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同分母与异分母分数加减法

同分母与异分母分数加减法
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2023-05-30 22:49
几何作图
本范例通过数轴和互动区域模型演示同分母与异分母分数的加减法。它展示了如何使用模型和图片解释过程，并记录结果。该范例使用了RandomUniform, Take, Element, If, Remove, Min, Max, PixelsToPoint, Sequence, Point, Numerator, Denominator, Mod, Polygon, Flatten, Vector, Zip, Join, Corner, PointToPixels, Translate, Segment, Text等GeoGebra命令。适合4-5年级学生学习分数和带分数的加减法。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.8819549171902377, 0.7839227597875107, 0.5885739173243362, 0.35688808870371314, 0.14699979483365885, 0.7203370503205309, 0.5421706189015314, 0.26007554442469644, 0.5069722313904086, 0.5402904061410444, 0.7124188600297885, 0.248289764945615, 0.39740508790627627, 0.554487950878196, 0.1950956043585404, 0.5150736139779096, 0.5559657631180086, 0.5266404941174392, 0.7411567190300394, 0.17260757109649313, 0.7799765701262624, 0.8556187673885347, 0.27333923991304626, 0.1276171281278989, 0.81493820942269, 0.12097945264792817, 0.7487160423857004, 0.16023836808512748, 0.08739933767083216, 0.6214928653189897, 0.6906780244572683, 0.2968149572855948, 0.3241390985995963, 0.7667221427463032, 0.07291014227203466, 0.767237182476234, 0.9466887494508995, 0.13806087802185338, 0.4104582471201836, 0.8480110355794895, 0.8757176535308915, 0.4279314939713765, 0.23894868651571952, 0.95375793887351, 0.8437438597059059, 0.8040787679290738, 0.30242879142264206, 0.5922978649134029, 0.8570027167688968, 0.1300629159416832, 0.1631366405423781, 0.8018563994640551, 0.1481174418291301, 0.2131641121684015, 0.4627887125691146, 0.08326320365600813, 0.14046400010265084, 0.3769554325071177, 0.9346904319248793, 0.7852724030643269, 0.44280728844558087, 0.007782879220801726, 0.5091291889953226, 0.5873371743117177, 0.3389097806624269, 0.13231227173416144, 0.10110068233305457, 0.44130876525452417, 0.37137360922195684, 0.707159040687846, 0.7194495857483831, 0.2616071757320607, 0.8319751809107528, 0.4114125863946256, 0.17997138645090494, 0.532423791816135, 0.4221872925675935, 0.5285991151392904, 0.15192732670769085, 0.6604674875416383, 0.1274563389763332, 0.9162966766869052, 0.9277654653718578, 0.16265489245281103, 0.5971133437567224, 0.6192236856904856, 0.009621202582045798, 0.3099709154574156, 0.488544614055499, 0.17516701684602332, 0.5833857995502904, 0.36149012161603883, 0.8994346713150783, 0.5525983349553416, 0.9617878338194759, 0.8462498003638487, 0.14551587517496276, 0.9842470516873482, 0.8620219859910966, 0.15530524405688662, 0.9633205710815496, 0.8622559726398208, 0.21099107026283312, 0.971873142360545, 0.22792939422032124, 0.42784019013353447, 0.8221922124224342, 0.10398302653202833, 0.3446446445994989, 0.921602918284856, 0.282683714764244, 0.2615077010984195, 0.34089108910501575, 0.4298309543934959, 0.6164100136885623, 0.8078325524393443, 0.250456951189008, 0.5272007808083443, 0.1814418025320602, 0.445749476945527, 0.5164357191210148, 0.7873706012018388, 0.743405590774825, 0.9674250321529766, 0.8019151524829004, 0.9199163424575415, 0.19553037348282373, 0.9594934269224575, 0.7885829332435027, 0.244989446702331, 0.4873314650777703, 0.8164639869699672, 0.05297885131573664, 0.23593179124057154, 0.39898121278236165, 0.6387082551368906, 0.7781214710117668, 0.7248778942126204, 