{"data":{"model":{"id":"116745","slug":"sablona-kvadratickych-funkci","name":"\u0160ablona kvadratick\u00fdch funkc\u00ed","authorship":null,"eduProject":{"id":"327","subject":{"id":"11","name":"Math","slug":"math","__typename":"SchoolSubjectType"},"language":{"id":"28","name":"Czech","__typename":"LanguageType"},"free":false,"timeDifficulty":"SHORT_TERM","audienceAge":"ADOLESCENT","complexity":"EASY","equipment":[{"id":"1","name":"3D modeling","__typename":"EquipmentType"},{"id":"4","name":"IT classroom","__typename":"EquipmentType"}],"suitablePrinters":[{"id":"18","name":"Prusa MINI / MINI+","__typename":"PrinterTypeType"},{"id":"1","name":"Prusa MK3/S/S+","__typename":"PrinterTypeType"}],"organisation":"Gymn\u00e1zium \u017d\u010f\u00e1r nad S\u00e1zavou","authors":"Mgr. V\u00e1clav \u010cern\u00edk, Gymn\u00e1zium \u017d\u010f\u00e1r nad S\u00e1zavou","targetGroupFocus":"

\u017d\u00e1ci st\u0159edn\u00ed \u0161koly \u2013 ide\u00e1ln\u011b druh\u00e9ho ro\u010dn\u00edku, ve kter\u00e9m se v matematice u\u010d\u00ed funkce a jejich grafy. Projekt je ide\u00e1ln\u00ed mezip\u0159edm\u011btovou aktivitou \u2013 propojuje informatiku, ve kter\u00e9 se studenti s 3D tiskem setk\u00e1vaj\u00ed nej\u010dast\u011bji, a matematiku.

Projekt je zvl\u00e1dnuteln\u00fd i mlad\u0161\u00edmi studenty, fin\u00e1ln\u00ed produkt (\u0161ablona funkc\u00ed) pro n\u011b ale nebude tak zaj\u00edmav\u00fd (vyu\u017eiteln\u00fd).

","knowledgeAndSkills":"

Matematika: co to jsou kvadratick\u00e9 funkce, jak\u00fd je p\u0159edpis funkc\u00ed, jak\u00e9 maj\u00ed vlastnosti (defini\u010dn\u00ed obor, obor hodnot), jak vypad\u00e1 graf

3D modelov\u00e1n\u00ed: z\u00e1kladn\u00ed modelov\u00e1n\u00ed v TinkerCADu, z\u00e1kladn\u00ed ovl\u00e1d\u00e1n\u00ed PrusaSliceru a 3D tisk\u00e1rny

","objectives":"

V\u00fdukov\u00fd c\u00edl: \u017d\u00e1ci uplatn\u00ed znalosti a dovednosti z matematiky (z\u00e1kladn\u00ed vlastnosti kvadratick\u00fdch funkc\u00ed a jejich graf\u016f, geometrick\u00e9 znalosti a dovednosti). B\u011bhem tvorby \u0161ablony se \u017e\u00e1ci procvi\u010d\u00ed v modelov\u00e1n\u00ed pomoc\u00ed TinkerCADu.

Hmatateln\u00fdm v\u00fdsledkem je vlastn\u00ed \u0161ablona kvadratick\u00fdch funkc\u00ed y=x\u00b2, y=2x\u00b2 a y=0.5x\u00b2, kterou mohou \u017e\u00e1ci n\u00e1sledn\u011b vyu\u017e\u00edt v hodin\u00e1ch matematiky p\u0159i tvorb\u011b graf\u016f kvadratick\u00fdch funkc\u00ed, ur\u010dov\u00e1n\u00ed jejich vlastnost\u00ed nebo p\u0159i tvorba graf\u016f funkc\u00ed inverzn\u00edch. Krom\u011b pocitu dob\u0159e odveden\u00e9 pr\u00e1ce p\u0159i v\u00fdrob\u011b vlastn\u00ed \u0161ablony \u017e\u00e1ci nav\u00edc mohou u\u0161et\u0159it, proto\u017ee si nebudou muset kupovat obdobnou pom\u016fcku v obchod\u011b \ud83d\ude0a

