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分数除法可视化模型

分数除法可视化模型
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2022-11-15 01:33
解析几何几何作图滑块动画函数图像
本范例通过可视化模型演示如何用分数除以另一个分数，特别适用于分母不同的分数。核心数学概念包括分数除法、可视化模型、分数比较。构造过程中使用了 GeoGebra 命令如 RandomUniform, Take, Element, If, Denominator, FractionText, Corner, cornerBox, Sequence, Flatten, Max, Zip, Join 等，用于生成随机分数、动画演示分数除法过程。适合小学高年级（4-5年级）学生学习分数除法运算。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.35512367939172695, 0.5942641245822663, 0.6850472070465758, 0.27852195128881324, 0.17395285301696572, 0.3821777071131764, 0.04619510876375086, 0.4073793753867612, 0.39496463751399413, 0.778519156371654, 0.3309659397334782, 0.18106551363316406, 0.13019776246438083, 0.0948518817022987, 0.8960905534778324, 0.6093650432786588, 0.20400792285014685, 0.8839754364360136, 0.02358478157598696, 0.8835806988647215, 0.19025646168649127, 0.5734171943077246, 0.6670488962041076, 0.11992273181155376, 0.14588951578118678, 0.2195688602799019, 0.665718895248951, 0.5320516535066343, 0.5281107620711637, 0.768632755543361, 0.12723764999040438, 0.5117280235176312, 0.5663644621402034, 0.7769793710548144, 0.5108459494828979, 0.7784267515296849, 0.19529661292456266, 0.9283897124431045, 0.4093633225688888, 0.044115830068944095, 0.6707509820609177, 0.4689677691006344, 0.26093643921171206, 0.7881784364557394, 0.9176825599162998, 0.24225498653807956, 0.34007722054708883, 0.5696740136387746, 0.4966350755427247, 0.41726540617079955, 0.5019956165277596, 0.8897885408870919, 0.2841299156098801, 0.23078270547530308, 0.1546517185375682, 0.21641548282657777, 0.9119529863191304, 0.8323207744524409, 0.3293094797782182, 0.8653391603377757, 0.0709017620988863, 0.42564764255211535, 0.7726690219677645, 0.5284576690707061, 0.7760686532701103, 0.8647084646435989, 0.3218870357900166, 0.8988884095713224, 0.2531881602439189, 0.8541555133061428, 0.9279648395554323, 0.5656395323417162, 0.5489633708198646, 0.23550461383989224, 0.40309075885583323, 0.5768109834234723, 0.9826145011288678, 0.3491847607063501, 0.6335687802850377, 0.21000545198102333, 0.10115472117582777, 0.70043364626994, 0.20194758686182815, 0.4917830199640369, 0.40710048487265527, 0.7431145969481205, 0.8998840605202689, 0.5245862621188245, 0.504462213756572, 0.700091231624062, 0.8671328723865707, 0.3595912248567927, 0.2169365812781989, 0.5217939555261508, 0.7618485499941742, 0.1474062195782957, 0.03123658402334383, 0.5560479615964936, 0.6031189726811788, 0.6754456146261837, 0.3584454058222155, 0.37210589292977947, 0.8383191153457344, 0.8111464366147534, 0.5771699731567018, 0.18013820469292846, 0.20548111026630245, 0.3339758893222351, 0.24409515313452906, 0.7341825288229448, 0.12442194641504166, 0.6763940605937965, 0.3803043317249606, 0.22173948817222433, 0.4698524314664355, 0.7045907849163845, 0.27543220429928755, 0.42682454035208556, 0.6851105658032692, 0.943906958469265, 0.6363551286404874, 0.005346328720627799, 0.32652068071101853, 0.17138049705645123, 0.7127001460157253, 0.7121806903761421, 0.5156739339948404, 0.9688234610797986, 0.39796742088363857, 0.7082436910776314, 0.8401583662902937, 0.024241327359433035, 0.12251234007909974, 0.6032415011509429, 0.6224369480100381, 0.9072471832874509, 0.9230217709744978, 0.6955845936738781, 0.6616789607886462, 0.2654029462894184, 0.83244539186056, 0.15520191154362956, 0.15439528119274926, 0.4831363643360193, 0.29460689802248086, 0.8676766643204114, 0.4467109012422718, 0.773037180388832, 0.35892036857965975, 0.01924774478865719, 0.194026766212617, 0.5309272207512352, 0.9627765567100453, 0.5017820691207135, 0.34268213139792175, 0.7411286515256322, 0.49223941846734015, 0.6348204929376597, 0.43302185159620205, 0.3568216486655269, 0.6357074046472979, 0.9482359053117492, 0.6340068109741471, 0.45228664061738844, 0.6301445309719699, 0.7239152523907918, 0.9261748101651135, 0.04916828844463565, 0.5553756401206551, 0.1381872525471355, 0.04236674989992229, 0.7776778322720493, 0.6087659489608507, 0.9384663387900588, 0.5741783845932846, 0.28586682380608713, 0.10036886825328213, 0.7077680987219287, 0.2865795686118837, 0.005759851259793014, 0.9073271574716428, 0.9393754525426246, 0.0735635705895765, 0.35422561258979346, 0.3659511472501875, 0.3409943717325231, 0.014045869470296776, 0.7189950185974504, 0.2304740263507914, 0.21323690112638014, 0.48952718603751094, 0.29620164361788537, 0.018997768634670054, 0.5012040646128322, 0.07326761952900644, 0.08522427504026459, 0.6195946404014481, 0.31031475682183995, 0.7348890519915882, 0.4694531749666695}
