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Änderungen von Dokument BPE 2.2 Prozent- und Zinsrechnung

Zuletzt geändert von Stephanie Wietzorek am 2025/11/28 08:03
Von Version 16.1
bearbeitet von Martina Wagner
am 2025/09/30 14:11
Änderungskommentar: Es gibt keinen Kommentar für diese Version
Auf Version 43.1
bearbeitet von Stephanie Wietzorek
am 2025/11/18 12:53
Änderungskommentar: Es gibt keinen Kommentar für diese Version

Zusammenfassung

Details

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Dokument-Autor
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1 -XWiki.martinawagner
1 +XWiki.wies
Inhalt
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3 3  [[Kompetenzen.K5]] Ich kann die Grundbegriffe der Prozent- und Zinsrechnung beschreiben.
4 4  [[Kompetenzen.K3]] [[Kompetenzen.K5]] Ich kann Prozentwert, Grundwert, Prozentsatz und Zins berechnen
5 5  
6 -{{aufgabe id="Umsatzsteigerung" afb="I" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
6 +
7 +
8 +{{aufgabe id="Zuordnen" afb="II" quelle="Simone Kanzler, Stephanie Wietzorek" kompetenzen="K1, K2, K3, K4, K5, K6" zeit="6" cc="by-sa" tags="mathebrücke"}}
9 +Ein Modegeschäft bietet auf Jeans einen Preisnachlass von 20% an.
10 +Ordne den Texten die entsprechende Berechnung zu und erläutere die Unterschiede.
11 + (% style="width: 100%; white-space: nowrap" class="border" %)
12 +|= Text |= Berechnung
13 +| Susi möchte wissen, wie hoch der Preisnachlass für eine Jeans im Wert von 90€ ist | {{formula}} G = 72 \cdot \frac{100}{20} {{/formula}}
14 +| Susi möchte den reduzierten Preis einer Jeans im Wert von 90€ wissen | {{formula}} P = 90 \cdot \frac{20}{100} {{/formula}}
15 +| Der reduzierte Preis beträgt 72€ und Susi möchte den regulären Preis wissen | {{formula}} 90 - 90 \cdot \frac{20}{100}{{/formula}}
16 +
17 +{{/aufgabe}}
18 +
19 +{{aufgabe id="Prozentmauer" afb="II" quelle="Simone Kanzler, Stephanie Wietzorek" kompetenzen="K1, K2, K3, K4, K5, K6" zeit="6" cc="by-sa"}}
20 +Fülle die Lücken, indem du nebeneinanderliegende Felder zur Berechnung des darüberliegenden Feldes benutzt.
21 + [[image:Mauer Aufgabe.svg||style="float:left;width:400px"]]
22 +
23 +{{/aufgabe}}
24 +
25 +
26 +
27 +{{aufgabe id="Instagramrabatt" afb="II" quelle="Simone Kanzler, Stephanie Wietzorek" kompetenzen="K1, K2, K3, K4, K5, K6" zeit="6" cc="by-sa"}}
28 +Mia sieht auf Instagram folgenden Post:
29 +
30 + [[image:Rabatt.svg||style="float:middle;width:400px"]]
31 +
32 +Aufgeregt erzählt sie ihrer Freundin Clara: "Das ist doch ein mega Angebot - da gibt es bis zu 75 % Rabatt auf die Hautpflege - da müssen wir zuschlagen."
33 +
34 +Nimm Stellung zu dieser Aussage.
35 +{{/aufgabe}}
36 +
37 +{{aufgabe id="Umsatzsteigerung" afb="I" quelle="Team Mathebrücke" kompetenzen="K5" zeit="4" cc="by-sa" tags="mathebrücke"}}
7 7  Ein Betrieb hatte 2010 einen Umsatz von 325.000 €.
8 8  Im Jahr 2011 sank der Umsatz um 18 %.
9 9  Für das Jahr 2012 meldet der Betriebsleiter eine Umsatzsteigerung von 25 %.
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12 12  1. Bestimme, um wie viel Prozent sich der Umsatz von 2010 bis 2012 verändert hat?
13 13  {{/aufgabe}}
14 14  
15 -{{aufgabe id="Zinsrechnung" afb="I" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
46 +{{aufgabe id="Zinsrechnung" afb="I" quelle="Team Mathebrücke" kompetenzen="K5" zeit="6" cc="by-sa" tags="mathebrücke"}}
16 16  Peter legt ein Kapital von 4000 € bei der Bank an. Dieses Kapital wird mit 2,5 % verzinst. Die Zinsen werden jährlich mitverzinst.
17 17  (%class=abc%)
18 18  1. Berechne den Betrag, der Peter nach sechs Jahren zur Verfügung steht.
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21 21  
22 22  {{/aufgabe}}
23 23  
24 -{{aufgabe id="Rabatt-Aktion bei Madio-Markt" afb="II" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
55 +{{aufgabe id="Rabatt-Aktion bei Madio-Markt" afb="II" quelle="Team Mathebrücke" kompetenzen="K1, K6" Zeit="5" cc="by-sa" tags="mathebrücke"}}
