Pangarau_A3Foldouts_FINAL.indd WHANAKETANGA 1a: PĀNGARAU Te Tino Wāhanga Pāngarau 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: 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-tahi1 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 whakaahuahanga2 me te raupapa o ngā tau • ngā tau rearua ki te 10 me ngā haurua e whai pānga ana • te mātauranga uara tū3 e hāngai ana, pēnei i ngā tauhono takirua4 o roto i te 5 me te 10, me ngā wāwāhitanga uara tū5. 1one to one counting strategies 2representation 3place value 4additive number pairs 5place value partitioning Te Ta ui ra m e t e P ān ga • te hanga me te whakaroa tauira tāruarua6. • te tautohu i te pūtake o te tauira e tāruaruatia ana. 6repetitive pattern Te In e m e t e H an ga • te whakatairite7 me te whakaraupapa i te rahi o ngā āhuatanga ine8 o ētahi mea e rua • te whakarōpū taonga i runga anō i ngā āhuatanga hanga9 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. 7compare 8measurement attributes 9geometric properties 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 10 • te whakamārama i te wāhi noho o tētahi mea. • ngā kupu ahunga11 māmā, pēnei i ēnei: whakamua, whakamuri, mauī, matau, me ētahi noa atu • ngā kupu whakaatu taunga12 māmā pēnei i ēnei: tata, tawhiti, taha, waenganui, mua, muri, me ētahi noa atu. 10movement 11direction 12position 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 raraunga13 māmā. 13data set W HANAKETANGA 1a: PĀNGARAU WHANAKETANGA 1e: PĀNGARAU W HANAKETANGA 1e: PĀNGARAU Te Tino Wāhanga Pāngarau 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: 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 māwhitiwhiti1, ngā rautaki tatau ake2, me ngā rautaki tohatoha ōrite4 hei whakaoti paheko tau. • ngā tauoti mai i te 0 ki te 100 me te mātauranga uara tū3 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 tau5 hei whārite6 • ngā kupu, ngā tohu, ngā whakaahuahanga7, me te tikanga o ngā haurua me ngā hauwhā. 1skip count strategy 2count on 3place value 4equal sharing strategy 5number-operation 6equation 7representation Te Ta ui ra m e t e P ān ga • te hanga me te whakaroa tauira raupapa āhuahanga8, tauira raupapa tau9 hoki • te hanga me te whakaroa tauira tāruarua, e rua ōna āhuatanga taurangi11 • te whiriwhiri huānga12 o roto i tētahi tauira tāruarua māmā. • te tipu o te tauira raupapa me te pūmautanga10 o te tipu. 8sequential geometric pattern 9sequential number pattern 10invariance 11variable 12element Te In e m e t e H an ga • te whakamahi waeine aro kē13 hei ine i tētahi mea • te whakamahi waeine aro whānui14 māmā hei ine i tētahi mea • ngā āhuatanga hanga15 o ngā taparau16 māmā me ngā matarau17 māmā. • ēnei āhuatanga e taea ana te ine – te hurihanga, te rōrahi/kītanga, me te horahanga • te pūmautanga o te waeine • te tāruarua18 i te waeine hei ine i tētahi mea, kāore he āputa19, kāore e inaki20 rānei • te wāhi tīmata me te wāhi mutu o tētahi inenga • ngā ingoa o ngā āhua ahu-221 māmā me ngā āhua ahu-322 māmā (pērā i te tapatoru, te tapawhā, te taimana, te porowhita, te tapawhā rite, te tapawhā hāngai, te pouaka, me te poi). 