积极 AI Logo 积极 AI

配方法：用代数瓦片选择表达式并完成平方

配方法：用代数瓦片选择表达式并完成平方
几何画板及绘图内容加载中，请稍等……
2024-04-03 07:29
函数几何作图滑块动画函数图像
该范例通过代数瓦片的可视化模型，让学习者“选择不同表达式”后观察配方法的逐步完成平方过程，并通过滑块改变系数来观察对应的表达式变化。核心数学概念包括二次项配方法、将ax^2+bx重写为a(x+m)^2+k的代数恒等变形、系数配平与等价表达式、以及为何向两边同时加入对应的常数以保持等式成立。作图与交互要点：利用随机数与种子驱动生成题目参数（RandomUniform、Sequence、Max、If等），用多种几何/绘图对象承载可视化界面与题干元素（Text、PointToPixels、PixelsToPoint、Vector、Segment、Point、Translate、Join、Zip、Flatten、Take、Corner），并通过界面对象与脚本控制显示/隐藏答案与提示（Element、showanswer/ showhint/ scriptResetApp、btnNew、scriptFixAllText、scriptEmptyInputBoxes等），同时用onboarding与文本排版偏移（onboardingTextOffset）构建学习引导。界面适合9-12年级或配方法入门到巩固练习阶段，用于课堂探究、分组讨论和形成性测评。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.8548254949126582, 0.8243255808539557, 0.7053537997663649, 0.5946431173553146, 0.1933366589400638, 0.5815387405495404, 0.7558949230858008, 0.4748264926115612, 0.4010455984507947, 0.7489214548777103, 0.9792670669916175, 0.044054862893809305, 0.019248765430733804, 0.22022913856092435, 0.249495865385833, 0.6319422221139752, 0.4593472751067925, 0.25020255148237586, 0.953566225962684, 0.7128823629942047, 0.0773307093276081, 0.42172646570247124, 0.4326254416052949, 0.21090037978669407, 0.8557573425616123, 0.9117201558238112, 0.9131135776330537, 0.23989808060489587, 0.681077783419194, 0.6263475956985084, 0.17503712671902794, 0.8112439515476332, 0.7240599301966252, 0.6119069270930962, 0.7356085429981243, 0.39127327189274, 0.7506736914291409, 0.3107177830470188, 0.5321673543985873, 0.9640667064196731, 0.1400806698260495, 0.8114716068108491, 0.958679272971693, 0.6498658285873696, 0.6653482484311628, 0.2908436901047139, 0.5551784752751239, 0.06666220593902177, 0.8711705791006473, 0.16768779621947907, 0.9792735629738891, 0.10186119548006432, 0.9612275066796402, 0.4628423673190306, 0.48328151128174984, 0.8324749744971062, 0.5058503031475466, 0.9464749522030766, 0.8396847387174243, 0.24603946179637454, 0.6683874758378703, 0.2809740428377824, 0.5814243301498342, 0.5303769754356413, 0.2160758852721784, 0.5006703006822191, 0.43204886196595793, 0.6084424517050515, 0.31832219721378885, 0.6001275403049549, 0.9639315611727436, 0.14479338227510524, 0.12208690193692093, 0.7203898980502166, 0.1006487383495816, 0.08271380204135219, 0.050537245096163044, 0.8074067785354367, 0.07218189843969866, 0.44570066450300133, 0.037298095962063314, 0.29887736994835506, 0.9288608178486034, 0.33388588938765107, 0.3244793779207024, 0.2649663826371737, 0.6119086922169998, 0.7350204831051192, 0.8481949669838652, 0.24473878660498175, 0.2750812887749394, 0.9208866904783966, 0.12051375903460239, 0.4637453397183963, 0.32321020491069485, 0.4434329389674912, 0.05169485879944131, 0.8489621524034654, 0.1494666518701368, 0.7905402684226256, 0.6311589018312113, 0.5752468688938315, 0.6438547610651368, 0.0391327504690752, 0.959934113274367, 0.24261971074125807, 0.7308252007426114, 0.2533342268736919, 0.9112911647074451, 0.12601290027408807, 0.2439674259941245, 0.9275512321700546, 0.8799421887242275, 0.9686517852555591, 0.08049526322088184, 0.7687275369725027, 0.9135290612567649, 0.9869418563534376, 0.05768375967028661, 0.30856832213859514, 