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  • Fakamatala Tonu Matematē

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Kātaki, ‘oku ‘ikai ma‘u ha vitiō.

  • Fakamatala Tonu Matematē
  • Maʻu ʻAonga mei he Ako Fakafaifekau Fakateokalatí
  • Fakamatala Meimei Tatau
  • Tonu Matematē mo Fakatupu Tuipau
    Ke Ke Kīvoi ʻi he Lautohí mo e Faiakó
  • Founga ʻo Hono Fai ʻa e Fekumí
    Maʻu ʻAonga mei he Ako Fakafaifekau Fakateokalatí
  • Maʻu ʻa e ʻAonga Kakato mei Hono Lau ʻa e Tohi Tapú
    Ko e Taua Leʻo ʻOku Fanongonongo Ai ʻa e Puleʻanga ʻo Sihová—2013
  • Malanga ke Ngaohi Ākonga
    Ko e Taua Leʻo ʻOku Fanongonongo Ai ʻa e Puleʻanga ʻo Sihová—2003
Sio ki he Me‘a Lahi Ange
Maʻu ʻAonga mei he Ako Fakafaifekau Fakateokalatí
be ako 40 p. 223-p. 225 pal. 3

AKO 40

Fakamatala Tonu Matematē

Ko e hā ʻoku fiemaʻu ke ke faí?

ʻOatu ha fakamatala ʻa ia ʻoku feongoongoi kakato mo e ngaahi moʻoniʻi meʻá.

Ko e hā ʻoku mahuʻinga aí?

Ko e tonu matematē ʻi he meʻa ʻokú ke leaʻakí ʻoku tapua lelei atu ai koe, ko e kautaha ʻa ia ʻokú ke tauhi ki aí, pea mo e ʻOtua ʻokú ke lotu ki aí.

KO E HĀ nai ʻe fai ai ʻe ha Kalisitiane ha fakamatala ʻa ia ʻoku ʻikai ke moʻoni? Te ne toe leaʻaki pē nai ha meʻa kuó ne fanongo ai, ʻo ʻikai vaheʻi ha taimi ke vakaiʻi ai ʻa e ngaahi foʻi moʻoní. Pe te ne fakamatala fakalahiʻi nai ha meʻa koeʻuhi ʻi he taʻeʻilo ki aí, ʻokú ne lauhalaʻi ha maʻuʻanga fakamatala. ʻI heʻetau fai ha tokanga lelei ki he tonu matematē naʻa mo e ʻi he fanga kiʻi meʻa īkí, ʻe ʻilo ai heʻetau kau fanongó ʻe lava ke nau maʻu ʻa e falala ki he moʻoni ʻo e ngaahi tafaʻaki mahuʻinga lahi ange ʻo ʻetau pōpoakí.

ʻI he Malaʻe Fakafaifekaú. ʻI hono ʻiloʻi ʻoku kei lahi ʻa e meʻa ke nau akó, ʻoku ongoʻi ilifia ai ʻa e tokolahi fekauʻaki mo e kamata ʻi he ngāue fakafaifekaú. Neongo ia, ʻoku ʻiloʻi vave ʻe he faʻahingá ni ʻoku nau malava ke fai ha fakamoʻoni ola lelei, naʻa mo hono fai ʻaki ha foʻi ʻilo tefito pē ʻo e moʻoní. Anga-fēfē? Ko e kií ko e teuteú.

Ki muʻa ke ʻalu ʻi he malaʻe ngāué, hoko ʻo maheni mo e tuʻunga-lea ʻokú ke loto ke lāulea ki aí. Feinga ke tomuʻa fakakaukau ki he ngaahi fehuʻi ʻe langaʻi hake nai ʻe hoʻo kau fanongó. Kumi ki ha ngaahi tali fakafiemālie makatuʻunga ʻi he Tohitapú. ʻE teuteuʻi koe ʻe he meʻá ni ke fai ha ngaahi tali tonu matematē ʻi ha tuʻunga fiemālie ʻo e ʻatamaí. Te ke fai ha ako Tohitapu? Fakamanatu lelei ʻa e fakamatala ki he akó. Fakapapauʻi ʻokú ke mahinoʻi ʻa e makatuʻunga Fakatohitapu ki he ngaahi tali ʻi he ngaahi fehuʻi kuo pulusí.

