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用可视化模型进行带分数加减法

用可视化模型进行带分数加减法
几何画板及绘图内容加载中，请稍等……
2023-09-06 09:27
该范例通过动态可视化模型演示带分数（混合数）的加法与减法运算过程。核心数学概念是带分数的加减法，包括整数部分与分数部分的分别处理、通分、以及结果化简。作图要点：利用GeoGebra的RandomUniform、Take、Element等命令生成随机题目，通过Polygon、Sequence、Translate等命令绘制分数条块模型，使用Numerator、Denominator、Mod等命令处理分数运算，并借助If、Remove、Min、Max等逻辑控制题目类型与答案验证。适合小学4-5年级学生，用于直观理解带分数运算的步骤，也可作为教师课堂演示或学生自主探索的互动资源。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.8852668807984533, 0.4896175041875582, 0.9004505281500474, 0.8138983790191049, 0.8743290129216643, 0.280047258804096, 0.688947078158236, 0.7314437083587516, 0.33015050254879785, 0.4374839454951024, 0.7865017680308626, 0.948456827350805, 0.9523338719634472, 0.8879031638956442, 0.326564356269377, 0.20191105737721926, 0.544155404387917, 0.37035095429884735, 0.9295919961041543, 0.26126065668314585, 0.2928170492551908, 0.43398286051044127, 0.1632876973859459, 0.6597332013015768, 0.5644923376034315, 0.28100317256816376, 0.7459109743954649, 0.4325136115536207, 0.645241401653553, 0.4807366049418677, 0.31820311969620046, 0.1336686650495682, 0.8055400541858188, 0.725407542104399, 0.7753592964670433, 0.946971717715064, 0.41877564181187255, 0.156980252385173, 0.8573045987205175, 0.5375352873303335, 0.55260672870276, 0.25663145516769814, 0.023295934101422333, 0.2813445819629811, 0.016566821355951007, 0.5440797083462516, 0.06557215775415652, 0.318408332547996, 0.4797115666653138, 0.04308882092974475, 0.8564136883888528, 0.16230382463626608, 0.068466770780014, 0.36199114272649835, 0.5535490430463219, 0.8043905977128843, 0.3571291887091137, 0.7940439125663369, 0.7903596154505329, 0.5549036764889184, 0.671704770058851, 0.8718357932151388, 0.6797846206030655, 0.1755094225087554, 0.18193857223359952, 0.1328024651837247, 0.2542175744783526, 0.01871812622383158, 0.09649849162578111, 0.5391898995578216, 0.4980109628830728, 0.708795307822319, 0.3423191176942597, 0.7855200147859026, 0.22447035925505318, 0.4764994512322494, 0.5710955856014176, 0.8397687354782861, 0.20541959262415144, 0.7460965714385699, 0.6338357465841632, 0.6010568230835057, 0.4985579781256158, 0.8376629087619224, 0.298237912042506, 0.2866849331463792, 0.005905990641803135, 0.5006850191229956, 0.1734552663763915, 0.014809326718981294, 0.715650185302284, 0.7964019406127016, 0.602540738463283, 0.5359604726533497, 0.6496489913083535, 0.5762071851874363, 0.5045364921735608, 0.44694766961485544, 0.5397494965506686, 0.7317390742667167, 0.9257789737833055, 0.16447225847292204, 0.19789211934840947, 0.0390357445808529, 0.573535762873985, 0.04298920538724174, 0.6177426667460697, 0.7143167039021513, 0.17457280858672006, 0.4720106774973076, 0.6292941465566924, 0.14257605628588838, 0.22667054075468812, 0.34213718185589415, 0.23251719427082926, 0.8822328235566445, 0.40246475171009877, 0.3866312155242223, 0.531716194988782, 0.24958212289126844, 0.41228303469988586, 0.08631500354211522, 0.6887605420749305, 0.7457261392997986, 0.14588029289839263, 0.36997847515154614, 0.8608121267773605, 0.46603714002709196, 