0.4668818754176847, 0.16530649334452244, 0.2446726434843402, 0.4071072070293129, 0.8678617107546956, 0.8669834456822373, 0.9306767486819383, 0.17657862511209418, 0.6047560075777552, 0.3402529153814694, 0.2922215900720383, 0.20768782980424555, 0.9849146313679229, 0.770716004696325, 0.3691159311197566, 0.3468317971925247, 0.9153944122346138, 0.7412222769576614, 0.2798647690005923, 0.8718480373617424, 0.4042486854593097, 0.0593037328695361, 0.42884564099219014, 0.5778158508588137, 0.8764185609190529, 0.787930413775981, 0.4256507683995801, 0.46406417002242784, 0.5352593807375366, 0.6042125762351815, 0.42205676715374935, 0.4695256568783557, 0.3267028737434456, 0.4521881378575192, 0.9860204042773846, 0.9518088303881909, 0.70245981606602, 0.07828489865974195, 0.1444710295893115, 0.8295306429467115, 0.13150935293652716, 0.741436503144056, 0.9074809750241145, 0.6975582277287161, 0.2154014157665573, 0.9241561132246363, 0.12564415374126026, 0.5008547139049326, 0.11261414854599752, 0.7961366628790396, 0.21017691479435044, 0.774605246677646, 0.010363880515256142, 0.7481468183362193, 0.7713802747023831, 0.7662203447136069, 0.8988559026826833, 0.39113097225077714, 0.44566151972770524, 0.29867017124689876, 0.7429942989374749, 0.7734974848236994}
  2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. Element(denAOps, denIndex) → denA
  4. If(denA ≟ 4, Element[{1, 3}, 1 + floor((currentRandomSeeds(2) * 2))], 1 + floor((currentRandomSeeds(2) * (denA - 1)))) → numerA
  5. Element(denBOps, denIndex) → denB
  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. If(isSubtract, numberLeft - numberRight, numberLeft + numberRight) → answerVal
  11. PixelsToPoint((xMin, yMin), (xMax, yMax), (800, 500), (50, layoutB)) → AnchorLineA
  12. Sequence(AnchorLineA + ((tickIncrement * A), 0), A, 0, (studentDen * 5)) → tickPositions
  13. Sequence((A * 1 / studentDen), A, 1, Length[tickPositions]) → possibleValues, {0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5}
  14. Point(tickPositions) → studentPoint
  15. PixelsToPoint((xMin, yMin), (xMax, yMax), (800, 500), (layoutXHint, layoutHint)) → HintAnchor
  16. Min((x(AnchorLineB) - x(HintAnchor) - (5 * gap)) / maxBlocks - gap, 4) → unitSize
  17. If(numberA > numberB, 1, 2) → indexLeft
  18. Element({numerA, numerB}, indexLeft) → numPartsLeft
  19. If(indexLeft ≟ 1, 2, 1) → indexRight
  20. Element({numerA, numerB}, indexRight) → numerRight
  21. Element({numerB, numerA}, indexRight) → numerLeft
  22. Element({denA, denB}, indexRight) → denRight
  23. Element({denA, denB}, indexLeft) → denLeft
  24. If(animateControl ≟ animateCount, 1, animateControl - floor(animateControl)) → animateCurrent
  25. Element({numUnitsA, If[testSum ≥ 5 ∧ (¬isSubtract), numUnitsB - 1, numUnitsB]}, indexRight) → numUnitsRight
  26. Element({numUnitsA, numUnitsB}, indexLeft) → numUnitsLeft
  27. If(sameDen, numerRight, (numerRight * denLeft)) → numCommonRight
  28. If(isBorrow, numUnitsLeft - 1, numUnitsLeft) → numUnitsLeft2
  29. If(animateCount < slideIndex, 0, If[animateCount > slideIndex, 1, animateCurrent]) → animateSlide
  30. If(sameDen, denLeft, (denLeft * denRight)) → denCommon
  31. Numerator(answerVal) → answerNumer
  32. Denominator(answerVal) → answerDen
  33. Mod(answerNumer, answerDen) → answerRemainder