Fēfē kapau ʻe ʻeke ʻe ha tokotaha-ʻapi pe ko ha kaungāngāue ha foʻi fehuʻi ʻoku ʻikai te ke mateuteu ke tali? Kapau ʻoku ʻikai te ke fakapapauʻi ʻa e ngaahi moʻoniʻi meʻá, talitekeʻi ʻa e fakatauele ke mateʻí. “Oku fakakaukau e he loto oe maonioni ae lea te ne tali aki.” (Pal. 15:​28, PM) Te ke maʻu nai ʻa e tokoni ʻokú ke fiemaʻú ʻi he tohi Reasoning From the Scriptures pe ʻi he “Ngaahi Tuʻunga Lea Faka-Tohitapu ke Fetalanoaʻaki Ai” kapau ʻoku ala maʻu ia ʻi hoʻo leá. Kapau ʻoku ʻikai ʻiate koe ha taha ʻo e ongo meʻá ni, fakahā ange te ke fai ha fekumi pea toe foki ange. Kapau ʻoku loto-moʻoni ʻa e tokotaha ʻokú ne fokotuʻu atu ʻa e fehuʻí, ʻe ʻikai te ne tokanga ki he tatali ke maʻu ʻa e tali totonú. Ko hono moʻoní, ʻe maongo nai ʻi ha tuʻunga lelei kiate ia ʻa hoʻo anga-fakatōkilaló.

Ko e ngāue ʻi he malaʻe fakafaifekaú fakataha mo e kau malanga taukeí ʻe lava ke ne tokoniʻi koe ke fakatupu ai ha pōtoʻi ʻi hono tofa totonu ʻo e Folofola ʻa e ʻOtuá. Siofi ʻa e ngaahi konga Tohitapu ʻoku nau ngāueʻakí mo e founga ʻo ʻenau fakaʻuhingaʻi iá. Tali anga-fakatōkilalo ha ngaahi fokotuʻu pe fakatonutonu pē ʻoku nau ʻomai. Ko e ākonga faivelenga ko ʻApolosí naʻá ne maʻu ʻaonga mei he tokoni naʻe maʻu mei he niʻihi kehé. Naʻe fakamatalaʻi ʻe Luke ʻa ʻApolosi ko e “[pōtoʻi] lea,” “boto lahi,” mo “loto faivelega,” ko ha tangata “naa ne lea mo ako lahi aki ae gaahi mea ae Eiki.” Neongo ia, naʻe ʻi ai ha palopalema ʻi heʻene mahinó. ʻI he taimi naʻe fakatokangaʻi ai eni ʻe ʻAkuila mo Pīsilá, naʻá na “maʻu ia, o na fakamatala [totonu] kiate ia o lahi ae hala oe Otua.”—Ng. 18:​24-28, PM.

“Buke ke Mau ae Lea Moʻoni.” Ko ʻetau ngaahi malanga ʻi he ngaahi fakatahá ʻoku totonu ke tapua mei ai ʻa e tokanga lahi ki he ngafa ʻo e fakatahaʻangá ʻi he tuʻunga “ko e pou mo e tuʻunga ʻo e Moʻoni.” (1 Tim. 3:15) Koeʻuhi ke poupouʻi ʻa e moʻoní, ʻoku mahuʻinga ke tau maʻu ʻa e ʻuhinga ʻo e ngaahi konga Tohitapu ʻoku tau palani ke ngāueʻaki ʻi he ngaahi malangá. Fakakaukau ki honau potutohí mo e taumuʻá.

Ko e meʻa ʻokú ke leaʻaki ʻi ha fakataha ʻa e fakatahaʻangá ʻe toe leaʻaki nai. Ko e moʻoni, “ʻoku lahi ʻa e meʻa ʻoku tau humu ai kotoa pe.” (Sem. 3:2) Ka te ke maʻu ʻaonga ʻi hono fakatupu ʻa e ngaahi tōʻonga ʻoku tānaki atu ki he lea tonu matemateé. Ko e fanga tokoua tokolahi ʻoku nau kau ʻi he Ako Fakafaifekau Fakateokalatí ʻe faifai pē ʻo nau hoko ko e kau mātuʻa. ʻOku ʻamanekina ʻa e meʻa “hulu atu” mei he faʻahinga kuo tuku ki ai ʻa e fatongia peheé. (Luke 12:48) Kapau ʻe fai taʻetokanga ʻe ha mātuʻa ha fakahinohino hala ʻo iku ai ki ha ngaahi palopalema mafatukituki ki he kau mēmipa ʻo e fakatahaʻangá, ʻe lava ke ʻomai ʻe he tokotaha mātuʻá ʻa e taʻehōifua ʻa e ʻOtuá. (Mt. 12:​36, 37) Ko ia ai, ko ha tokoua ʻoku taau ʻi he tuʻunga ko ha mātuʻá kuo pau ke ʻiloa ia ʻi he “buke ke mau ae lea mooni, o hage ko hono akonekina.”—Tai. 1:9, PM.

