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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 28.1
bearbeitet von Stephanie Wietzorek
am 2025/11/18 11:01
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Auf Version 59.1
bearbeitet von Stephanie Wietzorek
am 2025/11/28 08:03
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Inhalt
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1 1  {{seiteninhalt/}}
2 2  
3 3  [[Kompetenzen.K5]] Ich kann die Grundbegriffe der Prozent- und Zinsrechnung beschreiben.
4 -[[Kompetenzen.K3]] [[Kompetenzen.K5]] Ich kann Prozentwert, Grundwert, Prozentsatz und Zins berechnen
4 +[[Kompetenzen.K5]] Ich kann Prozentwert, Grundwert, Prozentsatz und Zins berechnen
5 5  
6 6  
7 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"}}
8 +{{aufgabe id="Zuordnen" afb="II" quelle="Simone Kanzler, Stephanie Wietzorek" kompetenzen="K4, K5, K6" zeit="6" cc="by-sa" tags="mathebrücke"}}
9 9  Ein Modegeschäft bietet auf Jeans einen Preisnachlass von 20% an.
10 -Ordne den Texten die entsprechende Berechnung zu und erläutere die Unterschiede.
10 +Gib zu jedem Berechnungswunsch von Susi die zugehörige Formel an. Erläutere die Unterschiede.
11 11   (% style="width: 100%; white-space: nowrap" class="border" %)
12 12  |= Text |= Berechnung
13 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 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}}
15 +| Susi möchte den regulären Preis wissen, wenn der reduzierte Preis 72€ beträgt | {{formula}} 90 - 90 \cdot \frac{20}{100}{{/formula}}
16 16  
17 17  {{/aufgabe}}
18 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.
19 +{{aufgabe id="Prozentmauer" afb="II" quelle="Simone Kanzler, Stephanie Wietzorek" kompetenzen="K1, K2, K5, K6" zeit="6" cc="by-sa"}}
20 +Bestimme die fehlenden Eintragungen der Felder, indem du nebeneinanderliegende Felder zur Berechnung des darüberliegenden Feldes benutzt.
21 + [[image:Mauer Aufgabe.svg||style="float:left;width:400px"]]
21 21  
22 22  {{/aufgabe}}
23 23  
25 +
26 +
27 +{{aufgabe id="Instagramrabatt" afb="II" quelle="Simone Kanzler, Stephanie Wietzorek" kompetenzen="K1, K5, K6" zeit="6" cc="by-sa"}}
28 +Mia sieht auf Instagram folgenden Post:
29 +
30 + [[image:BJUTI.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 +
24 24  {{aufgabe id="Umsatzsteigerung" afb="I" quelle="Team Mathebrücke" kompetenzen="K5" zeit="4" cc="by-sa" tags="mathebrücke"}}
25 25  Ein Betrieb hatte 2010 einen Umsatz von 325.000 €.
26 26  Im Jahr 2011 sank der Umsatz um 18 %.
... ... @@ -27,7 +27,7 @@
27 27  Für das Jahr 2012 meldet der Betriebsleiter eine Umsatzsteigerung von 25 %.
28 28  (%class=abc%)
29 29  1. Berechne den Umsatz für das Jahr 2012.
30 -1. Bestimme, um wie viel Prozent sich der Umsatz von 2010 bis 2012 verändert hat?
43 +1. Ermittle, um wie viel Prozent sich der Umsatz von 2010 bis 2012 verändert hat?
31 31  {{/aufgabe}}
32 32  
33 33  {{aufgabe id="Zinsrechnung" afb="I" quelle="Team Mathebrücke" kompetenzen="K5" zeit="6" cc="by-sa" tags="mathebrücke"}}
... ... @@ -39,39 +39,44 @@
39 39  
40 40  {{/aufgabe}}
41 41  
42 -{{aufgabe id="Rabatt-Aktion bei Madio-Markt" afb="II" quelle="Team Mathebrücke" kompetenzen="K1, K6" Zeit="5" cc="by-sa" tags="mathebrücke"}}
55 +{{aufgabe id="Rabatt-Aktion bei Madio-Markt" afb="II" quelle="Team Mathebrücke" kompetenzen="K1, K5, K6" Zeit="5" cc="by-sa" tags="mathebrücke"}}
43 43  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.