  34. Element({numerA, numerB}, indexRight) → numPartsRight
  35. Polygon({(0, 0), (0, unitSize), (unitSize, unitSize), (unitSize, 0)}) → templateUnitBox
  36. Sequence(AnchorLeft + ((K * spacing), 0), K, 0, 2) → anchorsLeft
  37. Flatten(Sequence[Sequence[AnchorSolnParts + ((i * unitSize / denLeft), (j * unitSize / If[sameDen, 1, denRight])), i, 0, denLeft - 1], j, 0, (2 * denRight)]) → anchorSolnPartsAll
  38. Vector(anchorSolnPartsAll(1), anchorSolnUnits(numUnitsSoln)) → vCarry
  39. If(animateCount < fade2Index + 1, 0, If[animateCount ≟ fade2Index + 1, animateCurrent, 1]) → animateCarry
  40. Sequence(AnchorRight + ((K * spacing), 0), K, 0, 2) → anchorsRight
  41. If(sameDen, 0, If[animateCount ≤ 3, 0, If[animateCount < 5, animateCurrent, 1]]) → animateStage1b
  42. 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
  43. Sequence(anchorsRight(3) + If[sameDen, ((A * unitSize / denRight), 0), (0, (A * unitSize / denRight))], A, 0, denRight - 1) → anchorRightParts
  44. Zip(Translate[templatePartRight, A], A, anchorRightParts) → outlinePartsRight
  45. Flatten(Sequence[Sequence[anchorsRight(3) + ((i * unitSize / denLeft), (j * unitSize / denRight)), i, 0, If[sameDen, numerRight - 1, denLeft - 1]], j, 0, If[sameDen, 0, numerRight - 1]]) → anchorRightPartsCD
  46. Flatten(Sequence[Sequence[anchorsLeft(2) + ((i * unitSize / denLeft), (j * unitSize / denRight)), i, 0, denLeft - 1], j, 0, If[sameDen, 0, denRight - 1]]) → anchorLeftPartsBorrow
  47. 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
  48. Take(anchorSolnPartsAll, 1, Length[anchorLeftPartsCD] + If[caseNum ≟ caseSUBTRACT, 0, Length[anchorRightPartsCD]]) → anchorSolnPartsCurrent
  49. If(animateCount < fade1Index + numUnitsRight, 0, If[animateCount ≥ fade1Index + numUnitsRight + numCommonRight, numCommonRight + If[animateCount ≥ fade2Index, 1, 0], animateCount - fade1Index - numUnitsRight]) → moveRightPart
  50. Polygon({(0, 0), (unitSize / denLeft, 0), (unitSize / denLeft, unitSize / If[sameDen, 1, denRight]), (0, unitSize / If[sameDen, 1, denRight])}) → templateCommon
  51. Vector(anchorSolnPartsCurrent(If[isSubtract, numCommonLeft - moveRightPart + 1, numCommonLeft + moveRightPart]) - anchorRightPartsCD(moveRightPart)) → vMovePartRight
  52. If(animateCount - sizeStageA ≤ 0, 0, If[animateCount - sizeStageA ≤ numUnitsLeft2, animateCount - sizeStageA, numUnitsLeft2 + 1]) → moveLeftUnit
  53. If(animateCount - sizeStageA ≤ moveLeftUnit, 0, If[moveLeftUnit < animateCount - sizeStageA ≤ moveLeftUnit + numCommonLeft, animateCount - sizeStageA - moveLeftUnit, numCommonLeft]) → moveLeftPart
  54. Sequence(anchorsRight(2 - A), A, 0, numUnitsRight - 1) → anchorUnitsRight
  55. If(animateCount ≤ fade1Index, 0, If[fade1Index < animateCount ≤ fade1Index + numUnitsRight, animateCount - fade1Index, numUnitsRight]) → moveRightUnit
  56. Sequence(anchorsLeft(2 - A), A, 0, numUnitsLeft - 1) → anchorUnitsLeft
  57. If(isBorrow, Element[{{}, {anchorUnitsLeft(2)}}, numUnitsLeft], anchorUnitsLeft) → anchorUnitsLeft2
  58. If(isSubtract, "\minus", "\plus") → caseOperator
  59. If(sameDen, "", (((((((((("\text{ \dfrac{" * fracLeftnumer) * "}{") * answerDen) * "} ") * caseOperator) * " \dfrac{") * fracRightNumer) * "}{") * answerDen) * "} = }")) → commonDenText
