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多位数减法的重组借位练习

多位数减法的重组借位练习
几何画板及绘图内容加载中，请稍等……
2023-10-04 02:27
函数几何作图滑块动画
该范例演示在进行两位数到三位数减法时，如何通过“重组/借位”策略保证逐位计算正确，并可生成多道练习题。核心数学概念包括位值表示、逐位减法、借位（尤其是十位与百位的借位链）以及对解的核对（是否存在期望的进/借位）。作图与交互要点：系统使用 RandomUniform 与 allRandomSeeds 生成随机题目，通过 NumDigits、digitHundredA/B、digitTenA/B、digitOneA/B 提取各位数字；再借助 Take、If、Sequence、Append、Flatten、Join 将输入与答案组织为可显示的形式；使用 TableText、Textfield、Text（onboardingTextOffset）呈现题干、提示与计算过程；通过 Element、Max、Min、Translate、Segment、Polygon 等对象对界面元素与局部提示进行布局；并用预设变量如 carryTens/carryHundreds、expectedCarries 与 carryHundredsOK 来检查借位逻辑是否满足，从而进行颜色标记与反馈（如 colorRedError）。适合4-5年级及小学中高年级用于计算策略训练，也可用于课堂讲解与作业生成。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.8492057074324373, 0.12433158968830253, 0.34215319866738986, 0.44231459234400966, 0.6473651295467706, 0.8856217160747685, 0.29113570036481773, 0.5157415198272105, 0.8092665561940475, 0.5381847843767462, 0.7952749042456214, 0.04609187862853864, 0.5413256383039124, 0.030850711602795056, 0.21267340908287974, 0.2901949834647718, 0.4322421087107492, 0.7793674680207053, 0.603884506140537, 0.7887210331329008, 0.9876069407078041, 0.6751356793936422, 0.8248243326110102, 0.7176168049138013, 0.7917196495084249, 0.4688903434803698, 0.03467044589428186, 0.5384260621983873, 0.1870975423439892, 0.4335207261654771, 0.43607931334086275, 0.148496586210677, 0.9717193435206259, 0.059075643861563505, 0.5100844160203446, 0.44515178211039624, 0.2720438395433533, 0.3777971767886727, 0.9465036368603207, 0.2219186649541273, 0.5262791950285559, 0.8377577781102008, 0.9525886645283406, 0.989855141396927, 0.3872523888561232, 0.2403460332722683, 0.057991106070516295, 0.5529082816859443, 0.23753811221771737, 0.6694532415014588, 0.33289934724917836, 0.6630609710742653, 0.43125487525005096, 0.30875864682130166, 0.3484166051912927, 0.5987887695335274, 0.21712154109107826, 0.017992603473123994, 0.0839056470970549, 0.9890494414459097, 0.7659904732749755, 0.9194779230614815, 0.2851165427122083, 0.6646662130678725, 0.5831342394316991, 0.37260625302509953, 0.28944402904117345, 0.07954255200527155, 0.2810604466454885, 0.6062017646254244, 0.8106269938465565, 0.1956592957035239, 0.2925653257774814, 0.2169564707240619, 0.6346076965991438, 0.7082565716205362, 0.3961095255863284, 0.14629169816328472, 0.0011093519817628372, 0.6609913062954162, 0.8464097389125678, 0.8581077656978697, 0.5217707292660816, 0.7351877629282921, 0.062388811503254364, 0.19592811705723234, 0.025392800734474537, 0.7825614415492149, 0.05231119120552951, 0.029927803248247762, 0.9240065610072525, 0.2869987137984263, 0.7320549327258961, 0.25225478448353955, 0.3900637922835167, 0.8181127068234463, 0.8770311422308358, 0.9329110458682173, 0.8950806406559428, 0.9473721008477354, 0.9112600312356101, 0.9882547140766904, 0.21353182146080585, 0.18661360357255205, 0.2785485440803763, 0.26991726364307495, 0.7126968237032798, 0.17869949553166814, 0.7505872819966136, 0.3735994458729148, 0.8395013936064804, 0.6909707068551378, 0.3750949364340533, 0.26481726547971207, 0.1191773141934596, 0.28397204516771946, 0.7438868862310932, 0.9722141224544769, 0.3477796895745042, 0.120689343284775, 0.4059297091808886, 0.7985377637326067, 0.17125562507428502, 0.975240499274474, 0.6340667755638437, 0.5148003460917473, 0.4778499217839783, 0.8645996572494968, 