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用带状图表示分数为单位分数乘积

用带状图表示分数为单位分数乘积
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2023-06-06 17:37
解析几何几何作图
本范例通过带状图展示分数如何表示为单位分数的乘积。核心数学概念包括分数、单位分数和乘积。使用了RandomUniform、Take、If、Textfield等GeoGebra命令。适合4-5年级学生进行分数概念的学习和练习。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.1605706529055802, 0.059587469534874926, 0.7786227152201088, 0.6214540822213908, 0.22980509207957628, 0.2637556001990956, 0.6669564314452548, 0.5758032988553746, 0.4555630442772438, 0.9300522089523213, 0.5311965122406954, 0.4422765271213055, 0.5773977145696311, 0.23615385663413427, 0.19159027210666335, 0.4774676530712184, 0.3759458194404581, 0.9594081784583802, 0.9336078783931248, 0.5993819513927756, 0.7979534101192534, 0.24638793253717106, 0.7099858319860489, 0.8589147122579053, 0.8570876814867509, 0.9219551843677749, 0.8475106655448671, 0.7540898347744328, 0.28065765307334295, 0.5455930800564112, 0.32164932943643715, 0.17557287252198228, 0.4323180214933633, 0.35263527223533164, 0.4638024126643802, 0.13231417430222595, 0.4117188123870255, 0.06633412763060227, 0.20356420046207346, 0.5099573378206562, 0.5238900027671334, 0.36345640202181434, 0.8919178167927666, 0.9018652709091762, 0.04391366963930275, 0.7612810051766862, 0.020777038424612544, 0.3132696129325788, 0.4661376870629523, 0.41749617250672383, 0.07970518324522498, 0.8831421766445302, 0.2218231842479668, 0.6265542721375913, 0.3120000766773593, 0.19591522360735222, 0.08469479486601902, 0.35654018961324163, 0.969627942792408, 0.31614528377034395, 0.4703757826478089, 0.6895450457453445, 0.15972229634561863, 0.08361862329449579, 0.18314181038618346, 0.41590976551143916, 0.5245334010205874, 0.1342387767159642, 0.8818152748563958, 0.008514025585720134, 0.4818213484242967, 0.9533156214905654, 0.44594897172108305, 0.1275334915324129, 0.773730962518308, 0.1325926125503079, 0.7237107120698163, 0.4987745207687644, 0.7591686600777263, 0.8505024480027392, 0.45408236578552175, 0.22981785120432205, 0.11762200246450626, 0.7167339206021266, 0.3781252665844474, 0.08776400614168975, 0.03121952338089604, 0.8772216332699876, 0.8471398202151957, 0.07037080422878632, 0.5966234881203566, 0.28413712546049386, 0.7995613222938717, 0.468808781925118, 0.36908092731902103, 0.45736409195491057, 0.9233845420736189, 0.06513382487983492, 0.7476277367059857, 0.3392827946268218, 0.8667991004674633, 0.5308866836454244, 0.39304867312201525, 0.04346705149390056, 0.10654296691203449, 0.2149765100457325, 0.34874019825815294, 0.00011490598261078011, 0.18124576564930558, 0.2491924241202381, 0.30910648211828007, 0.9666879430501166, 0.06573449509639911, 0.7783085986773698, 0.0405378195997549, 0.41132593888217844, 0.2619125207858283, 0.46881013819003814, 0.5863790713727829, 0.2991332843427224, 0.5624000731482345, 0.5557643513599922, 0.839589855889029, 0.227399697940743, 0.30463642251465717, 0.10129794061121658, 0.40503126457533206, 0.6252228561987416, 0.1655968618250226, 0.3705135195577491, 0.8874834277166967, 0.20584163475477002, 0.7506647281421315, 0.42148926695756955, 0.271605607641035, 0.41626851947220084, 0.3545262068495563, 0.7652540376497058, 0.8860961254073325, 0.5485261266843962, 0.43721830608796347, 0.6593153137485744, 0.5762904605998713, 0.24994740621915468, 0.8846620286206495, 0.014440704187175765, 0.2173576708262836, 0.6165905295673632, 0.08015175167477223, 0.018953959865624228, 0.9841107623226012, 0.9638492079530758, 0.28134691319929284, 0.7778050371235373, 0.6432429752288, 0.0018056183918447755, 