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指数简化练习 Level 1：将重复乘法改写为幂形式

指数简化练习 Level 1：将重复乘法改写为幂形式
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2024-04-24 21:32
函数数列滑块动画
所属专题 Potenzen - Einführung
本范例是一个面向初中生的交互式数学练习，演示如何将相同因数的重复乘法（如 2×2×2）改写为幂形式（如 2³），并验证学生对正整数指数含义的理解。核心数学概念是正整数指数的定义——指数表示底数重复相乘的次数，以及幂的读写与计算。作图要点：使用 GeoGebra 的 Join、Flatten、Sequence 等命令生成随机题目，通过 Textfield 和 InputBox1 接收学生输入，利用 TextToUnicode、If、Numerator、Denominator、Element 等命令解析并比较答案，配合 SpeechBubbleRight 和按钮（btnValidate、btnNew、btnTryAgain）提供即时反馈与重试机制。适合七年级至八年级学生，用于课堂练习或课后巩固，帮助学生从重复乘法过渡到指数表示，培养代数符号意识。

GeoGebra 命令及参数

  1. Join(Sequence[Shuffle[{1, 2}], k, 1, 100]) → CaseList
  2. Flatten(Join[{{1, 1}, Sequence[Shuffle[{1, 2, 3}], k, 1, 67]}]) → NumberCaseList
  3. Sequence(RandomElement[Remove[Sequence[-5 + (0.1 * k), k, 1, 100], {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}]], m, 1, 200) → DecimalList, {3.9000000000000004, 4.700000000000001, -4.1, -4.8, -2.3, 1.7000000000000002, 4.300000000000001, -0.2999999999999998, 3.200000000000001, 2.7, 1.1000000000000005, 4.700000000000001, -4.1, -4.6, 4.600000000000001, -1.1999999999999997, 4.5, 2.1000000000000005, -2.0999999999999996, -2.0999999999999996, -0.7999999999999998, 2.7, -4.4, 4.5, 1.6000000000000005, 0.5, -3.3, -3.9, -2.0999999999999996, -4.7, 3.8000000000000007, -2.6999999999999997, -1.7999999999999998, -1.4, -1.1999999999999997, 0.20000000000000018, 0.40000000000000036, -1.2999999999999998, -4.3, -0.09999999999999964, -3.5999999999999996, 1.5, 4.1, 4.200000000000001, 0.3000000000000007, 3.4000000000000004, 0.40000000000000036, -3.5999999999999996, 4.700000000000001, 1.9000000000000004, -1.6999999999999997, 4.1, -4.2, -4.9, -1.1999999999999997, 2.8000000000000007, -1.4, -0.5999999999999996, -4.3, 3.0999999999999996, -2.9, -1.5, -2.3, -1.4, 2.6000000000000005, -3.5, 0.5, -3.0999999999999996, -1.5, -0.1999999999999993, -0.1999999999999993, 4.5, 0.7000000000000002, -4.9, 3.3000000000000007, 3.5999999999999996, -0.5999999999999996, -4.1, 3.700000000000001, -0.1999999999999993, -1.0999999999999996, 3.9000000000000004, -4.2, 4.5, 1.2000000000000002, 2.2, -1.0999999999999996, 3.9000000000000004, 2.9000000000000004, -0.5, 2.6000000000000005, -1.4, 2.2, 0.7000000000000002, -3.3, -3.7, -1.4, 4.4, -3.5999999999999996, 1.9000000000000004, 3.200000000000001, -2.9, 4.800000000000001, -4.2, 3.0999999999999996, -0.39999999999999947, -4.8, -2.9, -1.5999999999999996, 0.6000000000000005, 3.0999999999999996, -0.09999999999999964, 0.20000000000000018, 3.0999999999999996, -1.2999999999999998, 0.10000000000000053, 0.40000000000000036, 2.8000000000000007, 2.9000000000000004, -1.9, 2.9000000000000004, 1.7000000000000002, -0.39999999999999947, -3.4, -0.7000000000000002, 3.5999999999999996, 1.8000000000000007, 4.9, 0.40000000000000036, -2.4, 0.8000000000000007, -1.5, -0.09999999999999964, 4.4, 2.8000000000000007, 4.300000000000001, -1.5, -1.4, -0.09999999999999964, -4.1, 1.4000000000000004, 