  2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. Element(Sequence[2, 9], 1 + floor((currentRandomSeeds(1) * 8))) → randomD1
  4. Element({{1}, {1}, {1, 2}, {1, 3}, {1, 2, 3, 4}, {1, 5}, {1, 2, 3, 4, 5, 6}, {1, 3, 5, 7}, {1, 2, 4, 5, 7, 8}}, randomD1) → possibleN1
  5. Element({{1}, {3, 5, 7, 9}, {2, 4, 5, 7}, {3, 5, 6, 7, 9}, {2, 3, 4, 6, 7, 8, 9}, {4, 5, 7, 8, 9}, {2, 3, 4, 5, 6, 8, 9}, {3, 5, 6, 7, 9}, {2, 4, 5, 7, 8}}, randomD1) → possibleD2
  6. Element({{1}, {1}, {1, 2}, {1, 3}, {1, 2, 3, 4}, {1, 5}, {1, 2, 3, 4, 5, 6}, {1, 3, 5, 7}, {1, 2, 4, 5, 7, 8}}, randomD2) → possibleN2
  7. If(randomFrac1 / (randomFrac2) < 3, randomFrac1, randomFrac2) → fracA
  8. If(fracA ≟ randomFrac1, randomFrac2, randomFrac1) → fracB
  9. If(animateStage2 > 1, 1, animateStage2) → animateFade
  10. If(animateStage2 > 1, animateStage2 - 1, 0) → animateGap
  11. Denominator(fracA) → denA
  12. Denominator(fracB) → denB
  13. If(animateStage1 > 1, 1, animateStage1) → animateDivisionsA
  14. FractionText(numB) → numBLatex
  15. Corner(5) → layoutAppSize
  16. cornerBox(AnchorB1, boxWidth, boxHeight) → frameB
  17. Sequence(AnchorA1 + ((B * (divisionWidth + x(gap))), 0), B, 0, denA - 1) → colPositionA
  18. Sequence(AnchorA1 + (0, ((-B) * (divisionHeight + y(gap)))), B, 0, denB - 1) → rowPositionA
  19. Flatten(Sequence[Sequence[(x(colPositionA(K)), y(rowPositionA(J))), J, 1, Length[rowPositionA]], K, 1, Length[colPositionA]]) → allA
  20. Take(allA, 1, numPiecesA) → visibleA
  21. Max(0, animateStage3 - 1) → animateMove
  22. If(animateMove ≟ 0, 0, floor(animateMove) + 1) → currentBoxIndex
  23. Zip(A + vMoveAB, A, colPositionA) → colPositionB
  24. Zip(A + vMoveAB, A, rowPositionA) → rowPositionB
  25. Flatten(Zip[Zip[(x(B), y(A)), B, colPositionB], A, rowPositionB]) → allB
  26. Take(allB, 1, numPiecesB) → visibleB
  27. Flatten(Zip[Translate[visibleB, A - AnchorB1], A, {AnchorC, AnchorC - (0, finalGroupHeight + (3 * y(gap))), AnchorC - (0, (2 * (finalGroupHeight + (3 * y(gap)))))}]) → finalPoints
  28. cornerBox(visibleA(currentBoxIndex) + (animateBox * (finalPoints(currentBoxIndex) - visibleA(currentBoxIndex))), divisionWidth, divisionHeight) → moveBoxA
  29. Zip(cornerBox[A, divisionWidth, divisionHeight], A, visibleB) → boxesB
  30. cornerBox(AnchorA1, boxWidth, boxHeight) → frameA
  31. Zip(cornerBox[A, divisionWidth, divisionHeight], A, visibleB) → boxFramesB
  32. Join({Zip[Segment[A, A + (animateDivisionsA * (boxWidth, 0))], A, rowPositionA], Zip[Segment[A, A + (boxWidth, 0)], A, rowPositionB]}) → divisionBarsA
  33. Sequence(cornerBox[finalPoints(A), divisionWidth, divisionHeight], A, 1, currentBoxIndex - 1) → finalBoxes
  34. If(animateStage1 > 1, animateStage1 - 1, 0) → animateDivisionB
  35. Join({Zip[Segment[A, A - (animateDivisionB * (0, boxHeight))], A, colPositionB], Zip[Segment[A, A - (0, boxHeight)], A, colPositionA]}) → divisionBarsB
  36. Take(finalPoints, 1, ((numFramesFinal * Numerator[fracB]) * Denominator[fracA])) → finalFramePoints
  37. Zip(cornerBox[A, divisionWidth, divisionHeight], A, finalFramePoints) → boxFramesFinal
  38. If(animateStage3 < 1, animateStage3, 1) → animateFadeStage3
  39. Zip(cornerBox[A, divisionWidth, divisionHeight], A, visibleB) → coverBox
  40. cornerBox(visibleA(currentBoxIndex) + (animateBox * (finalPoints(currentBoxIndex) - visibleA(currentBoxIndex))), divisionWidth, divisionHeight) → moveFrameA
  41. Zip(cornerBox[A, divisionWidth, divisionHeight], A, Take[visibleA, If[Defined[currentBoxIndex], currentBoxIndex + 1, 1]]) → boxesA
  42. Zip(cornerBox[A, divisionWidth, divisionHeight], A, Take[visibleA, If[Defined[currentBoxIndex], currentBoxIndex + 1, 1]]) → boxFramesA
  43. Element({4, 4, 15 / numPiecesA}, stage) → animateSpeed

AI 绘图提示语参考

该图形是一个分式除法的可视化模型，展示两个随机分数的除法过程。图形以一个中心点为基准，根据分母和分子生成网格线，形成分式条表示除法步骤，并放置分式框展示最终结果。图形由几何构造完成，使用坐标和网格布局，体现分数除法的直观理解。
以上提示语为根据原始绘图命令整理而来，仅供参考。