Matematik 1c: Skillnad mellan sidversioner

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Rad 78: Rad 78:
= Kapitel 2 - [[Algebra Ma1C|Algebra ]] =
= Kapitel 2 - [[Algebra Ma1C|Algebra ]] =


= Kapitel 3 - Geometri =
= Kapitel 3 - [[Geometri Ma1C|Geometri]] =
 
14 delavsnitt på två veckor?? Vi behöver mer tid.
 
Prov efter kapitlet?
 
Nåväl, vi siktar på att göra kapitel 3.1-3.2 under vecka 41 och 3.3-3.4 under vecka 42.
 
== lektion 20 - Geometriska satser och bevis ==
 
Första delen av Kapitel 2.1: Första lektionen gjorde vi sidorna 112-117 och arbetade till och med uppgift 3122.
 
Vi kommer att behöva mer tid för satser och befivis och även för definitioner och begrepp, ex likformig, biskektris mm.,
 
'''Definition:'''
En rak vinkel är 180<sup>o</sup>
 
'''Definition:'''
Två linjer är parallella om de likbenägna vinklarna är lika stora.
Alternatvinklar
Sidovinklar
 
'''Satser:'''
Vertiklavinklar
Likbelägna vinklar
Alternatvinklar
Sidovinklar
 
'''Övning:''' Titta på alla [http://www.geogebra.se/ma_a/geometri/vinklar/vinklar/vinklar_t_vl.html filmer om vinklar] på Geogebra
 
'''Sats:'''
Vinkelsumman i en triangel är 180<sup>o</sup>
 
'''Begrepp:'''
Likbent triangel
Liksidig triangel
Bisektris
 
== Lektion 21 - Geometriska figurer ==
 
Kvadrat
Romb
Parallelltrapets
Triangel
Cirkel
Cirkelsektor
Prisma
Cylinder
Pyramid
Kon
Klot
 
'''Cirkelns area'''
 
[http://www.geogebratube.org/student/m279 EN mycket bra GGB]
 
'''Triangelns area'''
 
Triangelns tyngdpunkt ligger i skärningspunkten för bisektriserna. Testa på [http://www.geogebra.se/ma_b/geometri/triangel_tyngdpunkt_t.html geogebra].
 
Arean för en triangel är basen * höjden / 2. Det gäller även om höjden faller utanför basen. Se exempel i geoGebra nedan:
 
<ggb_applet width="858" height="500"  version="3.2" ggbBase64="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" framePossible = "true" showResetIcon = "true" showAnimationButton = "true" enableRightClick = "true" errorDialogsActive = "true" enableLabelDrags = "true" showMenuBar = "true" showToolBar = "true" showToolBarHelp = "true" showAlgebraInput = "true" allowRescaling = "true" />
 
All bilder i galleriet nedan är CC [http://commons.wikimedia.org/wiki/Main_Page Från WikiMedia Commons].
<gallery>
Fil:1000px-Isosceles_triangle_area.svg.png
Fil:Triangle_area.gif
Fil:1000px-Triangle.Right.svg.png
Fil:1000px-Triangle.Isosceles.svg.png
Fil:1000px-Triangle.Equilateral.svg.png
Fil:Bisectrices.png
Fil:1000px-Square_definition.svg.png
Fil:1000px-Square_-_geometry.svg.png
Fil:1000px-Scale_one_to_thousand_volume.svg.png
Fil:1000px-CubeLitre.svg.png
Fil:1000px-Circle_area_by_reassembly.svg.png
Fil:Equation_in_circle_proved_by_the_method_of_indivisibles.gif
Fil:1000px-Volume_cylindre_parallelepipede_rectangle.svg.png
Fil:640px-PSM_V54_D324_Optical_illusion_with_cubes.png
Bild:640px-Fractal heptahedron.png | Fraktal figur
</gallery>
 
'''Bevis: Vinkelsumman i en triangel är 180<sup>o</sup>'''
 
* GeoGebras hemsida har ett [http://www.geogebra.se/ma_a/geometri/triangel_vinkelsumma_bevis/triangel_vinkelsumma_bevis/triangel_vinkelsumma_bevis_t_vl.html bevis att vinkelsumman är 180<sup>o</sup>]
*[http://www.mathopenref.com/triangleinternalangles.html testa vinkelsumman i praktiken]
 
'''Bevis:'''
Gör bevisen på sidan 116.
 