4.1, 1.8000000000000007, 2.1000000000000005, -4.7, 0.5, -2.6999999999999997, 4.200000000000001, -2.5, -0.7999999999999998, 1.1000000000000005, -3.8, -2.9, 4.4, 3.5, 3.5, -0.7999999999999998, 3.5, -4.7, -4.5, -0.09999999999999964, 2.5, -2.5, -3.3, 0.5, -1.0999999999999996, 2.6000000000000005, 1.1000000000000005, -2.5, 1.9000000000000004, -3.9, -2.5, -4.5, 0.7000000000000002, 3.9000000000000004, -2.9, -4.6, 1.4000000000000004, 2.2, -0.8999999999999995, 2.6000000000000005, 3.8000000000000007, -3.0999999999999996, -0.8999999999999995, -2.0999999999999996, -0.8999999999999995, -3.7, 2.1000000000000005, -3.0999999999999996, -3.9, 2.4000000000000004, 2.7, 3.5, 0.5, 3.700000000000001, -4.5, -4.5, 3.3000000000000007, 4.9, 4.800000000000001}
  4. Sequence(RandomElement[{1 / 9, 2 / 9, 4 / 9, 5 / 9, 7 / 9, 8 / 9, 1 / 8, 3 / 8, 5 / 8, 7 / 8, 1 / 7, 2 / 7, 3 / 7, 4 / 7, 5 / 7, 6 / 7, 1 / 6, 5 / 6, 1 / 5, 2 / 5, 3 / 5, 4 / 5, 1 / 4, 3 / 4, 1 / 3, 2 / 3, 1 / 2}], k, 1, 200) → FractionList, {0.125, 0.6666666666666666, 0.125, 0.6666666666666666, 0.6, 0.5555555555555556, 0.2857142857142857, 0.6666666666666666, 0.3333333333333333, 0.3333333333333333, 0.16666666666666666, 0.875, 0.875, 0.5714285714285714, 0.875, 0.14285714285714285, 0.875, 0.625, 0.2222222222222222, 0.75, 0.7777777777777778, 0.2222222222222222, 0.16666666666666666, 0.75, 0.7777777777777778, 0.8888888888888888, 0.8571428571428571, 0.16666666666666666, 0.16666666666666666, 0.7142857142857143, 0.2857142857142857, 0.4444444444444444, 0.4, 0.625, 0.4, 0.16666666666666666, 0.16666666666666666, 0.125, 0.875, 0.1111111111111111, 0.7777777777777778, 0.5555555555555556, 0.5555555555555556, 0.1111111111111111, 0.4, 0.7142857142857143, 0.7142857142857143, 0.14285714285714285, 0.6666666666666666, 0.42857142857142855, 0.7142857142857143, 0.1111111111111111, 0.125, 0.16666666666666666, 0.625, 0.3333333333333333, 0.8, 0.6666666666666666, 0.5555555555555556, 0.5, 0.2, 0.14285714285714285, 0.8, 0.375, 0.5555555555555556, 0.6, 0.2222222222222222, 0.2222222222222222, 0.5555555555555556, 0.5, 0.5555555555555556, 0.7142857142857143, 0.16666666666666666, 0.3333333333333333, 0.6666666666666666, 0.4, 0.5714285714285714, 0.4444444444444444, 0.2222222222222222, 0.5714285714285714, 0.16666666666666666, 0.125, 0.375, 0.625, 0.875, 0.14285714285714285, 0.7142857142857143, 0.2222222222222222, 0.875, 0.8571428571428571, 0.2222222222222222, 0.5555555555555556, 0.8, 0.6, 0.2222222222222222, 0.6, 0.2222222222222222, 0.5, 0.7777777777777778, 0.14285714285714285, 0.4444444444444444, 0.16666666666666666, 0.8888888888888888, 0.2222222222222222, 0.1111111111111111, 0.8, 0.7142857142857143, 0.875, 0.14285714285714285, 0.7777777777777778, 0.5714285714285714, 0.8, 0.2857142857142857, 0.5714285714285714, 0.5, 0.6, 0.6, 0.5714285714285714, 0.42857142857142855, 0.2222222222222222, 0.75, 0.5714285714285714, 0.7142857142857143, 0.2857142857142857, 0.625, 0.8333333333333334, 0.1111111111111111, 0.8571428571428571, 