0.0531639836688145, 0.5486304986232309, 0.5675459291182771, 0.11527221933934333, 0.8525085251753861, 0.1270978870697112, 0.1548566092465979, 0.9652373306669274, 0.12729100570757157, 0.6829016990785025, 0.9871364066528167, 0.5683222638123578, 0.9392603320560312, 0.46916012655826334, 0.7234019957848487, 0.7655463850048272, 0.7803624862695742, 0.6700036792665761, 0.13136997642820966, 0.4356033503445888, 0.8244000873154919, 0.11116046954923754, 0.8703699774281334, 0.16623979606697462, 0.3945972506363663, 0.27876108396134813, 0.19947819102265874, 0.9284166873729707, 0.3163423143536776, 0.6166581772674675, 0.08732638969460937, 0.9152227095280532, 0.9849174661191601, 0.9239523478548932, 0.6616716947755308, 0.20375039092575944, 0.21824908907079124, 0.08299986241677385, 0.5431315147793093, 0.08657254017683928, 0.014625085164798811, 0.18394927385308843, 0.16849315692100925, 0.12007200844870991, 0.39492439341264207, 0.30481314097976236, 0.6947014551479902, 0.6596809428751073, 0.48819181860507166, 0.6862270267003541, 0.5850085672655166, 0.01707536720601408, 0.3483650840113017, 0.1773826553124577, 0.6538381969251288, 0.701549029752595, 0.6686238615078947, 0.18414305647891713, 0.5466727047292412, 0.5871554471252861, 0.8981795231978387, 0.2020565423587069, 0.3957145440441569, 0.6787600811808708, 0.2543620371952242, 0.18588339645529334, 0.8312047697859359, 0.5638845538315781, 0.8605845250438718, 0.6333321030962124, 0.8520993554564408, 0.3631526445592118, 0.6981783974843492, 0.4539747834347205, 0.5283100280016995, 0.8802632335770939, 0.6871917891019502, 0.8047689904495958, 0.3599096425469103, 0.6027176562411295}
  2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. Corner(5) → layoutAppSize
  4. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, (xMin, yMin), (xMax, yMax), (800, 500)) → OnboardingTextOffset
  5. Element({-10, -8, -6, -4, -2, 2, 4, 6, 8, 10}, slideB) → coeffB
  6. PixelsToPoint((xMin, yMin), (xMax, yMax), (800, 500), (120, 250)) → AnchorSquared
  7. centerBox(xHeight, xHeight, AnchorSquared) → squaredBox
  8. Sequence(AnchorX + ((A * (xWidth + gap)), 0), A, 0, abs(absCoeffB) - 1) → anchorsX
  9. Max(Min[1, 1 + animateControl - ceil(animateControl)], 0) → animateCurrent
  10. If(floor(animateControl) < absCoeffB, 0, If[floor(animateControl) ≟ absCoeffB, animateControl - absCoeffB, 1]) → animateStage3A
  11. If(floor(animateControl) < absCoeffB, 0, If[floor(animateControl) ≟ absCoeffB, animateControl - absCoeffB, 1]) → animateStage3
  12. Vector(AnchorStage3 - AnchorStage1) → vShift
  13. Sequence(AnchorUnitStart + (A * (xWidth + gap, 0)) + (animateStage3A * vShift), A, 0, abs(absCoeffC)) → anchorUnits
  14. Sequence(AnchorSquared + ((0.5 * (xHeight + xWidth)) + gap + (A * (xWidth + gap)), 0), A, 0, floor(abs(absCoeffB) / 2) - 1) → anchorsXStage2A
  15. Sequence(AnchorSquared - (0, (0.5 * (xHeight + xWidth)) + gap + (A * (xWidth + gap))), A, 0, floor(abs(absCoeffB) / 2) - 1) → anchorsXStage2B
  16. Join({anchorsXStage2A, anchorsXStage2B}) → anchorsXStage2
  17. Zip(Vector[B - A], A, anchorsX, B, anchorsXStage2) → vMove
