Änderungen von Dokument BPE 3.3 Zeichnen, Steigung, Steigungsdreieck, y-Achsenabschnitt
Zuletzt geändert von Verena Schmid am 2026/02/03 15:52
Von Version 54.1
bearbeitet von Martin Rathgeb
am 2025/07/11 00:36
am 2025/07/11 00:36
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Auf Version 71.1
bearbeitet von Verena Schmid
am 2026/02/03 15:30
am 2026/02/03 15:30
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... ... @@ -1,1 +1,1 @@ 1 -XWiki. martinrathgeb1 +XWiki.sc25 - Inhalt
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... ... @@ -4,41 +4,38 @@ 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 5" zeit="3"cc="by-sa"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}} 11 11 12 12 Begründe, warum die rechts abgebildete Gerade weder {{formula}}g_1{{/formula}} noch {{formula}}g_2{{/formula}} darstellt. 13 - 14 -{{lehrende versteckt=1}} 13 +{{comment}} 15 15 Steigung und y-Achsenabschnitt aus der Geradengleichung und aus dem Schaubild ablesen 16 -{{/ lehrende}}15 +{{/comment}} 17 17 {{/aufgabe}} 18 18 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}} 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}} 23 23 * Geraden zeichnen 24 24 * Umgang mit Koordinatensystem 25 -{{/ lehrende}}23 +{{/comment}} 26 26 {{/aufgabe}} 27 27 28 28 {{aufgabe id="Achsen ergänzen" afb="II" quelle="Team Mathebrücke" kompetenzen="K2, K4, K5" zeit="5" cc="by-sa" tags="mathebrücke"}} 29 -[[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. 30 30 31 31 (% class=abc %) 32 - 1.Eine der beiden Geraden hat die Gleichung {{formula}}y=\frac{1}{4}x+1{{/formula}}.33 -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. 34 34 1. Bestimme die Gleichung der zweiten Geraden. 35 - 36 -{{lehrende versteckt=1}} 37 -Rückwärtsaufgabe: An Schaubilder Koordinatensystem anpassen 38 -{{/lehrende}} 33 +{{comment}} 34 +Rückwärtsaufgabe: Koordinatensystem an Schaubilder anpassen 35 +{{/comment}} 39 39 {{/aufgabe}} 40 40 41 -{{aufgabe id="Zeichnen von Geraden" afb="II" quelle="Team Mathebrücke" kompetenzen="K4, K5" zeit=" 5"cc="by-sa"tags="mathebrücke"}}38 +{{aufgabe id="Zeichnen von Geraden" afb="II" quelle="Team Mathebrücke" kompetenzen="K4, K5" zeit="7" tags="mathebrücke"}} 42 42 Zeichne die Gerade mit der Gleichung {{formula}}y=a\cdot(x-2)+3{{/formula}} für 43 43 (% class=abc %) 44 44 1. {{formula}}a=1{{/formula}} ... ... @@ -45,90 +45,68 @@ 45 45 1. {{formula}}a=-1{{/formula}} 46 46 1. {{formula}}a=\frac{1}{2}{{/formula}} 47 47 1. {{formula}}a=-\frac{3}{4}{{/formula}} 48 - 49 -{{lehrende versteckt=1}} 45 +{{comment}} 50 50 * Geradengleichung in Hauptform bringen 51 51 * Geraden zeichnen 52 -{{/ lehrende}}48 +{{/comment}} 53 53 {{/aufgabe}} 54 54 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? 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}} 58 58 59 -{{lehrende versteckt=1}} 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}} 60 60 * Fehlerursachen und Fehlerfortpflanzung verstehen 61 61 * Mit Geraden umgehen 62 62 * Eine Lösungsstrategie entwickeln 63 -{{/ lehrende}}64 +{{/comment}} 64 64 {{/aufgabe}} 65 65 66 -{{aufgabe id="Achsen beschriften" afb="I II" quelle="Team Mathebrücke" kompetenzen="K2, K5" 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"}} 67 67 [[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. 