'''Läs mer:'''
 
* [http://www.webbmatte.se/display_page.php?id=150&on_menu=802&page_id_to_fetch=2026&lang=swedish&no_cache=1209563336 Webbmatte om geometriska figurer]
 
== Lektion 22 - Pythagoras sats ==
 
'''Bevis:'''
 
[http://www.webbmatte.se/display_page.php?id=150&on_menu=802&page_id_to_fetch=2027&lang=swedish&no_cache=8585192 Webbmatte om Pythagoras sats]
[http://www.walter-fendt.de/m14e/pyththeorem.htm Fendt nr 2]
 
[http://www.walter-fendt.de/m14e/pyth2.htm Pythagoras, Walter Fendt]
 
<Gallery>
Fil:1000px-Pythagorean_theorem.svg.png
Fil:Pythagorean_theorem.jpg
Fil:443px-Perigal_TdP.gif
Fil:1000px-Pythagorean.svg.png
Fil:Pythagorean_Theorem_Proof.gif
Fil:1000px-Pythagorean_proof.svg.png
Fil:Pythagoras-2a.gif
</Gallery>
 
Även här kommer bilderna från commons.wikimedia.org
 
'''Uppgift:''' Titta själv igenom Geoegebras [http://www.geogebra.se/ma_b/geometri/pythagoras_sats_geometrisk_motivering_t.html film om pythagoras sats].
 
'''Uppgift:''' Hitta ditt eget favoritbevis på nätet och visa för oss andra.
'''
Bra övning:''' [http://www.geogebratube.org/student/m503 Upptäck Pythagoras] i GeoGebra.
 
== Lektion 23 - Likformighet ==
 
== Lektion 24 - Trigonometri ==
 
[[Fil:1000px-Trigono_sine_en2.svg.png|thumb|CC [http://commons.wikimedia.org/wiki/User:Dnu72 By]]]
[[Fil:1000px-Sinus.svg.png|thumb|CC Wikimedia.org]]
 
[http://www.geogebra.se/ma_a/trigonometri/sinv_ratvinklig_trigonometri_t.html GeoGebra om Sinus]
 
[http://sv.wikipedia.org/wiki/Sinus Läs mer om sinus på Wikipedia].
 
[http://en.wikipedia.org/wiki/Sine Engelska Wikipedia är ännu bättre på sinus].
 
http://www.walter-fendt.de/m14e/sincostan_e.htm Walter Fendt om trigonometri
 
[http://www.wolframalpha.com/input/?i=sine Detta svar får du om du skriver in sine på Wolfram Alpha]
 
'''Definitioner:'''
 
* Motstående katet
* Närliggande katet
* Sin v = motstående katet / hypotenusan
* Cos v = närliggande katet / hypotenusan
* Tangens v = motstående katet / närliggande katet
 
'''Digitalt'''
 
* Grader och radianer
* Miniräknare eller dator
* Datorns räknare
* [[Media:Sinus.xls|Excel - så här kan det se ut]]
 
'''Definition: Ta reda på vinkeln'''
 
Om y = roten ur x så är 'y''<sup>2</sup> = ''x''. Dessa två hänger ihop och den ena kan ses som den omvända av den andre. Detta kallas inversen, den inversa funktionen.
 
På samma sätt som det finns en invers funktion till kvadraten på ett tal, nämligen roten ur så finns det en invers funktion till sinus och cosinus.
 
Om sin v = a/h då är v = arcsin(a/h) eller sin<sup>-1</sup>(a/h)
Om cos v = b/h då är v = arccos(b/h) eller cos<sup>-1</sup>(b/h)
0ch på samma sätt för tangens
 
== Lektion 25 - Vektorer ==
 
'''vad är vektorer och vad ska man ha dem till?'''
 
http://sv.wikipedia.org/wiki/Vektorgrafik
 
[http://www.walter-fendt.de/m14e/vector3d.htm Walter om vektorer]
 
Vad är det för likhet mellan rebubbled och bilspelet xx?
 
Hur räknar man på kulans väg i CS?
 
Fysikerna ritar pilar för kraft och hastighet men inte för area eller temperatur.
 
Titta på Physics.fla
 
'''Den vetgirige''' tar en titt på [http://en.wikipedia.org/wiki/B%C3%A9zier_curve engelska] och [http://sv.wikipedia.org/wiki/B%C3%A9zier-kurva svenska] wikipedia om Bezierkurvor vilka används frekvent inom datorgrafiken.
 
Kolla vektorerna på fysiksidan.
 
=== Vad är en vektor? ===
 
Sid 144-147.
 
