Terme in 8

herr-fischer, 12 sept. 2025

[b]Die Lernumgebung ist konzipiert als Lernbegleiter für den traditionellen Unterricht mit Phasen entdeckenden Lernens in digitaler Form (Unterrichtskonzept: Entdeckendes Lernen mit mathematischer Kommunikation + Differenzierung + Feedback). [/b] Hinweis: Bei Übungsaufgaben mit anschließendem Textfeld sind die Schülerinnen und Schüler gehalten, die Aufgabe schriftlich (z.B. im Heft) anzufertigen. Mit Hilfe des Textfeldes (ein Buchstabe muss eingetragen werden, dann wird der Button „Antwort überprüfen“ aktiviert) kann die Lösung überprüft werden.

Table des matières

  1. Terme darstellen
    1. Terme am Würfelturm
  2. Terme addieren und subtrahieren
    1. Terme zusammenfassen
    2. Terme addieren und subtrahieren (verschiedene Variablen und höhere Potenzen)
  3. Terme multiplizieren
    1. Terme multiplizieren (verschiedene Variablen und höhere Potenzen)
  4. Summenterme addieren und subtrahieren: Klammern auflösen
    1. Plusklammer und Minusklammer
    2. Zusammenfassende Übung: Terme darstellen, zusammenfassen, multiplizieren, Plus- und Minusklammer
  5. Ausmultiplizieren und Ausklammern
    1. Ausmultiplizieren
    2. Ausklammern

1.

Terme darstellen

  • 1. Terme am Würfelturm

1.1.

Terme am Würfelturm

Sichtbare Quadrate
[b]Ein Würfel liegt auf dem Tisch. Du kannst ihn von den 4 Seiten und von oben betrachten. Das Quadrat am Tisch ist verdeckt.[br][br][/b]Zähle die sichtbaren Quadrate.
[b]Du kannst den Schieberegler betätigen und dir die ersten 10 Stockwerke betrachten.[br][/b] [br] [br]
Tabelle für die Anzahl der sichtbaren Quadrate
Stelle dir nun x-beliebige Stockwerke vor: gib die Anzahl der sichtbaren Quadrate mit Hilfe eines Terms an (Tipp: x steht für die Anzahl der Stockwerke).[br][br]Ergänze die Tabelle im Heft. 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– herr-fischer

2.

Terme addieren und subtrahieren

  • 1. Terme zusammenfassen
  • 2. Terme addieren und subtrahieren (verschiedene Variablen und höhere Potenzen)

2.1.

Terme zusammenfassen

[br] [br] [br]Löse die Learning-App und übernimm den Text am Ende der LearningApp als Hefteintrag mit der Überschrift: [br][b][u]Terme zusammenfassen[/u][/b]
Übung:
Übernimm die Terme in dein Heft und vereinfache durch Zusammenfassen gleichartiger Terme. ([math]x,y,a\in\mathbb{Q}[/math])[br][br]a) 13x + 6 – 7x [br][br]b) 14a + 2 – 2a[br][br]c) –12x + 12 – 3x[br][br]d) 7 + 3y – 2y[br][br]e) 4x – x + 4 [br][br]f) 15a + 2 – 2a[br] [br]g) 4x – 3x + 5 – x
– herr-fischer

2.2.

–

3.

Terme multiplizieren

  • 1. Terme multiplizieren (verschiedene Variablen und höhere Potenzen)

3.1.

Terme multiplizieren (verschiedene Variablen und höhere Potenzen)

Terme multiplizieren beim Berechnen des Quadervolumens:
Aufgabe 1:
[b]a) Übernimm das Schrägbild des Quaders in dein Heft.[br]b) Erstelle einen Term (mit x) für das Volumen des Quaders ([/b][math]x\in\mathbb{Q}[/math][b]).[/b]
Aufgabe 2:
Aufgabe 3:
Übernimm die Terme in dein Heft und vereinfache. ([math]x,y,a,b\in \mathbb{Q}[/math])[br][br]a) [math]7x\cdot3xy[/math][br][br]b) [math]12ab^2\cdot\frac{1}{2}a[/math][br][br]c) [math]\left(2b\right)^2\cdot2b^2[/math][br][br]d) [math]3x^2\cdot\left(-2y\right)^3\cdot x^{-4}\cdot y^6\cdot\left(-a\right)[/math]
– herr-fischer

4.