","equipmentDescription":"

p\u0159edem vyti\u0161t\u011bn\u00e9 \u0161ablony pro uk\u00e1zku
b\u011b\u017en\u00e9 vybaven\u00ed IT u\u010debny
3D tisk\u00e1rna
PETG filamenty - pr\u016fhledn\u00fd a tmav\u00fd (nap\u0159. \u0161ed\u00fd/\u010dern\u00fd)
prav\u00edtka s ryskou a tu\u017eky k r\u00fdsov\u00e1n\u00ed, pap\u00edry \u2013 pro testov\u00e1n\u00ed hotov\u00fdch \u0161ablon

","timeSchedule":"

tisk uk\u00e1zkov\u00fdch model\u016f (1 ks cca 20 min p\u0159i v\u00fd\u0161ce vrstvy 0,2 mm)
p\u0159\u00edprava projektu \u2013 modelov\u00e1n\u00ed 30\u201370 min
tisk \u017e\u00e1kovsk\u00fdch model\u016f (tak\u00e9 cca 20 min na 1 ks \u2013 pokud se v\u0161ichni budou dr\u017eet jednotn\u00fdch rozm\u011br\u016f v ose z, tak lze tisknout v\u00edce model\u016f v jednu chv\u00edli, co\u017e m\u016f\u017ee b\u00fdt ve v\u00fdsledku \u010dasov\u011b \u00fasporn\u011bj\u0161\u00ed)

","workflow":"

Na za\u010d\u00e1tku seznamte \u017e\u00e1ky s v\u00fdslednou pom\u016fckou \u2013 k \u010demu se bude v matematice hodit a jak se pou\u017e\u00edv\u00e1. Je dobr\u00e9 m\u00edt n\u011bkolik model\u016f p\u0159edem vyti\u0161t\u011bn\u00fdch, aby si je \u017e\u00e1ci mohli prohl\u00e9dnout a vyzkou\u0161et. Zmi\u0148te se o pou\u017eit\u00ed materi\u00e1lu PETG.

P\u0159ed samotnou v\u00fdrobou si p\u0159ipome\u0148te z\u00e1kladn\u00ed vlastnosti kvadratick\u00fdch funkc\u00ed, doporu\u010duji si vytvo\u0159it tabulku hodnot funkce v bodech -2, -1, 0, 1 a 2 pro funkce y=x\u00b2, y=2x\u00b2 a y=0.5x\u00b2.

Pro uk\u00e1zku graf\u016f doporu\u010duji vyu\u017e\u00edt webovou aplikaci https://www.desmos.com/

Postup k v\u00fdrob\u011b \u0161ablony lze rozd\u011blit do 3 \u010d\u00e1st\u00ed:
A) p\u0159\u00edprava grafu kvadratick\u00e9 funkce,
B) import a \u00fapravy grafu v TinkerCADu,
C) slicov\u00e1n\u00ed a tisk.

A) p\u0159\u00edprava grafu kvadratick\u00e9 funkce

C\u00edlem t\u00e9to \u010d\u00e1sti je p\u0159ipravit soubor, kter\u00fd obsahuje t\u011bleso nebo uzav\u0159en\u00fd 2D \u00fatvar, jeho\u017e okraj je tvo\u0159en \u010d\u00e1st\u00ed grafu kvadratick\u00e9 funkce.

Tento soubor mus\u00ed b\u00fdt importovateln\u00fd do TinkerCADu \u2013 v samotn\u00e9m TinkerCADu nen\u00ed mo\u017en\u00e9 generovat grafy funkc\u00ed, proto je nutn\u00e9 jej p\u0159ipravit jinde. Vzhledem k \u010dasov\u00fdm mo\u017enostem je mo\u017en\u00e9 zvolit:

rychlou a snadnou variantu \u2013 pou\u017e\u00edt p\u0159ilo\u017een\u00fd soubor graf.svg (a rovnou pokra\u010dovat na \u010d\u00e1st B)
m\u00edrn\u011b n\u00e1ro\u010dn\u011bj\u0161\u00ed variantu \u2013 pot\u0159ebn\u00fd soubor vytvo\u0159it \u2013 podrobn\u011bj\u0161\u00ed n\u00e1vod v souboru navod-priprava-grafu.pdf

