Änderungen von Dokument BPE 3.3 Zeichnen, Steigung, Steigungsdreieck, y-Achsenabschnitt

Zuletzt geändert von Verena Schmid am 2026/02/03 15:52

Von 51.2 nach 51.3 Von 72.1 nach 73.1

Von Version 51.3

bearbeitet von Martin Rathgeb
am 2025/07/08 10:54

Änderungskommentar: Es gibt keinen Kommentar für diese Version

Auf Version 72.1

bearbeitet von Cinzia Moser
am 2026/02/03 16:48

Änderungskommentar: Neues Bild Lösung 1.jpg hochladen

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- Bild3
- Lösung 1.jpg

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--XWiki.martinrathgeb
++XWiki.mr79

Inhalt

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  [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann die Steigung und den y-Achsenabschnitt von Geraden bestimmen.
  [[Kompetenzen.K4]] [[Kompetenzen.K5]] Ich kann Geraden in ein Koordinatensystem einzeichnen.
--{{aufgabe id="Darstellung von Geraden" afb="I" quelle="Team Mathebrücke" kompetenzen="K1, K5" zeit="3" cc="by-sa" tags="mathebrücke"}}
++{{aufgabe id="Darstellung von Geraden" afb="I" quelle="Team Mathebrücke" kompetenzen="K1, K4" zeit="4" tags="mathebrücke"}}
  [[image:Darstellung von Geraden.svg||width="400" style="float: right"]]Gegeben sind die Geraden {{formula}}g_1{{/formula}} und {{formula}}g_2{{/formula}}:
  {{formula}}g_1: y=-\frac{1}{2}x+1{{/formula}}
  {{formula}}g_2: 2y=x+1{{/formula}}
  Begründe, warum die rechts abgebildete Gerade weder {{formula}}g_1{{/formula}} noch {{formula}}g_2{{/formula}} darstellt.
--
--{{lehrende versteckt=1}}
++{{comment}}
  Steigung und y-Achsenabschnitt aus der Geradengleichung und aus dem Schaubild ablesen
--{{/lehrende}}
++{{/comment}}
  {{/aufgabe}}
--{{aufgabe id="Achse ergänzen" afb="II" quelle="Team Mathebrücke" kompetenzen="K2, K5" zeit="3"= cc="by-sa" tags="mathebrücke"}}
--[[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.
--
--{{lehrende versteckt=1}}
++{{aufgabe id="Achse ergänzen" afb="I" quelle="Team Mathebrücke" kompetenzen="K2, K4" zeit="3" tags="mathebrücke"}}
++[[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.
++{{comment}}
  * Geraden zeichnen
  * Umgang mit Koordinatensystem
--{{/lehrende}}
++{{/comment}}
  {{/aufgabe}}
  {{aufgabe id="Achsen ergänzen" afb="II" quelle="Team Mathebrücke" kompetenzen="K2, K4, K5" zeit="5" cc="by-sa" tags="mathebrücke"}}
--[[image:Achsen ergänzen.svg||width="400" style="float: right"]]Im nachfolgenden Gitternetz sind zwei Geraden dargestellt.
++[[image:Achsen ergänzen.svg||width="400" style="float: right"]]In nebenstehender Abbildung sind zwei Geraden dargestellt.
  (% class=abc %)
--1. Eine der beiden Geraden hat die Gleichung {{formula}}y=\frac{1}{4}x+1{{/formula}}.
--Zeichne das zugehörige Koordinatensystem ein.
++Eine der beiden Geraden hat die Gleichung {{formula}}y=\frac{1}{4}x+2{{/formula}}, die andere hat den y-Achsenabschnitt {{formula}}-4{{/formula}}.
++1. Zeichne ein mögliches zugehörendes Koordinatensystem mit Achsenskalierung ein.
 . Bestimme die Gleichung der zweiten Geraden.
--
--{{lehrende versteckt=1}}
--Rückwärtsaufgabe: An Schaubilder Koordinatensystem anpassen
--{{/lehrende}}
++{{comment}}
