Whārite Rārangi: Te Whakaoti

This is lesson 1 of 1 in the unit "Whārite Rārangi: Te Whakaoti". Lesson Title: Solve and Model Linear Equations Lesson Description: In this 90-minute, collaborative maths lesson, ākonga develop and apply the language of linear equations in a Māori-medium context. Begin by writing variable equations, testing whether a value satisfies an equation, and using the properties of equality to identify equivalent equations. Use algebra tiles and diagrams to model one-step and two-step equations, then progress to advanced equations, including variables on both sides. Ākonga complete partially solved equations, determine whether equations have one, no, or infinitely many solutions, and create examples of each. Apply strategies to consecutive-integer and other word problems before completing a mixed review. Learning is supported through mathematical kōrero, multiple representations, peer explanation, and culturally responsive contexts, reflecting Te Marautanga o Aotearoa emphasis on communication, reasoning, problem solving, and collaborative learning.

Overview

Ka hanga, ka whakamātau, ka whakaoti hoki ngā ākonga i ngā whārite rārangi, mai i ngā whārite kotahi-taahiraa ki ngā whārite uaua ake, tae atu ki ngā taurangi kei ngā taha e rua. Mā ngā tāpa algebra, ngā hoahoa, te kōrero pāngarau me ngā horopaki o te hapori ka whakawhanake rātou i te whakaaro whaitake, te whakaoti rapanga me te whakamārama rautaki.

Learning intentions

WALT te tuhi me te whakamātau i ngā whārite rārangi.
WALT te whakamahi i te āhuatanga o te taurite hei whakaoti whārite.
WALT te whakaatu whārite mā ngā tāpa algebra, ngā hoahoa me ngā tohu.
WALT te whakamārama me te aromatawai i ngā otinga o tētahi whārite.

Success criteria

Ka taea e au te whakaatu mēnā ka tutuki tētahi uara i tētahi whārite.
Ka taea e au te whakaoti whārite kotahi-taahiraa, rua-taahiraa hoki, me te tirotiro i taku whakautu.
Ka taea e au te whakaoti whārite me ngā taurangi kei ngā taha e rua.
Ka taea e au te whakamārama mēnā he kotahi, he kore, he mutunga-kore rānei ngā otinga.

Curriculum links

Pāngarau: Tau me te Taurangi — te whakamahi i ngā tohu, ngā whārite me ngā hononga taurite hei whakaoti rapanga.
Pāngarau: whakaaro whaitake, whakatauira, whakaoti rapanga me te whakamārama rautaki.
Te Reo Rangatira: whakarongo, kōrero, pānui me te tuhituhi i te reo pāngarau.
Marau ā-Kura: te whakamahi i ngā horopaki o te kura, te marae, te hapori me ngā wawata o te iwi hei whai tikanga ki te ako.

Lesson structure (90 minutes)