13non-standard unit 14standard unit 15geometric properties 16polygon 17polyhedron 18repeating 19gap 20overlap 212-dimensional shape 223-dimensional shape 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 hurihanga • te tautohu i te whakaatanga, te hurihanga, me te nekenga, o tētahi āhua māmā. • te hurihanga whakatekaraka, te hurihanga kōaro23, me ngā hurihanga hautanga māmā (1–4, 2–4, 3–4, 4–4, 5–4 …) • ngā āhuatanga ka noho pūmau24 i te panoni25 māmā. 23anti-clockwise 24invariant 25transformation Te Ta ua ng a • te hanga me te whakamāori26 whakaari raraunga27 māmā, pēnei i te kauwhata whakaahua. • te tatau raraunga whakarōpū28 hei whakaputa kōrero mō tētahi huinga raraunga • te tikanga o te whakamahi whakaahua hei tohu raraunga. 26interpret 27data display 28category data Te Tū po no ta ng a • te tūhura i ētahi pūāhua tūponotanga29 māmā • te matapae30 me te whakamātau31 i ngā putanga32 o tētahi pāpono tūponotanga 33. • ngā putanga ka taea i tētahi pāpono tūponotanga. 29probability situation 30predict 31trial 32outcome 33probability event Te Tino Wāhanga Pāngarau 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: 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 tau1 hei whakaoti paheko tau. • ngā tauoti mai i te 0 ki te 1 000, me te mātauranga uara tū2 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 tauraro3. 1part–whole strategies 2place value 3denominator Te Ta ui ra m e t e P ān ga • ngā tauira o roto i te wāwāhitanga tāpiripiri 4 o tētahi tau • te whakaatu pānga māmā7 • 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 whakaahuahanga5 tau, pēnei i te anga tekau6, te paparau, te anga pirepire8, me te rārangi tau • ngā momo whakaahuahanga pānga (pērā i te hoahoa pere9 me te tūtohi10) • ngā tauhono takirua11 o roto i tētahi tau. 4additive partitioning 5representation 6tens frame 7simple relations 8Slavonic abacus 9arrow diagram 10table 11additive pairs Te In e m e t e H an ga • te hanga me te whakamahi taputapu ine, waeine12 hoki e whaitake ana • te wāwāhi me te tāpiri inenga • te whakaputa whakaaro mō te whaitakenga15 o tētahi inenga, i runga anō i ngā whakataunga tata16 • ngā āhuatanga hanga17 o ngā taparau whānui me ngā matarau whānui. • te rahinga āwhiwhi13 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 whetoko14 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 matarau18 (pērā i ngā poro19 me ngā koeko20) • te rārangi hāngai21, te rārangi whakarara22 me te rārangi pūtahi23 • te koki hāngai24. 12unit of measurement 13approximate 14pace, stride 15reasonableness 16estimation 17geometric properties 18polyhedron 19prism 20pyramid 21perpendicular line 22parallel line 23intersecting line 24right angle Te W āh i, te A hu ng a, m e t e P an on i • te tautohu ahunga25 matua • te whakaatu taunga26 māmā ki te tukutuku27 • te whakaata28, 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 hangarite29 o tētahi āhua māmā. 25direction 26position 27grid 28refl ection 29symmetry Te Ta ua ng a • te whakatakoto pātai māmā me te kohikohi raraunga30 e hāngai ana, hei whakautu i ngā pātai • te hanga me te whakamāori32 whakaari raraunga33 e hāngai ana ki ngā raraunga i kohia. • te whakaatu raraunga ki te tūtohi tatau31 • te whakaputa kōrero mō ngā āhuatanga matua o tētahi huinga raraunga. 30data 31tally chart 32interpret 33data display Te Tū po no ta ng a • te reo māmā hei whakaahua i te tūponotanga o tētahi putanga34. . • te ōrite, te rerekē, te rangirua35 rānei o ngā putanga o tētahi pāpono36. 34outcome 35uncertainty 36event W HANAKETANGA 2a: PĀNGARAU WHANAKETANGA 2a: PĀNGARAU WHANAKETANGA 2e: PĀNGARAU W HANAKETANGA 2e: PĀNGARAU Te Tino Wāhanga Pāngarau 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: 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 tau1 me te rautaki paheko kōaro2 mō te tāpiritanga me te tangohanga • ngā rautaki tāpiri tāruarua4 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 tū3 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 whakaahuahanga5, me te tikanga o ngā haurua, ngā hautoru, ngā hauwhā, ngā haurima, ngā hauwaru, me ngā hautekau • te raupapa hautau waetahi6. 