44 44  Klara denkt: „Da stimmt doch was nicht. Ich bin doch nicht doof!“
45 45  
46 -Gib an, ob Klara recht hat. Begründe deine Entscheidung.
59 +Begründe, ob Klara recht hat.
47 47  {{/aufgabe}}
48 48  
49 -{{aufgabe id="Zinsversteuerung" afb="III" quelle="Team Mathebrücke" kompetenzen="K1,K5" cc="by-sa" tags="mathebrücke"}}
62 +{{aufgabe id="Skateboard" afb="II" quelle="Stephanie Wietzorek" kompetenzen="K1, K5, K6" Zeit="5" cc="by-sa"}}
63 + [[image:Skateboard.svg||style="float:middle;width:400px"]]
64 +
65 + Nimm Stellung dazu.
66 +{{/aufgabe}}
67 +
68 +
69 +{{aufgabe id="Zinsversteuerung" afb="III" quelle="Team Mathebrücke" kompetenzen="K1, K5, K3, K4, K6" Zeit="10" cc="by-sa" tags="mathebrücke"}}
50 50  Du möchtest ein Kapital von 10.000 € auf 20 Jahre anlegen. Die Bank schlägt dir zwei Anlagevarianten vor:
51 51  Anlage A bringt eine jährliche Verzinsung von 8 %. Von diesen Zinsen werden jährlich bei der Gutschrift sofort 25% Steuern abgezogen.
52 -Anlage B bringt ebenfalls eine jährliche Verzinsung von 8 %.
53 -
54 -Die Steuer von 25 % auf die Zinserträge wird jedoch erst am Ende der Anlagezeit abgezogen.
72 +Anlage B bringt ebenfalls eine jährliche Verzinsung von 8 %. Die Steuer von 25 % auf die Zinserträge wird jedoch erst am Ende der Anlagezeit abgezogen.
55 55  (%class=abc%)
56 56  1. Begründe für welche Anlagevariante du dich entscheiden würdest? Entscheide zuerst ohne zu rechnen. Berechne dann den Unterschied der beiden Varianten.
57 57  1. Berechne, wie groß der Unterschied wäre, wenn der Betrag als Altersvorsorge auf 50 Jahre angelegt wird?
58 58  {{/aufgabe}}
59 59  
60 -{{aufgabe id="Zinssätze" afb="II" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
78 +{{aufgabe id="Zinssätze" afb="II" quelle="Team Mathebrücke" kompetenzen="K5, K4" Zeit="10" cc="by-sa" tags="mathebrücke"}}
61 61  Bastian legt 10000 € bei der Bank an.
62 62  Nach drei Jahren beträgt sein Guthaben 10841,13 €.
63 63  Bastian weiß, dass der Zinssatz für das dritte Jahr 4 % betragen hat.
64 64  Die Zinssätze für das erste und zweite Jahr kennt er nicht.
65 65  (%class=abc%)
66 -1. Wie viel Guthaben hatte Bastian nach dem zweiten Jahr?
67 -1. Wie hoch war der Zinssatz im ersten und im zweiten Jahr, wenn in beiden Jahren der Zinssatz gleich war?
68 -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?
84 +1. Berechne, wie viel Guthaben Bastian nach dem zweiten Jahr hatte?
85 +1. Ermittle, wie hoch der Zinssatz im ersten und im zweiten Jahr sein muss, wenn in beiden Jahren der Zinssatz gleich war?
86 +1. Berechne, wie hoch die Zinssätze im ersten und im zweiten Jahr sein müssen, wenn der Zinssatz im zweiten Jahr doppelt so hoch war wie im ersten Jahr?
69 69  {{/aufgabe}}
70 70  
71 -{{aufgabe id="Richtig oder falsch?" afb="I" quelle="Team Mathebrücke" kompetenzen="" cc="by-sa" tags="mathebrücke"}}
72 -Wähle die richtige{{{(n)}}} Aussage{{{(n)}}} aus und begründe deine Entscheidung.
