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| (265 mellanliggande sidversioner av 4 användare visas inte) |
| Rad 1: |
Rad 1: |
| == [[Matte på öppet hus]] ==
| | __NOTOC__ |
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| == Ämnesövergripande samarbete matematik engelska == | | {{sway | [https://sway.com/myUNCB8ZIICKh9jn?ref{{=}}Link Inledning] }} |
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| [http://www.khanacademy.org/video/algebra--slope?playlist=Algebra exempel på film] på Khan där man kan välja och editera undertexter.
| | == Taluppfattning, aritmetik och algebra == |
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| == Allmänt ==
| | [[File:algebraic equation notation.svg|thumb|right|Algebraic expression notation:<br/> 1 – power (exponent)<br/> 2 – coefficient<br/> 3 – term<br/> 4 – operator<br/> 5 – constant term<br/> ''x'' ''y'' ''c'' – variables/constants]] |
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| * Miniräknare? [http://www.prim.su.se/matematik/kurs_1/lararinfo_kurs1c.pdf Instruktionen till Nationella provet] säger att digitala hjälpmedel (dator) är tillåtet på provet.
| | === [[Tal och talmängder]] === |
| * Ma 1c.[http://www.skolverket.se/forskola_och_skola/gymnasieutbildning/2.2954/amnesplaner_och_kurser_for_gymnasieskolan_2011/subject.htm?subjectCode=MAT&courseCode=MATMAT01c#anchor_MATMAT01c Kursplan]'
| |
| * Matte A kursen finns på [http://sv.wikibooks.org/wiki/Matematik/Matematik_A Wikibooks].
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| == Grovplanering == | | === [[Negativa tal]] === |
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| TEINF11 Matematik 1c, period 1, 2 (4 lekt/vecka)
| | === [[Tal i bråkform]] === |
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| Vi använder Libers matematikbok Matematik M1c, av Sjunnesson, Holmström, Smedhamre. Innehållsrubrikerna nedan är kapitel i boken.
| | === [[Faktorisering]] === |
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| '''Vecka Innehåll'''
| | === [[Primtal|Primtal]] === |
| 34-36 Taluppfattning och aritmetik
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| 37-40 Agebra och ekvationer
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| 41-42 Geometri
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| 43 MD+ Geometri
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| 44 Höstlov
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| 45-47 Samband och förändring
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| 48-50 Sannolikhet och statistik
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| 51-1 Jullov
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| == Extramatte == | | === [[Delbarhet|Delbarhet]] === |
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| '''Mål'''
| | === [[Potenser]] === |
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| Repetera det som hänt under veckan så att du hänger med.
| | === [[Positionssystemet och olika talbaser|Talbaser]] === |
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| '''Hur'''
| | == Algebra == |
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| Lösa alla svarta uppgifter. Prata om de svårigheter som kan ha varit.
| | === [[Begrepp inom algebran]] === |
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| '''Mål'''
| | === [[Algebraiska uttryck|Algebraiska uttryck]] === |
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| Repetera grunder
| | === [[Skapa uttryck]] === |
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| '''Hur'''
| | === [[Algebra och modeller]] === |
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| Testerna i boken
| | === [[Omskrivning av formler]] === |
| * Jobba metodiskt med ett avsnitt i taget.
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| * Interaktiva uppgifter finns på denna sida.
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| == Miniräknare == | | === [[Ekvationer]] === |
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| <html><script type="text/javascript" src="http://cdn.widgetserver.com/syndication/subscriber/InsertWidget.js"></script><script type="text/javascript">if (WIDGETBOX) WIDGETBOX.renderWidget('e63a9ee1-4e1c-4319-a84e-8ddf84e945d5');</script><noscript>Get the <a href="http://www.widgetbox.com/widget/whizz-scientific-calculator">Maths-Whizz Scientific Calculator</a> widget and many other <a href="http://www.widgetbox.com/">great free widgets</a> at <a href="http://www.widgetbox.com">Widgetbox</a>! Not seeing a widget? (<a href="http://support.widgetbox.com/">More info</a>)</noscript></html>
| | === [[Grafisk ekvationslösning]] === |
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| | === [[Linjär olikhet]] === |
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| Vi behöver inte skaffa räknare. Allt man kan göra på räknaren gör man lika bra eller bättre på datorn och datorn har vi alltid på lektionerna.
| | === [[Potensekvationer]] === |
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| Tidigare var miniräknaren nödvändig på nationella provet men från och med i år är det tillåtet att använda datorn på nationella provet.
| | === [[Problemlösning med ekvationer Ma1c |Problemlösning med ekvationer]] === |
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| Vi behöver göra vissa begränsningar av datorns kommunikationsförmåga under provet:
| | === [[Repetition av Ma1C Aritmetik och Algebra|Repetition]] === |
| * Nätverket stängs eller får nytt lösenord den aktuella dagen.
| | <br> |
| * Du stänger skype, msn, facebook.
| | [[File:Commutative Addition.svg|300px|Commutative Addition]] |
| * Du stänger ner nätverket och Bluetooth på din dator.
| | {{clear}} |
| * Du ser till att inte öppna anteckningar eller sådant som kan uppfattas som fusklappar.
