Änderungen von Dokument BPE 3.3 Zeichnen, Steigung, Steigungsdreieck, y-Achsenabschnitt
Zuletzt geändert von Verena Schmid am 2026/02/03 15:52
Von Version 71.1
bearbeitet von Verena Schmid
am 2026/02/03 15:30
am 2026/02/03 15:30
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Auf Version 52.1
bearbeitet von Martin Rathgeb
am 2025/07/08 11:14
am 2025/07/08 11:14
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Zusammenfassung
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... ... @@ -4,38 +4,41 @@ 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}} 11 11 12 12 Begründe, warum die rechts abgebildete Gerade weder {{formula}}g_1{{/formula}} noch {{formula}}g_2{{/formula}} darstellt. 13 -{{comment}} 13 + 14 +{{lehrende versteckt=1}} 14 14 Steigung und y-Achsenabschnitt aus der Geradengleichung und aus dem Schaubild ablesen 15 -{{/ comment}}16 +{{/lehrende}} 16 16 {{/aufgabe}} 17 17 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 -{{comment}} 19 +{{aufgabe id="Achse ergänzen" afb="II" quelle="Team Mathebrücke" kompetenzen="K2, K5" zeit="3"= cc="by-sa" tags="mathebrücke"}} 20 +[[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. 21 + 22 +{{lehrende versteckt=1}} 21 21 * Geraden zeichnen 22 22 * Umgang mit Koordinatensystem 23 -{{/ comment}}25 +{{/lehrende}} 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.29 +[[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.32 +1. Eine der beiden Geraden hat die Gleichung {{formula}}y=\frac{1}{4}x+1{{/formula}}. 33 +Zeichne das zugehörige Koordinatensystem ein. 32 32 1. Bestimme die Gleichung der zweiten Geraden. 33 -{{comment}} 34 -Rückwärtsaufgabe: Koordinatensystem an Schaubilder anpassen 35 -{{/comment}} 35 + 36 +{{lehrende versteckt=1}} 37 +Rückwärtsaufgabe: An Schaubilder Koordinatensystem anpassen 38 +{{/lehrende}} 36 36 {{/aufgabe}} 37 37 38 -{{aufgabe id="Zeichnen von Geraden" afb="II" quelle="Team Mathebrücke" kompetenzen="K4, K5" zeit=" 7" tags="mathebrücke"}}41 +{{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}} ... ... @@ -42,68 +42,87 @@ 42 42 1. {{formula}}a=-1{{/formula}} 43 43 1. {{formula}}a=\frac{1}{2}{{/formula}} 44 44 1. {{formula}}a=-\frac{3}{4}{{/formula}} 45 -{{comment}} 48 + 49 +{{lehrende versteckt=1}} 46 46 * Geradengleichung in Hauptform bringen 47 47 * Geraden zeichnen 48 -{{/ comment}}52 +{{/lehrende}} 49 49 {{/aufgabe}} 50 50 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}} 55 +{{aufgabe id="Folge ungenauen Zeichnens" afb="II" quelle="Team Mathebrücke" kompetenzen="K2, K5" zeit="4" cc="by-sa" tags="mathebrücke"}} 56 +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. 57 +Ermittle, wie groß ist die Abweichung bei {{formula}}x = 10{{/formula}} ist? 56 56 57 -{{aufgabe id="Folge ungenauen Zeichnens" afb="III" quelle="Team Mathebrücke" kompetenzen="K2,K4, K5" zeit="4" cc="by-sa" tags="mathebrücke"}} 58 -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. 59 -Ermittle, wie groß ist die Abweichung bei {{formula}}x = 10{{/formula}} ist. 60 -{{comment}} 59 +{{lehrende versteckt=1}} 61 61 * Fehlerursachen und Fehlerfortpflanzung verstehen 62 62 * Mit Geraden umgehen 63 63 * Eine Lösungsstrategie entwickeln 64 -{{/ comment}}63 +{{/lehrende}} 65 65 {{/aufgabe}} 66 66 67 -{{aufgabe id="Achsen beschriften" afb="I" quelle="Team Mathebrücke" kompetenzen="K 4, K5" zeit="6" cc="by-sa" tags="mathebrücke"}}66 +{{aufgabe id="Achsen beschriften" afb="III" quelle="Team Mathebrücke" kompetenzen="K2, K5" zeit="6" cc="by-sa" tags="mathebrücke"}} 68 68 [[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. 