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使用模型可视化等价分数

使用模型可视化等价分数
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2023-06-15 09:39
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本范例通过不同类型的可视化模型，帮助学生理解等价分数的概念。通过使用GeoGebra命令如RandomUniform、Zip等，学生可以探索分数之间的等价关系。适合4-5年级学生，帮助他们掌握使用模型写出等价分数的方法。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.6373122650890546, 0.9776953732500375, 0.6346612142726489, 0.26204278414600846, 0.021290995076380062, 0.6371531833988481, 0.7645708197700253, 0.939639958909575, 0.8935002243766219, 0.845519836530782, 0.907392413327278, 0.4986264071868864, 0.046978481451225025, 0.5596127791829371, 0.39595179303682515, 0.6519566232688773, 0.17159555157274844, 0.6336526142119085, 0.12312489195138818, 0.262269386385315, 0.3132180884105496, 0.13823931889150665, 0.4817437770439257, 0.12420634277886564, 0.3805892728375974, 0.9081417946830938, 0.5917821706160945, 0.07700706698261778, 0.4296371435736192, 0.46684463565047424, 0.6656625499462148, 0.6412577266342381, 0.5964779645126095, 0.03383335655890333, 0.9214235442269383, 0.8128004158822688, 0.4241219049575021, 0.5483237115337106, 0.7295696670024738, 0.8606293158641811, 0.49381573611459606, 0.5705531038958342, 0.9726976397020715, 0.7041053134575304, 0.9700723850092515, 0.018851331028000795, 0.9074520811021471, 0.9780140957484907, 0.5987403305154325, 0.48749569184928426, 0.7160100321569762, 0.8818738456482215, 0.11995547072559196, 0.1268289762745966, 0.14912759346249418, 0.7824666234401192, 0.032496552511678524, 0.8332822750241052, 0.4048037440362658, 0.8758237164620931, 0.7029296414213619, 0.5727931588855939, 0.36582484266349335, 0.40683849444560277, 0.5819806537366847, 0.36664723755351386, 0.8158507028615232, 0.4413111965811464, 0.22181475166963818, 0.9539959737612201, 0.1872859242856215, 0.9465481555937096, 0.4413289662563375, 0.3702151609801997, 0.5749528417903046, 0.5526443256504259, 0.6721804391374072, 0.9548687377828972, 0.6175404599590016, 0.3872710168020796, 0.816074287407726, 0.5473290421800154, 0.7039510588006836, 0.6121714962827077, 0.7138264109335452, 0.6020798897401299, 0.6739992597215665, 0.32963583239181976, 0.3188935221280547, 0.8093904527093776, 0.04244077032898788, 0.06198195295474577, 0.19242823457764302, 0.17039780045991706, 0.9420161825885587, 0.6365131641144103, 0.843469900931216, 0.2486728657229284, 0.09509219403828056, 0.9525537690169058, 0.7266217913174646, 0.5630696473685081, 0.5545665088807384, 0.9559819630255545, 0.34049322814682037, 0.6790687902100678, 0.4829739121433686, 0.35018565058998496, 0.1833002465618942, 0.2879272458646739, 0.0841903923332451, 0.6005602667721979, 0.6373216334766713, 0.594731946072979, 0.08477829991045364, 0.3225478871605749, 0.8913965402595917, 0.2479306893152471, 0.3118497571650051, 0.3907858355211829, 0.2803284216289033, 0.29407517142727874, 0.39134699457739125, 0.1291889968027872, 0.21192511184478915, 0.09236081544537054, 0.9448470089766153, 0.4187325534460418, 0.0464569693834592, 0.5540851702546467, 0.9143950261930502, 0.8313337767696624, 0.6395562977688592, 0.8123713878145845, 0.6334541975713607, 0.8045489869581545, 0.5080078328068841, 0.25741491718183585, 0.4978319995279049, 0.3128084738856295, 0.6284965777856314, 0.7921120175272666, 0.8734008161654251, 0.886604432401762, 0.9821806820467467, 0.602214731626445, 0.8075787641524838, 0.5114293239368005, 0.8429484251803024, 0.4941326474838802, 0.78886891196233, 0.4533288075186891, 0.5343953223126389, 