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有理数排序：正数、负数、小数与分数的比较练习

有理数排序：正数、负数、小数与分数的比较练习
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2023-03-26 04:40
数列不等式滑块动画函数图像
该GeoGebra范例演示了如何对有理数进行排序，涵盖正数、负数、小数和分数等多种形式。核心数学概念是有理数的大小比较与顺序排列，强调理解数轴上的位置关系以及不同表示形式之间的转换。作图要点包括使用RandomUniform生成随机数，通过Take、Zip、If、Sort、Sequence、IndexOf等命令构建题目列表和答案列表，并利用Polygon、Segment、Corner、Dilate等绘制可拖动的方框和点，实现交互式排序操作。适合6-8年级学生练习有理数的比较与排序，既可用于课堂演示，也可作为自主练习工具。

GeoGebra 命令及参数

  1. RandomUniform(-0.99, 0.99, 200) → allRandoms1, {-0.871267331064494, 0.6479897657213198, -0.9845341371927736, -0.28114577546691855, 0.6706536068314761, -0.459477749454432, 0.4950921685292964, 0.8701476752168107, 0.6395431954419137, -0.16867864936613852, -0.8492249991598843, -0.9039547413489356, -0.82584539646152, 0.6355743971872849, -0.5866965272402633, -0.32441819105342284, -0.43247521670432176, 0.07384782586934868, -0.2785441764549488, -0.4316053175746094, 0.5870320470731585, -0.1836319458713459, 0.6521476112331666, -0.6293707073300625, 0.14357811841945578, 0.6445227750082514, 0.26244212439425163, 0.7841201680425303, -0.13918531955849178, 0.8308488913544958, 0.45859111303528954, 0.001159643339897598, 0.824299041479857, -0.44991780755832744, 0.7046760008163702, 0.12441075618839603, 0.39130322057186073, -0.5079725668051515, -0.9773030670353134, -0.1843561214039945, 0.7947163790992271, 0.31206606847396823, 0.5771096905498319, 0.4779710822383043, 0.5990688153244759, -0.692947183679913, 0.6798378655012622, -0.43587568004278676, 0.44317253707483584, 0.4231596748976112, 0.39668938785329, 0.06806934053023839, -0.8877885529303666, -0.8320883402262473, 0.40288468100856356, 0.5788680191961737, 0.6423304963402761, -0.20878545748120414, 0.3040557074264274, -0.20580163217026792, -0.12713805799078015, -0.4203889461843928, -0.5903976572300841, 0.6663126173574883, 0.2252922169777154, 0.6543082443593882, -0.5823049712940961, 0.6854588509148667, 0.9639126384949357, -0.8432953182764964, 0.14549006068262926, 0.2549145449175596, -0.5391878352234472, 0.6452021646454944, -0.12572386239686872, 0.19777452621063163, 0.9474600047143753, -0.8459775762277968, 0.6972982599193744, 0.05850856432651996, 0.006590832877777508, 0.9785570311549783, 0.21790670814382063, 0.542048656691988, -0.41855487062506747, 0.6324616166652, -0.7125421779270575, -0.27021168735666024, 0.23463257783770786, 0.7492654942992505, 0.9160434362378451, -0.8346291278790443, -0.024025052055555163, -0.8442996381058672, 0.19465528193162318, -0.44648322825616216, -0.8223482277264088, 0.30526060112623465, -0.2652088500967018, -0.6776162388978908, -0.05419044725530153, 0.22869160213138517, -0.9192111494195232, -0.1959232483749559, -0.9194877132242285, -0.4668395344818411, 0.7413242803609483, -0.031080769592772284, 0.41049955586792386, -0.01620218669908824, -0.5404607717334231, 0.806969856968988, -0.9843162130763388, -0.8298923860326677, -0.18383440948936847, -0.054986968340534736, -0.21134195815582535, 0.8554251642022395, -0.32320996653294665, -0.6811256382111861, 0.23670037441547387, -0.10983700159158316, -0.8469432008615011, 0.42940763310142627, -0.7321486701837341, -0.1809830529237627, -0.8318682916670378, -0.8841296999533556, 0.878604718849501, 0.3486138193370869, 0.7591545664081516, 0.04265232335845104, 0.7665930969023149, 0.1252656768171343, -0.006316405821534143, 0.7144419167752534, -0.3106369531067492, -0.17744569017894452, 