69 -{{comment}} 68 + 69 +{{lehrende versteckt=1}} 70 70 * Aus der Geradengleichung Informationen wie z.B. y-Achsenabschnitt, Steigung ablesen und geometrisch umsetzen 71 -{{/ comment}}71 +{{/lehrende}} 72 72 {{/aufgabe}} 73 73 74 -{{aufgabe id="Zeichnen von Geraden 2" afb="III" quelle="Team Mathebrücke" kompetenzen="K 2,K4, K5" zeit="8" cc="by-sa" tags="mathebrücke"}}74 +{{aufgabe id="Zeichnen von Geraden 2" afb="III" quelle="Team Mathebrücke" kompetenzen="K4, K5" zeit="8" cc="by-sa" tags="mathebrücke"}} 75 75 Zeichne die Gerade mit der Gleichung {{formula}}a\cdot x+2y=5{{/formula}} für 76 + 76 76 (% class=abc %) 77 77 1. {{formula}}a=1{{/formula}} 78 78 1. {{formula}}a=-1{{/formula}} 79 79 1. {{formula}}a=2{{/formula}} 80 80 1. {{formula}}a=0{{/formula}} 81 -{{comment}} 82 + 83 +{{lehrende versteckt=1}} 82 82 * Geradengleichung in Hauptform bringen 83 83 * Geraden zeichnen 84 -{{/comment}} 86 +{{/lehrende}} 87 + 85 85 {{/aufgabe}} 86 86 87 -{{aufgabe id="Koordinatensystem zeichnen" afb="III" quelle="Team Mathebrücke" kompetenzen="K2, K 4" zeit="5" cc="by-sa" tags="mathebrücke"}}90 +{{aufgabe id="Koordinatensystem zeichnen" afb="III" quelle="Team Mathebrücke" kompetenzen="K2, K5" zeit="5" cc="by-sa" tags="mathebrücke"}} 88 88 [[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. 89 -{{comment}} 92 + 93 +{{lehrende versteckt=1}} 90 90 * Bedeutung des Koordinatensystems verstehen 91 91 * Steigung, y-Achsenabschnitt aus Gleichung ablesen und zeichnerisch umsetzen 92 -{{/ comment}}96 +{{/lehrende}} 93 93 {{/aufgabe}} 94 94 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. 99 +{{aufgabe id="Zuordnungsaufgabe Funktionsterm und Schaubild" afb="II" quelle="Team Mathebrücke" kompetenzen="K4,K5" cc="by-sa" tags="mathebrücke" zeit="7"}} 100 +Ordne den Schaubildern zu: 101 +a) {{formula}}y=-\frac{3}{4}x+2{{/formula}} b) {{formula}}y=\frac{1}{3}x{{/formula}} c) {{formula}}y=-\frac{4}{3}x+2{{/formula}} d) {{formula}}y=3x{{/formula}} 102 + 103 +(% class="border" style="width:70%" %) 104 +|1) [[image:4.png||width="250"]]|2)[[image:2.png||width="250"]] 105 +|3) [[image:3.png||width="250"]]|4) [[image:1.png||width="250"]] 106 + 107 +{{lehrende versteckt=1}} 108 +Zusammenhang Schaubild und Funktionsterm 109 +{{/lehrende}} 100 100 {{/aufgabe}} 101 101 102 -{{lehrende}} 103 -Gleichung von Geraden bestimmen ist redundant mit [[BPE 3.5 Aufstellen von Funktionstermen>>BPE_3_5]] 104 -Folgende Aufgabentypen könnten hier ergänzt werden: 105 -* Steigungsdreiecke einzeichnen und Steigung ablesen 106 -* Gleichung zu Schaubild bestimmen 112 +{{aufgabe id="Geradenbüschel" afb="II" quelle="Team Mathebrücke" kompetenzen="K1,K4,K5,K6" cc="by-sa" tags="mathebrücke" zeit="11"}} 113 +[[image:Geradenbüschel.PNG||width="350" style="display:block;margin-left:auto;margin-right:auto"]] 114 +Im obigen Koordinatensystem sind verschiedene Geraden eingezeichnet. 115 +(%class=abc%) 116 +1. Nenne eine Gemeinsamkeit aller dieser Geraden. 117 +1. Gib zu drei dieser Geraden die zugehörige Gleichung an. 118 +1. Wie lautet die Gleichung der Parallelen zur x-Achse bzw. zur y-Achse in diesem Bündel? 119 +1. Welche der beiden Gleichungen aus c) beschreibt keine Funktion? Begründe. 120 + 121 +{{lehrende versteckt=1}} 122 +**Sinn dieser Aufgabe:** 123 +* Ablesen der Steigungen über Steigungsdreiecke 124 +* Aufstellen von Geradengleichungen wiederholen 125 +* Erinnerung des Funktionsbegriffs 107 107 {{/lehrende}} 127 +{{/aufgabe}} 108 108 109 -{{seitenreflexion bildungsplan="5" kompetenzen="5" anforderungsbereiche="4" kriterien="5" menge="5"/}} 129 + 130 + 131 +{{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
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