0.4561602065486333, 0.3144978490645501, 0.6281625601183358, 0.3025115094687916, 0.9118931527790097, 0.46205925868476233, 0.19813974455699387, 0.0012650028625795873, 0.6454111881142608, 0.7329291430080169, 0.8946845161149596, 0.23444763642475705, 0.6313552020034536, 0.20185667040372937, 0.8914145282363927, 0.8421902666419658, 0.5176485345594986, 0.9710716108682219, 0.9033742485938229, 0.5597379995129623, 0.3626489539139008, 0.21107289273634944, 0.85422532501698, 0.020446873979050855, 0.6469619569542473, 0.5437376998958342, 0.547593362899837, 0.6655070395041174, 0.5413347936799605, 0.1403789764481463, 0.6158409745558905, 0.4948318409837209, 0.8016109704656857, 0.3162364829513284, 0.4845664894783321, 0.2866283078273339, 0.5697233538297015, 0.7976818995225494, 0.2395941846717285, 0.10717828123702239, 0.14613929696002445, 0.5991503029392172, 0.44512667810505585, 0.46731071588670287, 0.31404447890390175, 0.4434807670145869, 0.7070712638564993, 0.6179340430633931, 0.2588622303094726, 0.981956033422562, 0.3443318887830507, 0.28382410629398824, 0.938454055718174, 0.8088761031922224, 0.9430750827473381, 0.2226262187771998, 0.1095314281442766, 0.6099831187726399, 0.8246319738955656, 0.9647318376836743, 0.28443316744076863, 0.8744747035833056, 0.10679121419681811, 0.11932834166093773, 0.10948220231585443, 0.8267005608966846, 0.11076612522602591, 0.5824970163098714, 0.03163446119422874, 0.25593183963525495, 0.17208655617407873, 0.5047476359500183}
  2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. If(countQuestion ≟ 0, 2, 2 + floor((currentRandomSeeds(1) * 2))) → numDigits
  4. If(numDigits ≟ 2, 0, 1) → digitHundredB
  5. If(numDigits ≟ 2, 1 + floor((currentRandomSeeds(7) * (digitTenA - 3))), 5 + floor((currentRandomSeeds(7) * 5))) → digitTenB
  6. If(numDigits ≟ 2, 0, digitHundredB + If[carryHundreds, 2, 1] + floor((currentRandomSeeds(2) * 2))) → digitHundredA
  7. Zip(If[A ≟ B, 0, A], A, reverseSubtract, B, {0, digitHundredA, digitTenA, digitOneA}) → expectedCarries
  8. If(numDigits ≟ 2, {stringStudentTens, stringStudentUnits, stringCarryTens, stringCarryUnits}, {stringStudentHundreds, stringStudentTens, stringStudentUnits, stringCarryHundreds, stringCarryTens, stringCarryUnits}) → inputCurrent
  9. If((¬fillUnits) ∧ expectedCarries(4) ≠ 0, 3, If[(¬fillTens) ∧ expectedCarries(3) ≠ 0, 2, If[numDigits ≟ 3 ∧ (¬fillHundreds) ∧ expectedCarries(2) ≠ 0, 1, -1]]) → clickIndex
  10. Append(0, Zip[If[Defined[A], A, 0], A, {inputCarryHundreds, inputCarryTens, inputCarryUnits}]) → studentCarries
  11. If(¬unitsOK, 3, If[¬tensOK, 2, ¬hundredsOK, 1, 0]) → firstErrorIndex
  12. Zip(A ≠ 0, A, expectedCarries) → expectedSlashes
  13. If(expectedSlashes(3), If[(¬fillTens) ∨ inputCarryTens ≟ 10 + digitTenA, hintTenDouble, If[inputCarryTens ≟ digitTenA - 1, (((("Use place value to help subtract " * digitTenB) * " from ") * (digitTenA - 1)) * ". "), hintTenDouble]]) → hintTensNoCarry
  14. Sequence((((If[expectedCarries(A) > 0, "\cancel", ""] * "{") * numADigits(A)) * "}"), A, 1, 4) → numASolnCancel
  15. 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
  16. Corner(5) → layoutAppSize
  17. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  18. Textfield(studentHundreds) → inputStudentHundreds
  19. Textfield(inputCarryTens) → carryTensBox
  20. Textfield(inputCarryUnits) → carryUnitsBox