0.7432873493614052, -0.7490896733865374, -0.30007396175389134, 0.9354027328339558, -0.05453118094771936, 0.9848666579697971, -0.7287652007750371, -0.2989004469812099, 0.73500640120377, -0.4624181986474797, 0.89507563018749, 0.9384255461039901, -0.24242447435894487, 0.25159976687474095, -0.1939185188887117, 0.5535905544264683, -0.1878337391732552, -0.8551474536461119, -0.6213396656733627, -0.9338787208177936, -0.07566025461162862, -0.8697357007253339, 0.47359918085238295, -0.08084854716327738, 0.10976855217154569, -0.4377223746207982, 0.9119423811020877, -0.3232534261031047, 0.746783786378467, -0.47414433032945913, 0.526459060675956, 0.4159566929216918, 0.37780336297944905, -0.18549078208569658, -0.7543960720269851, 0.37322247676909903, -0.07745566554284233, 0.9517702311549996, 0.4013400435249841, 0.6435687631330802, -0.22917695956831352, -0.3447219008037219, -0.179467283926534, 0.5167045151941414, 0.30952553659326343, -0.33573295487533594, -0.22016171938853135, -0.7332949848172263, 0.9869825109504315, -0.39026166283490094, -0.0438987614348636, -0.30861336388521254, -0.5914898994667939, 0.5819726534381895, -0.09176212603250467, -0.3962063475285176, 0.3892805043471772, 0.16228406374688342, 0.40242494601059997, -0.5686014770922978, -0.07503595144418318, 0.975037551841434}
  2. Take(allRandoms, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. Zip(closestFraction[(n * 5), denominators], n, Take[currentRandomSeeds, 5, 8]) → problemListStart
  4. If(problemListStart ≟ Sort[problemListStart], Flatten[{Last[problemListStart, 2], First[problemListStart, 2]}], problemListStart) → problemList
  5. Sort(problemList) → answerList
  6. Zip(IndexOf[n, problemList], n, answerList) → correctOrder
  7. Sequence((x(CenterPoints(1)) + (1.25 * n), y(CenterPoints(1))) - (1.25 / 2, 0), n, 0, 4) → MidSnapPoints
  8. If(movingBox ≟ 1 ∨ movingBox ≟ 0 ∧ boxNum ≟ 1, x(ClosestPoint[MidSnapPoints, PointBox1]), x(ClosestPoint[CenterPoints, PointBoxDrag(1)])) → xInd1
  9. If(movingBox ≟ 2 ∨ movingBox ≟ 0 ∧ boxNum ≟ 2, x(ClosestPoint[MidSnapPoints, PointBox2]), x(ClosestPoint[CenterPoints, PointBoxDrag(2)])) → xInd2
  10. If(movingBox ≟ 3 ∨ movingBox ≟ 0 ∧ boxNum ≟ 3, x(ClosestPoint[MidSnapPoints, PointBox3]), x(ClosestPoint[CenterPoints, PointBoxDrag(3)])) → xInd3
  11. If(movingBox ≟ 4 ∨ movingBox ≟ 0 ∧ boxNum ≟ 4, x(ClosestPoint[MidSnapPoints, PointBox4]), x(ClosestPoint[CenterPoints, PointBoxDrag(4)])) → xInd4
  12. Sort({xInd1, xInd2, xInd3, xInd4}) → xIndOrdered
  13. IndexOf(xInd4, xIndOrdered) → ind4
  14. IndexOf(xInd3, xIndOrdered) → ind3
  15. IndexOf(xInd2, xIndOrdered) → ind2
  16. IndexOf(xInd1, xIndOrdered) → ind1
  17. Sequence(IndexOf[n, inds], n, 1, 4) → indOrder
  18. Zip(n ≟ m, n, correctOrder, m, indOrder) → correctByOrder
  19. RemoveUndefined(Sequence[If[correctByOrder(n), correctOrder(n)], n, 1, 4]) → greenInds
  20. Zip(IndexOf[n, indOrder], n, greenInds) → greenOrd
  21. Polygon({(-10, -10), (-10, -11), (-11, -11), (-11, -10)}) → box0
  22. centerBox(1.25, 1.25, PointBox4) → box4
  23. centerBox(1.25, 1.25, PointBox3) → box3
  24. centerBox(1.25, 1.25, PointBox2) → box2
  25. centerBox(1.25, 1.25, PointBox1) → box1
  26. Segment(StartNumLine + (0.5, 0), EndNumLine - (0.5, 0)) → segNumberArea
  27. Corner(sizePos, 4) → PointPos
  28. Corner(sizeNeg, 4) → PointNeg
  29. Segment(StartNumLine, EndNumLine) → numberLineSeg
  30. If(movingBox > 0, inds(movingBox), 0) → movingInd
