Pangarau_A2 Wallchart.indd WHANAKETANGA: PĀNGARAU (1a, 1e, 2a) Te Tino Wāhanga Pāngarau WHANAKETANGA 1a WHANAKETANGA 1e WHANAKETANGA 2a Ngā Whāinga Ka whakaoti rapanga te ākonga, ka whakamārama otinga, e whai wāhi mai ana: He tauira ēnei o ngā āhuatanga me mātua mōhio te ākonga e tutuki ai tana whakaoti rapanga: Ka whakaoti rapanga te ākonga, ka whakamārama otinga, e whai wāhi mai ana: He tauira ēnei o ngā āhuatanga me mātua mōhio te ākonga e tutuki ai tana whakaoti rapanga: Ka whakaoti rapanga te ākonga, ka whakamārama otinga, e whai wāhi mai ana: He tauira ēnei o ngā āhuatanga me mātua mōhio te ākonga e tutuki ai tana whakaoti rapanga: Te Ta u (T e M āt au ra ng a T au m e n gā R au ta ki Ta u) • ngā rautaki tatau pānga-tahi hei whakaoti paheko tau. • ngā tauoti mai i te 0 ki te 20, arā, ko ngā tohutau, ngā kupu tau, me te rahi o ngā tau • te whakaahuahanga me te raupapa o ngā tau • ngā tau rearua ki te 10 me ngā haurua e whai pānga ana • te mātauranga uara tū e hāngai ana, pēnei i ngā tauhono takirua o roto i te 5 me te 10, me ngā wāwāhitanga uara tū. • ngā rautaki tatau māwhitiwhiti, ngā rautaki tatau ake, me ngā rautaki tohatoha ōrite hei whakaoti paheko tau. • ngā tauoti mai i te 0 ki te 100 me te mātauranga uara tū e hāngai ana • te tatau mawhiti-2, mawhiti-5, mawhiti-10, whakamua, whakamuri hoki • ngā meka tāpiritanga ki te 10 me ngā tangohanga e whai pānga ana • ngā tau rearua ki te 20 me ngā haurua e whai pānga ana • te whakaatu paheko tau hei whārite • ngā kupu, ngā tohu, ngā whakaahuahanga, me te tikanga o ngā haurua me ngā hauwhā. • ngā rautaki wāwāhi tau hei whakaoti paheko tau. • ngā tauoti mai i te 0 ki te 1 000, me te mātauranga uara tū e hāngai ana • ngā hautau māmā • ngā meka tāpiritanga ki te 20 me ngā tangohanga e whai pānga ana • te raupapa hautau māmā mēnā he ōrite te tauraro. Te Ta ui ra m e t e P ān ga • te hanga me te whakaroa tauira tāruarua. • te tautohu i te pūtake o te tauira e tāruaruatia ana. • te hanga me te whakaroa tauira raupapa āhuahanga, tauira raupapa tau hoki • te hanga me te whakaroa tauira tāruarua, e rua ōna āhuatanga taurangi • te whiriwhiri huānga o roto i tētahi tauira tāruarua māmā. • te tipu o te tauira raupapa me te pūmautanga o te tipu. • ngā tauira o roto i te wāwāhitanga tāpiripiri o tētahi tau • te whakaatu pānga māmā • ngā tauira ka puta i te wāwāhi āhua • te whakamahi rauemi kē hei hanga tauira tāruarua e rite ana ki ētahi atu. • ngā tauira o roto i ngā momo whakaahuahanga tau, pēnei i te anga tekau, te paparau, te anga pirepire, me te rārangi tau • ngā momo whakaahuahanga pānga (pērā i te hoahoa pere me te tūtohi) • ngā tauhono takirua o roto i tētahi tau. Te In e m e t e H an ga • te whakatairite me te whakaraupapa i te rahi o ngā āhuatanga ine o ētahi mea e rua • te whakarōpū taonga i runga anō i ngā āhuatanga hanga o aua taonga. • ēnei āhuatanga e taea ana te ine: te roa, te taumaha, te wā, te paemahana, me te utu • te reo māmā hei whakatairite i ngā āhuatanga ine o ētahi mea • ēnei momo āhuatanga hanga māmā hei whakarōpū taonga: te rahi, te tae, te maha o ngā kokonga, ngā tapa, me ngā mata. • te whakamahi waeine aro kē hei ine i tētahi mea • te whakamahi waeine aro whānui māmā hei ine i tētahi mea • ngā āhuatanga hanga o ngā taparau māmā me ngā matarau māmā. • ēnei āhuatanga e taea ana te ine – te hurihanga, te rōrahi/ kītanga, me te horahanga • te pūmautanga o te waeine • te tāruarua i te waeine hei ine i tētahi mea, kāore he āputa, kāore e inaki rānei • te wāhi tīmata me te wāhi mutu o tētahi inenga • ngā ingoa o ngā āhua ahu-2 māmā me ngā āhua ahu-3 māmā (pērā i te tapatoru, te tapawhā, te taimana, te porowhita, te tapawhā rite, te tapawhā hāngai, te pouaka, me te poi). • te hanga me te whakamahi taputapu ine, waeine hoki e whaitake ana • te wāwāhi me te tāpiri inenga • te whakaputa whakaaro mō te whaitakenga o tētahi inenga, i runga anō i ngā whakataunga tata • ngā āhuatanga hanga o ngā taparau whānui me ngā matarau whānui. • te rahinga āwhiwhi o ngā waeine aro whānui