{"data":{"model":{"id":"178590","slug":"cavalieriho-princip-vyroba-modelu-pro-vyuku-hejneh","name":"Cavalieriho princip \u2013 v\u00fdroba modelu pro v\u00fduku Hejn\u00e9ho matematiky","authorship":null,"eduProject":{"id":"682","subject":{"id":"11","name":"Math","slug":"math","__typename":"SchoolSubjectType"},"language":{"id":"28","name":"Czech","__typename":"LanguageType"},"free":false,"timeDifficulty":"SHORT_TERM","audienceAge":"SCHOOL","complexity":"EASY","equipment":[],"suitablePrinters":[{"id":"18","name":"Prusa MINI / MINI+","__typename":"PrinterTypeType"}],"organisation":"Z\u0160 logopedick\u00e1 s. r. o.","authors":"Mgr. Lucie Barto\u0161ov\u00e1, Mgr. Petr Papavasilevk\u00fd, inspirac\u00ed k tomuto projektu byla u\u010debnice matematiky pro 2. stupe\u0148 a v\u00edcelet\u00e1 gymn\u00e1zia, pana prof. Hejn\u00e9ho a kolektivu autor\u016f - Matematika C, kapitola \u201eCavalieriho princip\u201c, kter\u00e1 rozv\u00edj\u00ed u d\u011bt\u00ed logick\u00e9 my\u0161len\u00ed a u\u010d\u00ed je nahl\u00ed\u017eet na probl\u00e9my v souvislostech.","targetGroupFocus":"

\u017d\u00e1ci druh\u00e9ho stupn\u011b se znalost\u00ed v\u00fdpo\u010dtu objemu krychle a kv\u00e1dru. Lze roz\u0161\u00ed\u0159it o hranoly s podstavou pravo\u00fahl\u00e9ho troj\u00faheln\u00edku, koso\u010dtverce, kosod\u00e9ln\u00edku, lichob\u011b\u017en\u00edku, nebo tak\u00e9 v\u00e1lce. Hotovou pom\u016fcku pak budou vyu\u017e\u00edvat \u017e\u00e1ci 7. a 8. ro\u010dn\u00edk\u016f v hodin\u00e1ch matematiky na demonstraci Cavalieriho principu.

","knowledgeAndSkills":"

Pro realizaci projektu nejsou nutn\u00e9 \u017e\u00e1dn\u00e9 speci\u00e1ln\u00ed znalosti ani dovednosti. Projekt je vhodn\u00fd pro \u00fapln\u00e9 za\u010d\u00e1te\u010dn\u00edky na sezn\u00e1men\u00ed s prost\u0159ed\u00edm programu Tinkercad, p\u0159\u00edp. i programu PrusaSlicer.

Vyu\u010duj\u00edc\u00ed by m\u011bl b\u00fdt obezn\u00e1men s principem tvorby n\u00e1vrh\u016f v programu Tinkercad a prac\u00ed s modely v programu PrusaSlicer.

","objectives":"

C\u00edlem projektu je vytvo\u0159it n\u00e1zornou matematickou pom\u016fcku na uk\u00e1zku a vysv\u011btlen\u00ed Cavalieriho principu. P\u0159i jej\u00ed v\u00fdrob\u011b se \u017e\u00e1ci sezn\u00e1m\u00ed s prost\u0159ed\u00edm program\u016f Tinkercad a PrusaSlicer, procvi\u010d\u00ed si znalosti o objemu kv\u00e1dru a krychle a z\u00edskaj\u00ed praktick\u00e9 zku\u0161enosti s \u0159e\u0161en\u00edm situac\u00ed p\u0159i n\u00e1vrhu a v\u00fdrob\u011b funk\u010dn\u00edch model\u016f.

","equipmentDescription":"

Notebook nebo tablet, programy Tinkercad a PrusaSlicer, 3D tisk\u00e1rna.

Nepovinn\u00e9 - krabi\u010dka \u010dtvercov\u00fdch rozm\u011br\u016f, tvrd\u00fd pap\u00edr, prav\u00edtko, tu\u017eka a n\u016f\u017eky (viz postup).

