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Zuletzt geändert von Verena Schmid am 2026/02/03 15:52
Von Version 70.1
bearbeitet von Verena Schmid
am 2026/02/03 15:29
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Auf Version 31.1
bearbeitet von Holger Engels
am 2025/07/04 08:45
Änderungskommentar: Neues Bild Darstellung von Geraden.svg hochladen

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1 -XWiki.sc25
1 +XWiki.holgerengels
Inhalt
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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" 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}}:
7 +{{aufgabe id="Darstellung von Geraden" afb="I" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
8 +[[image:Darstellung von Geraden.svg||width="200" style="float: right"]]
9 +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}}
14 +
15 +{{lehrende}}
16 +**Sinn dieser Aufgabe:**
14 14  Steigung und y-Achsenabschnitt aus der Geradengleichung und aus dem Schaubild ablesen
15 -{{/comment}}
18 +{{/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}}
21 +{{aufgabe id="Achse ergänzen" afb="II" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
22 +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.
23 +[[image:Achse ergänzen.svg||width="200" style="float: right"]]
24 +
25 +{{lehrende}}
26 +**Sinn dieser Aufgabe:**
21 21  * Geraden zeichnen
22 22  * Umgang mit Koordinatensystem
23 -{{/comment}}
29 +{{/lehrende}}
24 24  {{/aufgabe}}
25 25  
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.
32 +{{aufgabe id="Achsen ergänzen" afb="II" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
33 +Im nachfolgenden Gitternetz sind zwei Geraden dargestellt.
34 +[[image:Achsen ergänzen.svg||width="200" style="float: right"]]
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. Zeichne ein mögliches zugehörendes Koordinatensystem mit Achsenskalierung ein.
37 +1. Eine der beiden Geraden hat die Gleichung {{formula}}y=\frac{1}{4}x+1{{/formula}}.
38 +Zeichne das zugehörige Koordinatensystem ein.
32 32  1. Bestimme die Gleichung der zweiten Geraden.
33 -{{comment}}
34 -Rückwärtsaufgabe: Koordinatensystem an Schaubilder anpassen
35 -{{/comment}}
40 +
41 +{{lehrende}}
42 +**Sinn dieser Aufgabe:**
43 +Rückwärtsaufgabe: An Schaubilder Koordinatensystem anpassen
44 +{{/lehrende}}
36 36  {{/aufgabe}}
37 37  
38 -{{aufgabe id="Zeichnen von Geraden" afb="II" quelle="Team Mathebrücke" kompetenzen="K4, K5" zeit="7" tags="mathebrücke"}}
47 +{{aufgabe id="Zeichnen von Geraden" afb="II" quelle="Team Mathebrücke" kompetenzen="" 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}}
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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}}
54 +
55 +{{lehrende}}
56 +**Sinn dieser Aufgabe:**
46 46  * Geradengleichung in Hauptform bringen
47 47  * Geraden zeichnen
48 -{{/comment}}
59 +{{/lehrende}}
49 49  {{/aufgabe}}
50 -{{aufgabe id="Heißluftballon" afb="II" quelle="Cinzia Moser, Verena Schmid" kompetenzen="K3,K4, K5" zeit="6" cc="by-sa" tags=}}
51 -Ein roter Heißluftballon in 800m Höhe beginnt mit dem Sinkflug. Nach 20 Minuten ist der Ballon am Boden aufgekommen.
52 -Stelle das Ereignis in einem Schaubild dar und ermittle die passende Funktionsgleichung.
53 -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.
54 -{{/aufgabe}}
55 55  
56 -{{aufgabe id="Folge ungenauen Zeichnens" afb="III" quelle="Team Mathebrücke" kompetenzen="K2,K4, K5" zeit="4" cc="by-sa" tags="mathebrücke"}}
57 -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.
58 -Ermittle, wie groß ist die Abweichung bei {{formula}}x = 10{{/formula}} ist.
59 -{{comment}}
60 -* Fehlerursachen und Fehlerfortpflanzung verstehen
62 +{{aufgabe id="Folge ungenauen Zeichnens" afb="II" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
63 +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.
64 +Wie groß ist die Abweichung bei {{formula}}x = 10{{/formula}}?