0.4021460565302815, 0.15032504077535255, 0.9465588985332778, 0.17801544827895094, 0.6209646019823888, 0.8167624137930775, 0.5042900560736514, 0.007652824644084788, 0.5124533235765624, 0.26106222640222193, 0.9754129097592554, 0.14709782213881253, 0.7157870148723641, 0.49006659471257613, 0.21821159787337185, 0.36754255567844835, 0.24273646858496856, 0.10121177014645842, 0.8287873909098654, 0.5008103720380103, 0.5199059749839374, 0.7816678641054383, 0.0891962687906296, 0.8211230250325355, 0.8084507709442981, 0.8103609144423143, 0.5168123375009249, 0.28496022865210713, 0.7107862467754863, 0.05404750528781396, 0.6738984585312358, 0.7817987169337312, 0.5004720399719412, 0.17395421668747843, 0.06225229590014529, 0.3818274332493135, 0.2140607970983637, 0.18827321663783553, 0.3946236126410121, 0.00848434879018251, 0.2622464650942895, 0.7780222596098103, 0.3623614213926476, 0.5838454691174382, 0.742129478210496, 0.18943179469904872, 0.8274513181953294, 0.7835197169990287, 0.4928361218217288, 0.16511325256573864, 0.7767414083800084, 0.2947641368043649, 0.33308663523983156, 0.45879228952697887, 0.08673229443312182, 0.587031660389509, 0.031601837712440725, 0.5843574180885444, 0.4988191711668289, 0.4180993032965854, 0.8294699711022389, 0.009378842466115936, 0.29732635303525745, 0.6712978724235205, 0.6077660113362489, 0.9360936928890489, 0.12606204260583, 0.2801744277520937, 0.033822636762754515, 0.8291337774304036, 0.9434487799910692, 0.7461672527077756}
  2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. Element(denBOps, denIndex) → denB
  4. Element(denAOps, denIndex) → denA
  5. If(denA ≟ 4, Element[{1, 3}, 1 + floor((currentRandomSeeds(2) * 2))], 1 + floor((currentRandomSeeds(2) * (denA - 1)))) → numerA
  6. Remove(Element[{{}, {1}, {1, 2}, {1, 3}, {1, 2, 3, 4}, {}, {1, 2, 3, 4, 5, 6}}, denB], If[sameDen, {numerA}, {}]) → possibleNumerB
  7. Element(possibleNumerB, 1 + floor((currentRandomSeeds(3) * Length[possibleNumerB]))) → numerB
  8. Min(numberA, numberB) → numberRight
  9. Max(numberA, numberB) → numberLeft
  10. Element({3, 3, 2.6, 2.2}, totalBlocks - 2) → unitSize
  11. If(numberA > numberB, 1, 2) → indexLeft
  12. Element({numUnitsA, numUnitsB}, indexLeft) → numUnitsLeft
  13. If(indexLeft ≟ 1, 2, 1) → indexRight
  14. Element({numUnitsA, If[testSum ≥ 5 ∧ (¬isSubtract), numUnitsB - 1, numUnitsB]}, indexRight) → numUnitsRight
  15. Element({denA, denB}, indexRight) → denRight
  16. Sequence(AnchorRight + ((K * spacing), 0), K, 0, 2) → anchorsRight
  17. Element({numerA, numerB}, indexLeft) → numPartsLeft
  18. Element({numerA, numerB}, indexRight) → numPartsRight
  19. Element({numerA, numerB}, indexRight) → numerRight
  20. Element({numerB, numerA}, indexRight) → numerLeft
  21. Element({denA, denB}, indexLeft) → denLeft
  22. If(sameDen, denLeft, (denLeft * denRight)) → denCommon
  23. If(isSubtract, numberLeft - numberRight, numberLeft + numberRight) → answerVal
  24. Polygon({(0, 0), (0, unitSize), (unitSize, unitSize), (unitSize, 0)}) → templateUnitBox
