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Änderungen von Dokument BPE 8.1 Quadratische Zusammenhänge

Zuletzt geändert von Holger Engels am 2025/10/06 09:12
Von Version 5.1
bearbeitet von Sandra Vogt
am 2025/09/30 12:34
Änderungskommentar: Neues Bild Bilddatei_BPE8.1_Aufgabe2.svg hochladen
Auf Version 8.1
bearbeitet von Sandra Vogt
am 2025/09/30 13:59
Änderungskommentar: Es gibt keinen Kommentar für diese Version

Zusammenfassung

Details

Seiteneigenschaften
Inhalt
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5 5  
6 6  {{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
7 7  
8 +{{aufgabe id="Wertetabelle" afb="I" quelle="k. A." kompetenzen="K4" cc="by-sa" tags="mathebrücke" zeit="3"}}
9 +Untersuche die Werte in der Tabelle auf mögliche Muster oder Besonderheiten.
10 +Überlege, ob es einen Zusammenhang zwischen den x- und y-Werten gibt. Halte deine Überlegungen schriftlich fest.
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}}
17 +)))
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}}6{{/formula}}|{{formula}}3{{/formula}}|{{formula}}2{{/formula}}|{{formula}}3{{/formula}}|{{formula}}6{{/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 +
31 +{{/aufgabe}}
32 +
33 +{{aufgabe id="Schaubild" afb="I" quelle="k. A." kompetenzen="K4" cc="by-sa" tags="mathebrücke" zeit="7"}}
34 +Gegeben ist folgende Wertetabelle.
35 +
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.
45 +
46 +[[image:Bild_BPE8.1_A2.svg]]
47 +
48 +
49 + {{/aufgabe}}
50 +
51 +{{aufgabe id="Wie hoch fliegt der Ball?" afb="II" quelle="k. A." kompetenzen="K4" cc="by-sa" tags="mathebrücke" zeit="7"}}
52 +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.
53 +
54 +Dein Sportlehrer 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.
55 +
56 +Jetzt bist du dran: Schau dir die Werte in der Tabelle an und finde heraus, wie der Ball sich wirklich bewegt hat.
57 +
58 +(((
59 +(% style="table-layout: fixed; width: 800px; text-align: center; white-space: nowrap" class="border" %)
60 +|Zeit{{formula}}~t{{/formula}}~in Sekunden|{{formula}}0{{/formula}}|{{formula}}0,5{{/formula}}|{{formula}}1{{/formula}}|{{formula}}1,5{{/formula}}|{{formula}}2{{/formula}}
61 +|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}}
62 +)))
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 die Höhe berechnen könnte.
67 +
Bilddatei_BPE8.1_Aufgabe2.svg
Author
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1 -XWiki.sandravogt
Größe
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1 -8.9 KB
Inhalt
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