māmā me te hononga ki te rahi o tētahi mea e tino mōhiotia ana (pērā i te roa o te whetoko me te rōrahi o tētahi ipu miraka) • ngā hautanga māmā o tētahi waeine • ngā momo tapatoru • ngā kupu āhuahanga e hāngai ana (pērā i te akitu, te mata, me te tapa) • ngā momo matarau (pērā i ngā poro me ngā koeko) • te rārangi hāngai, te rārangi whakarara me te rārangi pūtahi • te koki hāngai. Te W āh i, te A hu ng a, m e t e P an on i • te whai me te hoatu tohutohu mō te nuku • te whakamārama i te wāhi noho o tētahi mea. • ngā kupu ahunga māmā, pēnei i ēnei: whakamua, whakamuri, mauī, matau, me ētahi noa atu • ngā kupu whakaatu taunga māmā pēnei i ēnei: tata, tawhiti, taha, waenganui, mua, muri, me ētahi noa atu. • te whai me te hoatu tohutohu mō te hurihanga • te tautohu i te whakaatanga, te hurihanga, me te nekenga, o tētahi āhua māmā. • te hurihanga whakatekaraka, te hurihanga kōaro, me ngā hurihanga hautanga māmā (1–4, 2–4, 3–4, 4–4, 5–4 …) • ngā āhuatanga ka noho pūmau i te panoni māmā. • te tautohu ahunga matua • te whakaatu taunga māmā ki te tukutuku • te whakaata, te neke, me te huri i tētahi āhua māmā. • ngā kupu whānui mō te ahunga me te taunga, pēnei i ēnei: uta, tai, rahaki, tua, me ētahi noa atu • ngā ahunga matua o te kāpehu • te hangarite o tētahi āhua māmā. Te Ta ua ng a • te whakarōpū raraunga māmā, e hāngai ana ki te ao o te tamaiti. • ngā momo whakarōpūtanga e taea ana mō tētahi huinga raraunga māmā. • te hanga me te whakamāori whakaari raraunga māmā, pēnei i te kauwhata whakaahua. • te tatau raraunga whakarōpū hei whakaputa kōrero mō tētahi huinga raraunga • te tikanga o te whakamahi whakaahua hei tohu raraunga. • te whakatakoto pātai māmā me te kohikohi raraunga e hāngai ana, hei whakautu i ngā pātai • te hanga me te whakamāori whakaari raraunga e hāngai ana ki ngā raraunga i kohia. • te whakaatu raraunga ki te tūtohi tatau • te whakaputa kōrero mō ngā āhuatanga matua o tētahi huinga raraunga. Te Tū po no ta ng a • te tūhura i ētahi pūāhua tūponotanga māmā • te matapae me te whakamātau i ngā putanga o tētahi pāpono tūponotanga. • ngā putanga ka taea i tētahi pāpono tūponotanga. • te reo māmā hei whakaahua i te tūponotanga o tētahi putanga. • te ōrite, te rerekē, te rangirua rānei o ngā putanga o tētahi pāpono. He Kupu Taka āhua ahu-2 .............................. 2-dimensional shape āhua ahu-3 .............................. 3-dimensional shape āhuatanga hanga .................... geometric properties āhuatanga ine .................... measurement attributes ahunga ......................................................... direction anga pirepire ................................... slavonic abacus anga tekau ............................................... tens frame āputa .................................................................... gap āwhiwihi ................................................. approximate hangarite .................................................... symmetry huānga .......................................................... element huinga raraunga ........................................... data set hoahoa pere ....................................... arrow diagram inaki ................................................................ overlap kōaro .................................................. anti-clockwise koeko ............................................................. pyramid koki hāngai .............................................. right angle matapae .......................................................... predict matarau ................................................... polyhedron nuku .......................................................... movement paheko tau ................................... number-operation pānga māmā .................................... simple relations panoni ............................................... transformation pāpono .............................................................. event pāpono tūponotanga ...................... probability event poro .................................................................... prism pūāhua tūponotanga ................. probability situation pūmau .......................................................... invariant pūmautanga .............................................. invariance putanga ........................................................ outcome rangirua ........................................................... uncertain rārangi hāngai .................................. perpendicular line rārangi pūtahi ...................................... intersecting line rārangi whakarara ..................................... parallel line raraunga ................................................................... data raraunga whakarōpū ................................ category data rautaki tatau māwhitiwhiti .............. skip count strategy rautaki tatau pānga-tahi ....... one to one counting strategies rautaki tohatoha ōrite ................ equal sharing strategy tatau ake ........................................................... count on tauhono takirua ......................................... additive pairs tauhono takirua ........................... additive number pairs tūtohi ........................................................................ table taparau ................................................................ polygon tauira tāruarua ................................... repetitive pattern taunga ................................................................. position taurangi ............................................................... variable tāruarua ........................................................... repeating tauira raupapa āhuahanga .... sequential geometric pattern tauira raupapa tau .............. sequential number pattern tukutuku .................................................................... grid tūtohi tatau ..................................................... tally chart uara tū ........................................................... place value waeine ........................................... unit of measurement waeine aro kē .................................... non-standard unit waeine aro whānui .................................... standard unit wāwāhitanga uara tū ................ place value partitioning wāwāhitanga tāpiripiri ................... additive partitioning whakaari raraunga ..................................... data display whakaahuahanga ................................... representation whakaata .................................................... refl ection whakamāori ................................................. interpret whakamātau ....................................................... trial whakatairite ................................................. compare whakataunga tata ..................................... estimation whārite ......................................................... equation whetoko ................................................... pace, stride NGĀ WHANAKETANGA ME NGĀ TAU KURA Tau kura 1 Tau kura 2 Tau kura 3 Tau kura 4 Tau kura 5 Tau kura 6 Tau kura 7 Tau kura 8 1a 1e 2a 2e 3a 3e 4a 4e 5a WHANAKETANGA: PĀNGARAU (2e, 3a, 3e) Te Tino Wāhanga Pāngarau WHANAKETANGA 2e WHANAKETANGA 3a WHANAKETANGA 3e Ngā Whāinga Ka whakaoti rapanga te ākonga, ka whakamārama otinga, e whai wāhi mai ana: He tauira ēnei o ngā āhuatanga me mātua mōhio te ākonga e tutuki ai tana whakaoti rapanga: Ka whakaoti rapanga te ākonga, ka whakamārama otinga, e whai wāhi mai ana: He tauira ēnei o ngā āhuatanga me mātua mōhio te ākonga e tutuki ai tana whakaoti rapanga: Ka whakaoti rapanga te ākonga, ka whakamārama otinga, e whai wāhi mai ana: He tauira ēnei o ngā āhuatanga me mātua mōhio te ākonga e tutuki ai tana whakaoti rapanga: Te Ta u (T e M āt au ra ng a T au m e n gā R au ta ki Ta u) • ngā rautaki wāwāhi tau me te rautaki paheko kōaro mō te tāpiritanga me te tangohanga • ngā rautaki tāpiri tāruarua mō te whakareatanga me te whakawehenga