  25. Sequence(AnchorLeft + ((K * spacing), 0), K, 0, 2) → anchorsLeft
  26. If(animateControl ≟ animateCount, 1, animateControl - floor(animateControl)) → animateCurrent
  27. Flatten(Sequence[Sequence[AnchorSolnParts + ((i * unitSize / denLeft), (j * unitSize / If[sameDen, 1, denRight])), i, 0, denLeft - 1], j, 0, (2 * denRight)]) → anchorSolnPartsAll
  28. If(sameDen, numerRight, (numerRight * denLeft)) → numCommonRight
  29. Vector(anchorSolnPartsAll(1), anchorSolnUnits(numUnitsSoln)) → vCarry
  30. If(isBorrow, numUnitsLeft - 1, numUnitsLeft) → numUnitsLeft2
  31. If(animateCount < fade2Index + 1, 0, If[animateCount ≟ fade2Index + 1, animateCurrent, 1]) → animateCarry
  32. If(sameDen, 0, If[animateCount ≤ 3, 0, If[animateCount < 5, animateCurrent, 1]]) → animateStage1b
  33. If(sameDen, Polygon[{(0, 0), (unitSize / denRight, 0), (unitSize / denRight, unitSize), (0, unitSize)}], Polygon[{(0, 0), (unitSize, 0), (unitSize, unitSize / denRight), (0, unitSize / denRight)}]) → templatePartRight
  34. Sequence(AnchorPartsRight + If[sameDen, ((A * unitSize / denRight), 0), (0, (A * unitSize / denRight))], A, 0, denRight - 1) → anchorRightParts
  35. Zip(Translate[templatePartRight, A], A, anchorRightParts) → outlinePartsRight
  36. Flatten(Sequence[Sequence[AnchorPartsRight + ((i * unitSize / denLeft), (j * unitSize / denRight)), i, 0, If[sameDen, numerRight - 1, denLeft - 1]], j, 0, If[sameDen, 0, numerRight - 1]]) → anchorRightPartsCD
  37. Flatten(Sequence[Sequence[anchorsLeft(2) + ((i * unitSize / denLeft), (j * unitSize / denRight)), i, 0, denLeft - 1], j, 0, If[sameDen, 0, denRight - 1]]) → anchorLeftPartsBorrow
  38. Join({Flatten[Sequence[Sequence[anchorsLeft(3) + ((i * unitSize / denLeft), (j * unitSize / denRight)), i, 0, numerLeft - 1], j, 0, If[sameDen, 0, denRight - 1]]], If[isBorrow, anchorLeftPartsBorrow, {}]}) → anchorLeftPartsCD
  39. Take(anchorSolnPartsAll, 1, Length[anchorLeftPartsCD] + If[caseNum ≟ caseSUBTRACT, 0, Length[anchorRightPartsCD]]) → anchorSolnPartsCurrent
  40. If(animateCount < fade1Index + numUnitsRight, 0, If[animateCount ≥ fade1Index + numUnitsRight + numCommonRight, numCommonRight + If[animateCount ≥ fade2Index, 1, 0], animateCount - fade1Index - numUnitsRight]) → moveRightPart
  41. Polygon({(0, 0), (unitSize / denLeft, 0), (unitSize / denLeft, unitSize / If[sameDen, 1, denRight]), (0, unitSize / If[sameDen, 1, denRight])}) → templateCommon
  42. Vector(anchorSolnPartsCurrent(If[isSubtract, numCommonLeft - moveRightPart + 1, numCommonLeft + moveRightPart]) - anchorRightPartsCD(moveRightPart)) → vMovePartRight
  43. If(animateCount - sizeStageA ≤ 0, 0, If[animateCount - sizeStageA ≤ numUnitsLeft2, animateCount - sizeStageA, numUnitsLeft2 + 1]) → moveLeftUnit
  44. If(animateCount - sizeStageA ≤ moveLeftUnit, 0, If[moveLeftUnit < animateCount - sizeStageA ≤ moveLeftUnit + numCommonLeft, animateCount - sizeStageA - moveLeftUnit, numCommonLeft]) → moveLeftPart
  45. Element({{}, {anchorsRight(1)}, {anchorsRight(2), anchorsRight(1)}}, numUnitsRight + 1) → anchorUnitsRight
