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小数数位意义探索

小数数位意义探索
几何画板及绘图内容加载中，请稍等……
2023-08-28 23:33
解析几何几何作图函数图像
本范例演示如何理解小数点后每位数字的具体数值，以千分位为例。涉及核心数学概念为数位价值与多位数中的数位识别。作图要点运用了GeoGebra命令如Sequence、Text、Segment等来展示数位与位置关系。适合小学4-5年级学生，用于培养数感与数位识别能力。

GeoGebra 命令及参数

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.6618749185791708, 0.7949794125208224, 0.21403506681465287, 0.984850528932058, 0.8188899778541004, 0.31508125321138336, 0.2345950091344206, 0.17724899791008425, 0.6044336384053195, 0.5955709798017984, 0.6003606351940349, 0.2699717941945454, 0.2831464857984519, 0.9815138712520406, 0.24180258827467688, 0.24648506633013803, 0.6628054536477772, 0.1751859241473669, 0.2365361247252865, 0.13463591262868219, 0.06504101567871023, 0.7929280631413281, 0.2166529042955606, 0.03168056332160433, 0.40585741779388024, 0.9072990349550759, 0.19693679681172652, 0.6948897396558191, 0.8099805209142742, 0.5094279046006611, 0.3946431261801593, 0.6189362902599937, 0.8291021567669569, 0.9561835113576699, 0.7467847588256258, 0.7489545745340198, 0.3060731597664159, 0.619932861798098, 0.10706952272552775, 0.9242851694960461, 0.895016256975459, 0.04525242645559824, 0.3417719544884228, 0.812478322626102, 0.07118816782819928, 0.18698485420391564, 0.07189894978674499, 0.5061279469294343, 0.35421479769575215, 0.8175014679452831, 0.7780219141535909, 0.42654343949983525, 0.7740557354333232, 0.7779341327409859, 0.8441000878221369, 0.9681395405928962, 0.2507246355519471, 0.07848279414080993, 0.05750735366428058, 0.4157352644336091, 0.7863990053942831, 0.9766836001654655, 0.8943018521791729, 0.9137005635273018, 0.682098182167373, 0.08973974480969005, 0.321541053445337, 0.23107545785397202, 0.5305904134333305, 0.8776713075663938, 0.01214587117119581, 0.45040884795919733, 0.582610186862107, 0.03813207617063841, 0.04245681883489984, 0.5601253051759256, 0.684824317066903, 0.5712708350565315, 0.11820037324766956, 0.8007256539589077, 0.5852795678902226, 0.32398133408074464, 0.3010982114778017, 0.844063372914055, 0.3752985262389682, 0.6372891356454671, 0.7658028430008159, 0.6623110724195184, 0.36595841315920974, 0.0884661454011021, 0.7752317126405527, 0.3990425376979971, 0.7423966003271322, 0.04074163150414521, 0.7216982341057161, 0.11910362270603712, 0.9302306143614917, 0.32819704894434704, 0.911501882876857, 0.20663064540201004, 0.7053630601242434, 0.9315842670051137, 0.43184026858646823, 0.3816984294217858, 0.7713619382892758, 0.4424006238649495, 0.22104556983540885, 0.7056399611675679, 0.7074640211378499, 0.3975820053285803, 0.42622282441164505, 0.7530788237437483, 0.815044095151636, 0.06564248526318509, 0.7963823524591038, 0.07514960114406817, 0.7711251681519216, 0.9469938344462386, 0.8641087416576245, 0.4032560709451454, 0.644174674049735, 0.46651894174400016, 0.5446983840085332, 0.7160261436069504, 0.23003924546983007, 0.4652536143753831, 0.7385230418669622, 0.9038717818900429, 0.4244153357793671, 0.04024703959927322, 0.5301409475521675, 0.20574664715869007, 0.8127355359886085, 0.847326499591908, 0.4563780309857983, 0.7713179240244328, 0.4287704355357932, 0.45058245643131895, 0.5652406576977795, 0.6688291482786919, 0.14960311259151782, 0.5049208954610687, 0.8680970666013017, 0.24442876099027733, 0.2069281780231334, 0.6239952418009034, 0.009078850865832091, 0.4626749028079211, 0.6428603718893164, 0.5452353801555307, 0.9781046442650116, 0.12029980603667373, 0.6826064701672157, 0.5965328308372435, 0.1873170019904077, 0.6361276427883182, 0.47646293621632757, 0.2154202042440719, 0.7750496205034527, 0.49928822899575226, 0.8296458320967585, 0.8313002029999905, 