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| * Du sitter med skärmen fullt synlig och provvakten sitter bakom eleverna så det blir fullt synligt vad som görs på datorn.
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| Om vi gör på detta sätt har vi begränsat möjligheterna till otillåten datoranvändning på de sätt vi kan. Om vi trots detta misstänker fusk kan vi analysera datortrafiken på skolans nät.
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| Miniräknare i datorn:
| | == Geometri == |
| | [[Fil:Chinese pythagoras.jpg|300px|höger]] |
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| * kalkylatorn i Windows, start - program - tillbehör
| | === [[Definition sats och bevis Ma1c|Definition, sats och bevis]] === |
| * WolframAlpha.org
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| * GeoGebra
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| * Excel
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| * Google Docs - kalkylark
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| * http://www.widgetbox.com/ som du ser ovan
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| = Kapitel 1 - [[Taluppfattning och Aritmetik]] = | | === [[Geometriska satser och bevis ma1c|Geometriska satser och bevis]] - Vinklar och vinkelsumma === |
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| = Kapitel 2 - [[Algebra Ma1C|Algebra ]] = | | === [[Grupparbete Geometri Ma1c]] Pythagoras sats === |
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| = Kapitel 3 - [[Geometri Ma1C|Geometri]] = | | === [[trigonometri_Ma1c|Trigonometri (sinus, cosinus, tangens)]] === |
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| = Kapitel 4 - [[Samband och förändring]] = | | === [[Vektorer|Vektor och dess representation (skalär/vektor)]] === |
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| = Kapitel 5 - Sannolikhet och statistik = | | === [[Addition och subtraktion av vektorer|Addition, subtraktion och multiplikation av vektorer]] === |
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| Kapitel 5 handlar om Sannolikhet och statistik och består av nio delar (en del har teori, exempel och uppgifter).
| | === [[NP muntligt övning]] === |
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| == 5.1 Hur stor är chansen? == | | === [[Problemllösning med trigonometri och vektorer]] === |
| | |
| | [[Fil:TrigonometryTriangle.svg|250px|vänster]]<br /> |
| | <br /> |
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| '''Intro'''
| | {{Gleerups|[[Media:Kapitel_2_Gleerups_Ma_1c.pdf|Lösningar till Gleerups kapitel 2 (pappersboken)]]}} |
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| [http://www.khanacademy.org/video/basic-probability?playlist=Probability Khan Academy] om Probability
| | {{clear}} |
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| <html><script type="text/javascript" src="http://s3.www.universalsubtitles.org/embed.js">
| | == Förändring och procent == |
| (
| | [[File:Proportional variables.svg|thumb|Variable ''y'' is directly proportional to the variable ''x''.]] |
| {"base_state": {}, "video_url": "http://www.youtube.com/watch?v=uzkc-qNVoOk"}
| |
| )
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| </script>
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| </html>
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|
| Här har jag börjat skriva undertexter (subtitles) på svenska. Det är enkelt, bara att skaffa ett konto på Universal Subtitles och sätta igång. Vi kommer att göra övningar på detta så småningom, där ni får en film var att översätta.
| | === [[Procent Ma1c|Procentbegreppet, promille, ppm, procentenheter]] === |
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| === Sidorna 244-248 === | | === [[Förändringsfaktor]] === |
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| fre - hemdiagnos denna fredag.
| | === [[Index, lån, amortering]] === |
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| '''Definition:'''
| | == Funktioner och samband == |
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| Sannolikheten för en händelse = antalet gynnsamma utfall / antal möjliga utfall
| | === [[Funktionsbegreppet|Funktion, definitions- och värdemängd]] === |
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| med P(A) menas sannolikheten för att händelse A ska inträffa.
| | === [[Representationer av funktioner]] === |
| A kan bestå av flera händelser, exempel vis att slå över tre på en tärning.