0–8 min · Kupu whakaoho me te horopaki. Ka whakaatu te kaiako i te pātai “E hia ngā mea kei ia rōpū?” me tētahi horopaki pērā i te whakarite tūru mō tētahi hui kura, mā ngā kiriata whakaoho me te pātai matua. Ka kōrero takirua ngā ākonga, ka tuhi i tētahi whārite hei whakaatu i te mōhiohio.
8–20 min · Te reo me te whakamātau. Ka whakamārama te kaiako i ngā kupu taurangi, tau tōmau, whārite, taha mauī, taha matau, otinga me te taurite; ka tauira i te whakamātau i te uara ki roto i te whārite. Ka mahi ngā ākonga i ngā tauira pērā i te (3x+2=14), ka whakaatu āe, kāo rānei me te take.
20–35 min · Te taurite me ngā tāpa. Ka whakamahi te kaiako i ngā tāpa algebra me te whakaahua i te whārite hei tauine: me mahi te mahi ōrite ki ngā taha e rua. Ka mahi ngā ākonga ki ngā whārite kotahi- me te rua-taahiraa, ā, ka whakamārama ki tō rātou hoa he aha i noho taurite ai te whārite. Ka tuhi rātou i ngā hīkoi ki te pepa mahi whakatauira me te whakaoti whārite.
35–52 min · Te whakaoti me te kōrero a te hoa. Ka whakarōpū te kaiako i ngā ākonga tokotoru, ka whakaatu i ngā whārite pērā i (2x+5=17), (4x-3=21), me (3x+2=x+14), mā ngā kiriata tauira me ngā tohutohu mahi rōpū. Ka whakaoti ngā rōpū, ka whakamahi i te tāpa, te hoahoa, te tohu rānei, ā, ka whakamārama tētahi mema i ia taahiraa.
52–67 min · Kotahi, kore, mutunga-kore. Ka arahi te kaiako i te whakataurite i (2x+4=10), (2x+4=2x+7), me (3(x+2)=3x+6). Ka tautohu ngā ākonga mēnā he kotahi, he kore, he mutunga-kore ngā otinga, kātahi ka hanga i tētahi tauira ake mō ia momo. Ka tuhia he whakamārama poto, kaua ko te whakautu anake.
67–80 min · Ngā rapanga kupu. Ka tuku te kaiako i ngā horopaki e rua: ngā tauoti whai muri, me te utu hui kura e whai ana i tētahi utu tīmatanga me tētahi utu mō ia tangata. Ka tuhi ngā ākonga i te taurangi, te whārite me te rerenga kōrero whakautu, ka tirotiro mēnā e tika ana te otinga i roto i te horopaki. Ka whakamahia ngā kiriata rapanga kupu me ngā pātai kōrero hei whakahāngai i te rautaki.
80–90 min · Arotake me te putanga. Ka whakahaere te kaiako i te arotake tere o ngā hapa noa, pērā i te whakarerekē i te taha kotahi anake, te kore tohatoha i te whakarea, me te kore tirotiro. Ka whakaoti takitahi ngā ākonga i te wāhanga arotake o te pepa mahi whakatauira me te whakaoti whārite, ā, ka tuku i te pātai putanga: “Whakaotia (5x-7=2x+8), tirohia te whakautu, ka whakamārama i tō rautaki.”

Resources

te rahoraho kotahi mō te akoranga katoa
te pepa mahi whakatauira me te whakaoti whārite
Tāpa algebra, tae atu ki ngā tāpa (x) me ngā tau tōmau
Pepa A3, pene tohu me ngā papa mā
Pene, rārangi tau me ngā pepa tuhi
Papa whakaatu mō ngā kupu pāngarau me ngā rerenga tīmatanga

Vocabulary / Kupu Pangarau

whārite — equation
rārangi — linear / line
taurangi — variable
tau tōpū — integer
whakarea — coefficient
tūtohu — constant
whakaoti — solve
ōrite — equal
tāpiri — add
tango — subtract
whakarea / whakareatia — multiply / multiplication
whakawehe — divide
kaupae — step

Sentence frames:

“Tuatahi, ka ___ i ngā taha e rua o te whārite.”
“Ko te kaupae e whai ake nei ko ___, nō reira ___.”
“Ka tirohia te otinga mā te whakakapi i ___ ki roto i te whārite.”

Assessment

Ka tirotiro te kaiako i ngā whārite tuatahi me te whakamahi a ngā ākonga i te reo tika.
I te mahi rōpū, ka ui: “He aha te take me mahi ōrite ki ngā taha e rua?” me “Me pēhea koe e tirotiro ai?”
Ka kohia te pepa mahi me te pātai putanga hei aromatawai i te whakaoti, te tirotiro me te whakamārama.

Differentiation

Mō te tautoko, whakaratoia he tauira hīkoi, he tāpa algebra, he rārangi tau me ngā rerenga tīmatanga: “Tuatahi…”, “Ka mahi au i te mahi ōrite ki…”, “Hei tirotiro…”.
Whakaurua ngā ākonga ki ngā rōpū whānui, ā, whakamahia te whakamārama ā-waha, te tuhi, te hoahoa rānei hei whakaatu māramatanga.
Mō ngā ākonga e hiahia ana ki te wero, whakamahia ngā hautau, ngā taiapa me ngā taurangi kei ngā taha e rua; tonoa rātou kia hanga whārite kotahi, kore, me te mutunga-kore ngā otinga, ā, kia whakamātauhia e tētahi hoa.
Mō ngā ākonga whai mate ako, whakaitihia te maha o ngā pātai engari kaua te taumata whakaaro, whakamahia ngā tohu tae mō ia taahiraa, ā, tuku wā hei kōrero i mua i te tuhi.

Teaching Instructions