māmā, hei whiriwhiri hoki i te hautanga māmā o tētahi tau. • ngā tauoti mai i te 0 ki te 10 000, me te mātauranga uara tū e hāngai ana • ngā meka whakareatanga o te 2, te 5, me te 10, me ngā whakawehenga e whai pānga ana • ngā kupu, ngā tohu, ngā whakaahuahanga, me te tikanga o ngā haurua, ngā hautoru, ngā hauwhā, ngā haurima, ngā hauwaru, me ngā hautekau • te raupapa hautau waetahi. • ngā rautaki wāwāhi tau whānui mō te tāpiritanga me te tangohanga • ngā rautaki whakarea māmā mō te whakareatanga, te whakawehenga, me te whiriwhiri hautanga māmā o tētahi tauoti. • ngā tauoti mai i te 0 ki te 100 000 me te mātauranga uara tū e hāngai ana • ngā hautau noa me ngā hautanga ā-ira (kia kotahi te mati ā-ira) • ngā meka whakareatanga ki te 10 x 10 me ngā whakawehenga e whai pānga ana • te raupapa hautau māmā • ngā momo whakaahuatanga hautanga ā-ira, me te hononga ki ngā hautau noa. • ngā rautaki whakarea mō te whakareatanga, te whakawehenga, me te whiriwhiri hautanga o tētahi tauoti. • ngā tauoti mai i te 0 ki te 1 000 000 me tua atu, ngā hautau noa, ngā tau ā-ira (kia 3 ngā mati ā-ira), me te mātauranga uara tū e hāngai ana • ngā hononga whānui o ngā meka matua pērā i te 3 x 0.4 = 1.2 • te whakaawhiwhi tauoti hei whakatau tata i te otinga o tētahi paheko tau • te raupapa hautau. Te Ta ui ra m e t e P ān ga • te whiriwhiri me te whakamahi i te ture o tētahi tauira māmā. • te whakamahi tohu hei whakaatu i te ture o tētahi tauira. • ngā tauira tāpiripiri, tauira whakarea māmā, me ngā tauira āhuahanga, pānga hoki • ngā tauira o roto i te wāwāhitanga whakarea o tētahi tau. • te pūmautanga o tētahi ture hei whakaahua i tētahi tauira, tētahi pānga rānei. • ngā rautaki taurangi māmā e hāngai ana ki tētahi tauira, ki tētahi pānga māmā rānei (pēnei i te pānga tāpiripiri me te pānga whakarea). • te tikanga o te taurangi hei whakaatu i tētahi rahinga kāore e mōhiotia ana, me te whakamahinga o te pū (reta) hei tohu taurangi. Te In e m e t e H an ga • te kōwhiri i ngā waeine e hāngai ana ki te horopaki me te tōtika anō o te inenga e whaitake ana • te tuhi hoahoa me te hanga tauira o ngā āhua ahu-2 me ngā āhua ahu-3. • te whakamahi i te rūri, te tāporowhita, me te koki hāngai hei ine, hei tuhi āhua. • ngā momo āwhata maha me ngā hautanga ā-ira o tētahi waeine • ngā raumata o ngā āhua ahu-3 māmā, pēnei i te mataono rite, te poro tapawhā hāngai, me te koeko tapawhā hāngai. • te whakamahi i ngā momo taputapu ine whānui (pērā i te ine-koki). • te whakatau tata me te whiriwhiri horahanga māmā, rōrahi māmā • te tuhi raumata o ngā āhua ahu-3 whānui. • ngā waeine e tika ana mō te horahanga me te rōrahi, pēnei i te cm2, te cm3, te m2, me te m3 • te whakamahi tukutuku hei whiriwhiri horahanga • te whakamahi mataono rite hei whiriwhiri rōrahi. Te W āh i, te A hu ng a, m e t e P an on i • te whakaatu ahunga, taunga hoki ki te mahere māmā, pērā i ngā mahere o ngā wāhi e mōhiotia ana • te whai me te hoatu tohutohu haere huarahi • te tautohu i ngā āhuatanga ka noho pūmau, me ngā āhuatanga ka rerekē i tētahi panoni. • ngā taunga me ngā ahunga o ngā āhuatanga kōhure o tōna wāhi noho, pēnei i te maunga, te awa, te marae, te kura, me ētahi noa atu. • te tukutuku, te takirua raupapa, ngā ahunga matua, me ngā mahere māmā hei whakaatu taunga, huarahi, panoni māmā hoki. • ngā ahunga matua e whā o te kāpehu me ngā ahunga kei waenganui i ērā (pērā i te rāwhiti-mā-tonga) • ngā tikanga o te whakaatu taunga ki tētahi pūnaha tukutuku. • te hanga me te whakamārama tauira ka hua mai i te panoni tāruarua • ngā panoni matua e hua mai ai te mātātuhi i tōna mātāoroko. • ngā tikanga mō te whakamārama panoni (pērā i te pū me te koki o te hurihanga, te rārangi whakaata, te rahi me te ahunga o te neke, me te taurahi o tētahi whakarahinga māmā). Te Ta ua ng a • te raraunga whakarōpū me te raraunga motumotu • te whakaputa kōrero mō ngā whakakitenga o tētahi tūhuratanga tauanga. • te whakaatu raraunga ki te kauwhata pou māmā, me te kauwhata ira • ngā tikanga matatika e hāngai ana (pērā i