89 +{{aufgabe id="Richtig oder falsch?" afb="I" quelle="Team Mathebrücke" kompetenzen="K1, K4, K5, K6" Zeit="4" cc="by-sa" tags="mathebrücke"}}
90 +Bestimme die richtige {{{(n)}}} Aussage {{{(n)}}}. Begründe deine Entscheidung.
73 73  
74 -Der Preis für einen Pullover wird erst um 20 % erhöht und anschließend um 20 % gesenkt. Wie verändert sich der ursprüngliche Preis?
92 +Der Preis für einen Pullover wird erst um 20 % erhöht und anschließend um 20 % gesenkt. Gib an, wie sich der ursprüngliche Preis verändert.
75 75  
76 76  ☐ Der Preis bleibt gleich, da {{formula}}100\% + 20\% = 120\%{{/formula}} und {{formula}}120\% - 20\% = 100\%{{/formula}}
77 77  ☐ Der Preis ist höher, da der Grundwert nach der Preiserhöhung höher ist.
... ... @@ -79,5 +79,21 @@
79 79  ☐ Der Preis ist niedriger, weil der Prozentwert nach der Preiserhöhung höher ist.
80 80  {{/aufgabe}}
81 81  
82 -{{seitenreflexion bildungsplan="" kompetenzen="" anforderungsbereiche="" kriterien="" menge=""/}}
100 +{{aufgabe id="arbeitendes Geld" afb="II" quelle="Team Mathebrücke" kompetenzen="K1, K2, K3, K5, K6" Zeit="15" cc="by-sa" tags="mathebrücke"}}
101 +Stell dir vor, du bekommst jeden Monat Taschengeld. Normalerweise gibst du es für Snacks, Apps oder neue Skins aus - klar. Aber was wäre, wenn dein Geld für dich arbeitet, während du chillst, zockst oder TikToks schaust.
102 +Charlotte, Kim, Anton und Joel unterhalten sich in der Pause darüber, wie sie ihr Geld für sich arbeiten lassen können. Die Eltern fanden die Idee, das Taschengeld zu sparen, super und haben den Schülern folgende Angebote gemacht:
103 +
104 + Charlotte bekommt 25€ Taschengeld im Monat. Ihre Eltern bieten ihr an, am Ende des Jahres 10% Zinsen oben drauf zu geben.
105 + Kim bekommt im Monat 28€ Taschengeld und würde am Ende des Jahres 1% weniger Zinsen bekommen wie Charlotte.
106 + Anton bekommt 30€ Taschengeld. Am Ende des Jahres würde er insgesamt von seinen Eltern 370€ bekommen.
107 + Joel bekommt am Ende des Jahres von seinen Eltern mit 8% Zinsen insgesamt 349,92€, welches sie selbstverständlich auf 350€ aufrunden.
108 +(%class=abc%)
109 +1. Erläutere, wie das Geld für die vier Freunde arbeitet.
110 +1. Begründe, welches Angebot du am besten fändest?
111 +1. Ein Jahr Sparen ist Joel zu lange. Er möchte die neue Switch Lite für 339 € kaufen, die in 4 Monaten rauskommt. Die Eltern bieten ihm eine Verkürzung des Sparzeitraums an, zahlen in diesem Fall die Zinsen aber nur anteilig aus. Begründe, dass er die Switch zu diesem Zeitpunkt noch nicht kaufen kann.
112 +1. Berechne, wie viele Tage Joel mindestens sparen muss, damit sein Geld inklusive Zinsen ausreicht, um die Switch zu kaufen?
83 83  
114 +{{/aufgabe}}
115 +
116 +{{seitenreflexion bildungsplan="4" kompetenzen="4" anforderungsbereiche="4" kriterien="4" menge="4"/}}
117 +
Mauer 1.svg
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BJUTI.svg
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Mauer Aufgabe.svg
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Mauer Lösung (2).svg
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