Summenterme addieren und subtrahieren: Klammern auflösen

  • 1. Plusklammer und Minusklammer
  • 2. Zusammenfassende Übung: Terme darstellen, zusammenfassen, multiplizieren, Plus- und Minusklammer

4.1.

Plusklammer und Minusklammer

Beispiel 1:
[size=200][color=#0000ff][b]7 + (+3 – 8) = [/b][/color][/size][br][br]Welchen Rechenweg würdest du wählen?
[br] [br][b][size=100][size=150]Die Klammer in der Aufgabe heißt Plusklammer, weil vor der Klammer ein Plus steht![/size][/size][/b][br][br][img]data:image/png;base64,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[/img][br][br][b][size=150]Die Plusklammer wird weggelassen. Die Zeichen in der Klammer bleiben gleich.[br][br][/size][/b]Rechenweg 1 ist also richtig: 7 [b]+ ([/b][color=#ff00ff]+3 – 8[/color][b])[/b] = 7 [color=#ff00ff]+ 3 – 8[/color] = 10 – 8 = 2[br][br]Rechenweg 2 ist ebenfalls richtig: 7 + (+3 – 8) = 7 [b]+ ([/b][color=#ff00ff]–5[/color][b]) [/b]= 7 [color=#ff00ff]– 5[/color] = 2[br] [br] [br] [br] [br] [br]
Beispiel 2:
[size=200][color=#0000ff][b]12 [b]–[/b] (+2 – 5) = [/b][/color][/size][br][br]Welchen Rechenweg würdest du wählen?
[br] [br][b][size=100][size=150]Die Klammer in der Aufgabe heißt Minusklammer, weil vor der Klammer ein Minus steht![/size][/size][/b][br][br][img]data:image/png;base64,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[/img][br][br][b][size=150]Die Minusklammer wird weggelassen. Die Zeichen in der Klammer werden umgekehrt.[br][br][/size][/b]Rechenweg 1 ist also richtig: 12 [b]– ([/b][color=#ff7700]+2 – 5[/color][b])[/b] = 12 [color=#ff7700]– 2 + 5[/color] = 10 + 5 = 15[br][br]Rechenweg 2 ist ebenfalls richtig: 12 – (+2 – 5) = 12 [b]– ([/b][color=#ff7700]–3[/color][b])[/b] = 12 [color=#ff7700]+ 3[/color] = 15[br] [br] [br] [br] [br] [br]
Übung:
Löse die Klammern auf und fasse zusammen.[br][br]a) 23 + (+7 – 11) [br][br]b) 6 – (–8 + 2)[br][br]c) 10 + (3 – 7)[br][br]d) –5 – (8 – 2)[br][br]e) 2 + (5 + x)[br][br]f) 15 – (–6 – x)[br][br]g) 7x – (9y + 3x)[br][br]h) 8x + (–2x + y)
– herr-fischer

4.2.

–

5.

Ausmultiplizieren und Ausklammern

  • 1. Ausmultiplizieren
  • 2. Ausklammern

5.1.

Ausmultiplizieren

x-beliebige 10er-Stelle:
[size=150] [br]Die 10er-Stelle soll nun eine [color=#0000ff]x-beliebige Zahl[/color] sein. ([math]x\in\mathbb{N}; x<10[/math])[br] [br][br]Wir können den Term dann so schreiben: [/size] [size=200][b]7 · ([color=#0000ff]x[/color]+[color=#ff0000]3[/color])[br][/b][/size] [br] [br]Notiere die richtige Termumformung im Heft: [b]7 · (x + 3) = ...[/b]
Übung
Multipliziere aus. ([math]x\in\mathbb{Q}[/math])[br][br]a) 5 · (x + 6) =[br][br]b) 15 · (2 + x) =[br][br]c) x · (8 + x) =[br][br]d) 9 · (x – 6) =[br][br]e) –2 · (4 – x) =
– herr-fischer

5.2.

–

Information