","timeSchedule":"

Na realizaci samotn\u00e9 hodiny s modely krychle a kv\u00e1dru posta\u010d\u00ed jedna standardn\u00ed vyu\u010dovac\u00ed hodina.

Tisk jednoho modelu, tedy 20 desti\u010dek a 1 krabi\u010dky, p\u0159i 100% rozm\u011brech, infillu 15% a v\u00fd\u0161ce vrstvy 0,2mm zabere 18 hodin 20 min. Rozm\u011bry je mo\u017en\u00e9 dle pot\u0159eby upravit, celkov\u00fd \u010das tisku se pak bude odv\u00edjet od v\u00fdsledn\u00e9ho zpracov\u00e1n\u00ed.

","workflow":"

1. Organizace hodiny:

\u017d\u00e1ky je vhodn\u00e9 p\u0159ed za\u010d\u00e1tkem samotn\u00e9 hodiny rozd\u011blit do skupin, kter\u00e9 budou spolupracovat a konzultovat sv\u00e9 n\u00e1pady a n\u00e1vrhy. V p\u0159\u00edpad\u011b mal\u00e9ho po\u010dtu \u017e\u00e1k\u016f m\u016f\u017ee ka\u017ed\u00fd \u017e\u00e1k pracovat s\u00e1m.

Ka\u017ed\u00e1 skupina \u010di \u017e\u00e1k m\u016f\u017ee tak\u00e9 pracovat na hranolu s jin\u00fdm tvarem podstavy (\u010dtverec, pravo\u00fahl\u00fd troj\u00faheln\u00edk, koso\u010dtverec, kosod\u00e9ln\u00edk, lichob\u011b\u017en\u00edk). V \u00favahu p\u0159ich\u00e1z\u00ed i v\u00e1lec.

2. Motivace:

Na za\u010d\u00e1tku hodiny uk\u00e1\u017ee vyu\u010duj\u00edc\u00ed \u017e\u00e1k\u016fm obr\u00e1zek dvou kv\u00e1dr\u016f roz\u0159ezan\u00fdch na jednotliv\u00e9 vrstvy r\u016fzn\u011b sestaven\u00e9 a vysv\u011btl\u00ed jim, \u017ee budou vyr\u00e1b\u011bt pom\u016fcku do hodiny matematiky (m\u016f\u017ee nebo nemus\u00ed je sezn\u00e1mit s Cavalieriho principem, tedy \u017ee oba objekty jsou v podstat\u011b kv\u00e1dry se stejn\u00fdmi rozm\u011bry a mus\u00ed m\u00edt tedy i stejn\u00fd objem).

3. Zad\u00e1n\u00ed \u00fakolu \u010d. 1 - Matematick\u00e1 \u00faloha

\u017d\u00e1ci dostanou zad\u00e1nu matematickou \u00falohu \u2013 Z kolika desti\u010dek o v\u00fd\u0161ce 4 mm, sestav\u00edm kv\u00e1dr se \u010dtvercovou podstavou o rozm\u011brech:

a = 6 cm, a objemu V = 288 cm3 (rozm\u011bry lze upravit )

Rychlej\u0161\u00ed \u017e\u00e1ci, \u010di skupinky \u017e\u00e1k\u016f, mohou pop\u0159em\u00fd\u0161let a navrhnout, kolik desti\u010dek by bylo vhodn\u00e9 vytisknout v jin\u00e9 barv\u011b, aby bylo mo\u017en\u00e9 hotov\u00fd n\u00e1vrh kv\u00e1dru jednodu\u0161e vyu\u017e\u00edt i pro demonstraci krychle.

4. Modelov\u00e1n\u00ed v Tinkercadu - desti\u010dka

\u017d\u00e1ci se p\u0159ihl\u00e1s\u00ed do programu Tinkercad, u\u010ditel jim p\u0159edstav\u00ed z\u00e1kladn\u00ed funkce a vysv\u011btl\u00ed princip ovl\u00e1d\u00e1n\u00ed. \u017d\u00e1ci si v programu vyzkou\u0161\u00ed vymodelovat jednu desti\u010dku modelu kv\u00e1dru s dan\u00fdmi parametry.

