Generator für das Addieren/Subtrahieren dreier ungleichnamiger Brüche
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168
aufgabengenerator_brueche_addieren_ungleichnamig_v6.py
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168
aufgabengenerator_brueche_addieren_ungleichnamig_v6.py
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import xml.etree.ElementTree as ET
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import random
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from math import gcd
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def create_cloze_question(name, questiontext, correct_answers, wrong_answers, feedback, tags):
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question = ET.Element('question', attrib={'type': 'cloze'})
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name_elem = ET.SubElement(question, 'name')
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text_elem = ET.SubElement(name_elem, 'text')
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text_elem.text = name
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questiontext_elem = ET.SubElement(question, 'questiontext', attrib={'format': 'html'})
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text_elem = ET.SubElement(questiontext_elem, 'text')
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# Erstelle die Tabelle für die Lücken
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cloze_text = "<table style='border-collapse: collapse;'>"
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cloze_text += "<tr>"
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cloze_text += f"<td style='border-bottom: 1px solid black; padding: 5px;'>Zähler: {{1:SHORTANSWER:={correct_answers[0]}~%0%{wrong_answers[0][0]}#{wrong_answers[0][1]}}}</td>"
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cloze_text += "</tr>"
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cloze_text += "<tr>"
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cloze_text += f"<td style='padding: 5px;'>Nenner: {{1:SHORTANSWER:={correct_answers[1]}~%0%{wrong_answers[1][0]}#{wrong_answers[1][1]}}}</td>"
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cloze_text += "</tr>"
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# Prüfe, ob der Bruch gekürzt werden kann
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if gcd(correct_answers[0], correct_answers[1]) > 1:
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common_divisor = gcd(correct_answers[0], correct_answers[1])
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reduced_numerator = correct_answers[0] // common_divisor
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reduced_denominator = correct_answers[1] // common_divisor
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cloze_text += "<tr>"
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cloze_text += f"<td style='border-bottom: 1px solid black; padding: 5px;'>Gekürzter Zähler: {{1:SHORTANSWER:={reduced_numerator}~%0%{wrong_answers[2][0]}#{wrong_answers[2][1]}}}</td>"
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cloze_text += "</tr>"
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cloze_text += "<tr>"
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cloze_text += f"<td style='padding: 5px;'>Gekürzter Nenner: {{1:SHORTANSWER:={reduced_denominator}~%0%{wrong_answers[3][0]}#{wrong_answers[3][1]}}}</td>"
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cloze_text += "</tr>"
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cloze_text += "</table>"
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# Füge die Frage hinzu
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text_elem.text = questiontext + " " + cloze_text
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generalfeedback_elem = ET.SubElement(question, 'generalfeedback', attrib={'format': 'html'})
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text_elem = ET.SubElement(generalfeedback_elem, 'text')
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# Musterlösung im LaTeX-Format
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if gcd(correct_answers[0], correct_answers[1]) > 1:
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solution = f"Die Musterlösung ist: \\( \\Large \\displaystyle \\frac{{{reduced_numerator}}}{{{reduced_denominator}}} \\)."
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else:
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solution = f"Die Musterlösung ist: \\( \\Large \\displaystyle \\frac{{{correct_answers[0]}}}{{{correct_answers[1]}}} \\)."