1part–whole strategy 2inverse operation strategy 3place value 4repeating addition 5representation 6unit fraction Te Ta ui ra me te Pā ng a • te whiriwhiri me te whakamahi i te ture o tētahi tauira māmā. • te whakamahi tohu hei whakaatu i te ture o tētahi tauira. Te In e m e t e H an ga • te kōwhiri i ngā waeine7 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-210 me ngā āhua ahu-3. • te whakamahi i te rūri, te tāporowhita8, me te koki hāngai9 hei ine, hei tuhi āhua. 7unit of measurement 8compass 9right angle 102-dimensional shape 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 pūmau12, me ngā āhuatanga ka rerekē i tētahi panoni13. • ngā taunga me ngā ahunga o ngā āhuatanga kōhure11 o tōna wāhi noho, pēnei i te maunga, te awa, te marae, te kura, me ētahi noa atu. 11distinctive features 12invariant 13transformation Te Ta ua ng a • te raraunga whakarōpū14 me te raraunga motumotu15 • te whakaputa kōrero mō ngā whakakitenga o tētahi tūhuratanga tauanga18. • te whakaatu raraunga ki te kauwhata pou16 māmā, me te kauwhata ira17 • ngā tikanga matatika19 e hāngai ana (pērā i ngā momo pātai e tika ana kia kore ai te kaiwhakautu e mamae, e whakaitia rānei). 14category data 15discrete data 16bar graph 17dot graph 18statistical investigation 19ethical conventions Te Tū po no ta ng a • te whakaatu tūponotanga ki tētahi āwhata20 • te whakamāori22 whakaari raraunga māmā hei matapae i te putanga o tētahi pāpono tūponotanga23. • te whakaatu putanga21 ki tētahi whakaari raraunga māmā (pērā i te kauwhata ira, te kauwhata whakaahua, me te kauwhata pou). 20scale 21outcome 22interpret 23probability event Te Tino Wāhanga Pāngarau 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: 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 whānui mō te tāpiritanga me te tangohanga • ngā rautaki whakarea2 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 tū1 e hāngai ana • ngā hautau noa me ngā hautanga ā-ira (kia kotahi te mati ā-ira3) • ngā meka whakareatanga ki te 10 x 10 me ngā whakawehenga e whai pānga ana • te raupapa hautau māmā • ngā momo whakaahuahanga4 hautanga ā-ira, me te hononga ki ngā hautau noa. 1place value 2multiplicative strategy 3decimal places 4representations Te Ta ui ra m e t e P ān ga • ngā tauira tāpiripiri5, tauira whakarea māmā, me ngā tauira āhuahanga6, pānga hoki • ngā tauira o roto i te wāwāhitanga whakarea7 o tētahi tau. • te pūmautanga o tētahi ture hei whakaahua i tētahi tauira, tētahi pānga rānei. 5additive pattern 6geometric pattern 7multiplicative partitioning Te In e m e t e H an ga • ngā momo āwhata8 maha me ngā hautanga ā-ira o tētahi waeine9 • ngā raumata11 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-koki10). 8scale 9unit of measurement 10protractor 11net Te W āh i, te A hu ng a, m e t e P an on i • te tukutuku12, te takirua raupapa13, ngā ahunga matua, me ngā mahere māmā hei whakaatu taunga, huarahi, panoni māmā hoki. • ngā ahunga matua e whā o te kāpehu14 me ngā ahunga kei waenganui i ērā (pērā i te rāwhiti-mā-tonga) • ngā tikanga o te whakaatu taunga ki tētahi pūnaha tukutuku. 