239 lines
10 KiB
Python
239 lines
10 KiB
Python
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import random
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from math import gcd
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import xml.etree.ElementTree as ET
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def lcm(a, b):
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"""Berechnet das kleinste gemeinsame Vielfache."""
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return abs(a * b) // gcd(a, b)
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def create_formula_question(numerator1, denominator1, numerator2, denominator2, n):
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"""Erzeugt eine Frage im Format 'Formulas'."""
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# GCD und das kleinste gemeinsame Vielfache für die Denominator
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common_denominator = lcm(denominator1, denominator2)
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new_numerator = (numerator1 * (common_denominator // denominator1)) - (numerator2 * (common_denominator // denominator2))
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gcd_result = gcd(new_numerator, common_denominator)
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if gcd_result > 1:
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print("kürzbar")
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shortable = True
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shortened_numerator = new_numerator // gcd_result
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shortened_denominator = common_denominator // gcd_result
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else:
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shortable = False
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question = ET.Element('question', attrib={'type': 'formulas'})
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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 = 'Subtraktion von 2 ungleichnamigen Brüchen {} E'.format(n)
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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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if shortable:
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text_elem.text = '''<![CDATA[ <p>Subtrahiere die Brüche und kürze das Ergebnis so weit wie möglich.</p>
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<p>{#A} </p> ]]> '''
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else:
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text_elem.text = '''<![CDATA[ <p>Subtrahiere die beiden Brüche.</p>
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<p>{#A} </p> ]]> '''
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# Allgemeines Feedback
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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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text_elem.text = ' '
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# Grundlegende Bewertungsinformationen
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ET.SubElement(question, 'defaultgrade').text = '1.0000000'
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ET.SubElement(question, 'penalty').text = '0.3333333'
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ET.SubElement(question, 'hidden').text = '0'
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ET.SubElement(question, 'idnumber').text = ' '
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# Feedback für korrekte und inkorrekte Antworten
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correctfeedback_elem = ET.SubElement(question, 'correctfeedback', attrib={'format': 'html'})
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text_elem = ET.SubElement(correctfeedback_elem, 'text')
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text_elem.text = '''<![CDATA[ <p>Die Antwort ist richtig.</p> ]]> '''
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partiallycorrectfeedback_elem = ET.SubElement(question, 'partiallycorrectfeedback', attrib={'format': 'html'})
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text_elem = ET.SubElement(partiallycorrectfeedback_elem, 'text')
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text_elem.text = '''<![CDATA[ <p>Die Antwort ist teilweise richtig.</p> ]]> '''
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incorrectfeedback_elem = ET.SubElement(question, 'incorrectfeedback', attrib={'format': 'html'})
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text_elem = ET.SubElement(incorrectfeedback_elem, 'text')
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text_elem.text = '''<![CDATA[ <p>Die Antwort ist falsch.</p> ]]>'''
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ET.SubElement(question, 'shownumcorrect')
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varsrandom_elem = ET.SubElement(question, 'varsrandom')
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text_elem = ET.SubElement(varsrandom_elem, 'text')
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text_elem.text = f' '
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# Globale Variablen definieren
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varsglobal_elem = ET.SubElement(question, 'varsglobal')
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text_elem = ET.SubElement(varsglobal_elem, 'text')
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text_elem.text = f'n = [{numerator1}, {numerator2}];\n d = [{denominator1}, {denominator2}];'
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answernumbering_elem = ET.SubElement(question, 'answernumbering')
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text_elem = ET.SubElement(answernumbering_elem, 'text')
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text_elem.text = 'ABCD'
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# Antworten definieren
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answers_elem = ET.SubElement(question, 'answers')
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# Indizes für die Antworten