B) modelov\u00e1n\u00ed \u0161ablony kvadratick\u00fdch funkc\u00ed v TinkerCADu

C\u00edlem t\u00e9to \u010d\u00e1sti je v TinkerCADu (na z\u00e1klad\u011b importovan\u00e9ho grafu kvadratick\u00e9 funkce z p\u0159edchoz\u00ed \u010d\u00e1sti) vytvo\u0159it model kompletn\u00ed \u0161ablony kvadratick\u00fdch funkc\u00ed. \u017d\u00e1k\u016fm poskytn\u011bte p\u0159ilo\u017een\u00fd n\u00e1vod (navod-modelovani-sablony.pdf) anebo je nechte pracovat samostatn\u011b (nechte je si na postup p\u0159ij\u00edt).

\u017d\u00e1ci si mohou vymodelovat na z\u00e1kladn\u00ed plo\u0161e \u0161ablony sv\u00e9 jm\u00e9no nebo zna\u010dku, d\u00edky kter\u00e9 si sv\u016fj model poznaj\u00ed. Jen je t\u0159eba d\u00e1t pozor na p\u0159\u00edli\u0161 drobn\u00e1 p\u00edsmena, kter\u00e1 by se nevytiskla s b\u011b\u017enou 0,4mm tryskou.

C) slicov\u00e1n\u00ed a tisk

Hotov\u00e9 modely naslicujte \u2013 doporu\u010duji n\u00e1sleduj\u00edc\u00ed nastaven\u00ed:

v\u00fd\u0161ka vrstvy 0,2 mm
materi\u00e1l PETG
zm\u011bna barvy ve v\u00fd\u0161ce 0,8 mm (tak, aby byl popis s vod\u00edc\u00edmi \u010d\u00e1rkami zv\u00fdrazn\u011bn\u00fd)

Tiskn\u011bte nejd\u0159\u00edve pr\u016fhledn\u00fdm filamentem PETG, n\u00e1sledn\u011b jej zm\u011b\u0148te na tmav\u00fd (nap\u0159. \u010dern\u00fd/\u0161ed\u00fd) PETG.

Pokud v\u0161echny modely dodr\u017e\u00ed doporu\u010den\u00ed (budou m\u00edt jednotnou v\u00fd\u0161ku z\u00e1kladn\u00ed plochy \u0161ablony 0,6 mm a dal\u0161\u00ed 0,4 mm budou popisky s vod\u00edc\u00edmi linkami), je mo\u017en\u00e9 ve sliceru na podlo\u017eku narovnat v\u00edce model\u016f.

Z\u00e1v\u011br

Po vyti\u0161t\u011bn\u00ed si s \u017e\u00e1ky vyzkou\u0161ejte pou\u017eit\u00ed jejich vlastn\u00edch \u0161ablon p\u0159i tvorb\u011b graf\u016f funkc\u00ed.

Je mo\u017en\u00e9, \u017ee n\u011bkdo zjist\u00ed, \u017ee jeho \u0161ablona v n\u011b\u010dem nevyhovuje a bude ji cht\u00edt upravit a znovu vytisknout. Doporu\u010duji s t\u00edmto p\u0159edem po\u010d\u00edtat a umo\u017enit z\u00e1jemc\u016fm \u00fapravu prototypu a op\u011btovn\u00e9 vyti\u0161t\u011bn\u00ed.

Porovnejte si vz\u00e1jemn\u011b vytvo\u0159en\u00e9 \u0161ablony \u2013 li\u0161\u00ed se v n\u011b\u010dem? Diskutujte s \u017e\u00e1ky, jestli je n\u011bkter\u00fd model vhodn\u011bj\u0161\u00ed ne\u017e jin\u00fd. Jsou modely skute\u010dn\u011b pou\u017eiteln\u00e9? P\u0159i\u0161el n\u011bkdo s inovac\u00ed, kter\u00e1 (navzdory n\u00e1vodu) zlep\u0161ila v\u00fdslednou \u0161ablonu?

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Šablona kvadratických funkcí

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