Änderungen von Dokument BPE 3.3 Zeichnen, Steigung, Steigungsdreieck, y-Achsenabschnitt
Zuletzt geändert von Verena Schmid am 2026/02/03 15:52
Von Version 69.2
bearbeitet von Verena Schmid
am 2026/02/03 15:09
am 2026/02/03 15:09
Änderungskommentar:
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Auf Version 58.2
bearbeitet von Holger Engels
am 2025/11/27 11:09
am 2025/11/27 11:09
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Zusammenfassung
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... ... @@ -1,1 +1,1 @@ 1 -XWiki.s c251 +XWiki.holgerengels - Inhalt
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... ... @@ -4,7 +4,7 @@ 4 4 [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann die Steigung und den y-Achsenabschnitt von Geraden bestimmen. 5 5 [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann Geraden in ein Koordinatensystem einzeichnen. 6 6 7 -{{aufgabe id="Darstellung von Geraden" afb="I" quelle="Team Mathebrücke" kompetenzen="K1, K 4" zeit="4" tags="mathebrücke"}}7 +{{aufgabe id="Darstellung von Geraden" afb="I" quelle="Team Mathebrücke" kompetenzen="K1, K5" zeit="3" cc="by-sa" tags="mathebrücke"}} 8 8 [[image:Darstellung von Geraden.svg||width="400" style="float: right"]]Gegeben sind die Geraden {{formula}}g_1{{/formula}} und {{formula}}g_2{{/formula}}: 9 9 {{formula}}g_1: y=-\frac{1}{2}x+1{{/formula}} 10 10 {{formula}}g_2: 2y=x+1{{/formula}} ... ... @@ -15,8 +15,8 @@ 15 15 {{/comment}} 16 16 {{/aufgabe}} 17 17 18 -{{aufgabe id="Achse ergänzen" afb="I" quelle="Team Mathebrücke" kompetenzen="K2, K 4" zeit="3" tags="mathebrücke"}}19 -[[image:Achse ergänzen.svg||width="400" style="float: right"]]Zeichne die fehlende x-Achse ein und bestimme eine passendeSkalierung,sodass die eingezeichnete Gerade die Gleichung {{formula}} y=\frac{1}{3}x+3{{/formula}} hat.18 +{{aufgabe id="Achse ergänzen" afb="II" quelle="Team Mathebrücke" kompetenzen="K2, K5" zeit="3"= cc="by-sa" tags="mathebrücke"}} 19 +[[image:Achse ergänzen.svg||width="400" style="float: right"]]Zeichne die fehlende x-Achse ein und bestimme eine Beschriftung für die Koordinatenachsen mit geeigneten Einheiten so, dass die eingezeichnete Gerade die Gleichung {{formula}} y=\frac{1}{3}x+3{{/formula}} hat. 20 20 {{comment}} 21 21 * Geraden zeichnen 22 22 * Umgang mit Koordinatensystem ... ... @@ -24,18 +24,18 @@ 24 24 {{/aufgabe}} 25 25 26 26 {{aufgabe id="Achsen ergänzen" afb="II" quelle="Team Mathebrücke" kompetenzen="K2, K4, K5" zeit="5" cc="by-sa" tags="mathebrücke"}} 27 -[[image:Achsen ergänzen.svg||width="400" style="float: right"]]I nnebenstehenderAbbildungsind zwei Geraden dargestellt.27 +[[image:Achsen ergänzen.svg||width="400" style="float: right"]]Im nachfolgenden Gitternetz sind zwei Geraden dargestellt. 28 28 29 29 (% class=abc %) 30 -Eine der beiden Geraden hat die Gleichung {{formula}}y=\frac{1}{4}x+ 2{{/formula}}, die andere hat den y-Achsenabschnitt {{formula}}-4{{/formula}}.31 - 1.Zeichneein mögliches zugehörendesKoordinatensystemmit Achsenskalierung ein.30 +1. Eine der beiden Geraden hat die Gleichung {{formula}}y=\frac{1}{4}x+1{{/formula}}. 31 +Zeichne das zugehörige Koordinatensystem ein. 32 32 1. Bestimme die Gleichung der zweiten Geraden. 33 33 {{comment}} 34 -Rückwärtsaufgabe: Koordinatensystem an Schaubilder anpassen34 +Rückwärtsaufgabe: An Schaubilder Koordinatensystem anpassen 35 35 {{/comment}} 36 36 {{/aufgabe}} 37 37 38 -{{aufgabe id="Zeichnen von Geraden" afb="II" quelle="Team Mathebrücke" kompetenzen="K4, K5" zeit=" 7" tags="mathebrücke"}}38 +{{aufgabe id="Zeichnen von Geraden" afb="II" quelle="Team Mathebrücke" kompetenzen="K4, K5" zeit="5" cc="by-sa" tags="mathebrücke"}} 39 39 Zeichne die Gerade mit der Gleichung {{formula}}y=a\cdot(x-2)+3{{/formula}} für 40 40 (% class=abc %) 41 41 1. {{formula}}a=1{{/formula}} ... ... @@ -48,9 +48,9 @@ 48 48 {{/comment}} 49 49 {{/aufgabe}} 50 50 51 -{{aufgabe id="Folge ungenauen Zeichnens" afb="II I" quelle="Team Mathebrücke" kompetenzen="K4, K5" zeit="4" cc="by-sa" tags="mathebrücke"}}52 -Achim zeichnet die Gerade mit der Gleichung {{formula}}y = 0,8 x + 2{{/formula}} recht ungenau in ein Koordinatensystem mit der Längeneinheit //1//. Den y-Achsenabschnitt hat er noch genau eingezeichnet, bei {{formula}}x = 3{{/formula}} liegt der gezeichnete Punkt schon//0,1 cm//zu hoch.53 -Ermittle, wie groß ist die Abweichung bei {{formula}}x = 10{{/formula}} ist .51 +{{aufgabe id="Folge ungenauen Zeichnens" afb="II" quelle="Team Mathebrücke" kompetenzen="K2, K5" zeit="4" cc="by-sa" tags="mathebrücke"}} 52 +Achim zeichnet die Gerade mit der Gleichung {{formula}}y = 0,8 x + 2{{/formula}} recht ungenau in ein Koordinatensystem mit der Längeneinheit 1cm. Den y-Achsenabschnitt hat er noch genau eingezeichnet, bei {{formula}}x = 3{{/formula}} liegt der gezeichnete Punkt schon 0,1 cm zu hoch. 53 +Ermittle, wie groß ist die Abweichung bei {{formula}}x = 10{{/formula}} ist? 54 54 {{comment}} 55 55 * Fehlerursachen und Fehlerfortpflanzung verstehen 56 56 * Mit Geraden umgehen ... ... @@ -58,7 +58,7 @@ 58 58 {{/comment}} 59 59 {{/aufgabe}} 60 60 61 -{{aufgabe id="Achsen beschriften" afb="I" quelle="Team Mathebrücke" kompetenzen="K2, K 4" zeit="6" cc="by-sa" tags="mathebrücke"}}61 +{{aufgabe id="Achsen beschriften" afb="III" quelle="Team Mathebrücke" kompetenzen="K2, K5" zeit="6" cc="by-sa" tags="mathebrücke"}} 62 62 [[image:Achsen beschriften.svg||width="400" style="float: right"]]Bestimme eine Beschriftung für die Koordinatenachsen mit geeigneten Einheiten so, dass die eingezeichnete Gerade die Gleichung {{formula}}y=2x+1{{/formula}} hat. 63 63 {{comment}} 64 64 * Aus der Geradengleichung Informationen wie z.B. y-Achsenabschnitt, Steigung ablesen und geometrisch umsetzen ... ... @@ -78,7 +78,7 @@ 78 78 {{/comment}} 79 79 {{/aufgabe}} 80 80 81 -{{aufgabe id="Koordinatensystem zeichnen" afb="III" quelle="Team Mathebrücke" kompetenzen="K2, K 4" zeit="5" cc="by-sa" tags="mathebrücke"}}81 +{{aufgabe id="Koordinatensystem zeichnen" afb="III" quelle="Team Mathebrücke" kompetenzen="K2, K5" zeit="5" cc="by-sa" tags="mathebrücke"}} 82 82 [[image:Koordinatensystem zeichnen.svg||width="400" style="float: right"]]Zeichne die fehlenden Koordinatenachsen ein und bestimme die Einheiten an den Achsen so, dass die gegebene Gerade bezüglich dieses Koordinatensystems die Gleichung {{formula}}y=-x+1{{/formula}} hat. 83 83 {{comment}} 84 84 * Bedeutung des Koordinatensystems verstehen ... ... @@ -86,18 +86,9 @@ 86 86 {{/comment}} 87 87 {{/aufgabe}} 88 88 89 -{{aufgabe id="Geradengleichungen bestimmen" afb="III" quelle="Cinzia Moser" kompetenzen="K1,K2,K5,K6" zeit="15" cc="by-sa"}} 90 -[[image:Bild3||width="400" style="float: right"]] 91 -(%class="abc"%) 92 -1. Bestimme die Geradengleichungen aus dem Schaubild. 93 -1. Erläutere, bei welchen Geradengleichungen es sich um einen funktionalen Zusammenhang handelt. Begründe deine Entscheidung. 94 -{{/aufgabe}} 95 - 96 96 {{lehrende}} 97 -Gleichung von Geraden bestimmen ist redundant mit [[BPE 3.5 Aufstellen von Funktionstermen>>BPE_3_5]] 98 -Folgende Aufgabentypen könnten hier ergänzt werden: 99 -* Steigungsdreiecke einzeichnen und Steigung ablesen 100 -* Gleichung zu Schaubild bestimmen 90 +Es fehlt isoliert Steigung und y-Achsenabschnitt von Geraden bestimmen 91 +Gleichung von Geraden bestimmen wird in [[BPE 3.5>>BPE_3_5]] behandelt 101 101 {{/lehrende}} 102 102 103 -{{seitenreflexion bildungsplan="4" kompetenzen="3" anforderungsbereiche=" 3" kriterien="5" menge="2"/}}94 +{{seitenreflexion bildungsplan="4" kompetenzen="3" anforderungsbereiche="4" kriterien="5" menge="2"/}}
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