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partindex_elem = ET.SubElement(answers_elem, 'partindex')
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ET.SubElement(partindex_elem, 'text').text = '0'
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placeholder_elem = ET.SubElement(answers_elem, 'placeholder')
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ET.SubElement(placeholder_elem, 'text').text = '#A'
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# Punktzahl auf Teilaufgabe
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answermark_elem = ET.SubElement(answers_elem, 'answermark')
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if shortable:
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ET.SubElement(answermark_elem, 'text').text = '2'
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else:
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ET.SubElement(answermark_elem, 'text').text = '1'
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answertype_elem = ET.SubElement(answers_elem, 'answertype')
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ET.SubElement(answertype_elem, 'text').text = '0'
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numbox_elem = ET.SubElement(answers_elem, 'numbox')
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ET.SubElement(numbox_elem, 'text').text = '2'
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# Berechnungsvariablen
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vars1_elem = ET.SubElement(answers_elem, 'vars1')
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if shortable:
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vars1_elem_text = "<![CDATA[ g = gcd(d[0],d[1]);\n cd = abs(d[0] * d[1]) / g;\n e = [cd / d[0], cd / d[1]];\n nums = [n[0]*e[0], n[1]*e[1]];\n thesumnum = nums[0] - nums[1];\n gcdres = gcd(thesumnum,cd);\n snum = thesumnum / gcdres;\n sdenom = cd / gcdres;]]>"
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else:
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vars1_elem_text = "<![CDATA[ g = gcd(d[0],d[1]);\ncd = abs(d[0] * d[1]) / g;\ne = [cd / d[0], cd / d[1]];\nnums = [n[0]*e[0], n[1]*e[1]];\nthesumnum = nums[0] - nums[1];]]>"
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ET.SubElement(vars1_elem, 'text').text = vars1_elem_text
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# Antwort
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answer_elem = ET.SubElement(answers_elem, 'answer')
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if shortable:
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answer_text = '[thesumnum, cd, snum, sdenom]'
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else:
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answer_text = '[thesumnum, cd]'
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ET.SubElement(answer_elem, 'text').text = answer_text
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answernotunique_elem = ET.SubElement(answers_elem, 'answernotunique')
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ET.SubElement(answernotunique_elem, 'text').text = '0'
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vars2_elem = ET.SubElement(answers_elem, 'vars2')
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if shortable:
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vars2_elem_text = "<![CDATA[ ga = _0 == thesumnum && _1 == cd;\n gb = (_0 / _1) == (thesumnum / cd);\n gsa = _2 == snum && _3 == sdenom;\n gsb = (_2 / _3) == (snum / sdenom); ]]>"
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else:
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vars2_elem_text = "<![CDATA[ ga = _0 == thesumnum && _1 == cd; gb = (_0 / _1) == (thesumnum / cd); ]]>"
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ET.SubElement(vars2_elem, 'text').text = vars2_elem_text
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correctness_elem = ET.SubElement(answers_elem, 'correctness')
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if shortable:
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ET.SubElement(correctness_elem, 'text').text = '0.25*ga + 0.25*gb + 0.25*gsa + 0.25*gsb'
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else:
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ET.SubElement(correctness_elem, 'text').text = '0.5*ga + 0.5*gb'
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unitpenalty_elem = ET.SubElement(answers_elem, 'unitpenalty')
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ET.SubElement(unitpenalty_elem, 'text').text = '1'
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postunit_elem = ET.SubElement(answers_elem, 'postunit')
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ET.SubElement(postunit_elem, 'text').text = ' '
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ruleid_elem = ET.SubElement(answers_elem, 'ruleid')
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ET.SubElement(ruleid_elem, 'text').text = '1'
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otherrule_elem = ET.SubElement(answers_elem, 'otherrule')
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ET.SubElement(otherrule_elem, 'text').text = ' '
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# Unterfragen-Text
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subqtext_elem = ET.SubElement(answers_elem, 'subqtext', attrib={'format': 'html'})
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if shortable:
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sub_question_text = '''<![CDATA[ <p>Berechne:</p> <p>\\(\\Large \\displaystyle \\frac{{n[0]}}{{d[0]}} - \\frac{{n[1]}}{{d[1]}} =\\) {_0} / {_1} = gekürzt: {_2} / {_3}</p> ]]> '''
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else:
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sub_question_text = '''<![CDATA[ <p>Berechne:</p> <p>\\(\\Large \\displaystyle \\frac{{n[0]}}{{d[0]}} - \\frac{{n[1]}}{{d[1]}} =\\) {_0} / {_1}</p> ]]> '''
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ET.SubElement(subqtext_elem, 'text').text = sub_question_text
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# Lösungshinweis
