" + # Musterlösung im LaTeX-Format + if gcd(correct_answers[0], correct_answers[1]) > 1: + solution += f"\\( {question_math} {calcstep_math} = \\frac{{{correct_answers[0]}}}{{{correct_answers[1]}}} = \\frac{{{reduced_numerator}}}{{{reduced_denominator}}} \\)." + else: + solution += f"\\( {question_math} {calcstep_math} = \\frac{{{correct_answers[0]}}}{{{correct_answers[1]}}} \\)" + solution += "
" + + text_elem.text = solution + + defaultgrade_elem = ET.SubElement(question, 'defaultgrade') + defaultgrade_elem.text = '1.0000000' + + penalty_elem = ET.SubElement(question, 'penalty') + penalty_elem.text = '0.3333333' + + hidden_elem = ET.SubElement(question, 'hidden') + hidden_elem.text = '0' + + # Tags hinzufügen + tags_elem = ET.SubElement(question, 'tags') + for tag in tags: + tag_elem = ET.SubElement(tags_elem, 'tag') + text_elem = ET.SubElement(tag_elem, 'text') + text_elem.text = tag + + return question + +def lcm(a, b): + return abs(a * b) // gcd(a, b) + +def create_quiz(questions): + quiz = ET.Element('quiz') + for q in questions: + quiz.append(q) + return quiz + +def save_to_file(xml_element, filename): + tree = ET.ElementTree(xml_element) + with open(filename, 'wb') as f: + tree.write(f, encoding='utf-8', xml_declaration=True) + +questions = [] + +# Generiere n Aufgaben zur Addition und Subtraktion von Brüchen mit verschiedenen Nennern +n = 20 +for i in range(1, (n+1)): + # Zähler und Nenner generieren + numerator1 = random.randint(1, 20) # Zähler zwischen 1 und 20 + numerator2 = random.randint(1, 20) # Zähler zwischen 1 und 20 + denominator1 = random.randint(2, 10) # Nenner zwischen 2 und 10 + denominator2 = random.randint(2, 10) # Nenner zwischen 2 und 10 + + # Berechne den gemeinsamen Nenner, der kleiner als 30 sein muss + common_denominator = lcm(denominator1, denominator2) + while common_denominator >= 30: + denominator1 = random.randint(2, 10) + denominator2 = random.randint(2, 10) + common_denominator = lcm(denominator1, denominator2) + + # Berechne die äquivalenten Zähler + equivalent_numerator1 = numerator1 * (common_denominator // denominator1) + equivalent_numerator2 = numerator2 * (common_denominator // denominator2) + + operation = random.choice(["+", "-"]) # Zufällige Operation + if operation == "+": + result_numerator = equivalent_numerator1 + equivalent_numerator2 + else: + result_numerator = equivalent_numerator1 - equivalent_numerator2 + + # Prüfe, ob der Bruch gekürzt werden kann + needs_reduction = gcd(result_numerator, common_denominator) > 1 + + question_puremath = f"\\Large \\displaystyle \\frac{{{numerator1}}}{{{denominator1}}} {operation} \\frac{{{numerator2}}}{{{denominator2}}} =" + + # Frage im LaTeX-Format + questiontext = (f"Berechne und kürze das Ergebnis, wenn möglich:
" + f"\\( {question_puremath} \\)
") + + # Feedback-Ausgabe für notwendigen Zwischenschritt + calculation_step_math = f"\\frac{{{equivalent_numerator1}}}{{{common_denominator}}} {operation} \\frac{{{equivalent_numerator2}}}{{{common_denominator}}}" + + # Antworten + correct_answers = [result_numerator, common_denominator] + if needs_reduction: + common_divisor = gcd(result_numerator, common_denominator) + reduced_numerator = result_numerator // common_divisor + reduced_denominator = common_denominator // common_divisor + + correct_answers.extend([reduced_numerator, reduced_denominator]) # Füge gekürzte Antworten hinzu + + wrong_answers = [ + (result_numerator + random.randint(1, 5), "Dieser Zähler ist zu hoch."), # Falscher Zähler + (result_numerator - random.randint(1, 5), "Dieser Zähler ist zu niedrig."), # Falscher Zähler + (reduced_numerator + random.randint(1, 3), "Dieser gekürzte Zähler ist nicht korrekt."), # Falscher gekürzter Zähler + (reduced_denominator - random.randint(1, 3), "Dieser gekürzte Nenner ist nicht korrekt.") # Falscher gekürzter Nenner + ] + else: + wrong_answers = [ + (result_numerator + random.randint(1, 5), "Dieser Zähler ist zu hoch."), # Falscher