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多位数退位减法互动练习

多位数退位减法互动练习
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2023-07-01 00:31
函数数列滑块动画
该范例是一个面向小学中高年级的多位数退位减法互动练习工具。它通过随机生成两个多位数，并利用退位（借位）方法进行减法运算，帮助学生掌握竖式减法中借位的核心概念。构造上使用了GeoGebra的RandomUniform、Sequence、Take、Zip、Flatten等命令生成随机数字和数位列表，通过expandedFormList将数字展开为位值形式，并利用Textfield、Polygon、TableText等对象构建交互界面和可视化展示。适合4-5年级学生在课堂或自主练习中使用，支持数字与文字应用题场景，并配有西班牙语翻译。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.6765099860589153, 0.2448906804719003, 0.965743662417109, 0.2700257935952639, 0.795603742092831, 0.18431861691713627, 0.9556890809533629, 0.6785957971735536, 0.47987926486332855, 0.2659917016360184, 0.6247586318271333, 0.7268310742277345, 0.0536008671884054, 0.7222673436693376, 0.8758357303442527, 0.841332385290648, 0.8642404583747006, 0.25348809985682497, 0.9262655468250942, 0.6533776313809219, 0.9240942421099986, 0.009915685044977382, 0.2697690182421031, 0.7328890288295509, 0.49136171092191294, 0.8702096185985724, 0.4804263281111081, 0.22731813835436213, 0.09640656615894279, 0.7600101700271955, 0.04417123111262404, 0.06728377604898082, 0.7951598788545767, 0.17440921012151328, 0.2818219617935929, 0.7471171744755178, 0.5500532745333303, 0.3980050875692775, 0.8634458247741386, 0.8094741278188502, 0.7994852361642794, 0.4458370970995477, 0.9768133744745555, 0.6288672671195586, 0.41962647901983563, 0.13778222139284443, 0.2828446652800553, 0.8493528044136188, 0.9873604641121773, 0.9379714530212493, 0.4782845062919538, 0.436673700972073, 0.3103326454305722, 0.8594451788023019, 0.030364026338105306, 0.2149180576615274, 0.67944783126232, 0.8926166011295132, 0.9499161868214598, 0.012194009964114193, 0.2807072521816503, 0.8441492741234046, 0.4083082007992278, 0.538953870389301, 0.3570173823490501, 0.7705797533603029, 0.7696388028376981, 0.7164181152534663, 0.526530238679826, 0.7684278130446397, 0.6129187023080517, 0.5210563476796649, 0.8121902267797292, 0.7896371521553631, 0.789412753769247, 0.30427485503181223, 0.24746520024698956, 0.8179757901018093, 0.25796777450243585, 0.27434207706967434, 0.16572976732936293, 0.06850059972900124, 0.005984691223554408, 0.870151112942159, 0.3154462636421543, 0.7683520152342334, 0.6057146337945756, 0.9636744302838373, 0.9301548196829516, 0.9129952155355825, 0.5547682064926909, 0.05990937202302385, 0.7613356072867707, 0.2675603349774407, 0.2961227426848774, 0.2497437680319011, 0.9334476625361596, 0.2581596204240087, 0.6064973681002017, 0.34248948052747374, 0.18387546436405383, 0.7629712223833854, 0.4127365322650348, 0.1408374245763089, 0.5761306369867655, 0.027478967789562277, 0.5238014708809159, 0.10168090647408379, 0.472457786804316, 0.8625444381134317, 0.3111164240671128, 0.5416354999838697, 0.7319848733809433, 0.10796254391069651, 0.36234947979079907, 0.8461510238674396, 0.6827351649165273, 0.9278137933846747, 0.5332299134444224, 0.5458683293905744, 0.5001841521326319, 0.2572759520970404, 0.7087127143405736, 0.7333156705648748, 0.7815962618149179, 0.2735949311210103, 0.668697704786411, 0.06717151704867991, 0.3041178233555574, 0.8766396544687214, 0.2845940281918776, 0.2901378083939857, 0.5855293795290686, 0.2968771043569987, 0.07129318445466037, 0.5899746921519107, 0.2396760057323325, 0.7507042326687905, 0.8245719191685629, 0.9214401640699491, 0.2538976151003215, 