5. Zad\u00e1n\u00ed \u00fakolu \u010d. 2 \u2013 Krabi\u010dka na \u00faschovu desti\u010dek

\u017d\u00e1ci prom\u00fd\u0161l\u00ed a diskutuj\u00ed, jak\u00e9 parametry by m\u011bla m\u00edt krabi\u010dka na \u00faschovu desti\u010dek. C\u00edlem t\u00e9to f\u00e1ze je doj\u00edt k my\u0161lenkov\u00e9 \u00favaze, \u017ee vnit\u0159n\u00ed rozm\u011bry krabi\u010dky (podstavy) by m\u011bly b\u00fdt cca o 2 mm v\u011bt\u0161\u00ed, ne\u017e jsou rozm\u011bry podstavy hranolu. P\u0159i n\u00e1vrhu krabi\u010dky je t\u0159eba po\u010d\u00edtat s t\u00edm, \u017ee desti\u010dky na sebe nemus\u00ed ide\u00e1ln\u011b nal\u00e9hat a jejich celkov\u00e1 v\u00fd\u0161ka po slo\u017een\u00ed bude vy\u0161\u0161\u00ed ne\u017e v\u00fd\u0161ka vypo\u010dten\u00e1 z objemu. Krabi\u010dka by proto m\u011bla b\u00fdt vy\u0161\u0161\u00ed nejm\u00e9n\u011b o v\u00fd\u0161ku jedn\u00e9 desti\u010dky. Do celkov\u00e9 v\u00fd\u0161ky krabi\u010dky je nutn\u00e9 neopomenout zapo\u010d\u00edtat tak\u00e9 tlou\u0161\u0165ku jej\u00edho dna.

Pro lep\u0161\u00ed pochopen\u00ed rozm\u011br\u016f krabi\u010dky je vhodn\u00e9 d\u011btem don\u00e9st jakoukoliv krabi\u010dku s nasouvac\u00edm v\u00edkem, kterou si \u017e\u00e1ci prom\u011b\u0159\u00ed. M\u016f\u017ee j\u00edt klidn\u011b o krabici od bot, nebo cokoliv, na \u010dem mohou \u017e\u00e1ci okoukat princip a re\u00e1ln\u00e9 rozm\u011bry t\u011bles, kter\u00e1 do sebe zapadaj\u00ed. V na\u0161em p\u0159\u00edpad\u011b jsme pou\u017eili pr\u00e1zdn\u00e9 obaly od apple pencil\u016f.

\u017d\u00e1ci si mohou po prom\u011b\u0159en\u00ed krabi\u010dky zkusit nakreslit a vyst\u0159ihnout vhodn\u011b velk\u00fd \u010dty\u0159\u00faheln\u00edk z tvrd\u00e9ho pap\u00edru, vlo\u017eit jej na dno krabi\u010dky a pozorovat jeho rozm\u011bry vzhledem k rozm\u011br\u016fm krabi\u010dky. Vz\u00e1jemn\u011b pak hodnot\u00ed, jak se jim s dan\u00fdm vyst\u0159i\u017een\u00fdm \u010dty\u0159\u00faheln\u00edkem v krabi\u010dce manipuluje. Svou \u00favahu diskutuj\u00ed a obhajuj\u00ed p\u0159ed vyu\u010duj\u00edc\u00edm a spolu\u017e\u00e1ky.

6. Modelov\u00e1n\u00ed v programu Tinkercad \u2013 krabi\u010dka na \u00faschovu desti\u010dek

\u017d\u00e1ci vymodeluj\u00ed krabi\u010dku na desti\u010dky pomoc\u00ed hranolu a do n\u011bj vlo\u017een\u00e9ho men\u0161\u00edho hranolu, \u201ed\u00edry\u201c. Soust\u0159ed\u00ed se na to, aby byly hranoly vycentrovan\u00e9, vyu\u017e\u00edvaj\u00ed k tomu jednotliv\u00e9 funkce programu Tinkercad.