0.012162963477127649, 0.603277969211881, 0.39769044740522774, 0.3899230920074844, 0.5152806316976216, 0.7281437146858816, 0.9323323168643257, 0.9619145881237825, 0.7416571476510482, 0.33279700637762893, 0.9550864582388647, 0.4096795165704812, 0.7668012098546974, 0.18156855393563462, 0.7398904857450145, 0.051792801472436166, 0.8986266508330806, 0.20792174488121018, 0.15390665075625606, 0.9665633406779935, 0.8598525792925401, 0.5289519842922386, 0.031380957551108306, 0.2846733849752836, 0.30492776362853474, 0.9071394809736877, 0.7078357599500309, 0.20051884773052567, 0.04514616542017785, 0.601076176703587, 0.6407575679190216, 0.9834588117128357, 0.35178198851913767, 0.4589095868525531, 0.19019793162991047, 0.9870477427880229, 0.252923270626839, 0.017454428694466582, 0.11464806846831507, 0.5633763869400541, 0.035218764520970725, 0.9063202592720455, 0.6541795098835086, 0.9008879175943797, 0.1869790198742244, 0.7599867117852037, 0.7741608586495669}
  2. Zip(currentNumer / A ≤ 4, A, {2, 3, 4, 5, 6}) → validDenoms
  3. If(caseNum ≟ 1, modelWidth / currentDenom, 4) → boxWidthLeft
  4. If(caseNum ≟ 1, 4, modelWidth / currentDenom) → boxHeightLeft
  5. Flatten(Sequence[Sequence[AnchorLeft + ((boxWidthLeft * i), ((-1.2 * boxHeightLeft) * j)), i, 0, currentDenom - 1], j, 0, 3]) → boxAnchorsLeftCase1
  6. If(caseNum ≟ 1, 4, modelWidth / rightDenom) → boxHeightRight
  7. Flatten(Sequence[Sequence[AnchorLeft + ((modelWidth / 2 * i), (((-modelWidth)) / 2 * j)), i, 0, 1], j, 0, 1]) → circAnchorsLeft
  8. Translate(circAnchorsLeft, AnchorRight - AnchorLeft) → circAnchorsRight
  9. Zip(Sequence[Rotate[A + ((0.24 * modelWidth), 0), K, A], K, 0, (2 * pi), (2 * pi / rightDenom)], A, circAnchorsRight) → sectorPointsRight
  10. Element({modelWidth / currentDenom, 0, modelWidth / currentDenom}, caseNum) → pieceSizeLeft
  11. If(caseNum ≟ 1, modelWidth / rightDenom, 4) → boxWidthRight
  12. Flatten(Sequence[Sequence[AnchorRight + ((boxWidthRight * i), ((-1.2 * boxHeightRight) * j)), i, 0, rightDenom - 1], j, 0, 3]) → boxAnchorsRightCase1
  13. Element({(x(AnchorRight), y(boxAnchorsLeftCase1(-1) - boxHeightRight)), sectorPointsRight(1, 1), AnchorRight}, caseNum) → SlideStartRight
  14. Sequence(A, A, 0, 45, 45 / 4) → unitLocations
  15. Unique(Remove[Flatten[Zip[Sequence[(A + B, 0), B, 0, unitLocations(2), unitLocations(2) / currentDenom], A, Take[unitLocations, 1, Length[unitLocations] - 1]]], {(0, 0)}]) → smallNumerLocations
  16. Flatten(Zip[Sequence[(A + B, 0), B, 0, unitLocations(2), unitLocations(2) / rightDenom], A, Take[unitLocations, 1, Length[unitLocations] - 1]]) → tickLocations
  17. Point(smallNumerLocations) → PEnd
  18. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  19. Corner(5) → layoutAppSize
  20. Flatten(Sequence[Sequence[AnchorRight + (((1.2 * boxWidthRight) * i), case3Offset - (boxHeightRight * j)), j, 0, rightDenom - 1], i, 0, 3]) → boxAnchorsRightCase3
  21. If(caseNum ≟ 1, boxAnchorsRightCase1, boxAnchorsRightCase3) → boxAnchorsRight
  22. Zip(Sequence[Rotate[A + ((0.24 * modelWidth), 0), K, A], K, 0, (2 * pi), (2 * pi / currentDenom)], A, circAnchorsLeft) → sectorPointsLeft
  23. Zip(Sequence[CircleSector[A, Element[B, K], Element[B, K + 1]], K, 1, Length[B] - 1], A, circAnchorsLeft, B, sectorPointsLeft) → sectorsLeft
  24. Take(Unique[Flatten[sectorsLeft]], 1, currentNumer) → filledSectorsLeft
  25. Translate(filledSectorsLeft, AnchorRight - AnchorLeft) → filledSectorsRight
