Änderungen von Dokument BPE 3.1 Eigenschaften und Formen
Zuletzt geändert von Martina Wagner am 2025/07/15 06:46
Von Version 112.1
bearbeitet von Holger Engels
am 2024/12/18 12:40
am 2024/12/18 12:40
Änderungskommentar:
Neues Bild 4-fach.svg hochladen
Auf Version 138.1
bearbeitet von Holger Engels
am 2025/02/18 17:58
am 2025/02/18 17:58
Änderungskommentar:
Neuen Anhang Arithmagon Quadratische Formen.pdf hochladen
Zusammenfassung
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Seiteneigenschaften (1 geändert, 0 hinzugefügt, 0 gelöscht)
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Anhänge (3 geändert, 7 hinzugefügt, 0 gelöscht)
Details
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- Inhalt
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... ... @@ -13,14 +13,33 @@ 13 13 Input: Vorgegebene Schaubilder vergleichen (Gemeinsamkeiten, Unterschiede) 14 14 "Beschreiben": Form 'fühlen' (Globalverhalten, Lokalverhalten); vgl. Buchstaben-Formen (N, W) Nulltellentypen (einfach vs mehrfach (gerade vs ungerade)) 15 15 16 +{{lehrende}} 17 +**Unterrichtsidee** [[Eingangsklasse.BPE_3_1.Stufenpyramiden zur Faktorisierung von Polynomfunktionen.WebHome]] 18 +{{/lehrende}} 19 + 16 16 {{lernende}} 17 17 [[Nullstellen und Vielfachheiten interaktiv>>https://kmap.eu/app/browser/Mathematik/Ganzrationale%20Funktionen/Produktform#erkunden]] 18 18 {{/lernende}} 19 19 20 -{{aufgabe id="Arithmagon Quadratische Formen" afb="I" kompetenzen="K4" quelle="Martina Wagner" cc="by-sa" zeit="5"}} 24 +{{aufgabe id="Vielfachheiten von Nullstellen" afb="I" kompetenzen="K4" quelle="Holger Engels" cc="by-sa" zeit="4"}} 25 +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]]. 26 +|[[image:3-fach.svg||width=100]]| |1-fach | 27 +|[[image:4-fach.svg||width=100]]| |2-fach | 28 +|[[image:2-fach.svg||width=100]]| |3-fach | 29 +|[[image:5-fach.svg||width=100]]| |4-fach | 30 +|[[image:1-fach.svg||width=100]]| |5-fach | 31 +{{/aufgabe}} 32 + 33 +{{aufgabe id="Arithmagon Quadratische Formen" afb="I" kompetenzen="K4, K5" quelle="Martina Wagner" cc="by-sa" zeit="5"}} 34 +Ermittle, welche Zahlen in die leeren Kästchen bei den Funktionsgleichungen eingetragen werden müssen. 21 21 [[image:Arithmagon Quadratische Formen.svg||width=500 style=float:left]] 22 22 {{/aufgabe}} 23 23 38 +{{aufgabe id="Arithmagon Darstellungsformen" afb="III" kompetenzen="K2, K4, K5" tags="problemlösen" quelle="Martina, Dirk, Caroline, Martin" cc="BY-SA" zeit="10"}} 39 +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. 40 +[[image:Arithmagon Polynomfunktion Formen.svg|| width=500]] 41 +{{/aufgabe}} 42 + 24 24 {{aufgabe id="Schaubilder zuordnen Teil 1" afb="II" kompetenzen="K4" quelle="Niklas Wunder, Katharina Schneider" cc="by-sa" zeit="5"}} 25 25 [[image:Polynome_zuordnen-Grad_drei.svg||width=500 style=float:right]]Ordne die Funktionsterme den 5 Schaubildern zu. Begründe deine Wahl. 26 26 (% style="list-style: alphastyle" %) ... ... @@ -77,21 +77,20 @@ 77 77 Hinweis: Die Funktion //f// besitzt nur die Nullstellen {{formula}} x_1 =-2, x_2=1 {{/formula}} und {{formula}} x_3 =3 {{/formula}}. 78 78 {{/aufgabe}} 79 79 80 -{{aufgabe id="Parabelmaschine" afb="II" kompetenzen="K2, K5" tags="problemlösen" quelle="Simon Oswald" cc="BY-SA" cc="by-sa" zeit="20"}} 81 -[[image:Parabelmaschine.PNG||width="240" style="float: right"]] 82 -Denke dir zwei Zahlen, eine positiv, eine negativ. 83 -Wenn du diese Zahlen quadrierst, erhältst du zwei Punkte auf der Normalparabel. 99 +{{aufgabe id="Parabelmaschine" afb="II" kompetenzen="K2, K5" tags="problemlösen" quelle="Simon Oswald" cc="by-sa" zeit="20"}} 100 +[[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. 84 84 85 85 Ermittle, wo die Verbindungslinie dieser zwei Punkte die y-Achse schneidet! 86 86 87 87 {{lehrende}} 88 -**Variante :** Offene Aufgabe für den Unterricht & für die Klassenarbeit 89 -Wo schneidet die Verbindungslinie dieser zwei Punkte die y-Achse? 105 +**Zusatzfrage:** Und wenn beide Zahlen positiv sind? 90 90 91 - Und wennbeideZahlenpositiv sind?107 +**Variante:** Aufgabe für die Klassenarbeit 92 92 93 - Zur Problemlösung legendirzweiMitschülerdieErgebnisse zweierLösungenvor.109 +Wo schneidet die Verbindungslinie dieser zwei Punkte die y-Achse? 94 94 111 +Zur Problemlösung legen dir zwei Mitschüler die Ergebnisse ihrer Lösungen vor. 112 + 95 95 Schüler 1: 96 96 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}}. 97 97 ... ... @@ -112,7 +112,6 @@ 112 112 {{/aufgabe}} 113 113 114 114 {{lehrende}} 115 -[[Polynomfunktionsgraphen begreifen]] 116 116 K3 soll hier nicht bedient werden .. das kommt in BPE 3.5 117 117 {{/lehrende}} 118 118
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- Arithmagon Polynomfunktion Formen.svg
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- Arithmagon Quadratische Formen Lösung.svg
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- Arithmagon Quadratische Formen.pdf
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- Vielfachheiten.ggb
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