Tokanga ke feongoongoi ʻa hoʻo ngaahi fakamulitukú mo e ‘anga ʻo e ngaahi lea moʻui’ ʻoku fakahaaʻi ʻi he sino kotoa ʻo e moʻoni Fakatohitapú. (2 Tim. 1:13) ʻOku ʻikai totonu ke fakailifiaʻi koe ʻe he meʻá ni. Mahalo pē ʻoku kei toe ke ke fakakakato ʻa hono lau ʻa e Tohitapú fakakātoa. Hokohoko atu ʻa e ngāue ki aí. Ka ʻi he taimi ní, fakatokangaʻi ʻa e founga ʻe lava ai ʻe he ngaahi fokotuʻu hokó ʻo tokoniʻi koe ke ʻanalaiso ai ʻa e fakamatala ʻokú ke fakakaukau fekauʻaki mo hano ngāueʻaki ʻi hoʻo faiakó.

ʻUluakí, ʻeke hifo kiate koe: ‘ʻOku fehoanakimālie ʻa e fakamatalá ni mo e meʻa kuó u ʻosi ako mei he Tohitapú? Te ne tohoakiʻi ʻa ʻeku kau fanongó kia Sihova, pe ʻokú ne fakamāʻolungaʻi ʻa e poto ʻo e māmaní, ʻo fakalotolahiʻi ʻa e kakaí ke tataki kinautolu ʻe he meʻa ko iá?’ Naʻe pehē ʻe Sīsū: “Ko e folofola aʻau ko e moʻoni ia.” (Sione 17:17; Teu. 13:​1-5; 1 Kol. 1:​19-21) Hokó, ngāueleleiʻaki ʻa e ngaahi meʻangāue fakaeako kuo tokonaki mai ʻe he kalasi tamaioʻeiki anga-tonu mo potó. ʻE tokoniʻi koe ʻe he ngaahi meʻá ni ke ʻikai ngata pē ʻi hono mahinoʻi totonu ʻa e ngaahi konga Tohitapú kae pehē foki ke ngāueʻaki kinautolu ʻaki ʻa e tuʻunga mafamafatatau mo ʻuhinga lelei. Kapau ʻokú ke fakatefito hoʻo ngaahi malangá ʻi he ‘anga ʻo e ngaahi lea moʻuí’ pea falala ki he fetuʻutakiʻanga ʻa Sihová ʻi hono fakamatalaʻi mo ngāueʻaki ʻa e ngaahi konga Tohitapú, ʻe hoko ai hoʻo ngaahi fakamatalá ʻo tonu matematē.

Vakaiʻi ʻa e Tonu Matematē ʻo e Fakamatalá. Ko e ngaahi meʻa ʻoku lolotonga hokó, ngaahi meʻa ʻoku fai ʻa e lave ki aí, mo e ngaahi meʻa ʻoku hokosiá ʻe lava ke ʻaonga ia ʻi hoʻo fakatātaaʻi mo ngāueʻaki ha ngaahi poini pau. ʻE lava fēfē ke ke fakapapauʻi ʻoku nau tonu matematē? Ko e founga ʻe taha ko hono maʻu ha ngaahi kupu pehē mei he ngaahi maʻuʻanga fakamatala falalaʻangá. Manatuʻi ke vakaiʻi pe ʻoku fakaeonopooni ʻa e fakamatalá. Ko e ngaahi fiká ʻoku hoko ia ʻo ʻikai kei ngāueʻaki; ko e ngaahi ʻilo fakasaienisí ʻoku vave ʻa ʻene fakalaká; pea ʻi he tupulaki ʻa e tangatá ʻi hono mahinoʻi ʻo e hisitōliá mo e ngaahi lea motuʻá, ko e ngaahi fakamulituku makatuʻunga ʻi he ʻilo ki muʻá ʻoku fiemaʻu ia ke toe fakaleleiʻi. Fai ha tokanga lahi kapau ʻokú ke fakakaukau ki hono ngāueʻaki ʻa e fakamatala mei he ngaahi nusipepá, televīsoné, letioó, meili fakaʻilekitulōniká, pe ko e ʻInitanetí. ʻOku akonaki ʻa e Palovepi 14:15: “Ko e hehemangofua ʻoku ne tui ki he lea kotoa; ka ko e fakapotopoto ʻoku ne fakakaukau ʻene laka.” ʻEke hifo kiate koe: ‘ʻOku maʻu ʻe he maʻuʻanga fakamatalá ha ongoongo ʻi he tonu matemateé? ʻE lava ʻa e fakamatalá ʻo fakapapauʻi ʻi ha toe ngaahi founga kehe?’ Kapau ʻokú ke veiveiua ʻi he moʻoni ʻo ha kupu, liʻaki ia.