Definition: vektor
 
'''GeoGebra:''' [http://www.geogebra.org/en/upload/files/UC_MAT/christybredestege/vector_for_dummies.html "Basic Vector Addition and Subtraction for Dummies"]
 
Definition: motsatta vektorer
 
Sats: Parallella vektorer
 
Definition: storleken av en vektor
 
'''''Mån 10.05-10.55'''''
 
=== Addition av vektorer ===
 
Sid 148-150.
 
Sats: Kommutativa lagen för vektorer
<br>
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<br>
 
 
=== Subtraktion av vektorer ===
 
Sid 151-154.
 
Definition: Subtraktion av vektorer
<br>
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<br>
Ovanstående GGB är skapad av Håkan Elderstig fria att använda enligt Creative Commons. Den finns att laddas ner från [http://www.geogebratube.org/material/show/id/2368 GeoGebratube].
<br>
 
=== Vektorer i koordinatsystem ===
 
Sid 155-158.
 
Definition: Basvektorer
 
Sats: Räkneregler för vektorer
 
Sats: Storleken av en vektor
 
'''''Fredag: Diagnos på hela kapitel 3'''''
 
=== 3.4 Vektorer och trigonometri===
 
Sid 159-163.
 
== [[GeoGebra]] ==
 
Länken går till min sida med GeoGebra-grejor.
 
Jag vill att ni ska ladda ner programmet och börja lära er det. Vi kommer att lära oss tillsammans för jag är själv ingen fena på det.
 
Här finns [http://www.geogebrainstitut.se/resurser/resurser.asp en GeoGebrafil med addition av vektorer]. Lek med den och försök göra något med vektorer och trigonometri.
 
== Kunskapskontroll kapitel 3 ==
 
Tyvärr var inte resultaten på Diagnos 6 och 7 tillräckligt bra för att vi ska kunna känna oss helt klara. Ni kommer därför att få en uppgift som ni ska göra individuellt och lämna in. Ni får göra den hemma eller i skolan på er lediga tid. Det är lämpligt att ni samarbetar. Uppgiften är att du ska lämna in snygga fullständiga lösningar på diagnos 6 och 7. Detta ska vara klart senast fredagen den 11 november.
 
Ni kan få papper på måndag men [[Media:Veckodiagnos_6_i_matematik_1c.pdf|Diagnos sex finns här]] och [[Media:Veckodiagnos_7_version2.pdf|Diagnos 7 finns här]] om du vill börja med en gång.
 
Detta är en kombination av hemtenta och samarbetsövning.
 
'''Uppgiften:''' Du ska göra om diagnos 6 och 7. Du kan jobba hemma eller på rasterna i skolan. Du ska jobba själv men ni får gärna samarbeta. Det är inget problem om det kommer in liknade lösningar men jag accepterar inga exakta kopior.
 
'''Krav för godkänt:''' Minst åtta poäng på varje diagnos. Extraberöm för snygga lösningar.
 
'''Mål:'''
* Ni ska kunna geometrin
* Ni ska öva er på att samarbeta och repetera med hjälp av boken.
* Ni ska upptäcka fördelarna med att plugga tillsammans
 
'''Snygga lösningar:'''
* Skriv alla dina lösningar på rutade papper i A4-format.
* Skriv ditt namn på varje blad. Skriv lösningens nummer.
* Använd luftiga marginaler.
* Ha luft mellan uppgifterna.
* Skriv av det viktiga från uppgiften.
* Använd figurer.
* Förklara vilka satser och formler du använder
* Redovisa dina beräkningar
* Stryk under svaret eller skriv "Svar:"


= Kapitel 4 - [[Samband och förändring]] =
= Kapitel 4 - [[Samband och förändring]] =

Versionen från 9 december 2011 kl. 08.58

Matte på öppet hus

Ämnesövergripande samarbete matematik engelska

exempel på film på Khan där man kan välja och editera undertexter.

Allmänt

Grovplanering

TEINF11 Matematik 1c, period 1, 2 (4 lekt/vecka)

Vi använder Libers matematikbok Matematik M1c, av Sjunnesson, Holmström, Smedhamre. Innehållsrubrikerna nedan är kapitel i boken.

Vecka	Innehåll
34-36	 Taluppfattning och aritmetik	
37-40	 Agebra och ekvationer
41-42	Geometri
43	MD+  Geometri
44	Höstlov	 
45-47	Samband och förändring	 
48-50	Sannolikhet och statistik
51-1	Jullov

Extramatte

Mål

Repetera det som hänt under veckan så att du hänger med.