0.3363273079987288, 0.7151088880125174, 0.8495338305919059, 0.7697773465017292, 0.722222984022284, 0.3087204440531212, 0.07923856657232765, 0.18485228443012516, 0.7608195182797876, 0.9237246497090383, 0.10148223916840848, 0.5829834921273972, 0.9773648735177941, 0.7584677225606146, 0.7620248797261898, 0.3184340069715371, 0.28156820362475177, 0.45194142945430515, 0.29324586144570614, 0.3380152808162451, 0.9234818666988222, 0.13495573244467116, 0.9396163608713919, 0.7206546657375544, 0.061596640969126384, 0.5995949196253473, 0.8092855575324721, 0.000356983065611699, 0.8060564105157293, 0.9519513624121237, 0.8397015771057044, 0.19159179482735306, 0.9564121737033401, 0.7220654231752597, 0.31842040995389154, 0.420542467125855, 0.4507862897021242, 0.5923741567078001, 0.4594257767437686, 0.24349452710552227, 0.8917067714677973, 0.19178136703807802, 0.9403909331779653, 0.41492070322254754}
  2. Take(allRandomSeeds, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. If(animateControl < 1, 0, Min[ceil(((animateControl - 1) * num)), num]) → solutionNum
  4. Textfield(input1) → InputBox1
  5. Textfield(input2) → InputBox2
  6. Corner(5) → layoutAppSize
  7. sectorPixels(A, B, C, haloPixels + 40, Corner[1], Corner[3], Corner[5]) → pulsingObject
  8. sectorPixels(A, B, C, 40, Corner[1], Corner[3], Corner[5]) → displayAngle
  9. PointToPixels(Corner[onboardingDisplayText, 2], Corner[1], Corner[3], Corner[5]) → layoutOnboarding
  10. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  11. makeBox(StartPt, fullLength, height) → fracBox
  12. Zip(Segment[A, A - (0, height)], A, Sequence[StartPt + ((fullLength / den, 0) * k), k, 1, den - 1]) → fracLines
  13. Sequence(StartPt + (k * (fullLength / den, 0)), k, 0, num - 1) → topPoints
  14. Zip(makeBox[A, fullLength / den, height], A, topPoints) → fracBoxes
  15. Vector(StartPt, solutionStartPt) → solutionVec
  16. Translate(fracBox, solutionVec) → solutionFracBox
  17. Translate(fracBoxes, solutionVec) → solutionFracBoxes
  18. Translate(topPoints, solutionVec) → solutionTopPoints
  19. Sequence(boxesStartPt + (k * (fullLength / den + spaceBetween, 0)), k, 0, solutionNum - 1) → solutionTopBoxPoints
  20. Zip(makeBox[A, fullLength / den, height], A, solutionTopBoxPoints) → upperFracBoxes
  21. Min(ceil((animateControl * den)), den) → solutionDen
  22. Zip(Segment[A, A - (0, height)], A, Sequence[solutionStartPt + ((fullLength / solutionDen, 0) * k), k, 1, solutionDen - 1]) → solutionFracLines
  23. Max(0, animateControl - 2) → moveBoxes
  24. Zip(Vector[A, B], A, solutionTopBoxPoints, B, solutionTopPoints) → moveVectors
  25. Zip(A + (B * moveBoxes), A, solutionTopBoxPoints, Vector[B], moveVectors) → movePoints
  26. Zip(makeBox[A, fullLength / den, height], A, movePoints) → movingBoxes
  27. Zip(makeBox[A, fullLength / den, height], A, solutionTopBoxPoints) → upperFracBoxOutline
  28. Segment(segStart + (0, segEndHeight / 2), segStart - (0, segEndHeight / 2)) → segLeftEnd
  29. Segment(segEnd + (0, segEndHeight / 2), segEnd - (0, segEndHeight / 2)) → segRightEnd
  30. Segment(segStart, segMid - (segMiddleSpace / 2, 0)) → segLeft
  31. Segment(segEnd, segMid + (segMiddleSpace / 2, 0)) → segRight
  32. Text("1", segMid, true, true, 0, 0) → segText1

AI 绘图提示语参考

绘制一个用于分数乘以单位分数的卷尺图（tape diagram）。画出一个长矩形分割成 den 等份的分数条，并在其上方依次给出每个等份对应的若干竖线与分割格。再在同一条带上方复制出若干“分数小盒”，让其中的分数条与上方分数盒对齐。接着从分数条的左端到右端用连续的线段刻画小盒边界的移动轨迹，并为分数条两侧端点画出竖向的半高线。最后在中间位置标注分数条的标记数字“1”，整体呈现“用单位分数的乘积来表示一个分数”的布局关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。