  46. If(animateCount ≤ fade1Index, 0, If[fade1Index < animateCount ≤ fade1Index + numUnitsRight, animateCount - fade1Index, numUnitsRight]) → moveRightUnit
  47. Sequence(anchorsLeft(2 - A), A, 0, numUnitsLeft - 1) → anchorUnitsLeft
  48. If(isBorrow, Element[{{}, {anchorUnitsLeft(2)}}, numUnitsLeft], anchorUnitsLeft) → anchorUnitsLeft2
  49. If(isSubtract, "\minus", "\plus") → caseOperator
  50. Numerator(answerVal) → answerNumer
  51. Denominator(answerVal) → answerDen
  52. If(sameDen, "", (((((((((("\text{ \dfrac{" * fracLeftnumer) * "}{") * answerDen) * "} ") * caseOperator) * " \dfrac{") * fracRightNumer) * "}{") * answerDen) * "} = }")) → commonDenText
  53. Mod(answerNumer, answerDen) → answerRemainder
  54. If(answerNumer < answerDen, "", (((("\text{ \dfrac{" * answerNumer) * "}{") * answerDen) * "} = }")) → improperText
  55. Vector(anchorSolnUnits(moveLeftUnit) - anchorUnitsLeft2(moveLeftUnit)) → vMoveLeftUnit
  56. If(sameDen, 0, 2) → lengthMoveBars
  57. If(sameDen, 0, 1) → denCase
  58. Corner(5) → layoutAppSize
  59. PointToPixels(Corner[onboardingDisplayText, 2], Corner[1], Corner[3], Corner[5]) → layoutOnboarding
  60. If(sameDen, "") → makeCommonDen
  61. Sequence(anchorsLeft(3) + (A, 0), A, 0, unitSize - unitSize / denLeft, unitSize / denLeft) → anchorLeftParts
  62. If(animateControl < 4, 0, animateControl - floor(animateControl)) → animateUnitBox
  63. Vector(anchorSolnUnits(If[isSubtract, numUnitsLeft2 - moveRightUnit + 1, numUnitsLeft2 + moveRightUnit]) - anchorUnitsRight(moveRightUnit)) → vMoveRightUnit
  64. Translate(templateUnitBox, anchorUnitsRight(moveRightUnit) + (animateCurrent * vMoveRightUnit)) → moveUnitRight
  65. Translate(templateUnitBox, anchorUnitsLeft2(moveLeftUnit) + (animateCurrent * vMoveLeftUnit)) → moveUnitLeft
  66. Element({If[sameDen, answerNumer, 2 + answerNumer] + 1, lengthMoveBars + 2 + numUnitsA + numUnitsB}, caseNum) → lengthSlider
  67. Polygon({(0, 0), (unitSize / denLeft, 0), (unitSize / denLeft, unitSize), (0, unitSize)}) → templatePartLeft
  68. Zip(Translate[templatePartLeft, A], A, Take[anchorLeftParts, 1, denLeft]) → outlinePartsLeft
  69. Zip(Translate[templatePartLeft, A], A, Take[anchorLeftParts, 1, numPartsLeft]) → fracPartsLeft
  70. Zip(Translate[templateUnitBox, A], A, anchorUnitsLeft) → unitBoxesLeft
  71. Zip(Translate[templateUnitBox, A], A, anchorUnitsRight) → unitBoxesRight
  72. If(animateCount < fade1Index ∨ (¬isSubtract), 0, If[animateCount > fade1Index, 1, animateCurrent]) → animateFade1
  73. If(animateCount < fade2Index, 0, If[animateCount > fade2Index, 1, animateCurrent]) → animateFade2
  74. Zip(Translate[templateUnitBox, A], A, Take[anchorSolnUnits, 1, numUnitsSoln]) → solnUnitBoxesFinal
  75. If(sameDen, 0, If[animateCount ≤ 1, 0, If[animateCount < 3, animateCurrent, 1]]) → animateStage1a
  76. Zip(Translate[A, (animateStage1b * (anchorsLeft(3) - AnchorPartsRight))], A, outlinePartsRight) → barsRight
  77. Zip(Translate[templatePartRight, A], A, Take[anchorRightParts, 1, numerRight]) → fracPartsRight