Doporu\u010den\u00e9 rozm\u011bry krabi\u010dky:

Vn\u011bj\u0161\u00ed hranol \u2013 65 mm x 65 mm x 87 mm

Vnit\u0159n\u00ed rozm\u011bry (d\u00edra) \u2013 62 mm x 62 mm x 84 mm

Z organiza\u010dn\u00edch d\u016fvod\u016f je vhodn\u00e9, aby desti\u010dka i krabi\u010dka byly modelov\u00e1ny zvl\u00e1\u0161\u0165 do samostatn\u00fdch n\u00e1vrh\u016f. Nen\u00ed v\u0161ak bezpodm\u00edne\u010dn\u011b nutn\u00e9.

Touto f\u00e1z\u00ed m\u016f\u017ee hodina skon\u010dit. Podle aktu\u00e1ln\u00edch \u010dasov\u00fdch mo\u017enost\u00ed m\u016f\u017ee vyu\u010duj\u00edc\u00ed pokra\u010dovat na body 7. a 8.

7. Export hotov\u00fdch model\u016f

\u017d\u00e1ci dle n\u00e1vodu vyu\u010duj\u00edc\u00edho vyexportuj\u00ed sv\u00e9 n\u00e1vrhy do form\u00e1tu *.stl.

Je vhodn\u00e9, aby m\u011bl vyu\u010duj\u00edc\u00ed zalo\u017eenou pro \u017e\u00e1ky jednodu\u0161e dostupnou slo\u017eku, do kter\u00e9 sv\u00e9 n\u00e1vrhy ulo\u017e\u00ed, a aby n\u00e1vrh desti\u010dky a krabi\u010dky byl vyexportov\u00e1n ka\u017ed\u00fd v samostatn\u00e9m souboru. Nen\u00ed to v\u0161ak nezbytn\u011b nutn\u00e9.

8. Zpracov\u00e1n\u00ed n\u00e1vrhu v programu PrusaSlicer

Vyu\u010duj\u00edc\u00ed vysv\u011btl\u00ed \u017e\u00e1k\u016fm, jak vlo\u017eit sv\u016fj n\u00e1vrh do programu PrusaSlicer a jak nastavit parametry pro tisk. Spole\u010dn\u011b mohou prodiskutovat praktick\u00e9 mo\u017enosti tisku n\u00e1vrhu (kolik desti\u010dek je mo\u017en\u00e9 v r\u00e1mci jednoho tisku vytisknout, jak\u00e9 nastaven\u00ed a kvalitu tisku pou\u017e\u00edt aj.).

9. Tisk a pr\u00e1ce vyti\u0161t\u011bn\u00fdm modelem

Po vyti\u0161t\u011bn\u00ed je mo\u017en\u00e9 nechat \u017e\u00e1ky porovnat skute\u010dnou v\u00fd\u0161ku poskl\u00e1dan\u00e9ho hranolu s v\u00fd\u0161kou vypo\u010dtenou z objemu a n\u00e1sledn\u011b rozvinout diskusi, pro\u010d je hranol poskl\u00e1dan\u00fd z desti\u010dek vy\u0161\u0161\u00ed (nap\u0159. kvalita a rovnost povrch\u016f, p\u0159esnost v\u00fdroby).

Kvalitu a rovnost povrch\u016f, jak p\u0159esn\u011b na sebe desti\u010dky dol\u00e9haj\u00ed, si mohou \u017e\u00e1ci ov\u011b\u0159it prohl\u00e9dnut\u00edm dvou desti\u010dek p\u0159ilo\u017een\u00fdch k sob\u011b proti sv\u011btlu.

Pozn\u00e1mky

Uk\u00e1zka Cavalieriho principu pro \u017e\u00e1ky

\u00daloha \u010d. 1:

Z kolika desti\u010dek o v\u00fd\u0161ce 4 mm, sestav\u00edm kv\u00e1dr se \u010dtvercovou podstavou o rozm\u011brech strany , a objemu

\u0158e\u0161en\u00ed \u00falohy \u010d. 1:

v\u00fdpo\u010det v\u00fd\u0161ky hranolu

\u2013 v\u00fd\u0161ka hranolu

po\u010det desti\u010dek

desti\u010dek

Jedna desti\u010dka \u010dtvercov\u00e9 podstavy bude m\u00edt rozm\u011bry:

Mo\u017en\u00e1 roz\u0161\u00ed\u0159en\u00ed zadan\u00e9 \u00falohy:

KRYCHLE:

Ur\u010di, kolik desti\u010dek se m\u00e1 vytisknout jinou barvou, aby \u0161lo z modelu jednodu\u0161e sestavit tak\u00e9 krychli.