0.37485972810051144, 0.6765934029979169, 0.10975957178883287, 0.6532703182373943, 0.0031136176275427096, 0.2820083626753632, 0.8038178806712054, 0.036148758860248334, 0.34959495661697576, 0.5241805237560518, 0.3495236576699713, 0.29736390359166376, 0.9239670258603321, 0.21526820631447663, 0.9307371246072056, 0.1894836808609246, 0.8941968926914857, 0.4952916512482578, 0.03678523311554704, 0.528784137211107, 0.5628907712808506, 0.9838990883420102, 0.6619054786827646, 0.25100655680676354, 0.23307852593402278, 0.49431579730136005, 0.7429655812652918, 0.5025910945521296, 0.9089306383789459, 0.211920152943246, 0.9875000440644964, 0.0658802442692488, 0.7861773976160189, 0.16003631874981322, 0.5544846737071255, 0.24177576807803985, 0.3559758898559794, 0.3228677947372728, 0.30533956119873373, 0.2705104482012354, 0.9446307129236909, 0.6300172527398942, 0.5924058743063402, 0.0005610403648394991, 0.6899259412423079, 0.5087471849348015, 0.426585816015751, 0.1772819496517835, 0.8928611415268487, 0.16903211212798272, 0.14496581154310198, 0.4265789693821649, 0.7213103404014838, 0.2225378041836353, 0.18306094388876154, 0.16487036704847452, 0.1595339019553315, 0.4799333088428205, 0.9748254288326283}
  2. Sequence(qCoordX + 80 + (52.5 * n), n, 0, 4) → qCoordsX, {130, 182.5, 235, 287.5, 340}
  3. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  4. Zip(1 + floor((A * 9)), A, Take[currentRandomSeeds, 3, 3 + numDigits1 - 1]) → digitsNum1Start
  5. Zip(1 + floor((A * 9)), A, Take[currentRandomSeeds, 3 + numDigits1 - 1, 3 + numDigits1 + numDigits2 - 2]) → digitsNum2Start
  6. Flatten({If[digitsNum1Start(1) ≠ digitsNum2Start(1), Min[digitsNum1Start(1), digitsNum2Start(1)], digitsNum1Start(1) - 1], Max[digitsNum1Start(2), digitsNum2Start(2)], Take[digitsNum1Start, 3]}) → digitsNum1
  7. Flatten({Max[digitsNum1Start(1), digitsNum2Start(1)], If[digitsNum1Start(2) ≠ digitsNum2Start(2), Min[digitsNum1Start(2), digitsNum2Start(2)], digitsNum1Start(2) - 1], Take[digitsNum2Start, 3]}) → digitsNum2
  8. Min(nums) → num2
  9. Length(Text[num2]) → digitMin
  10. expandedFormList(num2) → num2Expanded
  11. If(digitMin > 4, num2Expanded(digitMin - 4), 0) → A2
  12. If(digitMin > 3, num2Expanded(digitMin - 3), 0) → B2
  13. Max(nums) → num1
  14. Length(Text[num1]) → digitMax
  15. Sequence((floor(num1 / 10^(digitMax - n)) * 10^(digitMax - n)) - (floor(num1 / 10^(digitMax - n + 1)) * 10^(digitMax - n + 1)), n, 1, digitMax) → num1Expanded, {90000, 2000, 800, 70, 8}
  16. If(F4 < F2, E1 - 10^(E3), E1) → E4
  17. If(E4 < E2, E4 + 10^(E3 + 1), E4) → E5
  18. If(digitMax > 3, num1Expanded(digitMax - 3), 0) → B1
  19. If(digitMax > 4, num1Expanded(digitMax - 4), 0) → A1
  20. If(E4 < E2, D1 - 10^(D3), D1) → D4
  21. If(D4 < D2, D4 + 10^(D3 + 1), D4) → D5
  22. Last(startNum1List, digitMax) → num1ListInput
  23. If(D4 < D2, C1 - 10^(C3), C1) → C4
  24. If(C4 < C2, C4 + 10^(C3 + 1), C4) → C5
  25. If(C4 < C2, B1 - 10^(B3), B1) → B4
  26. If(B4 < B2, B4 + 10^(B3 + 1), B4) → B5
  27. If(B4 < B2, A1 - 10^(A3), A1) → A4
  28. If(A4 < A2, A4 + 10^(A3 + 1), A4) → A5
  29. Last(startTops, digitMax) → Tops
  30. KeepIf(k > 0, k, Sequence[If[num1ListInput(n) ≠ Tops(n), n, 0], n, 1, digitMax]) → allCancel
  31. Zip(PixelsToPoint[Corner[1], Corner[3], Corner[5], (qCoordsX(n) + 16.5, qCoordY + 35)], n, allCancel) → OnboardingPoints