  21. TableText(Zip[If[A ≟ 0, "", ("" * A)], A, expectedCarries], numASolnCancel, numBDigits, {"", If[numHundredsSoln > 0, ("" * numHundredsSoln), ""], ("" * ansTens), ("" * ansUnits)}, "c00_00010", 1, 30) → tableAns
  22. Textfield(inputCarryHundreds) → carryHundredsBox
  23. If(numDigits ≟ 2, (-62, 7), (-55.5, 7)) → AnchorAns
  24. Sequence(AnchorAns + ((A * 6.1), 0), A, 0, 3) → allAnsAnchors
  25. Zip(A + vTop, A, allAnsAnchors) → allCarryAnchors
  26. Textfield(studentTens) → inputStudentTens
  27. Textfield(studentUnits) → inputStudentUnits
  28. Polygon({(0, -8), (0, 25), (6, 25), (6, -8)}) → frameTemplate
  29. Polygon({(-3, -3), (-3, 3), (3, 3), (3, -3)}) → clickBoxTemplate
  30. Zip(A + (2.5, -7.2), A, allCarryAnchors) → allClickAnchors
  31. Sequence(Translate[clickBoxTemplate, allClickAnchors(A)], A, If[numDigits ≟ 3, 1, 2], 3) → allClickBoxes
  32. Zip(If[A, If[B, (((("\textcolor{" * colorRedError) * "}{\cancel{") * C) * "}}"), (((("\textcolor{" * colorRedError) * "}{\cancel{\textcolor{BLACK}{") * C) * "}}}")], (((If[B, (("\textcolor{" * colorRedError) * "}"), ""] * "{") * C) * "}")], A, studentSlashes, B, highlightSlash, C, numADigits) → numAStudentCancel
  33. If(numDigits ≟ 2, 104, 136) → onboardingX
  34. If(showsolution, colorA, colorWhite) → correctColor
  35. If(tensOK, "", If[carryTensOK, hintSubtract, If[¬(expectedSlashes(4)), If[expectedSlashes(3), If[¬fillTens, hintPlaceValue, hintCarry]], hintTensNoCarry]]) → hintTensThreeDigit
  36. If(hundredsOK, "", If[carryHundredsOK, hintSubtract, If[fillHundreds, hintNoUngroup, hintRemaining]]) → hintHundreds
  37. If(unitsOK, "", If[carryUnitsOK, hintSubtract, If[expectedSlashes(4), If[¬(studentSlashes(4)), hintPlaceValue, hintCarry], hintNoUngroup]]) → hintUnits
  38. If(tensOK, "", If[carryTensOK, hintSubtract, If[fillTens ∧ (¬fillUnits), hintNoUngroup, hintRemaining]]) → hintTensTwoDigit
  39. If(numDigits ≟ 3, hintTensThreeDigit, hintTensTwoDigit) → hintTens
  40. Element({hintHundreds, hintTens, hintUnits}, firstErrorIndex) → hintCurrent
  41. If(digitTenA ≥ digitTenB, digitHundredA, digitHundredA - 1) → numHundredsAfterCarry
  42. If(animateControl < startBorrowHundred, 0, If[animateControl > startBorrowHundred + 2, 2, animateControl - startBorrowHundred]) → animateBorrowHundredControl
  43. If(animateBorrowHundredControl < 1, animateBorrowHundredControl, 1) → animateBorrowHundredA
  44. Max(0, animateBorrowHundredControl - 1) → animateBorrowHundredB
  45. If(¬carryTens, 0, If[animateControl < 2, animateControl, 2]) → animateBorrowTensControl
  46. If(animateBorrowTensControl < 1, animateBorrowTensControl, 1) → animateBorrowTensA
  47. If(animateBorrowTensControl < 1, 0, animateBorrowTensControl - 1) → animateBorrowTensB
  48. If(carryHundreds, 4, 2) → startCarryHundreds
  49. If(carryTens, 2, 0) → startSubtractUnits
  50. If(digitHundredB ≟ 0, 0, If[animateControl < startSubtractHundred, 0, If[animateControl > startSubtractHundred + 2, 2, animateControl - startSubtractHundred]]) → animateSubtractHundredControl
  51. If(animateControl < startSubtractTen, 0, If[animateControl > startSubtractTen + 2, 2, animateControl - startSubtractTen]) → animateSubtractTensControl
  52. If(animateControl < startSubtractUnits, 0, If[animateControl > startSubtractUnits + 2, 2, animateControl - startSubtractUnits]) → animateSubtractUnitsControl