Zähler + (result_numerator - random.randint(1, 5), "Dieser Zähler ist zu niedrig.") # Falscher Zähler + ] + + feedback = "Richtig! Die Lösung ist korrekt." + + # Frage erstellen und hinzufügen + questions.append(create_cloze_question( + f"Addition/Subtraktion von 2 ungleichnamigen Brüchen {i}", + questiontext, + question_puremath, + calculation_step_math, + correct_answers, + wrong_answers, + feedback, + ["Mathematik", "Brüche", "Addition", "Subtraktion"] + )) + +# Erstelle das Quiz +quiz = create_quiz(questions) + +# Speichere die XML-Datei +save_to_file(quiz, 'cloze_f2raction_addition_subtraction_quiz.xml') + +print("Moodle-XML-Datei 'cloze_2fraction_addition_subtraction_quiz.xml' erfolgreich erstellt.") diff --git a/aufgabengenerator_4brueche_addieren_ungleichnamig_v6.py b/aufgabengenerator_4brueche_addieren_ungleichnamig_v6.py new file mode 100644 index 0000000..d50dd23 --- /dev/null +++ b/aufgabengenerator_4brueche_addieren_ungleichnamig_v6.py @@ -0,0 +1,212 @@ +import xml.etree.ElementTree as ET +import random +from math import gcd +import re + +def create_html_table_for_fracture_input(rows: list): + table_rows = [] + # Tabellenzeilen festlegen + for i, row in enumerate(rows): + if (i % 2) == 0: + table_row = "" + # Musterlösung im LaTeX-Format + if gcd(correct_answers[0], correct_answers[1]) > 1: + solution += f"\\( {question_math} {calcstep_math} = \\frac{{{correct_answers[0]}}}{{{correct_answers[1]}}} = \\frac{{{reduced_numerator}}}{{{reduced_denominator}}} \\)." + else: + solution += f"\\( {question_math} {calcstep_math} = \\frac{{{correct_answers[0]}}}{{{correct_answers[1]}}} \\)" + solution += "
" + + text_elem.text = solution + + defaultgrade_elem = ET.SubElement(question, 'defaultgrade') + defaultgrade_elem.text = '1.0000000' + + penalty_elem = ET.SubElement(question, 'penalty') + penalty_elem.text = '0.3333333' + + hidden_elem = ET.SubElement(question, 'hidden') + hidden_elem.text = '0' + + # Tags hinzufügen + tags_elem = ET.SubElement(question, 'tags') + for tag in tags: + tag_elem = ET.SubElement(tags_elem, 'tag') + text_elem = ET.SubElement(tag_elem, 'text') + text_elem.text = tag + + return question + +def lcm(a, b): + return abs(a * b) // gcd(a, b) + +def create_quiz(questions): + quiz = ET.Element('quiz') + for q in questions: + quiz.append(q) + return quiz + +def save_to_file(xml_element, filename): + tree = ET.ElementTree(xml_element) + with open(filename, 'wb') as f: + tree.write(f, encoding='utf-8', xml_declaration=True) + +questions = [] + +# Generiere n Aufgaben zur Addition und Subtraktion von Brüchen mit verschiedenen Nennern +n = 20 +for i in range(1, (n+1)): + # Zähler und Nenner generieren + numerator1 = random.randint(1, 20) # Zähler zwischen 1 und 20 + numerator2 = random.randint(1, 20) # Zähler zwischen 1 und 20 + numerator3 = random.randint(1, 20) # Zähler zwischen 1 und 20 + numerator4 = random.randint(1, 20) # Zähler zwischen 1 und 20 + denominator1 = random.randint(2, 10) # Nenner zwischen 2 und 10 + denominator2 = random.randint(2, 10) # Nenner zwischen 2 und 10 + denominator3 = random.randint(2, 10) # Nenner zwischen 2 und 10 + denominator4 = random.randint(2, 10) # Nenner zwischen 2 und 10 + + # Berechne den gemeinsamen Nenner, der kleiner als 30 sein muss + common_denominator = lcm(denominator1, lcm(denominator2, lcm(denominator3, denominator4))) + while common_denominator >= 30: + denominator1 = random.randint(2, 10) + denominator2 = random.randint(2, 10) + denominator3 = random.randint(2, 10) + denominator4 = random.randint(2, 10) + common_denominator = lcm(denominator1, lcm(denominator2, lcm(denominator3, denominator4))) + + # Berechne die äquivalenten Zähler + equivalent_numerator1 = numerator1 * (common_denominator // denominator1) + equivalent_numerator2 = numerator2 * (common_denominator // denominator2) + equivalent_numerator3 = numerator3 * (common_denominator // denominator3) + equivalent_numerator4 = numerator4 * (common_denominator // denominator4) + + operations = random.choice(["+ + +", "+ + -", "+ - +", "+ - -", "- + +", "- + -", "- - +", "- - -"]) # Zufällige Operationen + if operations == "+ + +": + result_numerator = equivalent_numerator1 + (equivalent_numerator2 + (equivalent_numerator3 + equivalent_numerator4)) + elif operations == "+ + -": + result_numerator = equivalent_numerator1 + (equivalent_numerator2 + (equivalent_numerator3 - equivalent_numerator4)) + elif operations == "+ - +": + result_numerator = equivalent_numerator1 + (equivalent_numerator2 - (equivalent_numerator3 + equivalent_numerator4)) + elif operations == "+ - -": + result_numerator = equivalent_numerator1 + (equivalent_numerator2 - (equivalent_numerator3 - equivalent_numerator4)) + elif operations == "- + +": + result_numerator = equivalent_numerator1 - (equivalent_numerator2 + (equivalent_numerator3 + equivalent_numerator4)) + elif operations == "- + -": + result_numerator = equivalent_numerator1 - (equivalent_numerator2 + (equivalent_numerator3 - equivalent_numerator4)) + elif operations == "- - +": + result_numerator = equivalent_numerator1 - (equivalent_numerator2 - (equivalent_numerator3 + equivalent_numerator4)) + else: + result_numerator = equivalent_numerator1 - (equivalent_numerator2 - (equivalent_numerator3 - equivalent_numerator4)) + + # Prüfe, ob der Bruch gekürzt werden kann + needs_reduction = gcd(result_numerator, common_denominator) > 1 + + question_puremath = f"\\Large \\displaystyle \\frac{{{numerator1}}}{{{denominator1}}} {operations[0]} \\left(\\frac{{{numerator2}}}{{{denominator2}}} {operations[2]} \\left(\\frac{{{numerator3}}}{{{denominator3}}} {operations[4]} \\frac{{{numerator4}}}{{{denominator4}}}\\right)\\right) =" + + # Frage im LaTeX-Format + questiontext = (f"Berechne und kürze das Ergebnis, wenn möglich:
" + f"\\( {question_puremath} \\)
") + + # Feedback-Ausgabe für notwendigen Zwischenschritt + calculation_step_math = (f"\\frac{{{equivalent_numerator1}}}{{{common_denominator}}} {operations[0]} " + f"\\left(\\frac{{{equivalent_numerator2}}}{{{common_denominator}}} {operations[2]} " + f"\\left(\\frac{{{equivalent_numerator3}}}{{{common_denominator}}} {operations[4]} " + f"\\frac{{{equivalent_numerator4}}}{{{common_denominator}}}\\right)\\right)") + + # Antworten + correct_answers = [result_numerator, common_denominator] + if needs_reduction: + common_divisor = gcd(result_numerator, common_denominator) + reduced_numerator = result_numerator // common_divisor + reduced_denominator = common_denominator // common_divisor + + correct_answers.extend([reduced_numerator, reduced_denominator]) # Füge gekürzte Antworten hinzu + + wrong_answers = [ + (result_numerator + random.randint(1, 5), "Dieser Zähler ist zu hoch."), # Falscher Zähler + (result_numerator - random.randint(1, 5), "Dieser Zähler ist zu niedrig."), # Falscher Zähler + (reduced_numerator + random.randint(1, 3), "Dieser gekürzte Zähler ist nicht korrekt."), # Falscher gekürzter Zähler + (reduced_denominator - random.randint(1, 3), "Dieser gekürzte Nenner ist nicht korrekt.") # Falscher gekürzter Nenner + ] + else: + wrong_answers = [ + (result_numerator + random.randint(1, 5), "Dieser Zähler ist zu hoch."), # Falscher Zähler + (result_numerator - random.randint(1, 5), "Dieser Zähler ist zu niedrig.") # Falscher Zähler + ] + + feedback = "Richtig! Die Lösung ist korrekt." + + # Frage erstellen und hinzufügen + questions.append(create_cloze_question( + f"Addition/Subtraktion von 4 ungleichnamigen Brüchen {i}", + questiontext, + question_puremath, + calculation_step_math, + correct_answers, + wrong_answers, + feedback, + ["Mathematik", "Brüche", "Addition", "Subtraktion"] + )) + +# Erstelle das Quiz +quiz = create_quiz(questions) + +# Speichere die XML-Datei +save_to_file(quiz, 'cloze_4fraction_addition_subtraction_quiz.xml') + +print("Moodle-XML-Datei 'cloze_4fraction_addition_subtraction_quiz.xml' erfolgreich erstellt.")