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Zuletzt geändert von Verena Schmid am 2026/02/03 15:52
Von Version 26.1
bearbeitet von akukin
am 2025/06/04 21:07
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Auf Version 72.1
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am 2026/02/03 16:48
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1 -XWiki.akukin
1 +XWiki.mr79
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2 2  
3 3  [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann die Gleichung von Geraden bestimmen.
4 4  [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann die Steigung und den y-Achsenabschnitt von Geraden bestimmen.
5 -[[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann Geraden in eine Koordinatensystem einzeichnen.
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="" cc="by-sa" tags="mathebrücke"}}
8 -[[image:DarstellungvonGeraden.PNG||width="150" style="float: right"]]
9 -Gegeben sind die Geraden {{formula}}g_1{{/formula}} und {{formula}}g_2{{/formula}}:
7 +{{aufgabe id="Darstellung von Geraden" afb="I" quelle="Team Mathebrücke" kompetenzen="K1, K4" zeit="4" tags="mathebrücke"}}
8 +[[image:Darstellung von Geraden.svg||width="400" style="float: right"]]Gegeben sind die Geraden {{formula}}g_1{{/formula}} und {{formula}}g_2{{/formula}}:
10 10  {{formula}}g_1: y=-\frac{1}{2}x+1{{/formula}}
11 11  {{formula}}g_2: 2y=x+1{{/formula}}
12 12  
13 13  Begründe, warum die rechts abgebildete Gerade weder {{formula}}g_1{{/formula}} noch {{formula}}g_2{{/formula}} darstellt.
14 -
15 -
16 -
17 -
18 -{{lehrende}}
19 -**Sinn dieser Aufgabe:**
13 +{{comment}}
20 20  Steigung und y-Achsenabschnitt aus der Geradengleichung und aus dem Schaubild ablesen
21 -{{/lehrende}}
22 -
15 +{{/comment}}
23 23  {{/aufgabe}}
24 24  
25 -{{aufgabe id="Gerade zeichnen" afb="II" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
26 -Zeichne die fehlende x-Achse so ein und beschrifte die Koordinatenachsen so mit geeigneten Einheiten, dass die eingezeichnete Gerade die Gleichung {{formula}} y=\frac{1}{3}x+3{{/formula}} besitzt.
27 -[[image:Geradezeichnen.PNG||width="600" style="display:block;margin-left:auto;margin-right:auto"]]
28 -
29 -
30 -
31 -{{lehrende}}
32 -**Sinn dieser Aufgabe:**
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}}
33 33  * Geraden zeichnen
34 34  * Umgang mit Koordinatensystem
35 -{{/lehrende}}
36 -
23 +{{/comment}}
37 37  {{/aufgabe}}
38 38  
39 -{{aufgabe id="Koordinatensystem zu Geraden zeichnen" afb="II" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
40 -Im nachfolgenden Gitternetz sind zwei Geraden dargestellt.
41 -[[image:Koordinatensystemzeichnen.PNG||width="500" style="display:block;margin-left:auto;margin-right:auto"]]
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"]]In nebenstehender Abbildung sind zwei Geraden dargestellt.
42 42  
43 43  (% class=abc %)
44 -1. Eine der beiden Geraden hat die Gleichung {{formula}}y=\frac{1}{4}x+1{{/formula}}.
45 -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.
46 46  1. Bestimme die Gleichung der zweiten Geraden.
47 -
48 -{{lehrende}}
49 -**Sinn dieser Aufgabe:**
50 -Rückwärtsaufgabe: An Schaubilder Koordinatensystem anpassen
51 -{{/lehrende}}
52 -
33 +{{comment}}
34 +Rückwärtsaufgabe: Koordinatensystem an Schaubilder anpassen
35 +{{/comment}}
53 53  {{/aufgabe}}
54 54  
55 -{{aufgabe id="Zeichnen von Geraden" afb="II" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
38 +{{aufgabe id="Zeichnen von Geraden" afb="II" quelle="Team Mathebrücke" kompetenzen="K4, K5" zeit="7" tags="mathebrücke"}}
56 56  Zeichne die Gerade mit der Gleichung {{formula}}y=a\cdot(x-2)+3{{/formula}} für
57 -
58 58  (% class=abc %)
59 59  1. {{formula}}a=1{{/formula}}
60 60  1. {{formula}}a=-1{{/formula}}
61 61  1. {{formula}}a=\frac{1}{2}{{/formula}}
62 62  1. {{formula}}a=-\frac{3}{4}{{/formula}}
63 -
64 -{{lehrende}}
65 -**Sinn dieser Aufgabe:**
45 +{{comment}}
66 66  * Geradengleichung in Hauptform bringen
67 67  * Geraden zeichnen
68 -{{/lehrende}}
48 +{{/comment}}
49 +{{/aufgabe}}
69 69  
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.