  53. Max(0, animateSubtractHundredControl - 1) → animateCancelHundred
  54. Min(animateSubtractTensControl, 1) → animateCancelTen
  55. If(animateSubtractUnitsControl < 1, animateSubtractUnitsControl, 1) → animateCancelUnits
  56. If(animateSubtractHundredControl < 1, 0, animateSubtractHundredControl - 1) → animateShowHundredsAnswer
  57. Max(0, animateSubtractTensControl - 1) → animateShowTensAnswer
  58. If(animateSubtractUnitsControl < 1, 0, animateSubtractUnitsControl - 1) → animateShowUnitAnswer
  59. Min(floor((animateCancelUnits * 10)), digitOneB) → numSlashes
  60. If(digitOneA ≥ digitOneB, digitTenA, digitTenA - 1) → numTensAfterCarry
  61. If(animateBorrowTensControl ≟ 0, digitTenA, numTensAfterCarry) → numTensCurrent
  62. Flatten(Sequence[Sequence[AnchorUnits + (3.5, 0) + (((i * 0.25) * blockWidth), ((j * 0.25) * blockWidth)), i, 0, 2], j, 0, 2]) → unitAnchors
  63. Join({Sequence[AnchorHundreds + (1, 0) + (((i * 1.2) * blockWidth), 0), i, 2, 0, -1], Sequence[AnchorHundreds + (1, (1.2 * blockWidth)) + (((i * 1.2) * blockWidth), 0), i, 2, 0, -1]}) → hundredAnchors
  64. TableText({"\textcolor{#0F8538}{Hundreds}", "\textcolor{#5145A8}{Tens}", "\textcolor{#C75000}{Ones}"}, {"\hspace{250px}", "\hspace{55px}", "\hspace{120px}"}, "c") → backTableCase2
  65. Sequence(AnchorTens + (1, 0) + ((((A - 1) * 2.5) * blockWidth / 10), 0), A, 1, 9) → tensAnchors
  66. Sequence(cornerBox[blockWidth, blockWidth, hundredAnchors(A) + num2Offset], A, 1, digitHundredB) → hundredsB
  67. Sequence(cornerBox[blockWidth / 10, blockWidth / 10, unitAnchors(A)], A, 1, digitOneA) → unitsA
  68. Sequence(cornerBox[blockWidth / 10, blockWidth / 10, unitAnchors(A) + num2Offset], A, 1, digitOneB) → unitsB
  69. Polygon({AnchorHundreds + (0, -13), AnchorTens + (0, -13), AnchorTens + (0, 23), AnchorHundreds + (0, 23)}) → hundredsBackground
  70. Polygon({AnchorTens + (0, -13), AnchorUnits + (0, -13), AnchorUnits + (0, 23), AnchorTens + (0, 23)}) → tensBackground
  71. Polygon({AnchorUnits + (0, -13), AnchorUnits + (11.4, -13), AnchorUnits + (11.4, 23), AnchorUnits + (0, 23)}) → unitsBackground
  72. Sequence(tensAnchors(1) + ((2.5 * (i - 1)), If[digitTenA ≟ 0, 0, 11.2]), i, 1, 10) → borrowAnchorTens
  73. Sequence(Vector[AnchorTens + (A - 1, 11), borrowAnchorTens(A)], A, 1, 10) → vMoveBorrowHundreds
  74. Sequence(cornerBox[blockWidth / 10, blockWidth, tensAnchors(A) + num2Offset], A, 1, digitTenB) → tensB
  75. Sequence(cornerBox[blockWidth, blockWidth, hundredAnchors(A)], A, 1, If[animateBorrowHundredA > 0, numHundredsAfterCarry, digitHundredA]) → hundredsA
  76. Segment((-0.3, -0.3), (1.3, 1.3)) → slashUnit
  77. If(carryHundreds, Join[{Take[tensAnchors, 1, digitTenA + If[carryTens, -1, 0]], borrowAnchorTens}], tensAnchors) → tensAnchorCurrent
  78. Sequence(AnchorUnits + (1, ((2.1 * A) * blockWidth / 10)), A, 0, 9) → borrowAnchorUnits
  79. Sequence(Vector[AnchorUnits + (0, A - 1), borrowAnchorUnits(A)], A, 1, 10) → vMoveBorrowTens
  80. If(carryTens, Join[{Take[unitAnchors, 1, digitOneA], borrowAnchorUnits}], Reverse[Take[unitAnchors, 1, digitOneA]]) → unitAnchorCurrent
  81. Sequence(Translate[slashUnit, unitAnchors(A) + num2Offset], A, 1, Min[(animateCancelUnits * 10), digitOneB]) → slashUnitsB
  82. Translate(unitAnchors, Vector[(2 * num2Offset)]) → unitAnchorsSoln