\u0158e\u0161en\u00ed:

Krychle m\u00e1 v\u0161echny hrany stejn\u011b dlouh\u00e9. P\u0159i rozm\u011brech podstavy , bude v\u00fd\u0161ka krychle .

po\u010det desti\u010dek

desti\u010dek

TROJBOK\u00dd HRANOL S PODSTAVOU PRAV\u00daHL\u00c9HO TROJ\u00daHELN\u00cdKU

Z kolika desti\u010dek o v\u00fd\u0161ce 4 mm, sestav\u00edm trojbok\u00fd hranol s podstavou tvaru pravo\u00fahl\u00e9ho troj\u00faheln\u00edku o d\u00e9lce ramen , a objemu
.

v\u00fdpo\u010det v\u00fd\u0161ky hranolu

\u2013 v\u00fd\u0161ka hranolu

po\u010det desti\u010dek

desti\u010dek

Dal\u0161\u00ed mo\u017enosti zad\u00e1n\u00ed:

HRANOL S PODSTAVOU KOSO\u010cTVERCE

Z kolika desti\u010dek o v\u00fd\u0161ce 4 mm, sestav\u00edm \u010dty\u0159bok\u00fd hranol se podstavou tvaru koso\u010dtverce a rozm\u011brech podstavy , a objemu .

v\u00fdpo\u010det v\u00fd\u0161ky hranolu

\u2013 v\u00fd\u0161ka hranolu

po\u010det desti\u010dek

desti\u010dek

V\u00c1LEC

Z kolika desti\u010dek o v\u00fd\u0161ce 4 mm, sestav\u00edm v\u00e1lec s pr\u016fm\u011brem podstavy
, a objemu (pro ).