  60. If(answerNumer < answerDen, "", (((("\text{ \dfrac{" * answerNumer) * "}{") * answerDen) * "} = }")) → improperText
  61. Vector(anchorSolnUnits(moveLeftUnit) - anchorUnitsLeft2(moveLeftUnit)) → vMoveLeftUnit
  62. If(sameDen, 0, 2) → lengthMoveBars
  63. If(sameDen, 0, 1) → denCase
  64. Corner(5) → layoutAppSize
  65. PointToPixels(Corner[onboardingDisplayText, 2], Corner[1], Corner[3], Corner[5]) → layoutOnboarding
  66. If(sameDen, "") → makeCommonDen
  67. Sequence(anchorsLeft(3) + (A, 0), A, 0, unitSize - unitSize / denLeft, unitSize / denLeft) → anchorLeftParts
  68. If(animateControl < 4, 0, animateControl - floor(animateControl)) → animateUnitBox
  69. Vector(anchorSolnUnits(If[isSubtract, numUnitsLeft2 - moveRightUnit + 1, numUnitsLeft2 + moveRightUnit]) - anchorUnitsRight(moveRightUnit)) → vMoveRightUnit
  70. Translate(templateUnitBox, anchorUnitsRight(moveRightUnit) + (animateCurrent * vMoveRightUnit)) → moveUnitRight
  71. Translate(templateUnitBox, anchorUnitsLeft2(moveLeftUnit) + (animateCurrent * vMoveLeftUnit)) → moveUnitLeft
  72. Element({If[sameDen, answerNumer, 2 + answerNumer] + 1, lengthMoveBars + 2 + numUnitsA + numUnitsB}, caseNum) → lengthSlider
  73. Polygon({(0, 0), (unitSize / denLeft, 0), (unitSize / denLeft, unitSize), (0, unitSize)}) → templatePartLeft
  74. Zip(Translate[templatePartLeft, A], A, Take[anchorLeftParts, 1, denLeft]) → outlinePartsLeft
  75. Zip(Translate[templatePartLeft, A], A, Take[anchorLeftParts, 1, numPartsLeft]) → fracPartsLeft
  76. Zip(Translate[templateUnitBox, A], A, anchorUnitsLeft) → unitBoxesLeft
  77. Zip(Translate[templateUnitBox, A], A, anchorUnitsRight) → unitBoxesRight
  78. If(animateCount < fade1Index ∨ (¬isSubtract), 0, If[animateCount > fade1Index, 1, animateCurrent]) → animateFade1
  79. If(animateCount < fade2Index, 0, If[animateCount > fade2Index, 1, animateCurrent]) → animateFade2
  80. Zip(Translate[templateUnitBox, A], A, Take[anchorSolnUnits, 1, numUnitsSoln]) → solnUnitBoxesFinal
  81. If(sameDen, 0, If[animateCount ≤ 1, 0, If[animateCount < 3, animateCurrent, 1]]) → animateStage1a
  82. Zip(Translate[A, (animateStage1a * (AnchorRight - AnchorLeft))], A, outlinePartsLeft) → barsLeft
  83. Zip(Translate[A, (animateStage1b * (AnchorLeft - AnchorRight))], A, outlinePartsRight) → barsRight
  84. Zip(Translate[templatePartRight, A], A, Take[anchorRightParts, 1, numerRight]) → fracPartsRight
  85. Zip(Translate[templateUnitBox, A], A, Join[{anchorUnitsLeft, anchorUnitsRight, {anchorsLeft(3), anchorsRight(3)}}]) → outlineUnits
  86. Translate(templateCommon, anchorRightPartsCD(moveRightPart) + (animateCurrent * vMovePartRight)) → movePartRight
  87. Translate(templateCommon, anchorLeftPartsCD(moveLeftPart) + (animateCurrent * vMoveLeftPart)) → movePartLeft
  88. If(isSubtract, numCommonLeft, numCommonLeft + 1) → indexStage3B
  89. If(moveRightUnit > 1 ∨ animateCount > numUnitsRight + fade1Index, Sequence[Translate[templateUnitBox, Vector[anchorSolnUnits(numUnitsLeft2 - A + 1)]], A, 1, If[animateCount > fade1Index + numUnitsRight, numUnitsRight, moveRightUnit - 1]], {}) → solnUnitBoxesRightSubtract
  90. If(moveRightUnit > 1 ∨ animateCount > numUnitsRight + fade1Index, Sequence[Translate[templateUnitBox, Vector[anchorSolnUnits(numUnitsLeft2 + A)]], A, 1, If[animateCount > fade1Index + numUnitsRight, numUnitsRight, moveRightUnit - 1]], {}) → solnUnitBoxesRight
