Änderungen von Dokument BPE 3.1 Eigenschaften und Formen

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

Von 105.1 nach 106.1 Von 137.3 nach 138.1

Von Version 106.1

bearbeitet von Holger Engels
am 2024/12/18 09:29

Änderungskommentar: Löschung des Bildes Polynome_zuordnen-Grad_vier.png

Auf Version 137.3

bearbeitet von Holger Engels
am 2025/02/12 13:04

Änderungskommentar: Es gibt keinen Kommentar für diese Version

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@@ -7,10 +7,39 @@
  [[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))
++
++{{lehrende}}
++**Unterrichtsidee** [[Eingangsklasse.BPE_3_1.Stufenpyramiden zur Faktorisierung von Polynomfunktionen.WebHome]]
++{{/lehrende}}
++
  {{lernende}}
  [[Nullstellen und Vielfachheiten interaktiv>>https://kmap.eu/app/browser/Mathematik/Ganzrationale%20Funktionen/Produktform#erkunden]]
  {{/lernende}}
++{{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, K5" quelle="Martina Wagner" cc="by-sa" zeit="5"}}
++Ermittle, welche Zahlen in die leeren Kästchen bei den Funktionsgleichungen eingetragen werden müssen.
++[[image:Arithmagon Quadratische Formen.svg||width=500 style=float:left]]
++{{/aufgabe}}
++
++{{aufgabe id="Arithmagon Darstellungsformen" afb="III" kompetenzen="K2, K4, K5" tags="problemlösen" quelle="Martina, Dirk, Caroline, Martin" cc="BY-SA" zeit="10"}}
++Ermittle, welche Zahlen in die leeren Kästchen bei den Funktionsgleichungen eingetragen werden müssen und beschreibe in den blau hinterlegten Kästchen die Vorgehensweise für die Umwandlung in die andere Funktionsgleichung.
++[[image:Arithmagon Polynomfunktion Formen.svg|| width=500]]
++{{/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" %)
@@ -67,21 +67,20 @@
  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" 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.
++{{aufgabe id="Parabelmaschine" afb="II" kompetenzen="K2, K5" tags="problemlösen" quelle="Simon Oswald" cc="by-sa" zeit="20"}}
++[[image:Parabelmaschine.PNG||width="240" style="float: right"]]Denke dir zwei Zahlen, eine positive, eine negative. Wenn du diese Zahlen quadrierst, erhältst du zwei Punkte auf der Normalparabel.
  Ermittle, wo die Verbindungslinie dieser zwei Punkte die y-Achse schneidet!
  {{lehrende}}
--**Variante :** Offene Aufgabe für den Unterricht & für die Klassenarbeit
--Wo schneidet die Verbindungslinie dieser zwei Punkte die y-Achse?
++**Zusatzfrage:** Und wenn beide Zahlen positiv sind?
--Und wenn beide Zahlen positiv sind?
++**Variante:** Aufgabe für die Klassenarbeit
--Zur Problemlösung legen dir zwei Mitschüler die Ergebnisse zweier Lösungen vor.
++Wo schneidet die Verbindungslinie dieser zwei Punkte die y-Achse?
++Zur Problemlösung legen dir zwei Mitschüler die Ergebnisse ihrer Lösungen vor.
++
  Schüler 1:
  Die Gerade durch die beiden Punkte {{formula}} P(a|a^2){{/formula}} und {{formula}}Q(b|b^2){{/formula}} schneidet die y-Achse bei {{formula}}S(0 | |a\cdot b|){{/formula}}.
@@ -102,7 +102,6 @@
  {{/aufgabe}}
  {{lehrende}}
--[[Polynomfunktionsgraphen begreifen]]
  K3 soll hier nicht bedient werden .. das kommt in BPE 3.5
  {{/lehrende}}

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Arithmagon Polynomfunktion Formen.svg

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Arithmagon Quadratische Formen Lösung.svg

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Arithmagon Quadratische Formen.svg

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