65 +
66 +{{lehrende}}
67 +**Sinn dieser Aufgabe:**
68 +* Fehlerursachen und Fehlerfortpflanzung verstehen
61 61  * Mit Geraden umgehen
62 62  * Eine Lösungsstrategie entwickeln
63 -{{/comment}}
71 +{{/lehrende}}
64 64  {{/aufgabe}}
65 65  
66 -{{aufgabe id="Achsen beschriften" afb="I" quelle="Team Mathebrücke" kompetenzen="K4, K5" zeit="6" cc="by-sa" tags="mathebrücke"}}
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 -{{comment}}
74 +{{aufgabe id="Achsen beschriften" afb="III" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
75 +Beschrifte die Koordinatenachsen so mit geeigneten Einheiten, dass die eingezeichnete Gerade die Gleichung {{formula}}y=2x+1{{/formula}} besitzt.
76 +[[image:Achsen beschriften.PNG||width="200" style="float: right"]]
77 +
78 +{{lehrende}}
79 +**Sinn dieser Aufgabe:**
69 69  * Aus der Geradengleichung Informationen wie z.B. y-Achsenabschnitt, Steigung ablesen und geometrisch umsetzen
70 -{{/comment}}
81 +{{/lehrende}}
71 71  {{/aufgabe}}
72 72  
73 -{{aufgabe id="Zeichnen von Geraden 2" afb="III" quelle="Team Mathebrücke" kompetenzen="K2,K4, K5" zeit="8" cc="by-sa" tags="mathebrücke"}}
84 +{{aufgabe id="Zeichnen von Geraden 2" afb="III" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
74 74  Zeichne die Gerade mit der Gleichung {{formula}}a\cdot x+2y=5{{/formula}} für
86 +
75 75  (% class=abc %)
76 76  1. {{formula}}a=1{{/formula}}
77 77  1. {{formula}}a=-1{{/formula}}
78 78  1. {{formula}}a=2{{/formula}}
79 79  1. {{formula}}a=0{{/formula}}
80 -{{comment}}
92 +
93 +{{lehrende}}
94 +**Sinn dieser Aufgabe:**
81 81  * Geradengleichung in Hauptform bringen
82 82  * Geraden zeichnen
83 -{{/comment}}
84 -{{/aufgabe}}
97 +{{/lehrende}}
85 85  
86 -{{aufgabe id="Koordinatensystem zeichnen" afb="III" quelle="Team Mathebrücke" kompetenzen="K2, K4" zeit="5" cc="by-sa" tags="mathebrücke"}}
87 -[[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.
88 -{{comment}}
89 -* Bedeutung des Koordinatensystems verstehen
90 -* Steigung, y-Achsenabschnitt aus Gleichung ablesen und zeichnerisch umsetzen
91 -{{/comment}}
92 92  {{/aufgabe}}
93 93  
94 -{{aufgabe id="Geradengleichungen bestimmen" afb="III" quelle="Cinzia Moser" kompetenzen="K1,K2,K5,K6" zeit="15" cc="by-sa"}}
95 -[[image:Bild3||width="400" style="float: right"]]
96 -(%class="abc"%)
97 -1. Bestimme die Geradengleichungen aus dem Schaubild.
98 -1. Erläutere, bei welchen Geradengleichungen es sich um einen funktionalen Zusammenhang handelt. Begründe deine Entscheidung.
99 -{{/aufgabe}}
101 +{{aufgabe id="Koordinatensystem zeichnen" afb="III" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
102 +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.
103 +[[image:Koordinatensystem zeichnen.svg||width="300" style="display:block;margin-left:auto;margin-right:auto"]]
100 100  
101 101  {{lehrende}}
102 -Gleichung von Geraden bestimmen ist redundant mit [[BPE 3.5 Aufstellen von Funktionstermen>>BPE_3_5]]
103 -Folgende Aufgabentypen könnten hier ergänzt werden:
104 -* Steigungsdreiecke einzeichnen und Steigung ablesen
105 -* Gleichung zu Schaubild bestimmen
106 +**Sinn dieser Aufgabe:**
107 +* Bedeutung des Koordinatensystems verstehen
108 +* Steigung, y-Achsenabschnitt aus Gleichung ablesen und zeichnerisch umsetzen
106 106  {{/lehrende}}
110 +{{/aufgabe}}
107 107  
108 -{{seitenreflexion bildungsplan="4" kompetenzen="3" anforderungsbereiche="3" kriterien="5" menge="2"/}}
112 +{{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
Alle Geraden.ggb
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Koordinatensystem zeichnen.svg
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