12grid 13ordered pair 14compass Te Ta ua ng a • te whakatakoto pātai e hāngai ana me te kohikohi raraunga hei tūhura i te pātai • te raraunga motukore15 (pērā i te raraunga houanga16) • 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 ia17, ngā tauira, me ngā āhuatanga kōhure18 o roto i ngā raraunga. 15continuous data 16time-series data 17trends 18distinctive features Te Tū po no ta ng a • te tūhura pūāhua tūponotanga 19 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 matapae20 me ngā putanga whakamātau21 o tētahi pāpono tūponotanga • te wehe kētanga22, te whakawhirinaki23, te aukati24 rānei o ētahi pāpono e rua. 19probability situation 20theoretical outcome 21experimental outcome 22independent 23dependent 24mutually exclusive W HANAKETANGA 3a: PĀNGARAU WHANAKETANGA 3a: PĀNGARAU WHANAKETANGA 3e: PĀNGARAU W HANAKETANGA 3e: PĀNGARAU Te Tino Wāhanga Pāngarau 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: 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 whakarea1 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 tū2 e hāngai ana • ngā hononga whānui o ngā meka matua pērā i te 3 x 0.4 = 1.2 • te whakaawhiwhi3 tauoti hei whakatau tata4 i te otinga o tētahi paheko tau5 • te raupapa hautau. 1multiplicative strategy 2place value 3round 4estimate 5number operation Te Ta ui ra me te Pā ng a • ngā rautaki taurangi6 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 taurangi7 hei whakaatu i tētahi rahinga8 kāore e mōhiotia ana, me te whakamahinga o te pū (reta) hei tohu taurangi. 6algebraic strategy 7variable 8quantity Te In e m e t e H an ga • te whakatau tata me te whiriwhiri horahanga māmā, rōrahi māmā • te tuhi raumata10 o ngā āhua ahu-311 whānui. • ngā waeine9 e tika ana mō te horahanga me te rōrahi, pēnei i te cm2, te cm3, te m2, me te m3 • te whakamahi tukutuku12 hei whiriwhiri horahanga • te whakamahi mataono rite13 hei whiriwhiri rōrahi. 9unit of measurement 10net 113-dimensional shape 12grid 13cube Te W āh i, te A hu ng a, m e t e P an on i • te hanga me te whakamārama tauira ka hua mai i te panoni tāruarua14 • ngā panoni matua e hua mai ai te mātātuhi15 i tōna mātāoroko16. • 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 taurahi17 o tētahi whakarahinga māmā). 14repetitive transformation 15image 16object 17scale factor Te Ta ua ng a • te raraunga whakarōpū matatini18 • te arotake i te whaihua o ngā momo whakaari raraunga21. • te whakaatu raraunga ki te kauwhata rautō19 me te kauwhata porowhita20 • ngā tikanga matatika22 e hāngai ana (pērā i te tikanga kia noho matatapu23 ngā kaiwhakautu pātai o tētahi tūhuratanga tauanga). 18multivariate category data 19stem-and-leaf graph 20pie graph 21data display 22ethical conventions 23anonymous Te Tū po no ta ng a • te reo me ngā whakaahuahanga24 whānui hei whakaatu tūponotanga. • te whakamahi rārangi hautau25 hei whakaatu tūponotanga • te hoahoa rākau26 hei whakaatu i ngā putanga27 o ētahi pāpono raupapa28. 24representation 25fraction line 26tree diagram 27outcome 28combined event Te Tino Wāhanga Pāngarau 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: 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 whakarea1 whānui mō te whiriwhiri ōrau, ōwehenga2 māmā hoki hei whakaatu pānga rahinga4. . • ngā tauoti me ngā tau hautanga, me te mātauranga uara tū3 e hāngai ana • ngā tikanga me te whakamahinga o te tau tōraro5 • te whakaawhiwhi6 tauoti, tau ā-ira hoki • ngā hautau ōrite (hautau, hautanga ā-ira, ōrau) • ngā tauwehe7 me ngā taurea8 o tētahi tau • ngā ōrau nui ake i te 100%. 