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Änderungen von Dokument BPE 8.1 Quadratische Zusammenhänge

Zuletzt geändert von Holger Engels am 2025/11/18 09:44
Von Version 40.1
bearbeitet von Holger Engels
am 2025/11/18 09:34
Änderungskommentar: Neues Bild Quadratischer Zusammenhang.svg hochladen
Auf Version 15.1
bearbeitet von Sandra Vogt
am 2025/09/30 14:39
Änderungskommentar: Es gibt keinen Kommentar für diese Version

Zusammenfassung

Details

Seiteneigenschaften
Dokument-Autor
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1 -XWiki.holgerengels
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Inhalt
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3 3  [[Kompetenzen.K4]] Ich kann quadratische Zusammenhänge aus Tabellen, Schaubildern oder Texten deuten.
4 4  [[Kompetenzen.K4]] Ich kann quadratische Zusammenhänge grafisch darstellen.
5 5  
6 -{{aufgabe id="Wertetabelle" afb="I" quelle="Sandra Vogt" kompetenzen="K4, K6" cc="by-sa" zeit="3"}}
6 +{{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
7 +
8 +{{aufgabe id="Wertetabelle" afb="I" quelle="k. A." kompetenzen="K4" cc="by-sa" tags="mathebrücke" zeit="3"}}
7 7  Untersuche die Werte in der Tabelle auf mögliche Muster oder Besonderheiten.
8 8  Überlege, ob es einen Zusammenhang zwischen den x- und y-Werten gibt. Halte deine Überlegungen schriftlich fest.
9 -
10 -(((
11 -(% class="border slim" %)
12 -|x |-2|-1|0|1|2
13 -|y |4|1|0|1|4
11 +
12 +(% class=abc %)
13 +1. (((
14 +(% style="table-layout: fixed; width:400px; text-align:center" class="border" %)
15 +|{{formula}}x {{/formula}}|{{formula}}-2 {{/formula}}|{{formula}}-1 {{/formula}}|{{formula}}0{{/formula}}|{{formula}}1{{/formula}}|{{formula}}2{{/formula}}
16 +|{{formula}}y {{/formula}}|{{formula}}4{{/formula}}|{{formula}}1{{/formula}}|{{formula}}0{{/formula}}|{{formula}}1{{/formula}}|{{formula}}4{{/formula}}
14 14  )))
15 -
18 +
19 + 1. (((
20 +(% style="table-layout: fixed; width: 400px; text-align:center; white-space: nowrap" class="border" %)
21 +|{{formula}}x{{/formula}}|{{formula}}-2{{/formula}}|{{formula}}-1{{/formula}}|{{formula}}0{{/formula}}|{{formula}}1{{/formula}}|{{formula}}2{{/formula}}
22 +|{{formula}}y{{/formula}}|{{formula}}0{{/formula}}|{{formula}}-3{{/formula}}|{{formula}}-4{{/formula}}|{{formula}}-3{{/formula}}|{{formula}}0{{/formula}}
23 +)))
24 +
25 + 1. (((
26 +(% style="table-layout: fixed; width: 400px; text-align: center; white-space: nowrap" class="border" %)
27 +|{{formula}}x{{/formula}}|{{formula}}0{{/formula}}|{{formula}}1{{/formula}}|{{formula}}2{{/formula}}|{{formula}}3{{/formula}}|{{formula}}4{{/formula}}
28 +|{{formula}}y{{/formula}}|{{formula}}4{{/formula}}|{{formula}}9{{/formula}}|{{formula}}16{{/formula}}|{{formula}}25{{/formula}}|{{formula}}36{{/formula}}
29 +)))
30 +
16 16  {{/aufgabe}}
17 17  
18 -{{aufgabe id="Quadratische Zusammenhänge am Schaubild" afb="I" kompetenzen="K1,K6" quelle="Bastian Knöpfle, Slavko Lamp" zeit="3" cc="by-sa"}}
19 -Begründe, dass es sich um einen quadratischen Zusammenhang handelt.
20 -[[image:Screenshot 2025-11-17 113715.png||width="500" style="display:block;margin-left:auto;margin-right:auto"]]
21 -{{/aufgabe}}
33 +{{aufgabe id="Schaubild" afb="I" quelle="k. A." kompetenzen="K4" cc="by-sa" tags="mathebrücke" zeit="7"}}
34 +Gegeben ist folgende Wertetabelle.
22 22  
36 +(((
37 +(% style="table-layout: fixed; width: 400px; text-align: center; white-space: nowrap" class="border" %)
38 +|{{formula}}x{{/formula}}|{{formula}}-3{{/formula}}|{{formula}}-2{{/formula}}|{{formula}}-1{{/formula}}|{{formula}}0{{/formula}}|{{formula}}1{{/formula}}|{{formula}}2{{/formula}}|{{formula}}3{{/formula}}
39 +|{{formula}}y{{/formula}}|{{formula}}9{{/formula}}|{{formula}}4{{/formula}}|{{formula}}1{{/formula}}|{{formula}}0{{/formula}}|{{formula}}1{{/formula}}|{{formula}}4{{/formula}}|{{formula}}9{{/formula}}
40 +)))
41 + a) Zeichne das passende Schaubild zur Wertetabelle für den Bereich [-3; 3].
