Änderungen von Dokument BPE 3.1 Eigenschaften und Formen

Zuletzt geändert von Holger Engels am 2025/04/09 13:57

Von 91.1 nach 92.1 Von 120.1 nach 121.1

Von Version 92.1

bearbeitet von Holger Engels
am 2024/12/17 18:01

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Auf Version 120.1

bearbeitet von Holger Engels
am 2024/12/18 14:18

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@@ -2,15 +2,36 @@
  [[Kompetenzen.K5]] Ich kenne die allgemeine Form der Polynomfunktion
  [[Kompetenzen.K4]] Ich kenne die Produktform der Polynomfunktion
--[[Kompetenzen.K3]] [[Kompetenzen.K4]] Ich kann die für den Anwendungsfall geeignete Darstellungsform wählen
--[[Kompetenzen.K1]] [[Kompetenzen.K4]] Ich kann die Wahl der Darstellungsform im Anwendungskontext begründen
++[[Kompetenzen.K4]] Ich kenne die Scheitelform der quadratischen Funktion [[→ BPE 2.2>>BPE_2_2]]
++[[Kompetenzen.K4]] Ich kann Polynomfunktionen mithilfe unterschiedlicher Darstellungsformen beschreiben
++[[Kompetenzen.K1]] [[Kompetenzen.K6]] Ich kann die Wahl der Form im mathematischen Kontext begründen
++[[Kompetenzen.K1]] [[Kompetenzen.K3]] [[Kompetenzen.K6]] Ich kann die Wahl der Form im anwendungsorientierten Kontext begründen [[→ BPE 3.5>>BPE_3_5]]
++Wiederholen (qF): Darstellungsformen von quadratischen Funktionen (SF, PF, HF)
++Wiederholen (qF): Eingehen auf verschiedene Eigenschaften (Vorteile, Nachteile) der DF
++Kennen: algebraische DF von PF, HF von Polynomfunktionen
++Input: Vorgegebene Schaubilder vergleichen (Gemeinsamkeiten, Unterschiede)
++"Beschreiben": Form 'fühlen' (Globalverhalten, Lokalverhalten); vgl. Buchstaben-Formen (N, W) Nulltellentypen (einfach vs mehrfach (gerade vs ungerade))
++
  {{lernende}}
  [[Nullstellen und Vielfachheiten interaktiv>>https://kmap.eu/app/browser/Mathematik/Ganzrationale%20Funktionen/Produktform#erkunden]]
  {{/lernende}}
--{{aufgabe id="Schaubilder zuordnen Teil 1" afb="II" kompetenzen="K4" quelle="Niklas Wunder, Katharina Schneider" zeit="5"}}
--[[image:geogebra_polynome_dritten_Grades.png||width=600 style=float:right]]Ordne die Funktionsterme den 5 Schaubildern zu. Begründe deine Wahl.
++{{aufgabe id="Vielfachheiten von Nullstellen" afb="I" kompetenzen="K4" quelle="Holger Engels" cc="by-sa" zeit="4"}}
++Ordne zu und schreibe dahinter jeweils "schneidet", "berührt" "schmiegt sich an", wobei //Anschmiegen// und //Schneiden// miteinander vereinbar sind, //Berühren// und //Schneiden// jedoch nicht. Siehe [[Vielfachheiten von Schnittstellen>>Glossar.WebHome||anchor=HVielfachheitenvonSchnittstellen]].
++|[[image:3-fach.svg||width=100]]|    |1-fach    |
++|[[image:4-fach.svg||width=100]]|    |2-fach    |
++|[[image:2-fach.svg||width=100]]|    |3-fach    |
++|[[image:5-fach.svg||width=100]]|    |4-fach    |
++|[[image:1-fach.svg||width=100]]|    |5-fach    |
++{{/aufgabe}}
++
++{{aufgabe id="Arithmagon Quadratische Formen" afb="I" kompetenzen="K4" quelle="Martina Wagner" cc="by-sa" zeit="5"}}
++[[image:Arithmagon Quadratische Formen.svg||width=500 style=float:left]]
++{{/aufgabe}}
++
++{{aufgabe id="Schaubilder zuordnen Teil 1" afb="II" kompetenzen="K4" quelle="Niklas Wunder, Katharina Schneider" cc="by-sa" zeit="5"}}
++[[image:Polynome_zuordnen-Grad_drei.svg||width=500 style=float:right]]Ordne die Funktionsterme den 5 Schaubildern zu. Begründe deine Wahl.
  (% style="list-style: alphastyle" %)
 . {{formula}}f_1(x)=x^3{{/formula}}
 . {{formula}}f_2(x)=-x^2\cdot(x-3){{/formula}}
@@ -19,11 +19,11 @@
 . {{formula}}f_5(x)=-x^3-2\,x^2+2{{/formula}}
  {{/aufgabe}}
--{{aufgabe id="Schaubilder zuordnen Teil 2" afb="II" kompetenzen="K4" quelle="Niklas Wunder, Katharina Schneider" zeit="5"}}
--[[image:Polynome_zuordnen-Grad_vier.png||width=600 style="float:right"]]Ordne die Funktionsterme den 5 Schaubildern zu. Begründe deine Wahl.
++{{aufgabe id="Schaubilder zuordnen Teil 2" afb="II" kompetenzen="K4" quelle="Niklas Wunder, Katharina Schneider" cc="by-sa" zeit="5"}}
++[[image:Polynome_zuordnen-Grad_vier.svg||width=500 style="float:right"]]Ordne die Funktionsterme den 5 Schaubildern zu. Begründe deine Wahl.
