Te Waihanga

Thanks for visiting NZMaths.
We are preparing to close this site by the end of August 2024. Maths content is still being migrated onto Tāhūrangi, and we will be progressively making enhancements to Tāhūrangi to improve the findability and presentation of content.

Hei Whakarāpopoto

Ko te kaupapa nei, he tūhura me pēhea te waihanga i ētahi āhua, me ngā āhuatanga hangarite o aua āhua.  Ka whakamahia te tāporowhita me te ruri hei waihanga āhua.

Achievement Objectives
6. Ka whakamahi taputapu ki te waihanga taparau māmā.
Te Hononga ki te Marautanga
Taumata 5
Te Ine me te Āhuahanga (Te Hanga)
Whāinga Paetae 6:
Ka whakamahi taputapu ki te waihanga taparau māmā.
Ngā Whāinga Ako
Kia mōhio te ākonga ki te:
• whakamahi tāporowhita hei waihanga tapatoru
• whakamahi tāporowhita hei waihanga koki hāngai
• whakamahi taputapu tā hei waihanga tauira āhuahanga, rōpinepine hoki
Ngā Rauemi

he ruri

Te Waihanga WM1

Te Waihanga WM2

he tāporowhita

Te Waihanga WM3

He Rārangi Kupu
 koki hāngai right angle pūtahitanga intersection pūwāhi point rōpinepine tesselation tapaono rite regular hexagon tapatoru hikuwaru scalene triangle tapatoru rite equilateral triangle tapatoru waerite isoceles triangle tāporowhita compass (for drawing circles tohu waihanga construction marks waihanga construct whakarara parallel

Hei Raupapa I Ngā Mahi Ako
1. Ko te mahi tuatahi he āta tirotiro i te whakamahinga o te tāporowhita hei waihanga tapatoru.
 Te mahi a te pouako He tauira kōrero mā te pouako Tonoa mā ngā tamariki e kimi me pēhea e oti ai tētahi tapatoru mā te whakamahi tāporowhita, ka whakamārama ai.    Mēnā ka raruraru, māu tonu e whakamārama.                     Hoatu te Te Waihanga WM1 (PDF, 89KB) hei whakaoti mā ngā ākonga. Tā koutou mahi, he tā i tētahi tapatoru.  Kia 6cm te roa o te pūtake, kia 3cm te roa o tētahi tapa, kia 5cm tētahi.  Ko te ruri, te tāporowhita me te pene rākau anake hei whakamahi mā koutou.    Whakamāramahia mai ngā hīkoi mō te tā i te tapatoru. Tuhia te rārangi pūtake o te tapatoru i te tuatahi.  Inea kia 6cm te roa.  Rohaina te tāporowhita kia 5cm te whātoro o ngā waewae. Poua te waewae koi ki tētahi pito o te rārangi pūtake, ka tā ai i te pewa ki runga ake o te rārangi pūtake. Rohaina te tāporowhita kia 3cm te whātoro o ngā waewae. Poua te waewae koi ki tērā atu pito o te rārangi pūtake.  Tāia he pewa anō. Honoa ngā pito e rua o te rārangi pūtake ki te wāhi e pūtahi ana ngā pewa e rua. Kua oti te tapatoru te waihanga.

2. He mahi whakarongo tēnei.  Ko tā ngā ākonga, he whai i āu tohutohu hei waihanga i tētahi koki hāngai.  Kia taunga ngā ākonga ki te waihanga koki hāngai, me hoatu te Te Waihanga WM2 (PDF, 108KB) hei whakaoti mā rātou.
 He tauira kōrero mā te pouako Ngā mahi a te ākonga Tuhia he rārangi hauroki ki tō whārangi.  Tohua tētahi pūwāhi kei te takiwā waenganui o te rārangi.   Whakamahia te tāporowhita.  Tuhia kia rua ngā tohu ki ia taha o te pūwāhi tuatahi (kia 2cm pea te roha o te tāporowhita).       Mai i ēnei tohu e rua, tāia he pewa ki runga ake o te pūwāhi tuatahi (kia 4cm pea te roha o te tāporowhita).       Honoa te pūtahitanga o ngā pewa e rua me te pūwāhi tuatahi.  Anā - he koki hāngai.