  18. Min(ceil(animateControl), absCoeffB) → animateIndexB
  19. If(animateIndexB ≤ absCoeffB / 2, 0, pi / 2) → rotateAngle
  20. Translate(Rotate[centerBox[xWidth, xHeight, anchorsX(animateIndexB)], (animateCurrent * rotateAngle), anchorsX(animateIndexB)], (animateCurrent * vMove(animateIndexB))) → moveBoxB
  21. Min(If[isNegativeC, 0, (absCoeffB / 2)^(2)], absCoeffC) → numUnitsMove
  22. Flatten(Sequence[Sequence[(x(anchorsXStage2A(i)), y(anchorsXStage2B(j))), i, 1, absCoeffB / 2], j, 1, absCoeffB / 2]) → anchorUnitsStage2
  23. If(floor(animateControl) < absCoeffB + 2, 0, If[floor(animateControl) ≟ absCoeffB + 2, animateControl - absCoeffB - 2, 1]) → animateStage4
  24. Flatten(Sequence[Sequence[anchorUnits(1) + ((A * (xWidth + gap)), ((-K) * (xWidth + gap))), A, 0, absCoeffB / 2 - 1], K, 1, absCoeffB / 2]) → anchorUnitsStage3
  25. If(floor(animateControl) < absCoeffB + 3, 0, If[floor(animateControl) ≟ absCoeffB + 3, animateControl - absCoeffB - 3, 1]) → animateStage5
  26. Translate(anchorUnitsStage3, Vector[((1 - animateStage5) * Vector[AnchorSubtractStage3 - AnchorStage3])]) → anchorsSubtractStage3
  27. Zip(Vector[B - A], A, anchorUnitsStage3, B, anchorUnitsStage2) → vMoveUnits
  28. Max(Min[ceil(animateControl) - absCoeffB - 4, numUnitsMove], 0) → animateIndexStage6
  29. Zip(centerBox[xWidth, xWidth, A], A, anchorUnitsStage2) → unitsStage2Frames
  30. Zip(Vector[B - A], A, anchorsSubtractStage3, B, anchorUnits) → vMoveSubtract
  31. Translate(centerBox[xWidth, xWidth, anchorsSubtractStage3(animateIndexStage6)], (animateCurrent * vMoveSubtract(animateIndexStage6))) → moveSubtractBox
  32. centerBox(squareWidth, squareWidth, CenterSquare) → squareFrame
  33. Text("x", AnchorSquared - (xHeight / 2, 0), true, true, -1, 0) → lblSideX
  34. Zip(centerBox[xWidth, xWidth, A], A, anchorUnitsStage3) → unitsStage4
  35. Zip(centerBox[xWidth, xWidth, A + (animateStage5 * B)], A, anchorUnitsStage3, Vector[B], vMoveUnits) → unitsStage5
  36. Sequence(centerBox[xWidth, xWidth, anchorUnits(A)], A, 1, absCoeffC) → unitsStage1
  37. Zip(centerBox[xWidth, xWidth, A], A, Take[anchorsSubtractStage3, animateIndexStage6 + 1]) → subtractStage3
  38. If(floor(animateControl) < absCoeffB + 4 + numUnitsMove, 0, If[floor(animateControl) ≟ absCoeffB + 4 + numUnitsMove, animateControl - absCoeffB - 4 - numUnitsMove, 1]) → animateStage7
  39. Take(unitsStage1, 1, If[animateStage7 ≟ 0, animateIndexStage6 - 1, numUnitsMove]) → unitsSubtractStage5
  40. PixelsToPoint((xMin, yMin), (xMax, yMax), (800, 500), (If[animateControl ≤ 4, 310, 16], 60)) → PExpr
  41. Element({("" * finalConstant), "", ("+" * finalConstant)}, sgn(finalConstant) + 2) → finalConstantLatex
  42. If(absCoeffC < 0, ("" * absCoeffC), If[absCoeffC ≟ 0, "", ("+" * absCoeffC)]) → coeffCLatex
  43. Text(fullExpression, PExpr, true, true, If[animateControl ≤ 4, 0, 1], -1) → displayExpr
  44. Segment((((-xWidth)) / 2, ((-xHeight)) / 2), (xWidth / 2, xHeight / 2)) → templateSlashX
  45. Sequence(centerBox[xWidth, xHeight, anchorsX(A)], A, animateIndexB + 1, abs(absCoeffB)) → xBlocksStart