++Rückwärtsaufgabe: Koordinatensystem an Schaubilder anpassen
++{{/comment}}
  {{/aufgabe}}
--{{aufgabe id="Zeichnen von Geraden" afb="II" quelle="Team Mathebrücke" kompetenzen="K4, K5" zeit="5" cc="by-sa" tags="mathebrücke"}}
++{{aufgabe id="Zeichnen von Geraden" afb="II" quelle="Team Mathebrücke" kompetenzen="K4, K5" zeit="7" tags="mathebrücke"}}
  Zeichne die Gerade mit der Gleichung {{formula}}y=a\cdot(x-2)+3{{/formula}} für
  (% class=abc %)
 . {{formula}}a=1{{/formula}}
@@ -45,87 +45,68 @@
 . {{formula}}a=-1{{/formula}}
 . {{formula}}a=\frac{1}{2}{{/formula}}
 . {{formula}}a=-\frac{3}{4}{{/formula}}
--
--{{lehrende versteckt=1}}
++{{comment}}
  * Geradengleichung in Hauptform bringen
  * Geraden zeichnen
--{{/lehrende}}
++{{/comment}}
  {{/aufgabe}}
--{{aufgabe id="Folge ungenauen Zeichnens" afb="II" quelle="Team Mathebrücke" kompetenzen="K2, K5" zeit="4" cc="by-sa" tags="mathebrücke"}}
--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.
--Ermittle, wie groß ist die Abweichung bei {{formula}}x = 10{{/formula}} ist?
++{{aufgabe id="Heißluftballon" afb="II" quelle="Cinzia Moser, Verena Schmid" kompetenzen="K3,K4, K5" zeit="6" cc="by-sa"}}
++Ein roter Heißluftballon in 800m Höhe beginnt mit dem Sinkflug. Nach 20 Minuten ist der Ballon am Boden aufgekommen.
++Stelle das Ereignis in einem Schaubild dar und ermittle die passende Funktionsgleichung.
++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.
++{{/aufgabe}}
--{{lehrende versteckt=1}}
++{{aufgabe id="Folge ungenauen Zeichnens" afb="III" quelle="Team Mathebrücke" kompetenzen="K2,K4, K5" zeit="4" cc="by-sa" tags="mathebrücke"}}
++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.
++Ermittle, wie groß ist die Abweichung bei {{formula}}x = 10{{/formula}} ist.
++{{comment}}
  * Fehlerursachen und Fehlerfortpflanzung verstehen
  * Mit Geraden umgehen
  * Eine Lösungsstrategie entwickeln
--{{/lehrende}}
++{{/comment}}
  {{/aufgabe}}
--{{aufgabe id="Achsen beschriften" afb="III" quelle="Team Mathebrücke" kompetenzen="K2, K5" zeit="6" cc="by-sa" tags="mathebrücke"}}
++{{aufgabe id="Achsen beschriften" afb="I" quelle="Team Mathebrücke" kompetenzen="K4, K5" zeit="6" cc="by-sa" tags="mathebrücke"}}
  [[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.
--
--{{lehrende versteckt=1}}
++{{comment}}
  * Aus der Geradengleichung Informationen wie z.B. y-Achsenabschnitt, Steigung ablesen und geometrisch umsetzen
--{{/lehrende}}
++{{/comment}}
  {{/aufgabe}}
--{{aufgabe id="Zeichnen von Geraden 2" afb="III" quelle="Team Mathebrücke" kompetenzen="K4, K5" zeit="8" cc="by-sa" tags="mathebrücke"}}
++{{aufgabe id="Zeichnen von Geraden 2" afb="III" quelle="Team Mathebrücke" kompetenzen="K2,K4, K5" zeit="8" cc="by-sa" tags="mathebrücke"}}
  Zeichne die Gerade mit der Gleichung {{formula}}a\cdot x+2y=5{{/formula}} für
--
  (% class=abc %)
 . {{formula}}a=1{{/formula}}
 . {{formula}}a=-1{{/formula}}
 . {{formula}}a=2{{/formula}}
 . {{formula}}a=0{{/formula}}
--
--{{lehrende versteckt=1}}
++{{comment}}
  * Geradengleichung in Hauptform bringen
  * Geraden zeichnen
--{{/lehrende}}
--
++{{/comment}}
  {{/aufgabe}}