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| P(A eller B) = P(A) + P(B)
| | === [[Skillnaden mellan ekvation, olikhet, algebraiskt uttryck, funktion]] === |
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| == 5.2 Oberoende händelser == | | === [[Proportionalitet]] === |
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| === Sidorna 249-251 === | | === [[Linjära funktioner|Egenskaper hos linjära funktioner]] === |
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| fre
| | === [[Potensfunktioner]] === |
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| '''exempel 1, sid 249'''
| | === [[Exponentialfunktioner Ma1c|Exponentialfunktioner]] === |
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| <ggb_applet width="629" height="465" version="4.0" ggbBase64="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" framePossible = "true" showResetIcon = "true" showAnimationButton = "true" enableRightClick = "true" errorDialogsActive = "true" enableLabelDrags = "true" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" />
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| <br>
| |
| Kolla gärna Mikael Bondestam som förklarar kast med två tärningar = sannolikhet vid oberoende händelser:
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| <Youtube>EANNJSjare</Youtube>
| | === [[Mönster och talföljder]] === |
|
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|
| <br> | | <br> |
| Här kommer en bild som är lämplig att projicera och sedan rita på om man diskuterar sannolikheter vid två tärningsslag:
| | [[Fil:Doubling time vs half life.svg|400px|vänster]] |
| <br>
| | {{clear}} |
| <ggb_applet width="540" height="413" version="4.0" ggbBase64="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" framePossible = "false" showResetIcon = "false" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" />
| |
| <br>
| |
| | |
| == Khan Academy ==
| |
| | |
| Däremot får alla gå in en kort stund på '''[http://www.khanacademy.org/ KhanAcademy]''' på slutet av lektionen. Alla ska välja mig som coach så jag kan se hur det går. När du gör övningarna kan du klicka på Add coach längst ned på sidan. Gör det och adda mig.
| |
| | |
| Mitt ID är hakan.elderstig@gmail.com
| |
| | |
| == 5.3 Händelser i flera steg ==
| |
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| === Sidorna 252-255 ===
| |
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| må
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| Khan om oberoende händelser i flera steg:
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| <youtube>xSc4oLA9e8o</youtube>
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| Sedan en kul grej bara.
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| Rulla tärning från http://www.geogebratube.org/student/m712:
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| <br>
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| Mikael Bondestam om träddiagram för händelser i flera steg:
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| <br>
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| <youtube>qN64hazQ5-Q</youtube>
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| === Beroende händelser i flera steg, 256-258 ===
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| ti
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| MB
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| === Komplementhändelse, 259-260 ===
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| ti
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| [http://sv.wikipedia.org/wiki/De_M%C3%A9r%C3%A9s_problem De Meres problem]
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| <ggb_applet width="835" height="381" version="4.0" ggbBase64="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" framePossible = "true" showResetIcon = "true" showAnimationButton = "true" enableRightClick = "true" errorDialogsActive = "true" enableLabelDrags = "true" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" />
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| == Repetition inför provet ==
| |
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| onsdag
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| [[Media:Lösningar_till_några_uppgifter_vi_övade_på_inför_provet_på_geometri,_funktioner_och_sannolikhet.pdf|Några lösningar till uppgifter vi gjorde på sista lektionen]]. | |
| | |
| '''Khan Academy'''
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| * [http://www.khanacademy.org/exercise/trigonometry_1 Khan Academy om Trigonometri]
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| * [http://www.khanacademy.org/exercise/probability_1 Khan uppgifter om Sannolikhet]
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| * [http://www.khanacademy.org/exercise/probability_1 Khan om vektorer]
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| * [http://www.khanacademy.org/exercise/linear_equations_1 Khan om funktioner]
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| | |
| '''Veckodiagnos 10'''
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| Detta är en lösning till uppgift 4 på [[Media:Veckodiagnos_10.pdf|veckodiagnos 10]].
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| == Prov kapitel fyra samt mindre delar av 3 och 5 ==
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| fredag
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| [[Media:Prov_Matte_1c_kapitel_3,_4_och_5,_version_1_2-facit.pdf|Lösningar till provet]] | | == Sannolikhet och statistik == |
| | [[File:Svg-cards-pair.svg|thumb|Tre exempel på pokerhänder med ''ett par'']] |
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| '''Provgränser'''
| | === [[Statistik i samhälle och vetenskap|Statistiska metoder i samhället]] === |
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| * Betyg E krävs 12 poäng
| | === [[Oberoende händelse]] === |
| * Betyg C krävs dessutom 6 C-poäng
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| * Betyg A krävs 11 C-poäng och 3 A-poäng
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| == 5.4 Hur ofta inträffar en händelse? == | | === [[Beroende händelse]] === |
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| === Relativ frekvens === | | === [[Spel, risk- och säkerhetsbedömningar]] === |
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| Sid 262-264
| | === [[Valet 2018]] === |
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| Intro från: [http://www.geogebratube.org/student/m784 GGBtube]. Dub'''Fet text'''belklicka för att se hela simuleringen.
