mā tēnā, mā tēnā.
• E $34 te utu mō tētahi kōpae pūoro. Ka whakahekea tēnei utu mā te 25%. He aha te utu hou?

rautaki tāpiripiri

Hei tauira:

• 2 3/4 – 1 2/3 = (2 – 1) + (3/4 – 2/3) = 1 + (9/12 – 8/12) = 1 1/12 (te wāwāhi me te hautau ōrite)

rautaki whakarea

Hei tauira:

• -261.20 ÷ 4 = (-261.20 ÷ 2) ÷ 2 = -130.60 ÷ 2 = -65.30 (te wāwāhi)
• 3.6 x 0.75 = 3/4 o te 3.6 = (1/4 o te 3.6) x 3 = 0.9 x 3 = 2.7 (te huri kōaro me te wāwāhi hautau)

rautaki pānga riterite

Hei tauira:

• 75% o te 34 = box → 50% o te 34 = 17, 25% o te 34 = 8.5, nō reira 75% o te 34 = 25.5 (te wāwāhi ōrau)
• Hei whakatairite i ngā ōwehenga e toru nei: 3:1, 5:2, 9:4 (te ōwehenga ōrite)

tauwehe pātahi

Hei tauira:
Koia nei ngā tauwehe o te 8: {1, 2, 4, 8}
Koia nei ngā tauwehe o te 12: {1, 2, 3, 4, 6, 12}
Nō reira, ko ngā tauwehe pātahi o te 8 me te 12: {1, 2, 4}

taurea pātahi

Hei tauira:
Koia nei ngā taurea o te 3: {3, 6, 9, 12, 15, 18, 21, 24, ...}
Koia nei ngā taurea o te 4: {4, 8, 12, 16, 20, 24, ...}
Nō reira, ko ngā taurea pātahi o te 3 me te 4: {12, 24, 36, ...}

5. Ka tuhi whārite rārangi ki te whakatauira pūāhua whaitake, ka whakaoti hoki i te whārite
6. Ka whakawhānui i ngā tikanga o roto i ngā rautaki tau hei tūāpapa mō ngā tikanga taurangi
7. Ka whakaatu i te ōritenga o ngā ture e hāngai ana ki tētahi pānga rārangi kotahi
8. Ka rāwekeweke kīanga i runga i ngā tikanga taurangi
9. Ka whakaatu pānga rārangi, pānga pūrua, pānga taupū ki te kauwhata hei whakatauira i tētahi pūāhua whaitake

whārite rārangi

Hei tauira:
$12 te utu mō te hunga pakeke, e $4.50 te utu mō te tamariki ki te haere ki te pikitia. Ko te whārite hei tātai i te utu:
U = 12p + 4.5t (p = te tokomaha o ngā pakeke, t = te tokomaha o ngā tamariki)
Ka whakamahia tēnei whārite hei tātai i te utu mēnā e 50 ngā pakeke, e 30 ngā tamariki:
U = 12 x 50 + 4.5 x 30
       = 600 + 135
       = $735

Ka whakawhānui i ngā tikanga o roto i ngā rautaki tau hei tūāpapa mō ngā tikanga taurangi

Hei tauira:

te ōritenga o ngā ture e hāngai ana ki tētahi pānga rārangi kotahi

Hei tauira:

rāwekeweke kīanga

Hei tauira:
3a + 4e + 7a = 10 a + 4e
3t = 72, nō reira:
t = 72 ÷ 3
t = 24
3a + 4 = 25, nō reira:
3a = (25 – 4)
3a = 21
a = 21 ÷ 3
a = 7
4(p – 6) = 12, nō reira:
p – 6 = 12 ÷ 4
p – 6 = 3
p = 3 + 6
p = 9

Ka whakaatu pānga rārangi, pānga pūrua, pānga taupū ki te kauwhata

Hei tauira:
pānga rārangi

pānga pūrua

pānga taupū