Hur

Lösa alla svarta uppgifter. Prata om de svårigheter som kan ha varit.

Mål

Repetera grunder

Hur

Testerna i boken

  • Jobba metodiskt med ett avsnitt i taget.
  • Interaktiva uppgifter finns på denna sida.

Miniräknare


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.

Tidigare var miniräknaren nödvändig på nationella provet men från och med i år är det tillåtet att använda datorn på nationella provet.

Vi behöver göra vissa begränsningar av datorns kommunikationsförmåga under provet:

  • Nätverket stängs eller får nytt lösenord den aktuella dagen.
  • Du stänger skype, msn, facebook.
  • Du stänger ner nätverket och Bluetooth på din dator.
  • Du ser till att inte öppna anteckningar eller sådant som kan uppfattas som fusklappar.
  • Du sitter med skärmen fullt synlig och provvakten sitter bakom eleverna så det blir fullt synligt vad som görs på datorn.

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.

Miniräknare i datorn:

  • kalkylatorn i Windows, start - program - tillbehör
  • WolframAlpha.org
  • GeoGebra
  • Excel
  • Google Docs - kalkylark
  • http://www.widgetbox.com/ som du ser ovan

Kapitel 1 - Taluppfattning och Aritmetik

Kapitel 2 - Algebra

Kapitel 3 - Geometri

Kapitel 4 - Samband och förändring

Kapitel 5 - Sannolikhet och statistik

Kapitel 5 handlar om Sannolikhet och statistik och består av nio delar (en del har teori, exempel och uppgifter).

5.1 Hur stor är chansen?

Intro

Khan Academy om Probability

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.

Sidorna 244-248

fre - hemdiagnos denna fredag.

Definition:

Sannolikheten för en händelse = antalet gynnsamma utfall / antal möjliga utfall
med P(A) menas sannolikheten för att händelse A ska inträffa.
A kan bestå av flera händelser, exempel vis att slå över tre på en tärning.
P(A eller B) = P(A) + P(B)

5.2 Oberoende händelser

Sidorna 249-251

fre

exempel 1, sid 249

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Kolla gärna Mikael Bondestam som förklarar kast med två tärningar = sannolikhet vid oberoende händelser:


Här kommer en bild som är lämplig att projicera och sedan rita på om man diskuterar sannolikheter vid två tärningsslag:
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Khan Academy

Däremot får alla gå in en kort stund på 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

Sidorna 252-255

Khan om oberoende händelser i flera steg:

Sedan en kul grej bara.

Rulla tärning från http://www.geogebratube.org/student/m712:

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Mikael Bondestam om träddiagram för händelser i flera steg:

Beroende händelser i flera steg, 256-258

ti

MB

Komplementhändelse, 259-260

ti

De Meres problem

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Repetition inför provet

onsdag

Några lösningar till uppgifter vi gjorde på sista lektionen.

Khan Academy

Veckodiagnos 10

Detta är en lösning till uppgift 4 på veckodiagnos 10.

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Prov kapitel fyra samt mindre delar av 3 och 5

fredag

Lösningar till provet

Provgränser

  • Betyg E krävs 12 poäng
  • Betyg C krävs dessutom 6 C-poäng
  • Betyg A krävs 11 C-poäng och 3 A-poäng

5.4 Hur ofta inträffar en händelse?

Relativ frekvens

Sid 262-264

Intro från: GGBtube. DubFet textbelklicka för att se hela simuleringen.

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Sidorna 261-266

ons

Här är det lämpligt med några laborationer. Kanske olika uppgifter som gruperna får redovisa på nätet.

5.5 Statistik i samhälle och vetenskap

Sidorna 267-275

fre

Här kan man tänka sig att eleverna gör egna undersökningar och redovisar...

Medelvärde och standardavvikelse

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Fri att använda. Från GeoGebraInstitutet

Gapminder - övning

www.gapminder.org

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.

Praktiskt experiment för att testa om det stämmer.

Redovisa

http://sv.wikipedia.org/wiki/Monty_Hall-problemet

5.6 Vilseledande statistik

Sidorna 276-277

5.7 Några statistiska lägesmått

Sidorna 278-282

ti

Nationellt prov Ma1C - Onsdagen den 14 december

Behovet av repetition gör att vi kan senarelägga avsnitt 5.6 och 5.7

Muntligt Nationellt prov

Egna undersökningar och gruppövningar

  • Sannolikheterna bakom "Kasta gris"
  • GapMinder