  31. If(movingInd > 0, CenterPoints(movingInd), CenterPoints(1)) → PointHighlight
  32. Polygon(Zip[PixelsToPoint[Corner[1], Corner[3], Corner[5], A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, y(Corner[5]) - pixelsBottom), Corner[5] - (pixelsRight, pixelsBottom), (x(Corner[5]) - pixelsRight, pixelsTop)}]) → borderBox
  33. Corner(5) → layoutAppSize
  34. Zip(Vector[PointSize, n], n, CornerSize) → cornerVectors
  35. centerBox(1.25, 1.25, CenterPoints(1)) → borderBox1
  36. centerBox(1.25, 1.25, CenterPoints(2)) → borderBox2
  37. centerBox(1.25, 1.25, CenterPoints(3)) → borderBox3
  38. centerBox(1.25, 1.25, CenterPoints(4)) → borderBox4
  39. Zip(¬(n ∈ CenterPoints), n, {PointBox1, PointBox2, PointBox3, PointBox4}) → boxesMoving
  40. centerBox(1.25, 1.25, PointHighlight) → borderHighlight1
  41. Sequence(StartNumLine + (0.5, 0) + ((n * (lenSeg - 2) / (dist - 1)), 0), n, 0, dist - 1) → PointNums
  42. Zip(Segment[n + (0, 0.12), n + (0, -0.12)], n, PointNums) → tickBig
  43. Sequence(StartNumLine + (0.5, 0) + ((n * (lenSeg - 2) / ((2 * (dist - 1)))), 0), n, 0, (2 * (dist - 1))) → PointMids
  44. Zip(Segment[n + (0, 0.1), n + (0, -0.1)], n, PointMids) → tickMid
  45. Sequence(StartNumLine + (0.5, 0) + ((n * (lenSeg - 2) / ((10 * (dist - 1)))), 0), n, 0, (10 * (dist - 1))) → PointSmalls
  46. Zip(Segment[n + (0, 0.05), n + (0, -0.05)], n, PointSmalls) → tickSmall
  47. Sequence(n, n, minNumLine, maxNumLine) → textNums
  48. Zip(Text[n, k - (0, 0.25) + If[n < 0, (((-oSizeNeg(2))) / 4, 0) + oSizeNeg(1), (((-oSizePos(2))) / 4, 0) + oSizePos(1)], true, true], n, textNums, k, PointNums) → textNumLine
  49. Zip(abs((minNumLine - n) / (dist - 1)), n, answerList) → ratioNums
  50. Zip(StartNumLine + (0.5, 0) + ((n * (lenSeg - 2)), 0), n, ratioNums) → PointsSolution
  51. Zip(textUnOrdered(n), n, correctOrder) → textOrdered
  52. Zip((((-x(solSizes(n)))) / 2, y(solSizes(n)) / 2), n, correctOrder) → positionsOrdered
  53. Sequence(If[showanswer ∨ showsolution ∨ validate ∧ correct, If[n ∈ greenInds, {210, 228, 226} / 255, {241, 210, 216} / 255], boxesMoving(n), {226, 223, 248} / 255, {238, 238, 238} / 255], n, 1, 4) → rgbInd
  54. Zip(StartNumLine + (0.5, 0) + ((n * (lenSeg - 2)), 0), n, ratioNums) → hintPoints
  55. Dilate({borderBox1, borderBox2, borderBox3, borderBox4}, 0.5, (0, -1.3)) → boxesSol
  56. Dilate(CenterPoints, 0.5, (0, -1.3)) → CenterSolutions
  57. Zip(Text[n, p + k - cornerVectors(1), true, true], n, textOrdered, p, CenterSolutions, k, positionsOrdered) → textSolNums
  58. Zip(n - (0, 1.25 / 4), n, CenterSolutions) → BottomSolutions
  59. Zip(n - (0, 1.25 / 2), n, CenterPoints) → BottomPoints
  60. Zip(Segment[n, m], n, If[validate ∧ correct, BottomPoints, BottomSolutions], m, PointsSolution) → solutionLines
  61. Element({box0, box1, box2, box3, box4}, movingBox + 1) → topBox
  62. If(movingBox > 0, PointTexts(movingBox), (-10, -10)) → PointPosition
  63. Sequence(If[showanswer ∨ showsolution ∨ validate ∧ correct, If[n ∈ greenOrd, {0, 103, 88} / 255, {176, 0, 32} / 255], {101, 87, 210} / 255], n, 1, 4) → outlineRGB
  64. Zip(problemText(n), n, inds) → readText

AI 绘图提示语参考

绘制一个用于练习排序有理数的交互式图形。图形包含一个数字线，上面有刻度标记和数字标签。数字线上方有四个可拖拽的方框，每个方框对应一个有理数问题（正数、负数、小数或分数）。方框下方有可拖拽的点，用于放置答案。图形中央有一个方框作为示例。数字线两端延伸出刻度标记。图形底部有文本标签，标注有理数排序的规则。整体构造顺序为：先生成随机有理数列表，创建方框和点，绘制数字线，添加刻度和文本，最后添加排序指示。
以上提示语为根据原始绘图命令整理而来，仅供参考。