  91. Zip(Translate[templateCommon, A], A, Reverse[Take[anchorSolnPartsCurrent, numCommonLeft + 2 - moveRightPart]]) → solnPartBoxesRightSubtract
  92. Zip(Translate[templateCommon, A], A, Take[anchorLeftPartsCD, moveLeftPart + 1]) → remainingLeftParts
  93. Zip(Translate[templateUnitBox, A], A, Take[anchorUnitsLeft2, moveLeftUnit + 1]) → remainingLeftUnits
  94. Zip(Translate[templateUnitBox, A], A, Take[anchorUnitsRight, moveRightUnit + 1]) → remainingRightUnits
  95. Translate(templateUnitBox, anchorSolnPartsAll(1) + (If[Defined[IndexOf[answerVal, {1, 2, 3}]], 0, animateCarry] * vCarry)) → unitCarry
  96. If(sameDen, 0, 5) → startStage1c
  97. If(¬isBorrow, 0, If[animateCount < startStage1c, 0, If[animateCount ≤ startStage1c + 1, animateCurrent, 1]]) → animateStage1c
  98. Zip(Translate[templateUnitBox, A], A, Take[anchorSolnUnits, 1, moveLeftUnit - 1]) → solnUnitsLeft
  99. Zip(Translate[templateCommon, A], A, Take[anchorSolnPartsCurrent, 1, Min[numCommonLeft, animateCount - sizeStageA - numUnitsLeft2 - 2]]) → solnPartBoxesLeft
  100. Zip(Translate[templateCommon, A], A, Take[anchorSolnPartsCurrent, numCommonLeft + 1, numCommonLeft + moveRightPart - 1]) → solnPartBoxesRightAdd
  101. Zip(Translate[templateCommon, A], A, Take[anchorRightPartsCD, moveRightPart + 1]) → remainingRightParts
  102. Zip(Translate[templateUnitBox, A], A, Take[anchorSolnUnits, 1, numUnitsSoln - If[isCarry, 1, 0]]) → solnUnitsFinal
  103. Zip(Translate[templateCommon, A - If[isCarry, (0, (-unitSize) + (animateCarry * unitSize)), (0, 0)]], A, Take[anchorSolnPartsAll, 1, numPartsSoln]) → solnPartsFinal
  104. PointToPixels(AnchorLineA, Corner[1], Corner[3], Corner[5]) → LineStartPX
  105. Segment(AnchorLineA - (1, 0), AnchorLineB + (1, 0)) → numberLine
  106. Zip(Segment[A - (0, 0.2), A + (0, 0.2)], A, tickPositions) → smallTicks
  107. Sequence(Text[("" * Element[{0, 1, 2, 3, 4, 5}, A + 1]), tickPositions((A * studentDen) + 1) + (0, 1), true, true, 0, 0], A, 0, 5, 1) → lblLine
  108. Text(("" * MixedNumber[numberLeft]), LblPosLeft, true, true, 0, 0) → lblLeft
  109. Text(("" * MixedNumber[numberRight]), LblPosRight, true, true, 0, 0) → lblRight
  110. Text(("" * caseOperator), Midpoint[LblPosLeft, LblPosRight], true, true, 0, 0) → opHint
  111. circlePixels(studentPoint, 7 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingPoint
  112. Element({(AnchorSolnParts * 1), anchorSolnUnits(1), anchorSolnUnits(2)}, Min[2, numUnitsSoln] + 1) → FirstSolnPoint
  113. Element({-2, -1, 0}, ceil(numberLeft)) → test
  114. Text(caseOperator, AnchorLeft + ((3.25 * unitSize) + (2 * gap), (0.5 * unitSize)), true, true, 0, 0) → hintOperator
  115. Text("=", AnchorRight + ((3.25 * unitSize) + (2 * gap), (0.5 * unitSize)), true, true, 0, 0) → hintEqual
  116. Sequence(Segment[tickPositions(A + 1) - (0, 0.3), tickPositions(A + 1) + (0, 0.3)], A, 0, (5 * studentDen), studentDen) → bigTicks

AI 绘图提示语参考

在画布上先放置一条水平数轴，并在数轴上用等分刻度标出若干可能的数值；在数轴下方安排两个由小方格组成的区域模型方块，方块可表示两个分数的分母与分子对应的取值单位。左侧用同一分母的分割方式画出第一个分数的取色小单元，再在右侧按另一个分数的分割方式画出对应小单元；若分母相同则直接把两者相应部分组合，若分母不同则把右侧单位按公共分母等量细分以便对齐。随后根据是加法或减法，利用对齐后的取色单元表示运算结果，并在图上保留最终的分数形式作为标注。
以上提示语为根据原始绘图命令整理而来，仅供参考。