ngā momo pātai e tika ana kia kore ai te kaiwhakautu e mamae, e whakaitia rānei). • te whakatakoto pātai e hāngai ana me te kohikohi raraunga hei tūhura i te pātai • te raraunga motukore (pērā i te raraunga houanga) • te whakaputa kōrero mō ngā tauira, ngā ia, me ngā āhuatanga kōhure o tētahi huinga raraunga. • te whakaatu raraunga ki te kauwhata rārangi • te āhua o te whakaaringa raraunga hei whakaatu i ngā ia, ngā tauira, me ngā āhuatanga kōhure o roto i ngā raraunga. • te raraunga whakarōpū matatini • te arotake i te whaihua o ngā momo whakaari raraunga. • te whakaatu raraunga ki te kauwhata rautō me te kauwhata porowhita • ngā tikanga matatika e hāngai ana (pērā i te tikanga kia noho matatapu ngā kaiwhakautu pātai o tētahi tūhuratanga tauanga). Te Tū po no ta ng a • te whakaatu tūponotanga ki tētahi āwhata • te whakamāori whakaari raraunga māmā hei matapae i te putanga o tētahi pāpono tūponotanga. • te whakaatu putanga ki tētahi whakaari raraunga māmā (pērā i te kauwhata ira, te kauwhata whakaahua, me te kauwhata pou). • te tūhura pūāhua tūponotanga māmā, pēnei i te piu i tētahi uka, me te pīrori i tētahi mataono tau • te whakaatu tūponotanga hei hautau māmā i waenganui i te kore me te kotahi. • te whakatairite i ngā putanga matapae me ngā putanga whakamātau o tētahi pāpono tūponotanga • te wehe kētanga, te whakawhirinaki, te aukati rānei o ētahi pāpono e rua. • te reo me ngā whakaahuahanga whānui hei whakaatu tūponotanga. • te whakamahi rārangi hautau hei whakaatu tūponotanga • te hoahoa rākau hei whakaatu i ngā putanga o ētahi pāpono raupapa. He Kupu Taka āhuatanga kōhure ......................................... distinctive features aukati .............................................................. mutually exclusive āwhata ................................................................................... scale hautau waetahi ......................................................... unit fraction hoahoa rākau ........................................................... tree diagram ia ......................................................................................... trends ine-koki ........................................................................ protractor kauwhata ira ................................................................. dot graph kauwhata porowhita ...................................................... pie graph kauwhata pou ............................................................... bar graph kauwhata rautō .......................................... stem-and-leaf graph koki hāngai ................................................................. right angle mataono rite ......................................................................... cube mātāoroko ........................................................................... object matatapu .................................................................... anonymous mātātuhi .............................................................................. image mati ā-ira ............................................................. decimal places paheko tau ...................................................... number operation panoni tāruarua ................................... repetitive transformation pāpono raupapa .................................................. combined event pūmau ............................................................................. invariant putanga matapae ........................................ theoretical outcome putanga whakamātau ............................. experimental outcome rahinga ............................................................................. quantity rārangi hautau .......................................................... fraction line raraunga houanga ............................................. time-series data raraunga motukore ............................................ continuous data raraunga motumotu ................................................ discrete data raraunga whakarōpū matatini ................... multivariate category data raumata ................................................................................... net rautaki paheko kōaro ........................ inverse operation strategy rautaki taurangi .............................................. algebraic strategy rautaki wāwāhi tau ...................................... part–whole strategy rautaki whakarea .................................... multiplicative strategy takirua raupapa ........................................................ ordered pair tāpiri tāruarua ................................................ repeating addition tāporowhita .................................................................... compass tauira āhuahanga ........................................... geometric pattern tauira tāpiripiri ................................................... additive pattern taurahi ........................................................................ scale factor tikanga matatika .......................................... ethical conventions tūhuratanga tauanga .............................. statistical investigation wāwāhitanga whakarea ..................... multiplicative partitioning wehe kētanga ........................................................... independent whakaawhiwhi ..................................................................... round whakatau tata ................................................................. estimate whakawhirinaki ........................................................... dependent NGĀ WHANAKETANGA ME NGĀ TAU KURA Tau kura 1 Tau kura 2 Tau kura 3 Tau kura 4 Tau kura 5 Tau kura 6 Tau kura 7 Tau kura 8 1a 1e 2a 2e 3a 3e 4a 4e 5a WHANAKETANGA: PĀNGARAU (4a, 4e, 5a) Te Tino Wāhanga Pāngarau WHANAKETANGA 4a WHANAKETANGA 4e WHANAKETANGA 5a Ngā Whāinga Ka whakaoti rapanga te ākonga, ka whakamārama otinga, e whai wāhi mai ana: He tauira ēnei o ngā āhuatanga me mātua mōhio te ākonga e tutuki ai tana whakaoti rapanga: Ka whakaoti rapanga te ākonga, ka whakamārama otinga, e whai wāhi mai ana: He tauira ēnei o ngā āhuatanga me mātua mōhio te ākonga e tutuki ai tana whakaoti rapanga: Ka whakaoti rapanga te ākonga, ka whakamārama otinga, e whai wāhi mai ana: He tauira ēnei o ngā āhuatanga me mātua mōhio te ākonga e tutuki ai tana whakaoti rapanga: Te Ta u (T e M āt au ra ng a T au m e n gā R au ta ki Ta u) • ngā rautaki whakarea whānui mō te whiriwhiri ōrau, ōwehenga māmā hoki hei whakaatu pānga rahinga. • ngā tauoti me ngā tau hautanga, me te mātauranga uara tū e hāngai ana • ngā tikanga me te whakamahinga o te tau tōraro • te whakaawhiwhi tauoti, tau ā-ira hoki • ngā hautau ōrite (hautau, hautanga ā-ira, ōrau) • ngā tauwehe me ngā taurea o tētahi tau • ngā ōrau nui ake i te 100%. • ngā tau tōpū me ngā tau hautanga (hautau noa, hautau ā-ira, ōrau) • ngā rautaki tāpiripiri, whakarea hoki e hāngai ana ki ngā horopaki pānga riterite (pērā i te ōwehenga me te pāpātanga māmā). • te taupū māmā (pērā i te pūrua me te pūtakerua) • te tōtika me te whaitakenga o ngā whakataunga tata me ngā tātaitanga • ngā huarahi e tino whaihua ana hei whakaoti tātaitanga i ngā horopaki maha. • ngā tau tōpū me ngā tau hautanga • te kōwhiri i te rautaki paheko tau e tino hāngai ana ki te horopaki. • ngā tikanga me te whakamahinga o te tānga ngahuru hei tohu i ngā tau tino nui, tino iti hoki • ngā momo hātepe whakaoti paheko hautau. Te Ta ui ra m e t e P ān ga • te whakaatu pānga māmā hei whārite taurangi, hei kauwhata anō hoki. • te hua o te huri i tētahi taurangi me te pānga ki taurangi kē. • te whakaatu pānga hei kupu, hei tūtohi, hei kauwhata, hei whārite hoki • te whakaoti whārite taurangi māmā, pērā i te 3t + 5 = 47. • te whakamahinga o te āhuatanga kōaro, te āhuatanga herekore, me te āhuatanga tohatoha hei whakaoti whārite • te tikanga o te tuaka pou, te tuaka pae, me te takirua raupapa hei whakaatu i te pānga o ētahi taurangi e rua ki te kauwhata • te tikanga o te rārangi o tētahi kauwhata