Änderungen von Dokument BPE 3.3 Zeichnen, Steigung, Steigungsdreieck, y-Achsenabschnitt
Zuletzt geändert von Verena Schmid am 2026/02/03 15:52
Von Version 59.1
bearbeitet von Holger Engels
am 2025/11/27 11:37
am 2025/11/27 11:37
Änderungskommentar:
Es gibt keinen Kommentar für diese Version
Auf Version 72.1
bearbeitet von Cinzia Moser
am 2026/02/03 16:48
am 2026/02/03 16:48
Änderungskommentar:
Neues Bild Lösung 1.jpg hochladen
Zusammenfassung
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... ... @@ -1,1 +1,1 @@ 1 -XWiki. holgerengels1 +XWiki.mr79 - 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, K4 , K5" zeit="4" tags="mathebrücke"}}7 +{{aufgabe id="Darstellung von Geraden" afb="I" quelle="Team Mathebrücke" kompetenzen="K1, K4" zeit="4" 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 I" quelle="Team Mathebrücke" kompetenzen="K2, K4" zeit="3" tags="mathebrücke"}}19 -[[image:Achse ergänzen.svg||width="400" style="float: right"]]Zeichne die fehlende x-Achse ein und bestimme eine Beschriftung fürdieKoordinatenachsen mit geeignetenEinheitenso,dass die eingezeichnete Gerade die Gleichung {{formula}} y=\frac{1}{3}x+3{{/formula}} hat.18 +{{aufgabe id="Achse ergänzen" afb="I" quelle="Team Mathebrücke" kompetenzen="K2, K4" zeit="3" tags="mathebrücke"}} 19 +[[image:Achse ergänzen.svg||width="400" style="float: right"]]Zeichne die fehlende x-Achse ein und bestimme eine passende Skalierung, sodass 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 mnachfolgendenGitternetzsind zwei Geraden dargestellt.27 +[[image:Achsen ergänzen.svg||width="400" style="float: right"]]In nebenstehender Abbildung sind zwei Geraden dargestellt. 28 28 29 29 (% class=abc %) 30 - 1.Eine der beiden Geraden hat die Gleichung {{formula}}y=\frac{1}{4}x+1{{/formula}}.31 -Zeichne das zugehörige Koordinatensystem ein.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. Zeichne ein mögliches zugehörendes Koordinatensystem mit Achsenskalierung ein. 32 32 1. Bestimme die Gleichung der zweiten Geraden. 33 33 {{comment}} 34 -Rückwärtsaufgabe: An SchaubilderKoordinatensystem anpassen34 +Rückwärtsaufgabe: Koordinatensystem an Schaubilder anpassen 35 35 {{/comment}} 36 36 {{/aufgabe}} 37 37 38 -{{aufgabe id="Zeichnen von Geraden" afb="I" 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="7" 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}} ... ... @@ -48,7 +48,13 @@ 48 48 {{/comment}} 49 49 {{/aufgabe}} 50 50 51 -{{aufgabe id="Folge ungenauen Zeichnens" afb="II" quelle="Team Mathebrücke" kompetenzen="K4, K5" zeit="4" cc="by-sa" tags="mathebrücke"}} 51 +{{aufgabe id="Heißluftballon" afb="II" quelle="Cinzia Moser, Verena Schmid" kompetenzen="K3,K4, K5" zeit="6" cc="by-sa"}} 52 +Ein roter Heißluftballon in 800m Höhe beginnt mit dem Sinkflug. Nach 20 Minuten ist der Ballon am Boden aufgekommen. 53 +Stelle das Ereignis in einem Schaubild dar und ermittle die passende Funktionsgleichung. 54 +Ein blauer Heißluftballon setzt ebenfalls zur Landung an, dieser landet bei gleicher Geschwindigkeit nach 15 Minuten. In welcher Höhe startete der blaue Ballon das Sinkmanöver? Begründe mit einer passenden Darstellungsmethode. 55 +{{/aufgabe}} 56 + 57 +{{aufgabe id="Folge ungenauen Zeichnens" afb="III" quelle="Team Mathebrücke" kompetenzen="K2,K4, K5" zeit="4" cc="by-sa" tags="mathebrücke"}} 52 52 Achim zeichnet die Gerade mit der Gleichung {{formula}}y = 0,8 x + 2{{/formula}} recht ungenau in ein Koordinatensystem mit der Längeneinheit //1 cm//. Den y-Achsenabschnitt hat er noch genau eingezeichnet, bei {{formula}}x = 3{{/formula}} liegt der gezeichnete Punkt schon //0,1 cm// zu hoch. 53 53 Ermittle, wie groß ist die Abweichung bei {{formula}}x = 10{{/formula}} ist. 54 54 {{comment}} ... ... @@ -58,7 +58,7 @@ 58 58 {{/comment}} 59 59 {{/aufgabe}} 60 60 61 -{{aufgabe id="Achsen beschriften" afb="I" quelle="Team Mathebrücke" kompetenzen="K 2, K4" zeit="6" cc="by-sa" tags="mathebrücke"}}67 +{{aufgabe id="Achsen beschriften" afb="I" quelle="Team Mathebrücke" kompetenzen="K4, 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 ... ... @@ -65,7 +65,7 @@ 65 65 {{/comment}} 66 66 {{/aufgabe}} 67 67 68 -{{aufgabe id="Zeichnen von Geraden 2" afb="I" quelle="Team Mathebrücke" kompetenzen="K4, K5" zeit="8" cc="by-sa" tags="mathebrücke"}} 74 +{{aufgabe id="Zeichnen von Geraden 2" afb="III" quelle="Team Mathebrücke" kompetenzen="K2,K4, K5" zeit="8" cc="by-sa" tags="mathebrücke"}} 69 69 Zeichne die Gerade mit der Gleichung {{formula}}a\cdot x+2y=5{{/formula}} für 70 70 (% class=abc %) 71 71 1. {{formula}}a=1{{/formula}} ... ... @@ -86,6 +86,13 @@ 86 86 {{/comment}} 87 87 {{/aufgabe}} 88 88 95 +{{aufgabe id="Geradengleichungen bestimmen" afb="III" quelle="Cinzia Moser" kompetenzen="K1,K2,K5,K6" zeit="15" cc="by-sa"}} 96 +[[image:Bild3||width="400" style="float: right"]] 97 +(%class="abc"%) 98 +1. Bestimme die Geradengleichungen aus dem Schaubild. 99 +1. Erläutere, bei welchen Geradengleichungen es sich um einen funktionalen Zusammenhang handelt. Begründe deine Entscheidung. 100 +{{/aufgabe}} 101 + 89 89 {{lehrende}} 90 90 Gleichung von Geraden bestimmen ist redundant mit [[BPE 3.5 Aufstellen von Funktionstermen>>BPE_3_5]] 91 91 Folgende Aufgabentypen könnten hier ergänzt werden: ... ... @@ -93,4 +93,4 @@ 93 93 * Gleichung zu Schaubild bestimmen 94 94 {{/lehrende}} 95 95 96 -{{seitenreflexion bildungsplan=" 4" kompetenzen="3" anforderungsbereiche="3" kriterien="5" menge="2"/}}109 +{{seitenreflexion bildungsplan="5" kompetenzen="4" anforderungsbereiche="5" kriterien="5" menge="5"/}}
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... ... @@ -1,0 +1,1 @@ 1 +XWiki.mr79 - Größe
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