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feedback_elem = ET.SubElement(answers_elem, 'feedback', attrib={'format': 'html'})
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if shortable:
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feedback_text = '''<![CDATA[ <h4>Lösungshinweis</h4>
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<p>Die korrekte Lösung ist:</p>
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<p>\\(\\Large \\displaystyle \\frac{{n[0]}}{{d[0]}} - \\frac{{n[1]}}{{d[1]}} = \\frac{{nums[0]}}{{cd}} - \\frac{{nums[1]}}{{cd}} = \\frac{{thesumnum}}{{cd}} = \\frac{{snum}}{{sdenom}} \\) </p> ]]>'''
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else:
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feedback_text = '''<![CDATA[ <h4>Lösungshinweis</h4>
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<p>Die korrekte Lösung ist:</p>
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<p>\\(\\Large \\displaystyle \\frac{{n[0]}}{{d[0]}} - \\frac{{n[1]}}{{d[1]}} = \\frac{{nums[0]}}{{cd}} - \\frac{{nums[1]}}{{cd}} = \\frac{{thesumnum}}{{cd}} \\) </p> ]]>'''
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ET.SubElement(feedback_elem, 'text').text = feedback_text
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# correctfeedback
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correctfeedback_elem = ET.SubElement(answers_elem, 'correctfeedback', attrib={'format': 'html'})
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correctfeedback_text = '''<![CDATA[ <p>Richtig!</p>]]>'''
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ET.SubElement(correctfeedback_elem, 'text').text = correctfeedback_text
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# partially correct feedback
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pcorrectfeedback_elem = ET.SubElement(answers_elem, 'partiallycorrectfeedback', attrib={'format': 'html'})
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pcorrectfeedback_text = '''<![CDATA[ <p>Teilweise richtig.</p>]]>'''
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ET.SubElement(pcorrectfeedback_elem, 'text').text = pcorrectfeedback_text
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# incorrect feedback
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incorrectfeedback_elem = ET.SubElement(answers_elem, 'incorrectfeedback', attrib={'format': 'html'})
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incorrectfeedback_text = '''<![CDATA[ <p>Leider nicht richtig.</p>]]>'''
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ET.SubElement(incorrectfeedback_elem, 'text').text = incorrectfeedback_text
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return question
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def generate_questions(num_questions):
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"""Generiert Aufgaben für die Addition ungleichnamiger Brüche."""
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questions = []
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for i in range(num_questions):
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numerator1 = random.randint(1, 10)
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denominator1 = random.randint(2, 10)
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numerator2 = random.randint(1, 10)
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denominator2 = random.randint(2, 10)
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# Sicherstellen, dass die Nenner unterschiedlich sind
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while denominator1 == denominator2:
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denominator2 = random.randint(2, 10)
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question = create_formula_question(numerator1, denominator1, numerator2, denominator2, i)
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questions.append(question)
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return questions
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def create_quiz(questions):
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"""Erzeugt die gesamte Quiz-Struktur."""
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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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"""Speichert das XML-Dokument in einer Datei."""
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tree = ET.ElementTree(xml_element)
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ET.indent(tree)
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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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def ersetze_vars2(xml_file):
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# XML-Datei lesen
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with open(xml_file, 'r') as f:
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text = f.read()
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text = text.replace("&","&")
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text = text.replace("<","<")
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text = text.replace(">",">")
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with open(xml_file, 'w') as f:
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f.write(text)
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# Hauptprogramm
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if __name__ == "__main__":
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num_questions = 20 # Anzahl der zu generierenden Aufgaben
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questions = generate_questions(num_questions)
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quiz = create_quiz(questions)
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save_to_file(quiz, 'formulas_fraction_addition_quiz.xml')
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ersetze_vars2('formulas_fraction_addition_quiz.xml')
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print("Moodle-XML-Datei 'formulas_fraction_addition_quiz.xml' erfolgreich erstellt.")
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