Tānaki atu ki hono vakaiʻi ʻa e tuʻunga falalaʻanga ʻo e ngaahi maʻuʻanga fakamatalá, fakakaukau lelei ki he founga ʻo hoʻo palani ke ngāueʻaki ʻa e fakamatalá. Fakapapauʻi ko hoʻo ngāueʻaki ʻa e ngaahi fakamatalá mo e ngaahi fiká ʻoku fehoanakimālie ia mo e potutohi ʻoku toʻo kinautolu mei aí. ʻI ha feinga ke fakamamafaʻi hoʻo poiní, tokanga ke ʻoua ʻe hoko ʻa e meʻa fekauʻaki mo ha “kakai ʻe niʻihi” ko ha meʻa ia ki he “kakai tokolahi,” pea ko e “kakai tokolahí” ke ʻoua ʻe hoko ia ko e “tokotaha kotoa,” pea ʻi he “ngaahi tuʻunga ʻe niʻihi” ke ʻoua ʻe hoko ia “ko e tuʻunga kotoa pē.” Ko hono fakamamafaʻi tōtuʻa ʻa e ngaahi meʻá pe fakalahiʻi ʻa e ngaahi līpooti fekauʻaki mo e fiká, lahí, pe tuʻunga mafatukitukí ʻoku langaʻi hake ai ʻa e ngaahi fehuʻi fekauʻaki mo e alafalalaʻangá.

ʻI hoʻo tonu matematē hokohoko ʻi he meʻa ʻokú ke leaʻakí, te ke hoko ai ʻo ʻiloa ko ha tokotaha ʻoku ʻapasia ki he moʻoní. ʻOku tapua lelei atu ʻa e meʻá ni ʻi he Kau Fakamoʻoni ʻa Sihová ʻi he tuʻunga ko ha kulupú. Ko e meʻa ʻoku toe mahuʻinga angé, ʻoku fakalāngilangiʻi ai ʻa “Sihova, ʻa e ʻOtua moʻonia.”—Sāme 31:5.

FOUNGA KE FAI AI IÁ

  • Talitekeʻi ʻa e tenge ke fai ha tali ʻi he taimi ʻokú ke veiveiua aí.

  • Fakatuʻunga hoʻo ngaahi fakamatalá ʻi he “anga ʻo e ngaahi lea moʻui” ʻi he Tohitapú.

  • Fai ha fekumi ʻi hoʻo tuʻunga-leá.

  • Vakaiʻi ʻa e tonu matematē ʻo e ngaahi fiká, ngaahi hiki fakamatalá, mo e ngaahi meʻa ʻoku hokosiá, pea ngāueʻaki kinautolu ʻo ʻikai fakalahiʻi. Fakaʻehiʻehi mei he mateʻi ʻa e ngaahi fakaikiiki ʻoku ʻikai te ke manatuʻi leleí.

MEʻA KE FAI: Kole ki ha tokotaha Fakamoʻoni matuʻotuʻa ke fanongo mo vakaiʻi ʻa e tonu matematē ʻo e meʻa ʻokú ke leaʻakí ʻi hoʻo fakamatalaʻi ʻa e ngaahi meʻa hono hokó ʻi he ngaahi lea pē ʻaʻaú: (1) Ko e faʻahinga tokotaha fēfē ʻa Sihova, pea ʻoku anga-fēfē hoʻo ʻiloʻí? (2) Ko e hā naʻe foaki ai ʻe Sīsū ʻa ʻene moʻuí ʻi he feilaulaú, pea ʻe lava fēfē ke tau maʻu ʻaonga mei he meʻá ni? (3) Talu mei hono fakanofo ko e Tuʻí, ko e hā kuo fai ʻe Sīsū Kalaisí?

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