1multiplicative strategy 2ratio 3place value 4quantitative relationship 5negative number 6round 7factor 8multiple Te Ta ui ra m e t e P ān ga • te whakaatu pānga māmā hei whārite taurangi9, hei kauwhata anō hoki. • te hua o te huri i tētahi taurangi me te pānga ki taurangi kē. 9algebraic equation Te In e m e t e H an ga • te whakawhitiwhiti waeine • ngā inenga tapa me ngā ture hei tātai paenga10, horahanga, rōrahi hoki o ngā āhua māmā • te pāpātanga14 hei ine i tētahi mea (pēnei i te km/h hei ine i te tere) • te whakaatu āhua ahu-315 hei hoahoa ahu-2 (pērā i te tuhinga hoahoa inerite16) • 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 ōwehenga11 me te taurahi12 hei tuhi hoahoa āwhata13. 10perimeter 11ratio 12scale factor 13scale diagram 14rate 153-dimensional shape 16isometric diagram Te W āh i, te A hu ng a, m e t e P an on i • ngā koki o te kāpehu17 hei whakaatu ahunga • te hangarite panoni18 o tētahi āhua. • te hononga o ngā koki ki ngā ahunga matua o te kāpehu • ngā tikanga o te hangarite rārangi19 me te hangarite hurihanga20 o tētahi āhua. 17compass 18transformation symmetry 19line symmetry 20rotational symmetry Te Ta ua ng a • te whakatakoto pātai, tāpaetanga kōrero21 rānei hei tūāpapa mō tētahi tūhuratanga tauanga • te whakatairite i te tuari26 o ētahi huinga raraunga • te whakamahi wēanga28. • te tātai toharite22, tau waenga23, inenga whānui24, tau tānui25 o tētahi huinga raraunga, me te whakaatu ki te whakaari raraunga • te whakaatu raraunga ki te kauwhata pou whakaapaapa27 • te tautohu i ngā taurangi29 o tētahi tūhuratanga tauanga, te kohikohi me te whakaari raraunga mō aua taurangi. 21assertion 22mean 23median 24range 25mode 26distribution 27stacked bar graph 28measure of central tendency 29variable Te Tū po no ta ng a • te tōkeke30, te haukume31 rānei o tētahi pāpono tūponotanga32. • te whakaatu tūponotanga hei ōrau. 30fairness 31bias 32probability event W HANAKETANGA 4a: PĀNGARAU WHANAKETANGA 4a: PĀNGARAU WHANAKETANGA 4e: PĀNGARAU W HANAKETANGA 4e: PĀNGARAU Te Tino Wāhanga Pāngarau 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: Te Ta u (T e M āt au ra ng a T au m e n gā R au ta ki Ta u) • ngā tau tōpū1 me ngā tau hautanga (hautau noa, hautau ā-ira, ōrau) • ngā rautaki tāpiripiri, whakarea hoki e hāngai ana ki ngā horopaki pānga riterite5 (pērā i te ōwehenga7 me te pāpātanga8 māmā). • te taupū2 māmā (pērā i te pūrua3 me te pūtakerua4) • te tōtika me te whaitakenga6 o ngā whakataunga tata me ngā tātaitanga • ngā huarahi e tino whaihua ana hei whakaoti tātaitanga i ngā horopaki maha. 1integer 2exponent 3square (power of two) 4square root 5proportional context 6reasonableness 7ratio 8rate Te Ta ui ra m e t e P ān ga • te whakaatu pānga hei kupu, hei tūtohi, hei kauwhata, hei whārite hoki • te whakaoti whārite taurangi11 māmā, pērā i te 3t + 5 = 47. • te whakamahinga o te āhuatanga kōaro9, te āhuatanga herekore10, me te āhuatanga tohatoha12 hei whakaoti whārite • te tikanga o te tuaka pou, te tuaka pae, me te takirua raupapa hei whakaatu i te pānga o ētahi taurangi13 e rua ki te kauwhata • te tikanga o te rārangi o tētahi kauwhata hei whakaatu i te pānga o ētahi taurangi e rua. 9commutative property 10associative property 11algebraic equation 12distributive property 13variable Te In e m e t e H an ga • 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 whakahāngai14, te koki whakarārangi15, te koki whakahuripū16, te koki tāhapa17, me te koki hāpūpū18. 