  26. Segment((-2, 0), (47, 0)) → numberLine
  27. Zip(Text[("" * A), (B, -0.5), true, true, 0, -1], A, Sequence[("" * A), A, 0, Length[unitLocations]], B, unitLocations) → numbers
  28. Zip(Sequence[Segment[(A + B, 0), (A + B, -0.5)], B, 0, unitLocations(2), unitLocations(2) / rightDenom], A, Take[unitLocations, 1, Length[unitLocations] - 1]) → smallTicks
  29. Zip(Segment[(A, 1), (A, -1)], A, unitLocations) → bigTicks
  30. Zip(Sequence[Segment[(A + B, 0.75), (A + B, 0)], B, 0, unitLocations(2), unitLocations(2) / currentDenom], A, Take[unitLocations, 1, Length[unitLocations] - 1]) → mediumTicks
  31. Segment((0, 0), PEnd) → fractionSegment
  32. Element({(x(AnchorLeft), y(boxAnchorsLeftCase1(-1) - boxHeightRight)), sectorPointsLeft(1, 1), AnchorLeft}, caseNum) → SlideStartLeft
  33. Element({SlideStartRight + (pieceSizeLeft / 2, 0), Rotate[SlideStartRight, pi / currentDenom, AnchorRight], SlideStartRight + (0, ((-pieceSizeLeft)) / 2)}, caseNum) → SlideEndRight
  34. Element({SlideStartLeft + (modelWidth / 2, 0), Rotate[SlideStartLeft, pi, AnchorLeft], SlideStartLeft + (0, ((-modelWidth)) / 2)}, caseNum) → SlideEndLeft
  35. Sequence(Element[{SlideStartRight + ((2 / A * (x(SlideEndRight) - x(SlideStartRight))), 0), Rotate[SlideStartRight, (2 * Angle[SlideStartRight, AnchorRight, SlideEndRight] / A), AnchorRight], SlideStartRight + (0, (2 / A * (y(SlideEndRight) - y(SlideStartRight))))}, caseNum], A, 6, 2, -1) → denPointsRight
  36. Point(denPointsRight) → PMoveRight
  37. Sequence(Element[{SlideStartLeft + ((1 / A * modelWidth), 0), Rotate[SlideStartLeft, (2 * pi / A), AnchorLeft], SlideStartLeft + (0, (-1 / A * modelWidth))}, caseNum], A, 6, minDenom, -1) → denPointsLeft
  38. Point(denPointsLeft) → PMoveLeft
  39. Zip(topBox[boxHeightRight, boxWidthRight, A], A, boxAnchorsRight) → boxesRight
  40. Flatten(Sequence[Sequence[AnchorLeft + (((1.2 * boxWidthLeft) * i), ((-boxHeightLeft) * j)), j, 0, currentDenom - 1], i, 0, 3]) → boxAnchorsLeftCase3
  41. If(caseNum ≟ 1, boxAnchorsLeftCase1, boxAnchorsLeftCase3) → boxAnchorsLeft
  42. Zip(topBox[boxHeightLeft, boxWidthLeft, A], A, boxAnchorsLeft) → boxesLeft
  43. Take(boxesLeft, 1, currentNumer) → filledLeft
  44. Translate(filledLeft, AnchorRight - AnchorLeft) → filledRight
  45. Zip(Sequence[CircleSector[A, Element[B, K], Element[B, K + 1]], K, 1, Length[B] - 1], A, circAnchorsRight, B, sectorPointsRight) → sectorsRight
  46. TableText({((fracDisplayLeft * "=") * fracDisplayRight)}, "c", 200, 5) → fracDisplay
  47. IndexOf(PEnd, Unique[smallNumerLocations]) → movingNumer
  48. Segment(denPointsLeft(1), denPointsLeft(-1)) → slideSegmentLeft
  49. CircleArc(AnchorLeft, denPointsLeft(1), denPointsLeft(-1)) → slideArcLeft
  50. CircleArc(AnchorRight, denPointsRight(1), denPointsRight(-1)) → slideArcRight
  51. Segment(denPointsRight(1), denPointsRight(-1)) → slideSegmentRight
  52. onboardingTextOffset(Corner[onboardingText1, 1], Corner[onboardingText1, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingOffset
  53. circlePixels(PMoveLeft, 7 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObject1
  54. circlePixels(PEnd, 7 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObject2

AI 绘图提示语参考

绘制一个等价分数的可视化教学图形，包含三种不同的视觉模型：方块模型、圆形扇形模型和数轴模型。左侧显示原始分数，右侧显示其等价分数。数轴水平放置，上方有刻度线和数字标记。方块模型将整体分成若干行，每行包含若干个小方块，分子对应的方块填充颜色。圆形模型将圆分成若干扇形，分子对应的扇形填充颜色。通过平移和旋转操作，将左边的模型复制到右边，形成对比。使用表格文本在下方显示分数等式，如「2/4 = 1/2」。整个图形包含小刻度、中刻度和大刻度，以及表示分数值的动态线段。
以上提示语为根据原始绘图命令整理而来，仅供参考。