  32. Length(Tops) → lenTops
  33. Max(RemoveUndefined[Sequence[If[¬(boolColorTop(n)), n], n, 1, lenTops]]) → topLastIncorrect
  34. Sequence(If[n ≟ topLastIncorrect, true, false], n, 1, 5) → hintColorTop
  35. Zip(n ∧ k, n, hintColorTop, k, numFill) → boolTopBox
  36. Last(startAnswers, digitMax) → Answers
  37. Length(Answers) → lenAnswer
  38. Max(RemoveUndefined[Sequence[If[¬(boolColorBottom(n)), n], n, 1, lenAnswer]]) → bottomLastIncorrect
  39. First({inputTop1, inputTop2, inputTop3, inputTop4, inputTop5}, digitMax) → startInputTops
  40. Zip(If[Defined[n], n, k], n, startInputTops, k, num1ListInput) → inputTops
  41. If(Defined[num1ListInput(bottomLastIncorrect)], {num1ListInput(bottomLastIncorrect), Tops(bottomLastIncorrect), inputTops(bottomLastIncorrect)}, {0, 0, 0}) → cancelCurrent
  42. If(Defined[num1ListInput(bottomLastIncorrect + 1)], {num1ListInput(bottomLastIncorrect + 1), Tops(bottomLastIncorrect + 1), inputTops(bottomLastIncorrect + 1)}, {-1, -1, -1}) → cancelNext
  43. If(Defined[topLastIncorrect], num1ListInput(topLastIncorrect), 0) → num1T1
  44. Last(Flatten[{Sequence[0, n, 1, 5 - digitMin], Sequence[num2Expanded(n) / 10^(digitMin - n), n, 1, digitMin]}], digitMax) → num2ListNums
  45. If(Defined[num2ListNums(bottomLastIncorrect)], num2ListNums(bottomLastIncorrect), 0) → num2ValCurrent
  46. If(Defined[num2ListNums(bottomLastIncorrect + 1)], num2ListNums(bottomLastIncorrect + 1), -1) → num2ValNext
  47. If(Defined[num1ListInput(bottomLastIncorrect - 1)], {num1ListInput(bottomLastIncorrect - 1), Tops(bottomLastIncorrect - 1), inputTops(bottomLastIncorrect - 1), num2ListNums(bottomLastIncorrect - 1)}, {100, 100, 100, 100}) → cancelBefore
  48. If(¬Defined[bottomLastIncorrect], 7, If[num1CC2 ≟ num1CC3, If[num1CN2 ≟ num1CN3, 3, 1], num1CC2 ≟ num1CC3 - 1, 6, num1CC2 ≟ num1CC3 + 1 ∨ num1CC3 ≟ num1CC2 + 10, 8, num1CN1 ≟ num1CN2, 2, num1CB1 < num2CB4, 4, 5]) → answerCase
  49. If(answerCase ≟ 1, num2ValNext, num2ValCurrent) → num2Val
  50. If(cancelNext(2) ≟ cancelNext(3), cancelNext(1), cancelCurrent(1)) → num1ValNext_{1}
  51. Max(Sequence[If[num1ListInput(n) ≠ Tops(n), n, 0], n, 1, digitMax]) → maxCancel
  52. Flatten({"", Answers}) → numAnswerList
  53. Flatten({"", Zip[If[n ≟ k, "", "" + (k)], n, num1ListInput, k, Tops]}) → num1Tops
  54. First({input1, input2, input3, input4, input5}, digitMax) → inputAnswers
  55. Flatten({Zip[n ≟ k, n, inputAnswers, k, Answers], Last[{false, false, false, false, false}, 5 - lenAnswer]}) → topValidateAns
  56. Flatten({"", Zip[If[n ≟ k, "" + (k), "\cancel{" + (k) + "}"], k, num1ListInput, n, Tops]}) → num1Cancel
  57. Zip(If[n, "#8CBAB4", "#DB8C9A"], n, boolColorBottom) → colorsBottomSol
  58. Sequence(If[Defined[bottomLastIncorrect] ∧ n < bottomLastIncorrect, true, boolColorBottom(n)], n, 1, 5) → boolColorBottomHint
  59. Sequence(If[boolColorBottomHint(n), If[n > bottomLastIncorrect, "#8CBAB4", "#ffffff"], "#E6B08C"], n, 1, 5) → colorsBottomHint
  60. Flatten({Sequence[0, n, 1, 5 - digitMax], Sequence[num1Expanded(n) / 10^(digitMax - n), n, 1, digitMax]}) → num1ListNums
  61. Flatten({"-", Sequence["", n, 1, digitMax - digitMin], Sequence[num2Expanded(n) / 10^(digitMin - n), n, 1, digitMin]}) → num2Sub
  62. Sequence(If[hintColorValidate(n), "#C75000", "#252525"], n, 1, 5) → hintColors