25 25  Der Elektronik-Discounter Madio-Markt startet eine Rabatt-Aktion unter dem Motto „Alles 19 % billiger!“. Tatsächlich wird in der Rabatt-Woche alles zum Netto-Preis, also ohne die 19 % Mehrwertsteuer verkauft.
26 26  Klara denkt: „Da stimmt doch was nicht. Ich bin doch nicht doof!“
27 27  
28 -Was meinst du dazu?
59 +Gib an, ob Klara recht hat. Begründe deine Entscheidung.
29 29  {{/aufgabe}}
30 30  
31 -{{aufgabe id="Zinsversteuerung" afb="III" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
62 +{{aufgabe id="Zinsversteuerung" afb="III" quelle="Team Mathebrücke" kompetenzen="K1,K5" cc="by-sa" tags="mathebrücke"}}
32 32  Du möchtest ein Kapital von 10.000 € auf 20 Jahre anlegen. Die Bank schlägt dir zwei Anlagevarianten vor:
33 33  Anlage A bringt eine jährliche Verzinsung von 8 %. Von diesen Zinsen werden jährlich bei der Gutschrift sofort 25% Steuern abgezogen.
34 34  Anlage B bringt ebenfalls eine jährliche Verzinsung von 8 %.
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35 35  
36 36  Die Steuer von 25 % auf die Zinserträge wird jedoch erst am Ende der Anlagezeit abgezogen.
37 37  (%class=abc%)
38 -1. Für welche Anlagevariante würdest du dich entscheiden? Überlege zuerst ohne zu rechnen und berechne dann den Unterschied der beiden Varianten.
39 -1. Wie groß wäre der Unterschied, wenn der Betrag als Altersvorsorge auf 50 Jahre angelegt wird?
69 +1. Begründe für welche Anlagevariante du dich entscheiden würdest? Entscheide zuerst ohne zu rechnen. Berechne dann den Unterschied der beiden Varianten.
70 +1. Berechne, wie groß der Unterschied wäre, wenn der Betrag als Altersvorsorge auf 50 Jahre angelegt wird?
40 40  {{/aufgabe}}
41 41  
42 42  {{aufgabe id="Zinssätze" afb="II" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
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47 47  (%class=abc%)
48 48  1. Wie viel Guthaben hatte Bastian nach dem zweiten Jahr?
49 49  1. Wie hoch war der Zinssatz im ersten und im zweiten Jahr, wenn in beiden Jahren der Zinssatz gleich war?
50 -1. Wie hoch waren die Zinssätze im ersten und im zweiten Jahr, wenn der Zinssatz im zweiten Jahr doppelt so hoch war wie im ersten Jahr?
81 +1. Wie hoch waren die Zinssätze im ersten und im zweiten Jahr, wenn der Zinssatz im zweiten Jahr doppelt so hoch war wie im ersten Jahr?
51 51  {{/aufgabe}}
52 52  
53 53  {{aufgabe id="Richtig oder falsch?" afb="I" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
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55 55  
56 56  Der Preis für einen Pullover wird erst um 20 % erhöht und anschließend um 20 % gesenkt. Wie verändert sich der ursprüngliche Preis?
57 57  
58 -□ Der Preis bleibt gleich, da {{formula}}100\% + 20\% = 120\%{{/formula}} und {{formula}}120\% - 20\% = 100\%{{/formula}}
59 -□ Der Preis ist höher, da der Grundwert nach der Preiserhöhung höher ist.
60 -□ Der Preis ist niedriger, da der Grundwert vor der Preiserhöhung niedriger ist.
61 -□ Der Preis ist niedriger, weil der Prozentwert nach der Preiserhöhung höher ist.
89 +☐ Der Preis bleibt gleich, da {{formula}}100\% + 20\% = 120\%{{/formula}} und {{formula}}120\% - 20\% = 100\%{{/formula}}
90 +☐ Der Preis ist höher, da der Grundwert nach der Preiserhöhung höher ist.
91 +☐ Der Preis ist niedriger, da der Grundwert vor der Preiserhöhung niedriger ist.
92 +☐ Der Preis ist niedriger, weil der Prozentwert nach der Preiserhöhung höher ist.
62 62  {{/aufgabe}}
63 63  
64 64  {{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
Mauer Aufgabe.svg
Author
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1 +XWiki.wies
Größe
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1 +29.8 KB
Inhalt
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Mauer Lösung (2).svg
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Rabatt.svg
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