v\u00fdpo\u010det v\u00fd\u0161ky hranolu

\u2013 v\u00fd\u0161ka v\u00e1lce

po\u010det desti\u010dek

desti\u010dek

","approved":true,"publishedStatus":"PUBLISHED","__typename":"EduProjectType"},"user":{"id":"139574","handle":"ZSklokanek_139574","verified":false,"dateVerified":null,"publicUsername":"ZS-klokanek","avatarFilePath":"","badgesProfileLevel":{"profileLevel":4,"__typename":"BadgesProfileLevelType"},"__typename":"UserType","isFollowedByMe":false,"canBeFollowed":true,"billingAccountType":"personal","lowestTierPrice":null,"designer":false,"stripeAccountActive":null,"membership":null},"ratingAvg":"0E-10","myRating":null,"ratingCount":0,"description":"","category":null,"modified":"2022-06-20T14:22:24.424575+00:00","firstPublish":"2022-06-20T14:22:24.424465+00:00","datePublished":"2022-06-20T14:22:24.424465+00:00","dateCreatedThingiverse":null,"nsfw":false,"summary":"Studenti vypo\u010d\u00edtaj\u00ed po\u010det desti\u010dek pot\u0159ebn\u00fdch k sestaven\u00ed kv\u00e1dru \u010dtvercov\u00e9ho p\u016fdorysu, promysl\u00ed, jak\u00e9 rozm\u011bry by m\u011bla m\u00edt krabi\u010dka na jejich p\u0159epravu a skladov\u00e1n\u00ed. Jednu desti\u010dku i krabi\u010dku vymodeluj\u00ed","likesCount":1,"makesCount":0,"liked":null,"printDuration":"5.00","numPieces":2,"weight":"66.00","nozzleDiameters":["0.40"],"usedMaterial":null,"layerHeights":["0.20"],"mmu":false,"materials":[{"id":"1","name":"PLA","__typename":"MaterialTypeType"}],"dateFeatured":null,"downloadCount":1,"displayCount":170,"filesCount":4,"privateCollectionsCount":0,"publicCollectionsCount":0,"pdfFilePath":"media/prints/178590/pdfs/178590-cavalieriho-princip-vyroba-modelu-pro-vyuku-hejneho-matematiky-f1bac6c1-16aa-4bb3-b328-ec82de74908c.pdf","commentCount":0,"userGcodeCount":0,"remixCount":0,"canBeRated":false,"printer":{"id":"18","name":"Prusa MINI / MINI+","__typename":"PrinterTypeType"},"image":{"id":"995867","filePath":"media/prints/178590/images/2026396_7f569491-cda2-46cf-9cc6-4606fa1de585/1_img_6353.webp","rotation":0,"imageHash":"bfgJBYKo93Z+h4VvhzSIh5Du/ev0","imageWidth":1600,"imageHeight":1200,"__typename":"PrintImageType"},"images":[{"id":"995867","filePath":"media/prints/178590/images/2026396_7f569491-cda2-46cf-9cc6-4606fa1de585/1_img_6353.webp","rotation":0,"imageHash":"bfgJBYKo93Z+h4VvhzSIh5Du/ev0","imageWidth":1600,"imageHeight":1200,"__typename":"PrintImageType"},{"id":"995874","filePath":"media/prints/178590/images/2026401_c21ef392-6acf-406e-a0d0-d5e995943b3e/3_img_6597.webp","rotation":0,"imageHash":null,"imageWidth":null,"imageHeight":null,"__typename":"PrintImageType"},{"id":"995875","filePath":"media/prints/178590/images/2026400_eed33cb3-2aca-4e73-8b0b-41dc563a238b/4_img_6591.webp","rotation":0,"imageHash":null,"imageWidth":null,"imageHeight":null,"__typename":"PrintImageType"},{"id":"995868","filePath":"media/prints/178590/images/2026399_aa4edc9e-9ae7-4e53-9f2b-a3ad36def53d/5_cavalieriho_princip-ucebnice.webp","rotation":0,"imageHash":null,"imageWidth":null,"imageHeight":null,"__typename":"PrintImageType"},{"id":"995871","filePath":"media/prints/178590/images/2026404_414456fa-b87a-4d52-a29e-85e62474db2e/8_img_6369.webp","rotation":0,"imageHash":null,"imageWidth":null,"imageHeight":null,"__typename":"PrintImageType"},{"id":"995870","filePath":"media/prints/178590/images/2026398_e467a966-bbc4-4e3b-b3fd-f00dce42b6bf/6_img_6378.webp","rotation":0,"imageHash":null,"imageWidth":null,"imageHeight":null,"__typename":"PrintImageType"},{"id":"995869","filePath":"media/prints/178590/images/2026403_5d3b2c1a-58c9-4b12-8d18-4f757f6d9404/7_img_6370.webp","rotation":0,"imageHash":null,"imageWidth":null,"imageHeight":null,"__typename":"PrintImageType"},{"id":"995872","filePath":"media/prints/178590/images/2026402_fd673a7b-7353-497f-8d01-404b0cc40b0a/2_img_6368.webp","rotation":0,"imageHash":null,"imageWidth":null,"imageHeight":null,"__typename":"PrintImageType"}],"tags":[{"name":"matematika","id":"50189","__typename":"TagType"},{"name":"objem","id":"58569","__typename":"TagType"},{"name":"cavalierihoprincip","id":"71329","__typename":"TagType"}],"thingiverseLink":null,"filesType":"GCODE","previewFile":{"id":"84833","filePreviewPath":"media/prints/178590/gcodes/2026416_1bcc0c04-1719-4a6c-a190-5c7c75db656e/desticka_02mm_pla_mini_41m_preview.png","__typename":"GCodeType"},"license":{"id":"4","disallowRemixing":false,"__typename":"LicenseType"},"remixParents":[],"remixDescription":null,"__typename":"PrintType"}}}

Cavalieriho princip – výroba modelu pro výuku Hejného matematiky

Comments