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text_elem.text = solution
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defaultgrade_elem = ET.SubElement(question, 'defaultgrade')
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defaultgrade_elem.text = '1.0000000'
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penalty_elem = ET.SubElement(question, 'penalty')
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penalty_elem.text = '0.3333333'
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hidden_elem = ET.SubElement(question, 'hidden')
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hidden_elem.text = '0'
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# Tags hinzufügen
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tags_elem = ET.SubElement(question, 'tags')
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for tag in tags:
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tag_elem = ET.SubElement(tags_elem, 'tag')
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text_elem = ET.SubElement(tag_elem, 'text')
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text_elem.text = tag
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return question
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def lcm(a, b):
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return abs(a * b) // gcd(a, b)
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def create_quiz(questions):
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quiz = ET.Element('quiz')
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for q in questions:
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quiz.append(q)
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return quiz
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def save_to_file(xml_element, filename):
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tree = ET.ElementTree(xml_element)
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with open(filename, 'wb') as f:
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tree.write(f, encoding='utf-8', xml_declaration=True)
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questions = []
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# Generiere n Aufgaben zur Addition und Subtraktion von Brüchen mit verschiedenen Nennern
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n = 20
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for i in range(1, (n+1)):
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# Zähler und Nenner generieren
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numerator1 = random.randint(1, 20) # Zähler zwischen 1 und 20
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numerator2 = random.randint(1, 20) # Zähler zwischen 1 und 20
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numerator3 = random.randint(1, 20) # Zähler zwischen 1 und 20
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denominator1 = random.randint(2, 10) # Nenner zwischen 2 und 10
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denominator2 = random.randint(2, 10) # Nenner zwischen 2 und 10
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denominator3 = random.randint(2, 10) # Nenner zwischen 2 und 10
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# Berechne den gemeinsamen Nenner, der kleiner als 30 sein muss
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common_denominator = lcm(denominator1, lcm(denominator2, denominator3))
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while common_denominator >= 30:
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denominator1 = random.randint(2, 10)
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denominator2 = random.randint(2, 10)
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denominator3 = random.randint(2, 10)
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common_denominator = lcm(denominator1, lcm(denominator2, denominator3))
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# Berechne die äquivalenten Zähler
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equivalent_numerator1 = numerator1 * (common_denominator // denominator1)
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equivalent_numerator2 = numerator2 * (common_denominator // denominator2)
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equivalent_numerator3 = numerator3 * (common_denominator // denominator3)
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operations = random.choice(["+ +", "+ -", "- +", "- -"]) # Zufällige Operationen
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if operations == "+ +":
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result_numerator = equivalent_numerator1 + (equivalent_numerator2 + equivalent_numerator3)
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elif operations == "+ -":
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result_numerator = equivalent_numerator1 + (equivalent_numerator2 - equivalent_numerator3)
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elif operations == "- +":
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result_numerator = equivalent_numerator1 - (equivalent_numerator2 + equivalent_numerator3)
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else:
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result_numerator = equivalent_numerator1 - (equivalent_numerator2 - equivalent_numerator3)
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# Prüfe, ob der Bruch gekürzt werden kann
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needs_reduction = gcd(result_numerator, common_denominator) > 1
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# Frage im LaTeX-Format
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questiontext = (f"<p>Berechne und kürze das Ergebnis, wenn möglich:</p> "
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f"<p> \\( \\Large \\displaystyle \\frac{{{numerator1}}}{{{denominator1}}} {operations[0]} "
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f"\\left(\\frac{{{numerator2}}}{{{denominator2}}} {operations[2]} \\frac{{{numerator3}}}{{{denominator3}}}\\right) = \\) </p>")
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# Antworten
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correct_answers = [result_numerator, common_denominator]
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if needs_reduction:
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common_divisor = gcd(result_numerator, common_denominator)
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reduced_numerator = result_numerator // common_divisor
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reduced_denominator = common_denominator // common_divisor
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correct_answers.extend([reduced_numerator, reduced_denominator]) # Füge gekürzte Antworten hinzu
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wrong_answers = [
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(result_numerator + random.randint(1, 5), "Dieser Zähler ist zu hoch."), # Falscher Zähler
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(result_numerator - random.randint(1, 5), "Dieser Zähler ist zu niedrig."), # Falscher Zähler
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(reduced_numerator + random.randint(1, 3), "Dieser gekürzte Zähler ist nicht korrekt."), # Falscher gekürzter Zähler
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(reduced_denominator - random.randint(1, 3), "Dieser gekürzte Nenner ist nicht korrekt.") # Falscher gekürzter Nenner
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]
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else:
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wrong_answers = [
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(result_numerator + random.randint(1, 5), "Dieser Zähler ist zu hoch."), # Falscher Zähler
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(result_numerator - random.randint(1, 5), "Dieser Zähler ist zu niedrig.") # Falscher Zähler
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]
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feedback = "Richtig! Die Lösung ist korrekt."
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# Frage erstellen und hinzufügen
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questions.append(create_cloze_question(
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f"Addition/Subtraktion von 3 ungleichnamigen Brüchen {i}",
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questiontext,
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correct_answers,
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wrong_answers,
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feedback,
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["Mathematik", "Brüche", "Addition", "Subtraktion"]
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))
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# Erstelle das Quiz
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quiz = create_quiz(questions)
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# Speichere die XML-Datei
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save_to_file(quiz, 'cloze_fraction_addition_subtraction_quiz.xml')
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print("Moodle-XML-Datei 'cloze_fraction_addition_subtraction_quiz.xml' erfolgreich erstellt.")
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