  63. Flatten({Sequence["", n, 1, 5 - digitMax], Sequence[num1Expanded(n) / 10^(digitMax - n), n, 1, digitMax]}) → num1List
  64. Sequence(Corner[textnum1a, n], n, 1, 4) → CornersOnboarding
  65. Midpoint(CornersOnboarding(1), CornersOnboarding(3)) → InputPoint
  66. Flatten({Sequence["", n, 1, 5 - digitMin], Sequence[num2Expanded(n) / 10^(digitMin - n), n, 1, digitMin]}) → num2List
  67. Flatten({Sequence[0, n, 1, digitMax - digitMin], num2Expanded}) → num2Expanded0
  68. Flatten({inputAnswers, inputTops}) → inputCurrent
  69. Textfield(input1) → InputBox1
  70. Textfield(input2) → InputBox2
  71. Polygon(Zip[PixelsToPoint[Corner[1], Corner[3], Corner[5], A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, y(Corner[5]) - pixelsBottom), Corner[5] - (pixelsRight, pixelsBottom), (x(Corner[5]) - pixelsRight, pixelsTop)}]) → borderBox
  72. Corner(5) → layoutAppSize
  73. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  74. If(E4 ≠ E1, If[E5 ≠ E4, 2, 1], E5 ≠ E4, 1, 0) → E6
  75. If(E4 ≠ E1, If[E5 ≠ E4, 2, 1], E5 ≠ E4, 1, 0) → A6
  76. If(B4 ≠ B1, If[B5 ≠ B4, 2, 1], B5 ≠ B4, 1, 0) → B6
  77. If(C4 ≠ C1, If[C5 ≠ C4, 2, 1], C5 ≠ C4, 1, 0) → C6
  78. If(D4 ≠ D1, If[D5 ≠ D4, 2, 1], D5 ≠ D4, 1, 0) → D6
  79. Flatten({"", Sequence["\phantom{" + (num1Expanded(n) / 10^(digitMax - n)) + "}", n, 1, digitMax]}) → num1Sub
  80. Sequence(qCoordX + 75 + (52.5 * n), n, 0, 4) → solCoordsX, {125, 177.5, 230, 282.5, 335}
  81. Textfield(input3) → InputBox3
  82. Textfield(input4) → InputBox4
  83. Textfield(input5) → InputBox5
  84. Textfield(inputTop1) → InputTopBox1
  85. Textfield(inputTop2) → InputTopBox2
  86. Textfield(inputTop3) → InputTopBox3
  87. Textfield(inputTop4) → InputTopBox4
  88. Textfield(inputTop5) → InputTopBox5
  89. Flatten({Zip[n ≟ k, n, inputTops, k, Tops], Last[{false, false, false, false, false}, 5 - lenTops]}) → topValidateTop
  90. TableText({num1Tops, num1Cancel, num2Sub, numAnswerList}, "c00_00010", 1, 30) → tableAns
  91. Sequence(If[n ≟ bottomLastIncorrect, true, false], n, 1, 5) → hintColor
  92. PixelsToPoint(Corner[1], Corner[3], Corner[5], (qCoordsX(digitMax), qCoordY + 12)) → Cornernum1
  93. If(showsolution, colorsBottomSol, colorsBottomHint) → colorsBottom
  94. Sequence(If[Defined[topLastIncorrect] ∧ n < topLastIncorrect, true, boolColorTop(n)], n, 1, 5) → boolColorTopHint
  95. Zip(If[n, "#8CBAB4", "#DB8C9A"], n, boolColorTop) → colorsTopSol
  96. Sequence(If[¬(boolTopBox(n)), If[n > topLastIncorrect, "#8CBAB4", "#ffffff"], "#E6B08C"], n, 1, 5) → colorsTopHint
  97. If(showsolution, colorsTopSol, colorsTopHint) → colorsTop
  98. PixelsToPoint(Corner[1], Corner[3], Corner[5], (qCoordsX(maxCancel), qCoordY + 12)) → OnboardingCorner
  99. If(Defined[topLastIncorrect], Flatten[{Sequence["#252525", n, 1, topLastIncorrect - 1], "#C75000", Sequence["#252525", n, 1, lenTops - topLastIncorrect]}], Sequence["#252525", n, 1, lenTops]) → topColors
  100. circlePixels(If[Defined[OnboardingPoints(pulsingIndDisplay)], OnboardingPoints(pulsingIndDisplay), InputPoint], 9 + (9 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObject

AI 绘图提示语参考

这是一个用于练习多位数减法（进位法）的交互式竖式减法图形。图形包含两个随机生成的多位数输入框，每个输入框显示一个数字，并显示其各位数字的展开形式。竖式减法步骤以垂直排列的数字对呈现，从被减数到减数，每一步都标明进位操作。图形还包含一个提示区域，当输入错误时显示提示信息，以及一个结果显示区域。构造顺序是：先随机生成两个多位数，然后显示它们的展开形式，接着绘制竖式减法步骤，最后添加提示和结果区域。
以上提示语为根据原始绘图命令整理而来，仅供参考。