42 + b) Das Schaubild ist achsensymmetrisch. Zeichne die Symmetrieachse farbig in das Koordinatensystem.
43 + c) Beschreibe weitere Eigenschaften des Schaubilds.
44 + d) Beschreibe, wie eine mögliche Rechenvorschrift für {{formula}}y{{/formula}} in Abhängigkeit von {{formula}}x{{/formula}} lautet.
23 23  
24 -{{aufgabe id="Schaubild" afb="I" quelle="Sandra Vogt" kompetenzen="K4,K5,K6" cc="by-sa" zeit="7"}}
25 -Gegeben ist folgende Wertetabelle.
26 -(% class="border slim" %)
27 -|x|-3|-2|-1|0|1|2|3
28 -|y|9|4|1|0|1|4|9
29 -(%class=abc%)
30 -1. Zeichne das passende Schaubild zur Wertetabelle für den Bereich [-3; 3].
31 -1. Das Schaubild ist achsensymmetrisch. Zeichne die Symmetrieachse farbig in das Koordinatensystem.
32 -1. Beschreibe weitere Eigenschaften des Schaubilds.
33 -1. Beschreibe, wie eine mögliche Rechenvorschrift für //y// in Abhängigkeit von //x// lautet.
34 -{{/aufgabe}}
46 +[[image:Bild_BPE8.1_A2.svg]]
47 +
48 +
49 + {{/aufgabe}}
35 35  
36 -{{aufgabe id="Wie hoch fliegt der Ball?" afb="II" quelle="Sandra Vogt" kompetenzen="K3,K4" cc="by-sa" zeit="7"}}
51 +{{aufgabe id="Wie hoch fliegt der Ball?" afb="II" quelle="k. A." kompetenzen="K4" cc="by-sa" tags="mathebrücke" zeit="7"}}
37 37  Stell dir vor: In der Pause wirft jemand auf dem Schulhof einen Basketball senkrecht in die Luft – richtig hoch! Du schaust zu. Der Ball steigt schnell auf, wird langsamer, bleibt ganz kurz wie eingefroren in der Luft – und fällt dann wieder runter.
38 38  
39 -Deine Sportlehrerin hat das Ganze mit einer App aufgenommen und genau gemessen, wie hoch der Ball in bestimmten Momenten war. Die Ergebnisse hat sie in eine Tabelle eingetragen.
54 +Deine Sportlehrerin hat das Ganze mit einer App aufgenommen und genau gemessen, wie hoch der Ball in bestimmten Momenten war. Die Ergebnisse hat er in eine Tabelle eingetragen.
40 40  
41 41  Jetzt bist du dran: Schau dir die Werte in der Tabelle an und finde heraus, wie der Ball sich wirklich bewegt hat.
42 -
43 -(% class="border slim" %)
57 +
58 +(((
59 +(% style="table-layout: fixed; width: 800px; text-align: center; white-space: nowrap" class="border" %)
44 44  |Zeit{{formula}}~t\ {{/formula}}~in Sekunden|{{formula}}0{{/formula}}|{{formula}}0,5{{/formula}}|{{formula}}1{{/formula}}|{{formula}}1,5{{/formula}}|{{formula}}2{{/formula}}
45 45  |Höhe{{formula}}~h\ {{/formula}}~in Metern|{{formula}}1,5{{/formula}}|{{formula}}2,5{{/formula}}|{{formula}}3{{/formula}}|{{formula}}2,5{{/formula}}|{{formula}}1,5{{/formula}}
46 -
47 -(%class=abc%)
48 -1. Beschreibe in Worten, wie sich die Höhe des Balls mit der Zeit verändert.
49 -1. Beschreibe, wann der Ball seine maximale Höhe erreicht. Wie könnte die Bewegung weitergehen? Beschreibe.
50 -{{/aufgabe}}
51 -
52 -{{aufgabe id="Wertetabelle" afb="III" quelle="Sandra Vogt" kompetenzen="K4, K6" cc="by-sa" zeit="4"}}
53 -Untersuche die Werte in der Tabelle auf mögliche Muster oder Besonderheiten.
54 -Überlege, ob es einen Zusammenhang zwischen den x- und y-Werten gibt. Halte deine Überlegungen schriftlich fest.
55 -(% class=abc %)
56 -1. (((
57 -(% class="border slim" %)
58 -|x|-2|-1|0|1|2
59 -|y|0|-3|-4|-3|0
60 60  )))
61 -1. (((
62 -(% class="border slim" %)
63 -|x|0|1|2|3|4
64 -|y|4|9|16|25|36
65 -)))
66 -{{/aufgabe}}
63 +
64 +a) Beschreibe in Worten, wie sich die Höhe des Balls mit der Zeit verändert.
65 +b) Beschreibe, wann der Ball seine maximale Höhe erreicht. Wie könnte die Bewegung weitergehen? Beschreibe.
66 +c) Versuche, eine Regel in Worten oder mit Zahlen aufzustellen. Überlege dir hierzu, wie man aus der Zeit {{formula}}t{{/formula}} die Höhe {{formula}}h{{/formula}} berechnen könnte.
67 67  
68 -
69 -{{seitenreflexion bildungsplan="5" kompetenzen="4" anforderungsbereiche="5" kriterien="5" menge="5"/}}
Quadratischer Zusammenhang.ggb
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Bild_BPE8.1_A2.svg
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