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" 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| <br>
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| <br>
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| <br> | | <br> |
| <html><iframe src="http://phet.colorado.edu/sims/plinko-probability/plinko-probability_en.html" width="800" height="600"></iframe></html>
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|
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| === Sidorna 261-266 ===
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|
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| ons
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| Här är det lämpligt med några laborationer. Kanske olika uppgifter som gruperna får redovisa på nätet.
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| == 5.5 Statistik i samhälle och vetenskap ==
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|
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| === Sidorna 267-275 ===
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|
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| fre
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|
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| Här kan man tänka sig att eleverna gör egna undersökningar och redovisar...
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|
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| '''Medelvärde och standardavvikelse'''
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|
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| Fri att använda. Från [http://geogebrainstitut.se/resurser/resurser.asp#MaA GeoGebraInstitutet]
| |
|
| |
| === Gapminder - övning ===
| |
|
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| www.gapminder.org
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|
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| samtidigt som vi kör muntliga nationella prov får elevernas uppgifter på gapminder att jobba med.
| |
|
| |
| === Film - undertexter ===
| |
|
| |
| En tanke är att eleverna får en film var från Khan Academy och att de gör en översättning till svenska av den engelska undertexten.
| |
|
| |
| == Monty Hall ==
| |
|
| |
| Lös det teoretiskt eller leta rätt på en lösning på nätet.
| |
|
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| Praktiskt experiment för att testa om det stämmer.
| |
|
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|
| Redovisa
| | [[File:Mikemoral-time stats.jpg|300px|left|Mikemoral-time stats]] |
| | {{clear}} |
|
| |
|
| http://sv.wikipedia.org/wiki/Monty_Hall-problemet
| | == Problemlösning == |
|
| |
|
| == 5.6 Vilseledande statistik == | | === [[Strategier för matematisk problemlösning inklusive användning av digitala medier och verktyg]]. === |
| | === [[Matematiska problem av betydelse för privatekonomi, samhällsliv och tillämpningar i andra ämnen]]. === |
| | === [[Matematiska problem med anknytning till matematikens kulturhistoria]]. === |
|
| |
|
| === Sidorna 276-277 === | | == [[Repetition av Ma1C]] == |
|
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|
| må
| | Mest gamla prov, länkar till Khan Academy, etc. |
|
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|
| == 5.7 Några statistiska lägesmått == | | == Relevansförmågan == |
|
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|
| === Sidorna 278-282 ===
| | : Vi jobbar på olika sätt med den [[Intro till Global uppvärmning|globala uppvärmningen]]. Vad kan vara mer relevant? |
|
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|
| ti
| | '''Huvuduppgift''': |
| | : [https://wikiskola.se/index.php?title=Intro_till_Global_uppv%C3%A4rmning#Se_filmen_Before_the_Flood Uppgiften som ska lämnas in finns här.] |
|
| |
|
| == [[Nationellt prov Ma1C]] - Onsdagen den 14 december ==
| | '''Alternativ uppgift''': |
| | : [[Relevansuppgift: Globala temperaturavvikelser från 1880 till och med 2014]] |
|
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|
| Behovet av repetition gör att vi kan senarelägga avsnitt 5.6 och 5.7
| | == [[Julemys]] == |
|
| |
|
| == Muntligt Nationellt prov ==
| | För den händelse du vill öka dina kunskaper och vässa dina förmågor avslutar vi Ma1c med dessa övningar. Det är nyttigheter för var och en men ett måste för er som vill höja era betyg (ni vet om ifall ni ligger nära gränsen). Om ni vill höja er kommer det att komma ett test när skolan börjar i januari. |
|
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|
| Egna undersökningar och gruppövningar
| | Gå in på denna sida så hittar ni uppgifterna och övningarna: [[Julemys]] |
|
| |
|
| * Sannolikheterna bakom "Kasta gris"
| | Övningarna består av texter och uppgifter i skön förening. Jobba med ett undersökande arbetssätt. Det kan hända att du har nytta av dina anteckningar, program eller resultat vid bedömingstillfället. |
| * GapMinder
| |
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