  (% style="list-style: alphastyle" %)
 . {{formula}}f_1(x)=-0{,}25\,x^4{{/formula}}
--1. {{formula}}f_2(x)=-0{,}5\,x^4-1{,}5\,x^3-1{,}5\,x^2-1{{/formula}}
++1. {{formula}}f_2(x)=-0{,}5\,x^4-1{,}5\,x^3-1{,}5\,x^2+1{{/formula}}
 . {{formula}}f_3(x)=-x^4{{/formula}}
 . {{formula}}f_4(x)=-x^4-x^3+2x^2+2{{/formula}}
 . {{formula}}f_5(x)=-0{,}3\cdot (x+2)^2\cdot(x-2)^2+4{{/formula}}
@@ -34,14 +34,7 @@
  [[image:Graphen Produktform.png||width=600]]
  {{/aufgabe}}
--{{aufgabe id="Skizzieren" afb="I" kompetenzen="K4" quelle="Juliane Maier" cc="BY-SA"}}
--Gegeben ist die Funktion {{formula}}f{{/formula}} mit {{formula}}D=\mathbb{R}{{/formula}}. Skizziere den Funktionsgraphen.
--(% class="abc" %)
--1. {{formula}}f(x)=(x-2)^3{{/formula}}
--1. {{formula}}f(x)=x^4-x^2{{/formula}}
--{{/aufgabe}}
--
--{{aufgabe id="Immer, manchmal, nie" afb="III" kompetenzen="K1,K5" quelle="Niklas Wunder, Katharina Schneider" zeit="12"}}
++{{aufgabe id="Immer, manchmal, nie" afb="III" kompetenzen="K1,K5" quelle="Niklas Wunder, Katharina Schneider" cc="by-sa" zeit="12"}}
  Beurteile, ob die folgenden Aussagen immer, nie oder manchmal unter bestimmten Bedingungen zutreffen. Begründe deine Entscheidung.
  (% style="list-style: alphastyle" %)
 . Der Graph von {{formula}}f{{/formula}} mit {{formula}}f(x)=-3\cdot x^n {{/formula}} verläuft für ein gerades n von links unten nach rechts unten.
@@ -52,8 +52,16 @@
 . Durch die beiden Punkte P(-2|1) und Q(2|2) verläuft kein Graph einer Funktion vierten Grades.
  {{/aufgabe}}
++{{aufgabe id="Vieta" afb="II" kompetenzen="K2,K5" quelle="Martin Rathgeb, Martina Wagner" cc="BY-SA" zeit="10"}}
++Ermittle die fehlenden Zahlen bzw. Terme.
++(% class="abc" %)
++1. {{formula}}x^2+\square x + \square=(x-5)(x+7){{/formula}}
++1. {{formula}}x^2+\square x - 12=(x-4)(x-\square){{/formula}}
++1. {{formula}}x^2-12 x + \square=(x-4)(x-\square){{/formula}}
++1. {{formula}}x^2+\square x + \square=(x-a)(x-b){{/formula}}
++{{/aufgabe}}
--{{aufgabe id="Darstellungsformen umwandeln" afb="II" kompetenzen="K5" quelle="Niklas Wunder, Katharina Schneider" zeit="15"}}
++{{aufgabe id="Darstellungsformen umwandeln" afb="II" kompetenzen="K5" quelle="Niklas Wunder, Katharina Schneider" cc="by-sa" zeit="15"}}
  Wandle in die entsprechend andere Darstellungsform um (Hauptform bzw. Produktform).
  (% style="list-style: alphastyle" %)
 . {{formula}}f(x)=-\frac{1}{16}\cdot (x-2)^2\cdot (x-8){{/formula}}
@@ -64,12 +64,12 @@
  Hinweis: Die Funktion //f// besitzt nur die Nullstellen {{formula}} x_1 =-2, x_2=1 {{/formula}} und {{formula}} x_3 =3 {{/formula}}.
  {{/aufgabe}}
--{{aufgabe id="Parabelmaschine" afb="II" kompetenzen="K2, K5" tags="problemlösen" quelle="Simon Oswald" cc="BY-SA" zeit="20"}}
++{{aufgabe id="Parabelmaschine" afb="II" kompetenzen="K2, K5" tags="problemlösen" quelle="Simon Oswald" cc="BY-SA" cc="by-sa" zeit="20"}}
  [[image:Parabelmaschine.PNG||width="240" style="float: right"]]
  Denke dir zwei Zahlen, eine positiv, eine negativ.
  Wenn du diese Zahlen quadrierst, erhältst du zwei Punkte auf der Normalparabel.
--Ermitteln Sie, wo die Verbindungslinie dieser zwei Punkte die y-Achse schneidet!
++Ermittle, wo die Verbindungslinie dieser zwei Punkte die y-Achse schneidet!
  {{lehrende}}
  **Variante :** Offene Aufgabe für den Unterricht & für die Klassenarbeit
@@ -100,6 +100,7 @@
  {{lehrende}}
  [[Polynomfunktionsgraphen begreifen]]
++K3 soll hier nicht bedient werden .. das kommt in BPE 3.5
  {{/lehrende}}
--{{seitenreflexion bildungsplan="4" kompetenzen="2" anforderungsbereiche="3" kriterien="1" menge="0"/}}
++{{seitenreflexion bildungsplan="4" kompetenzen="4" anforderungsbereiche="5" kriterien="4" menge="5"/}}

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Arithmagon Quadratische Formen.svg

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Vielfachheiten.ggb

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Änderungen von Dokument BPE 3.1 Eigenschaften und Formen

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