  78. Translate(templateCommon, anchorRightPartsCD(moveRightPart) + (animateCurrent * vMovePartRight)) → movePartRight
  79. Translate(templateCommon, anchorLeftPartsCD(moveLeftPart) + (animateCurrent * vMoveLeftPart)) → movePartLeft
  80. If(isSubtract, numCommonLeft, numCommonLeft + 1) → indexStage3B
  81. If(moveRightUnit > 1 ∨ animateCount > numUnitsRight + fade1Index, Sequence[Translate[templateUnitBox, Vector[anchorSolnUnits(numUnitsLeft2 - A + 1)]], A, 1, If[animateCount > fade1Index + numUnitsRight, numUnitsRight, moveRightUnit - 1]], {}) → solnUnitBoxesRightSubtract
  82. If(moveRightUnit > 1 ∨ animateCount > numUnitsRight + fade1Index, Sequence[Translate[templateUnitBox, Vector[anchorSolnUnits(numUnitsLeft2 + A)]], A, 1, If[animateCount > fade1Index + numUnitsRight, numUnitsRight, moveRightUnit - 1]], {}) → solnUnitBoxesRight
  83. Zip(Translate[templateCommon, A], A, Reverse[Take[anchorSolnPartsCurrent, numCommonLeft + 2 - moveRightPart]]) → solnPartBoxesRightSubtract
  84. Zip(Translate[templateCommon, A], A, Take[anchorLeftPartsCD, moveLeftPart + 1]) → remainingLeftParts
  85. Zip(Translate[templateUnitBox, A], A, Take[anchorUnitsLeft2, moveLeftUnit + 1]) → remainingLeftUnits
  86. Zip(Translate[templateUnitBox, A], A, Take[anchorUnitsRight, moveRightUnit + 1]) → remainingRightUnits
  87. Translate(templateUnitBox, anchorSolnPartsAll(1) + (If[IsInteger[answerVal] ∧ answerVal ≠ 4, 0, animateCarry] * vCarry)) → unitCarry
  88. If(sameDen, 0, 5) → startStage1c
  89. If(¬isBorrow, 0, If[animateCount < startStage1c, 0, If[animateCount ≤ startStage1c, animateCurrent, 1]]) → animateStage1c
  90. Zip(Translate[templateUnitBox, A], A, Take[anchorSolnUnits, 1, moveLeftUnit - 1]) → solnUnitsLeft
  91. Zip(Translate[templateCommon, A], A, Take[anchorSolnPartsCurrent, 1, Min[numCommonLeft, animateCount - sizeStageA - numUnitsLeft2 - 2]]) → solnPartBoxesLeft
  92. Zip(Translate[templateCommon, A], A, Take[anchorSolnPartsCurrent, numCommonLeft + 1, numCommonLeft + moveRightPart - 1]) → solnPartBoxesRightAdd
  93. Zip(Translate[templateCommon, A], A, Take[anchorRightPartsCD, moveRightPart + 1]) → remainingRightParts
  94. Zip(Translate[templateUnitBox, A], A, Take[anchorSolnUnits, 1, numUnitsSoln - If[isCarry, 1, 0]]) → solnUnitsFinal
  95. Zip(Translate[templateCommon, A - If[isCarry, (0, (-unitSize) + (animateCarry * unitSize)), (0, 0)]], A, Take[anchorSolnPartsAll, 1, numPartsSoln]) → solnPartsFinal
  96. PointToPixels(AnchorLineA, Corner[1], Corner[3], Corner[5]) → LineStartPX
  97. Zip(Translate[templateUnitBox, A], A, Join[{anchorUnitsLeft, anchorUnitsRight, {anchorsLeft(3), AnchorPartsRight}}]) → outlineUnits
  98. Zip(Translate[A, (animateStage1a * (AnchorPartsRight - anchorsLeft(3)))], A, outlinePartsLeft) → barsLeft

AI 绘图提示语参考

描述一个基于分数条模型的图形，用于展示混合数的加减法。图形包含一个单位条，以及多个分数条，这些分数条代表混合数中的整数部分和分数部分。图形中可能有一个加法示例，展示如何将两个混合数相加，通过将分数部分对齐并相加，整数部分相加。图形还包括一个减法示例，展示如何从较大的混合数中减去较小的混合数，可能涉及借位。图形中的分数条通过颜色或位置区分整数部分和分数部分。构造顺序：先绘制单位条，然后根据随机生成的混合数创建分数条，将整数部分和分数部分分开，最后将分数条组合成混合数图形，并标注加减步骤。
以上提示语为根据原始绘图命令整理而来，仅供参考。