  46. Sequence(centerBox[If[A > abs(absCoeffB) / 2, xHeight, xWidth], If[A > abs(absCoeffB) / 2, xWidth, xHeight], anchorsXStage2(A)], A, 1, Min[ceil(animateControl) - 1, abs(absCoeffB)]) → xBlocksStage2
  47. Vector(AnchorStage1 - AnchorStage3) → vSlideSubtract
  48. Append((1000, 1000), Take[anchorUnits, 1, Min[animateIndexStage6, numUnitsMove]]) → anchorsCrosses
  49. Sequence(Translate[crossTemplate, anchorUnits(A)], A, 1, absCoeffC) → possibleCrosses
  50. Flatten(Take[possibleCrosses, 1, If[animateStage7 ≟ 0, animateIndexStage6 - 1, numUnitsMove]]) → displayCrosses
  51. Sequence(centerBox[(1.4 * xWidth), (1.4 * xWidth), anchorUnits(A)], A, 1, absCoeffC) → possibleFades
  52. Take(possibleFades, 1, If[animateStage7 ≟ 0, animateIndexStage6 - 1, numUnitsMove]) → fadeBoxes
  53. Zip(centerBox[xWidth - (2 * borderWidth), xWidth - (2 * borderWidth), A], A, Take[anchorsSubtractStage3, animateIndexStage6 + 1]) → subtractStage3Centers
  54. Translate(centerBox[xWidth - (2 * borderWidth), xWidth - (2 * borderWidth), anchorsSubtractStage3(animateIndexStage6)], (animateCurrent * vMoveSubtract(animateIndexStage6))) → moveSubtractCenter
  55. Zip(centerBox[xWidth, xWidth, A], A, Join[{anchorUnitsStage3, anchorsSubtractStage3}]) → fadeCoverStage4
  56. Sequence(centerBox[xWidth - (2 * gap), xWidth - (2 * gap), anchorUnits(A)], A, 1, absCoeffC) → negativeUnitsStage1
  57. Sequence(centerBox[xWidth - (2 * gap), xHeight - (2 * gap), anchorsX(A)], A, animateIndexB + 1, abs(absCoeffB)) → negativeXStage1
  58. Translate(Rotate[centerBox[xWidth - (2 * gap), xHeight - (2 * gap), anchorsX(animateIndexB)], (animateCurrent * rotateAngle), anchorsX(animateIndexB)], (animateCurrent * vMove(animateIndexB))) → negativeMoveBox
  59. PointToPixels((xMin, yMin), (xMax, yMax), (800, 500), CenterX) → CenterXPX
  60. PointToPixels((xMin, yMin), (xMax, yMax), (800, 500), AnchorUnitStart) → CenterUnitsPX
  61. Sequence(centerBox[If[A > abs(absCoeffB) / 2, xHeight - (2 * gap), xWidth - (2 * gap)], If[A > abs(absCoeffB) / 2, xWidth - (2 * gap), xHeight - (2 * gap)], anchorsXStage2(A)], A, 1, Min[ceil(animateControl) - 1, abs(absCoeffB)]) → negativeXStage2
  62. Text("\vphantom{4}x", AnchorSquared + (0, xHeight / 2), true, true, 0, 1) → lblTopA
  63. Text(("\vphantom{x^2}" * LaTeX[((If[isNegativeB, "-", ""] * absCoeffB) * "x")]), CenterX + (0, ((-xHeight)) / 2), true, true, 0, -1) → captionSlideB
  64. Text(("\vphantom{x^2}" * LaTeX[(If[isNegativeC, "-", ""] * absCoeffC)]), CenterUnit + (0, ((-xHeight)) / 2), true, true, 0, -1) → captionSlideC
  65. Text(("" * coeffB / 2), AnchorSquared - ((0.5 * xHeight), (xHeight * 0.5) + (xWidth * absCoeffB / 4)), true, true, -1, 0) → lblSideB
  66. Text(("" * coeffB / 2), AnchorSquared + ((0.5 * xHeight) + (xWidth * absCoeffB / 4), (0.5 * xHeight)), true, true, 0, 1) → lblTopB
  67. Text("x^2", AnchorSquared + (0, ((-xHeight)) / 2), true, true, 0, -1) → lblSqStage1

AI 绘图提示语参考

这是一个展示代数平方法则的可视化图形。图形由一系列代数块组成，初始时呈现一个二次表达式。用户通过拖动和添加代数块，逐步将表达式转化为完全平方形式。图形中包含一个中心区域，用于表示完全平方部分，以及一些标签和文本，标注当前表达式和步骤。代数块按照特定顺序排列，展示如何通过添加和移动块来调整系数，最终得到等价的完全平方表达式。整个图形动态展示代数平方的过程，帮助理解如何通过添加常数项来完成平方。
以上提示语为根据原始绘图命令整理而来，仅供参考。