hei whakaatu i te pānga o ētahi taurangi e rua. • te whārite me te kauwhata rārangi hei whakaatu pānga. • te tikanga o ngā haukotinga tuaka me te rōnaki o tētahi kauwhata rārangi, me te puta o ēnei i rō whārite. Te In e m e t e H an ga • te whakawhitiwhiti waeine • ngā inenga tapa me ngā ture hei tātai paenga, horahanga, rōrahi hoki o ngā āhua māmā • te pāpātanga hei ine i tētahi mea (pēnei i te km/h hei ine i te tere) • te whakaatu āhua ahu-3 hei hoahoa ahu-2 (pērā i te tuhinga hoahoa inerite) • te tuhi hoahoa āwhata. • ngā momo tirohanga ki tētahi mea, pērā i te tirohanga ā-manu, te tirohanga mua, me te tirohanga mauī • te whakamahinga o te ōwehenga me te taurahi hei tuhi hoahoa āwhata. • ngā momo wātaka whānui • te whiriwhiri i te rahi o tētahi koki. • te tātai i te takanga o te wā • te whakaatu wā-24 • te tikanga o te koki whakahāngai, te koki whakarārangi, te koki whakahuripū, te koki tāhapa, me te koki hāpūpū. • ngā ture hei tātai tapa, paenga, horahanga, koki, horahanga mata, rōrahi hoki o ngā āhua whānui • ngā tikanga koki o te rārangi pūtahi, te rārangi whakarara, me ngā taparau. • te whakamahi i te ture a Pythagoras • te tikanga o te koki tauroto, te koki tauaro, te koki taurite, me te koki tauwhiti. Te W āh i, te A hu ng a, m e t e P an on i • ngā koki o te kāpehu hei whakaatu ahunga • te hangarite panoni o tētahi āhua. • te hononga o ngā koki ki ngā ahunga matua o te kāpehu • ngā tikanga o te hangarite rārangi me te hangarite hurihanga o tētahi āhua. • te ōwehenga hei tātai taurahi, hei tātai hoki i te rahi o tētahi mātātuhi whakarahi • tētahi raupapatanga panoni. • te hua o te whakarahi āhua (pērā i te pānga ki te roa o ngā tapa, te horahanga me te rōrahi). • te hangarite o ngā koki o ngā rārangi pūtahi, ngā rārangi whakarara, ngā taparau, me ngā matarau • te whakaatu me te whakamārama panoni ki te papa kauwhata. • te whakamahi pere hei whakaatu nekehanga • te whakamahi mahere me ōna āhuatanga katoa (pērā i te tukutuku me te āwhata) hei whakaahua huarahi. Te Ta ua ng a • te whakatakoto pātai, tāpaetanga kōrero rānei hei tūāpapa mō tētahi tūhuratanga tauanga • te whakatairite i te tuari o ētahi huinga raraunga • te whakamahi wēanga. • te tātai toharite, tau waenga, inenga whānui, tau tānui o tētahi huinga raraunga, me te whakaatu ki te whakaari raraunga • te whakaatu raraunga ki te kauwhata pou whakaapaapa • te tautohu i ngā taurangi o tētahi tūhuratanga tauanga, te kohikohi me te whakaari raraunga mō aua taurangi. • te tātari i ngā whakakitenga o tētahi tūhuratanga tauanga • te arohaehae i te tōtika o te tukanga kohikohi raraunga, me te whakaari i ngā raraunga o tētahi tīpako, hei whakaatu i te āhua o tētahi taupori. • te whakaatu raraunga ki te kauwhata pouhere • ngā tikanga matatika e hāngai ana (pērā i te whakamōhio atu ki te kaiwhakautu pātai i te whakamahinga o ngā raraunga ka puta i te tūhuratanga tauanga). • te whakatakoto pātai, tāpaetanga kōrero rānei, te whakahaere tūhuratanga tauanga, me te whakaputa pūrongo • te arotake i ngā kōrero ka puta i tētahi tūhuratanga tauanga • te whakaputa kōrero mō te pānga o tētahi taurangi ki tētahi. • te whakaatu raraunga ki te kauwhata kauamo me te kauwhata marara • te whaitake me te whaihua o ngā momo whakaari raraunga • ngā tikanga matatika e hāngai ana (pērā i te tikanga kia kaua e haukumea te āhua o ngā pātai). Te Tū po no ta ng a • te tōkeke, te haukume rānei o tētahi pāpono tūponotanga. • te whakaatu tūponotanga hei ōrau. • te whakatairite i te tuari o ngā putanga matapae me ngā putanga whakamātau. • ngā take e taurangi ai ngā putanga o tētahi whakamātau tūponotanga. • tētahi pūāhua tūponotanga papa-maha. • te tātai tūponotanga o tētahi pāpono raupapa. He Kupu Taka āhuatanga herekore ................. associative property āhuatanga kōaro .................... commutative property āhuatanga tohatoha ................. distributive property arohaehae ...................................................... critique hangarite panoni ............. transformation symmetry hātepe ........................................................ algorithm haukotinga tuaka ................................. axis intercept haukume ............................................................. bias haukumea .................................................. be biased hoahoa āwhata ................................... scale diagram hoahoa inerite ............................. isometric diagram horopaki pānga riterite ............ proportional context inenga whānui .................................................. range kauwhata kauamo .............. box-and-whisker graph kauwhata marara ................................... scatter plot kauwhata pou whakaapaapa ...... stacked bar graph kauwhata pouhere .................................... histogram koki hāpūpū .......................................... obtuse angle koki tāhapa ............................................. acute angle koki tauaro ......................................... opposite angle koki taurite ............................. corresponding angles koki tauroto ........................................ interior angles koki tauwhiti ................................... alternate angles koki whakahāngai ................... complimentary angle koki whakahuripū ............................ conjugate angle koki whakarārangi .................. supplementary angle mātātuhi ........................................................... image ōwehenga ............................................................ ratio paenga ....................................................... perimeter pānga rahinga .................... quantitative relationship papa-maha .............................................. multi-level pāpātanga ............................................................. rate pāpono raupapa ............................... combined event pere .................................................................. vector pūrua ............................................................... square pūtakerua ............................................... square root rārangi pūtahi ................................ intersecting lines raupapatanga panoni ...... combined transformation rōnaki ................................................................ slope tānga ngahuru .................................... standard form tāpaetanga kōrero ...................................... assertion tātari ............................................................... analyse tau tānui ............................................................ mode tau tōpū .......................................................... integer tau tōraro ....................................... negative number tau waenga ......................................................... median taupori ............................................................ population taupū ................................................................. exponent taurahi .......................................................... scale factor taurea ................................................................. multiple tauwehe ................................................................. factor tikanga matatika ............................. ethical conventions tīpako ................................................................... sample toharite .................................................................. mean tōkeke ........................................................................ fair tuari ............................................................... distribution tukanga kohikohi raraunga ....... data collection process ture .................................................................... formulae wēanga .............................. measure of central tendency whārite taurangi ............................... algebraic equation NGĀ WHANAKETANGA ME NGĀ TAU KURA Tau kura 1 Tau kura 2 Tau kura 3 Tau kura 4 Tau kura 5 Tau kura 6 Tau kura 7 Tau kura 8 1a 1e 2a 2e 3a 3e 4a 4e 5a