3. I konei, ka whakamahia te tāporowhita me te ruri, ka whai i ngā tohutohu hei tā i tētahi tauira tāniko.
 He tauira kōrero mā te pouako Ngā mahi a te ākonga Ka whakamahia te tāporowhita me te ruri hei waihanga i tētahi tauira tāniko.  He tauira tāniko mō tētahi tīpare.   Tuhia he rārangi mai i tētahi taha o te whārangi ki tētahi.  Koinei hei rārangi pūtake o te tāniko.   Tohua te pūwāhi waenganui o tēnei rārangi pūtake.   Inea kia 2cm ki ia taha o tēnei pūwāhi waenganui.  Koinei hei pūtake mō tētahi tapatoru waerite.  E 4cm te roa o te pūtake.   Whakamahia te tāporowhita hei waihanga i te tapatoru waerite, kia 5cm te roa o ngā tapa waerite.       Whakamahia te tāporowhita me te ruri, ka tuhi ai i tētahi tapatoru waerite anō.  He iti ake tēnei tapatoru waerite, ā, ka noho ki roto i te tapatoru tuatahi.  Anei ngā tohutohu mō tēnei tapatoru:   E hoki ki te pūwāhi waenganui o te rārangi pūtake.  Tuhia he tohu kia 1cm ki ia taha o tēnei pūwāhi.  Koirā te pūtake o te tapatoru iti nei.  Hangaia te tapatoru kia 2.5cm te roa o ngā tapa waerite.   Tuhia he rārangi ki runga ake o te rārangi pūtake, kia pā tēnei rārangi ki te tihi o te tapatoru waerite nui.  Kia noho whakarara ki te rārangi pūtake.   Tuhia he tohu ki te rārangi pūtake, kia 0.5cm mai i ia taha o te pūtake o te tapatoru nui.  Tuhia hoki he tohu kia 0.5cm ki ia taha o te tihi o te tapatoru nui.    Honoa ngā tohu kei ia taha o te tapatoru, mai i runga ki raro.           Kua oti te tānga matua o te tauira tāniko.  Ko te mahi ināianei, he nuku i tēnei tānga matua ki ia taha, ka tā anō ai.

4. Ko tāu mahi ināianei, he waihanga i tāu ake tauira tāniko, me te tuhi anō i ngā tohutohu hei whaitanga mā tētahi atu tangata, hei tuhi māna i tō tauira.  Kia māmā noa iho te āhua o te tauira.  Kia oti āu tohutohu te tuhi, me kōrero ā-waha ki tētahi hoa, ka ārahi i a ia ki te waihanga i tō tauira.  Māna hoki koe e ārahi ki te tuhi i tāna.

5. I konei ka whakamahia te tāporowhita hei waihanga tapaono rite.  Ka tāia hoki he rōpinepine e whai wāhi mai ana te tapaono rite me te tapatoru rite.
 He tauira kōrero mā te pouako Ngā mahi a te ākonga Rohaina te tāporowhita kia 5cm te whātoro o ngā waewae.  Tuhia he porowhita ki tō whārangi.   Poua te tāporowhita ki tētahi wāhi i te paenga o te porowhita, ka tohu ai i tētahi anō wāhi i te paenga o te porowhita.         Poua tō taputapu tuhi porowhita ki te wāhi hou i tohua i te paenga o te porowhita, ka tohu ai i tētahi anō wāhi i te paenga o te porowhita.   Kia pērā tonu tō mahi kia hoki rā anō koe ki te wāhi i tīmata ai koe.  E hia ngā wāhi i te paenga o te porowhita kua tohua e koe?   Honoa ngā wāhi kua tohua ki te paenga o te porowhita, tētahi ki tētahi.  He aha te āhua ka puta?

Kia taunga rā anō ngā ākonga ki te tuhi tapaono rite kātahi ka hoatu i te Te Waihanga WM3  (PDF, 119KB) hei whakaoti mā rātou.  He tuhi rōpinepine tētahi o ngā mahi.
Attachments