  83. Translate(tensAnchors, Vector[(2 * num2Offset)]) → tensAnchorSoln
  84. Translate(hundredAnchors, Vector[(2 * num2Offset)]) → hundredsAnchorSoln
  85. If(carryTens, Take[unitAnchorCurrent, digitOneB + 1, numUnitsSoln + digitOneB], Reverse[Take[unitAnchorCurrent, digitOneB + 1, numUnitsSoln + digitOneB]]) → moveUnitsStart
  86. Zip(cornerBox[blockWidth / 10, blockWidth / 10, A + (animateShowUnitAnswer * (B - A))], A, moveUnitsStart, B, unitAnchorsSoln) → movingSolnUnits
  87. Take(tensAnchorCurrent, digitTenB + 1, numTensSoln + digitTenB) → movingTensStart
  88. Translate(tensAnchors, Vector[(2 * num2Offset)]) → tenAnchorsSoln
  89. Zip(cornerBox[blockWidth / 10, blockWidth, A + (animateShowTensAnswer * (B - A))], A, movingTensStart, B, tenAnchorsSoln) → movingSolnTens
  90. Take(hundredAnchors, 1, numHundredsSoln) → movingHundredsStart
  91. Zip(cornerBox[blockWidth, blockWidth, A + (animateShowHundredsAnswer * (B - A))], B, hundredsAnchorSoln, A, movingHundredsStart) → movingSolnHundreds
  92. Segment((-0.4, -0.4), (1.4, 10.4)) → slashTen
  93. Segment((-0.5, -0.5), (10.5, 10.5)) → slashHundredTemplate
  94. Sequence(Translate[slashTen, tensAnchors(A) + num2Offset], A, 1, Min[(animateCancelTen * 10), digitTenB]) → slashTensB
  95. Sequence(Translate[slashTen, tensAnchorCurrent(A)], A, 1, Min[(animateCancelTen * 10), digitTenB]) → slashTens
  96. If(animateBorrowTensControl < 1, animateBorrowTensControl, 1) → animateBorrowTenA
  97. Translate(cornerBox[blockWidth / 10, blockWidth, tensAnchors(digitTenA)], (animateBorrowTenA * (AnchorUnits - tensAnchors(digitTenA)))) → borrowTenA
  98. If(animateBorrowTensControl < 1, 0, animateBorrowTensControl - 1) → animateBorrowTenB
  99. Zip(cornerBox[blockWidth / 10, blockWidth / 10, AnchorUnits + (0, B) + (animateBorrowTenB * A)], Vector[A], vMoveBorrowTens, B, Sequence[K, K, 0, 9]) → borrowTenB
  100. Sequence(cornerBox[blockWidth / 10, blockWidth, tensAnchors(A)], A, 1, numTensCurrent) → tensA
  101. cornerBox(blockWidth, blockWidth, hundredAnchors(digitHundredA) + (animateBorrowHundredA * (AnchorTens + (0, 11) - hundredAnchors(digitHundredA)))) → borrowHundredA
  102. Sequence(cornerBox[blockWidth / 10, blockWidth, AnchorTens + (A - 1, 11) + (animateBorrowHundredB * vMoveBorrowHundreds(A))], A, 1, 10) → borrowHundredB
  103. Sequence(Translate[slashUnit, unitAnchorCurrent(A)], A, 1, numSlashes) → slashUnits
  104. TableText({"\textcolor{#5145A8}{Tens}", "\textcolor{#C75000}{Ones}"}, {"\hspace{75px}", "\hspace{80px}"}, "c") → backTableCase1
  105. Segment(AnchorHundreds - (0, 1), (x(Vertex[unitsBackground, 2]), y(AnchorHundreds) - 1)) → divisionLine
  106. Translate(slashHundredTemplate, hundredAnchors(If[carryHundreds, digitHundredA - 1, digitHundredA])) → slashHundredsA
  107. Translate(slashHundredTemplate, hundredAnchors(digitHundredB) + num2Offset) → slashHundredsB
  108. Take(numAStudentCancel, 4 - numDigits) → tableRowA
  109. Append("-", Take[numBDigits, 5 - numDigits]) → tableRowB
  110. If(showsolution, colorB, If[validate, colorC, colorWhite]) → wrongColor
  111. circlePixels(allClickAnchors(clickIndex), 9 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingRegroup

AI 绘图提示语参考

一个用于多位数减法练习的图形界面，包含学生输入数字的区域、答案显示区域和错误提示信息。界面会根据随机生成的减法问题自动调整布局，展示输入数字、答案和可能的提示。
以上提示语为根据原始绘图命令整理而来，仅供参考。