0.1111111111111111, 0.8333333333333334, 0.2222222222222222, 0.5714285714285714, 0.1111111111111111, 0.5714285714285714, 0.7142857142857143, 0.4444444444444444, 0.16666666666666666, 0.25, 0.2857142857142857, 0.75, 0.8333333333333334, 0.7142857142857143, 0.14285714285714285, 0.14285714285714285, 0.1111111111111111, 0.42857142857142855, 0.8333333333333334, 0.5714285714285714, 0.25, 0.5555555555555556, 0.6666666666666666, 0.75, 0.42857142857142855, 0.5, 0.7777777777777778, 0.1111111111111111, 0.125, 0.5714285714285714, 0.4, 0.375, 0.125, 0.6666666666666666, 0.6, 0.5714285714285714, 0.2857142857142857, 0.4444444444444444, 0.7777777777777778, 0.125, 0.8571428571428571, 0.4, 0.125, 0.7142857142857143, 0.8333333333333334, 0.7777777777777778, 0.375, 0.125, 0.625, 0.16666666666666666, 0.375, 0.4, 0.1111111111111111, 0.5, 0.8333333333333334, 0.5714285714285714, 0.5555555555555556, 0.7142857142857143, 0.2, 0.8571428571428571, 0.2857142857142857, 0.14285714285714285, 0.2222222222222222, 0.4, 0.6666666666666666, 0.5, 0.625, 0.8888888888888888, 0.4444444444444444, 0.42857142857142855, 0.6666666666666666, 0.8}
  5. Textfield(input1) → InputBox1
  6. Join({{RandomElement[2…10], RandomElement[2…10]}, Sequence[RandomElement[{-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}], k, 1, 198]}) → IntegerList
  7. Sequence(RandomElement[{2, 3, 4, 5, 6}], k, 1, 200) → FactorExpList, {3, 3, 4, 2, 6, 3, 2, 6, 4, 2, 3, 6, 3, 6, 6, 2, 3, 3, 4, 3, 4, 3, 2, 4, 5, 6, 6, 2, 4, 3, 5, 5, 3, 4, 2, 2, 5, 2, 4, 4, 3, 2, 4, 6, 6, 3, 5, 6, 6, 2, 2, 6, 5, 6, 2, 4, 2, 3, 4, 2, 4, 6, 5, 2, 4, 2, 4, 4, 4, 2, 6, 3, 6, 2, 6, 5, 6, 6, 6, 2, 5, 5, 3, 3, 6, 4, 6, 6, 5, 5, 4, 6, 5, 4, 3, 2, 4, 5, 5, 3, 4, 6, 5, 4, 5, 6, 6, 4, 2, 3, 2, 2, 2, 4, 2, 2, 5, 3, 2, 3, 4, 6, 4, 6, 2, 2, 6, 5, 3, 6, 6, 4, 5, 4, 2, 6, 3, 4, 2, 4, 4, 5, 5, 4, 6, 5, 4, 5, 4, 5, 2, 6, 3, 2, 3, 5, 2, 5, 4, 4, 5, 2, 2, 6, 2, 5, 3, 2, 5, 3, 5, 3, 6, 4, 2, 6, 3, 5, 5, 4, 5, 5, 6, 4, 2, 2, 3, 6, 2, 5, 5, 4, 4, 2, 6, 3, 4, 5, 6, 4}
  8. TextToUnicode((InputBox1 * "")) → uniUser
  9. If(NumberCase ≟ 1, IntegerList(counter), NumberCase ≟ 2, DecimalList(counter), FractionList(counter)) → num
  10. If(Case ≟ 1, (expo * num), num^(expo)) → sol
  11. Numerator(frac) → fracN
  12. Denominator(frac) → fracD
  13. If(NumberCase ≠ 3, TextToUnicode[("" * num)], {LetterToUnicode[("" * fracN)], 47, LetterToUnicode[("" * fracD)]}) → uniNum
  14. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {8, 3, 6, 7, 2, 9, 5, 8, 9, 1}
  15. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  16. TextToUnicode("*") → uniMultList
  17. Join({TextToUnicode["^²³"], {8308, 8309, 8310, 8311, 8312, 8313}}) → uniExpList
  18. If(Case ≟ 1, "+", "\cdot") → symb
  19. If(NumberCase ≟ 1, txtInt, NumberCase ≟ 2, txtDec, txtFrac) → txtNum
  20. SpeechBubbleRight(PosSB, sbwidth, sbheight) → poly1

AI 绘图提示语参考

画一个数学练习题，包含10个随机的整数、小数和分数，每个数后面跟着一个随机的指数，例如2^3或1.5^4。整数用加号连接，小数和分数用乘号连接，最后将每个表达式转换为指数形式，如2×2×2变为2³。
以上提示语为根据原始绘图命令整理而来，仅供参考。