70 70  {{/aufgabe}}
71 71  
72 -{{aufgabe id="Folge ungenauen Zeichnens" afb="II" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
73 -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.
74 -Wie groß ist die Abweichung bei {{formula}}x = 10{{/formula}}?
75 -
76 -{{lehrende}}
77 -**Sinn dieser Aufgabe:**
78 -* Fehlerursachen und Fehlerfortpflanzung verstehen
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}}
61 +* Fehlerursachen und Fehlerfortpflanzung verstehen
79 79  * Mit Geraden umgehen
80 80  * Eine Lösungsstrategie entwickeln
81 -{{/lehrende}}
82 -
64 +{{/comment}}
83 83  {{/aufgabe}}
84 84  
85 -{{aufgabe id="Darstellung von Geraden 2" afb="III" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
86 -Beschrifte die Koordinatenachsen so mit geeigneten Einheiten, dass die eingezeichnete Gerade die Gleichung {{formula}}y=2x+1{{/formula}} besitzt.
87 -[[image:2x+1.PNG||width="350" style="display:block;margin-left:auto;margin-right:auto"]]
88 -
89 -{{lehrende}}
90 -**Sinn dieser Aufgabe:**
67 +{{aufgabe id="Achsen beschriften" afb="I" quelle="Team Mathebrücke" kompetenzen="K4, K5" zeit="6" cc="by-sa" tags="mathebrücke"}}
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}}
91 91  * Aus der Geradengleichung Informationen wie z.B. y-Achsenabschnitt, Steigung ablesen und geometrisch umsetzen
92 -{{/lehrende}}
93 -
71 +{{/comment}}
94 94  {{/aufgabe}}
95 95  
96 -{{aufgabe id="Zeichnen von Geraden 2" afb="III" quelle="Team Mathebrücke" kompetenzen="" 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"}}
97 97  Zeichne die Gerade mit der Gleichung {{formula}}a\cdot x+2y=5{{/formula}} für
98 -
99 99  (% class=abc %)
100 100  1. {{formula}}a=1{{/formula}}
101 101  1. {{formula}}a=-1{{/formula}}
102 102  1. {{formula}}a=2{{/formula}}
103 103  1. {{formula}}a=0{{/formula}}
104 -
105 -{{lehrende}}
106 -**Sinn dieser Aufgabe:**
81 +{{comment}}
107 107  * Geradengleichung in Hauptform bringen
108 108  * Geraden zeichnen
109 -{{/lehrende}}
84 +{{/comment}}
85 +{{/aufgabe}}
110 110  
87 +{{aufgabe id="Koordinatensystem zeichnen" afb="III" quelle="Team Mathebrücke" kompetenzen="K2, K4" zeit="5" cc="by-sa" tags="mathebrücke"}}
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}}
90 +* Bedeutung des Koordinatensystems verstehen
91 +* Steigung, y-Achsenabschnitt aus Gleichung ablesen und zeichnerisch umsetzen
92 +{{/comment}}
111 111  {{/aufgabe}}
112 112  
113 -{{aufgabe id="Darstellung im Koordinatensystem" afb="III" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
114 -Zeichne Koordinatenachsen so ein und lege die Einheiten an den Achsen so fest, dass die gegebene Gerade bezüglich dieses Koordinatensystems die Gleichung {{formula}}y=-x+1{{/formula}} besitzt.
115 -[[image:Darstellung im Koordinatensystem.PNG||width="300" 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"]]
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}}
116 116  
117 117  {{lehrende}}
118 -**Sinn dieser Aufgabe:**
119 -* Bedeutung des Koordinatensystems verstehen
120 -* Steigung, y-Achsenabschnitt aus Gleichung ablesen und zeichnerisch umsetzen
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
121 121  {{/lehrende}}
122 122  
123 -{{/aufgabe}}
124 -
125 -{{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
126 -
109 +{{seitenreflexion bildungsplan="5" kompetenzen="4" anforderungsbereiche="5" kriterien="5" menge="5"/}}
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Achsen ergänzen.svg
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Alle Geraden.ggb
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Bild3
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Koordinatensystem zeichnen.svg
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