--{{aufgabe id="Koordinatensystem zeichnen" afb="III" quelle="Team Mathebrücke" kompetenzen="K2, K5" zeit="5" cc="by-sa" tags="mathebrücke"}}
++{{aufgabe id="Koordinatensystem zeichnen" afb="III" quelle="Team Mathebrücke" kompetenzen="K2, K4" zeit="5" cc="by-sa" tags="mathebrücke"}}
  [[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.
--
--{{lehrende versteckt=1}}
++{{comment}}
  * Bedeutung des Koordinatensystems verstehen
  * Steigung, y-Achsenabschnitt aus Gleichung ablesen und zeichnerisch umsetzen
--{{/lehrende}}
++{{/comment}}
  {{/aufgabe}}
--{{aufgabe id="Zuordnungsaufgabe Funktionsterm und Schaubild" afb="II" quelle="Team Mathebrücke" kompetenzen="K4,K5" cc="by-sa" tags="mathebrücke" zeit="7"}}
--Ordne den Schaubildern zu:
--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}}
--
--(% class="border" style="width:70%" %)
--|1) [[image:4.png||width="250"]]|2)[[image:2.png||width="250"]]
--|3) [[image:3.png||width="250"]]|4) [[image:1.png||width="250"]]
--
--{{lehrende versteckt=1}}
--Zusammenhang Schaubild und Funktionsterm
--{{/lehrende}}
++{{aufgabe id="Geradengleichungen bestimmen" afb="III" quelle="Cinzia Moser" kompetenzen="K1,K2,K5,K6" zeit="15" cc="by-sa"}}
++[[image:Bild3||width="400" style="float: right"]]
++(%class="abc"%)
++1. Bestimme die Geradengleichungen aus dem Schaubild.
++1. Erläutere, bei welchen Geradengleichungen es sich um einen funktionalen Zusammenhang handelt. Begründe deine Entscheidung.
  {{/aufgabe}}
--{{aufgabe id="Geradenbüschel" afb="II" quelle="Team Mathebrücke" kompetenzen="K1,K4,K5,K6" cc="by-sa" tags="mathebrücke" zeit="11"}}
--[[image:Geradenbüschel.PNG||width="350" style="display:block;margin-left:auto;margin-right:auto"]]
--Im obigen Koordinatensystem sind verschiedene Geraden eingezeichnet.
--(%class=abc%)
--1. Nenne eine Gemeinsamkeit aller dieser Geraden.
--1. Gib zu drei dieser Geraden die zugehörige Gleichung an.
--1. Wie lautet die Gleichung der Parallelen zur x-Achse bzw. zur y-Achse in diesem Bündel?
--1. Welche der beiden Gleichungen aus c) beschreibt keine Funktion? Begründe.
--
--{{lehrende versteckt=1}}
--**Sinn dieser Aufgabe:**
--* Ablesen der Steigungen über Steigungsdreiecke
--* Aufstellen von Geradengleichungen wiederholen
--* Erinnerung des Funktionsbegriffs
++{{lehrende}}
++Gleichung von Geraden bestimmen ist redundant mit [[BPE 3.5 Aufstellen von Funktionstermen>>BPE_3_5]]
++Folgende Aufgabentypen könnten hier ergänzt werden:
++* Steigungsdreiecke einzeichnen und Steigung ablesen
++* Gleichung zu Schaubild bestimmen
  {{/lehrende}}
--{{/aufgabe}}
--
--
--{{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
++{{seitenreflexion bildungsplan="5" kompetenzen="4" anforderungsbereiche="5" kriterien="5" menge="5"/}}

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	1	+XWiki.mr79

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Lösung 1.jpg

Author

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	1	+XWiki.mr79

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Inhalt

Änderungen von Dokument BPE 3.3 Zeichnen, Steigung, Steigungsdreieck, y-Achsenabschnitt

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