14complimentary angle 15supplementary angle 16conjugate angle 17acute angle 18obtuse angle Te W āh i, te A hu ng a, m e t e P an on i • te ōwehenga hei tātai taurahi19, hei tātai hoki i te rahi o tētahi mātātuhi20 whakarahi • tētahi raupapatanga panoni21. • te hua o te whakarahi āhua (pērā i te pānga ki te roa o ngā tapa, te horahanga me te rōrahi). 19scale factor 20image 21combined transformation Te Ta ua ng a • te tātari22 i ngā whakakitenga o tētahi tūhuratanga tauanga • te arohaehae24 i te tōtika o te tukanga kohikohi raraunga25, me te whakaari i ngā raraunga o tētahi tīpako27, hei whakaatu i te āhua o tētahi taupori28. • te whakaatu raraunga ki te kauwhata pouhere23 • ngā tikanga matatika26 e hāngai ana (pērā i te whakamōhio atu ki te kaiwhakautu pātai i te whakamahinga o ngā raraunga ka puta i te tūhuratanga tauanga). 22analyse 23histogram 24critique 25data collection process 26ethical conventions 27sample 28population Te Tū po no ta ng a • te whakatairite i te tuari29 o ngā putanga matapae30 me ngā putanga whakamātau31. • ngā take e taurangi32 ai ngā putanga o tētahi whakamātau tūponotanga. 29distribution 30theoretical outcome 31experimental outcome 32variable Te Tino Wāhanga Pāngarau 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: Te Ta u (T e M āt au ra ng a T au m e n gā R au ta ki Ta u) • ngā tau tōpū1 me ngā tau hautanga • te kōwhiri i te rautaki paheko tau3 e tino hāngai ana ki te horopaki. • ngā tikanga me te whakamahinga o te tānga ngahuru2 hei tohu i ngā tau tino nui, tino iti hoki • ngā momo hātepe4 whakaoti paheko hautau. 1integer 2standard form 3number operation 4algorithm Te Ta uir a me te Pā ng a • te whārite me te kauwhata rārangi hei whakaatu pānga. • te tikanga o ngā haukotinga tuaka5 me te rōnaki6 o tētahi kauwhata rārangi, me te puta o ēnei i rō whārite. 5axis intercept 6slope Te In e m e t e H an ga • ngā ture7 hei tātai tapa, paenga, horahanga, koki, horahanga mata, rōrahi hoki o ngā āhua whānui • ngā tikanga koki o te rārangi pūtahi12, te rārangi whakarara, me ngā taparau. • te whakamahi i te ture a Pythagoras • te tikanga o te koki tauroto8, te koki tauaro9, te koki taurite10, me te koki tauwhiti11. 7formulae 8interior angles 9opposite angle 10corresponding angles 11alternate angles 12intersecting lines Te W āh i, te A hu ng a, m e t e P an on i • te hangarite13 o ngā koki o ngā rārangi pūtahi14, ngā rārangi whakarara15, ngā taparau, me ngā matarau • te whakaatu me te whakamārama panoni ki te papa kauwhata. • te whakamahi pere16 hei whakaatu nekehanga • te whakamahi mahere me ōna āhuatanga katoa (pērā i te tukutuku17 me te āwhata18) hei whakaahua huarahi. 13symmetry 14intersecting lines 15parallel lines 16vector 17grid 18scale Te Ta ua ng a • te whakatakoto pātai, tāpaetanga kōrero19 rānei, te whakahaere tūhuratanga tauanga, me te whakaputa pūrongo • te arotake23 i ngā kōrero ka puta i tētahi tūhuratanga tauanga • te whakaputa kōrero mō te pānga o tētahi taurangi26 ki tētahi. • te whakaatu raraunga ki te kauwhata kauamo20 me te kauwhata marara21 • te whaitake me te whaihua o ngā momo whakaari raraunga22 • ngā tikanga matatika24 e hāngai ana (pērā i te tikanga kia kaua e haukumea25 te āhua o ngā pātai). 19assertion 20box-and-whisker graph 21scatter plot 22data display 23evaluate 24ethical conventions 25be biased 26variable Te Tū po no ta ng a • tētahi pūāhua tūponotanga papa-maha27. • te tātai tūponotanga o tētahi pāpono raupapa28. 27multi-level 28combined event W HANAKETANGA 5a: PĀNGARAU WHANAKETANGA 5a: PĀNGARAU