68 - 69 -{{lehrende versteckt=1}} 69 +{{comment}} 70 70 * Aus der Geradengleichung Informationen wie z.B. y-Achsenabschnitt, Steigung ablesen und geometrisch umsetzen 71 -{{/ lehrende}}71 +{{/comment}} 72 72 {{/aufgabe}} 73 73 74 -{{aufgabe id="Zeichnen von Geraden 2" afb="III" 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"}} 75 75 Zeichne die Gerade mit der Gleichung {{formula}}a\cdot x+2y=5{{/formula}} für 76 - 77 77 (% class=abc %) 78 78 1. {{formula}}a=1{{/formula}} 79 79 1. {{formula}}a=-1{{/formula}} 80 80 1. {{formula}}a=2{{/formula}} 81 81 1. {{formula}}a=0{{/formula}} 82 - 83 -{{lehrende versteckt=1}} 81 +{{comment}} 84 84 * Geradengleichung in Hauptform bringen 85 85 * Geraden zeichnen 86 -{{/lehrende}} 87 - 84 +{{/comment}} 88 88 {{/aufgabe}} 89 89 90 -{{aufgabe id="Koordinatensystem zeichnen" afb="III" quelle="Team Mathebrücke" kompetenzen="K2, K 5" zeit="5" cc="by-sa" tags="mathebrücke"}}87 +{{aufgabe id="Koordinatensystem zeichnen" afb="III" quelle="Team Mathebrücke" kompetenzen="K2, K4" zeit="5" cc="by-sa" tags="mathebrücke"}} 91 91 [[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. 92 - 93 -{{lehrende versteckt=1}} 89 +{{comment}} 94 94 * Bedeutung des Koordinatensystems verstehen 95 95 * Steigung, y-Achsenabschnitt aus Gleichung ablesen und zeichnerisch umsetzen 96 -{{/ lehrende}}92 +{{/comment}} 97 97 {{/aufgabe}} 98 98 99 -{{aufgabe id="Richtig-Falsch-Aufgabe zu Schaubildern linearer Funktionen" afb="II" quelle="Team Mathebrücke" kompetenzen="K4,K5,K6" cc="by-sa" tags="mathebrücke" zeit="10"}} 100 -Kreuze jeweils an, ob die Aussage richtig oder falsch ist. 101 -Stelle die falschen Aussagen richtig! 102 -[[image:richtig-falschlinear.PNG||width="450" style="display:block;margin-left:auto;margin-right:auto"]] 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"]] 103 103 (%class="abc"%) 104 -1. Gerade a hat die Steigung {{formula}}\frac{1}{3}{{/formula}}. 105 -☐ richtig ☐ falsch 106 -1. Der y-Achsenabschnitt der Geraden c beträgt 3,5. 107 -☐ richtig ☐ falsch 108 -1. Die Gerade b hat die Steigung 1. 109 -☐ richtig ☐ falsch 110 -1. Die Geraden a und b schneiden sich im Punkt {{formula}}S\left(-\frac{33}{8}\Bigl|\frac{17}{8}\right){{/formula}} 111 -☐ richtig ☐ falsch 112 -1. Die Geraden c und e schneiden sich nie. 113 -☐ richtig ☐ falsch 114 -1. Die Gerade e hat die Gleichung {{formula}}y=3{{/formula}}. 115 -☐ richtig ☐ falsch 116 -1. Die Gerade d ist das Schaubild einer Funktion, da jedem x-Wert genau ein y-Wert zugeordnet wird. 117 -☐ richtig ☐ falsch 118 -1. Die Geraden b und e schneiden sich im Punkt {{formula}}S(3|-5,5){{/formula}} 119 -☐ richtig ☐ falsch 120 -1. Die Geraden a und f unterscheiden sich nur durch ihren y-Achsenabschnitt. 121 -☐ richtig ☐ falsch 122 -1. Eine Gerade, die orthogonal (senkrecht) auf der Geraden c stehen würde, hätte die Steigung {{formula}}\frac{1}{3}{{/formula}}. 123 -☐ richtig ☐ falsch 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}} 124 124 125 -{{lehrende versteckt=1}}126 - **Sinn dieser Aufgabe**:127 - * Steigungenundy-AchsenschnittpunktevonSchaubildernlinearer Funktionenablesen128 -* Geradenschnittpunkte berechnen129 -* LagenvonGeradenunterscheiden102 +{{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 130 130 {{/lehrende}} 131 -{{/aufgabe}} 132 132 133 - 134 -{{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}} 109 +{{seitenreflexion bildungsplan="5" kompetenzen="5" anforderungsbereiche="4" kriterien="5" menge="5"/}}
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