0.14670562881158244, 0.45555379607161695, 0.12044205773188549, 0.024433455891119178, 0.02812899864356851, 0.5877495143305488, 0.6250914209506699, 0.6919866783153382, 0.47418963228594363, 0.10074915402378112, 0.5116656916700779, 0.5114711276706704, 0.9733791614390189, 0.954564876407137, 0.44500628476587034, 0.005369304413083852, 0.4582274826466301, 0.17047595686790534, 0.03051457174238481, 0.7176509885329141, 0.29130227904395534, 0.975014399147982, 0.18625826243108395, 0.963222245549957, 0.847441325032866, 0.7549355795727279, 0.6104654621122075, 0.6651300648848545, 0.5746944443969529, 0.28305044309917454, 0.6550224478069917, 0.9315620310570707, 0.9492151265534493, 0.10998128202661175, 0.8950734985096223, 0.5153350811176477, 0.45304313916844063, 0.43052586663224385}
  2. Take(allRandomSeeds, maxRandIndex - numRandoms + 1, maxRandIndex) → unTruncatedSeeds
  3. Corner(1) → C1
  4. Corner(3) → C3
  5. Corner(5) → C5
  6. Zip(round(A, 6), A, unTruncatedSeeds) → currentRandomSeeds
  7. IndexOf(".", textNumber) → decLocation
  8. IndexOf(true, HintClicked) → indexClicked
  9. Element(textNumber, 10) → Digit10
  10. Element(textNumber, 9) → Digit9
  11. Element(textNumber, 8) → Digit8
  12. Element(textNumber, 7) → Digit7
  13. Element(textNumber, 6) → Digit6
  14. Element(textNumber, 5) → Digit5
  15. Element(textNumber, 4) → Digit4
  16. Element(textNumber, 3) → Digit3
  17. Element(textNumber, 2) → Digit2
  18. Element(textNumber, 1) → Digit1
  19. Insert(colorBlack, {colorPink, colorRedError, colorPurpleDark, colorPurpleButton, colorBlue, colorTealSuccess, colorGreen, colorOrange, colorBrown}, decLocation) → colorsRainbow
  20. Take({"hundred thousands", "ten thousands", "thousands", "hundreds", "tens", "ones", "decimal point", "tenths", "hundredths", "thousandths"}, 8 - decLocation) → placeList
  21. Length(textNumber) → numDigits
  22. Zip(HintStart + (k * (boxWidthHint, 0)), k, Sequence[j, j, 0, numDigits - 1]) → HintPointsList
  23. ParseToNumber(digitClicked) → digitClickedNum
  24. Remove(Sequence[k, k, 1, numDigits], {decLocation}) → placeIndexOps
  25. Element(placeIndexOps, 1 + floor((currentRandomSeeds(3) * Length[placeIndexOps]))) → placeIndex
  26. Corner(5) → layoutAppSize
  27. PointToPixels(Corner[onboardingDisplayText, 2], Corner[1], Corner[3], Corner[5]) → layoutOnboarding
  28. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  29. Element(placeList, placeIndex) → place
  30. Sequence(k, k, 1, numDigits) → digitNum
  31. centerBox(boxWidthHint, boxHeightHint, Element[HintPointsList, 1]) → Box1Hint
  32. centerBox(boxWidthHint, boxHeightHint, Element[HintPointsList, 2]) → Box2Hint
  33. centerBox(boxWidthHint, boxHeightHint, Element[HintPointsList, 3]) → Box3Hint
  34. centerBox(boxWidthHint, boxHeightHint, Element[HintPointsList, 4]) → Box4Hint
  35. centerBox(boxWidthHint, boxHeightHint, Element[HintPointsList, 5]) → Box5Hint
  36. centerBox(boxWidthHint, boxHeightHint, Element[HintPointsList, 6]) → Box6Hint
  37. centerBox(boxWidthHint, boxHeightHint, Element[HintPointsList, 7]) → Box7Hint
  38. centerBox(boxWidthHint, boxHeightHint, Element[HintPointsList, 8]) → Box8Hint
  39. centerBox(boxWidthHint, boxHeightHint, Element[HintPointsList, 9]) → Box9Hint
  40. centerBox(boxWidthHint, boxHeightHint, Element[HintPointsList, 10]) → Box10Hint
  41. centerBox(boxWidthHint, boxHeightHintLabel, Element[HintPointsList, 1] + (0, (boxHeightHintLabel + boxHeightHint) / 2)) → Box1HintLabel
  42. centerBox(boxWidthHint, boxHeightHintLabel, Element[HintPointsList, 2] + (0, (boxHeightHintLabel + boxHeightHint) / 2)) → Box2HintLabel
  43. centerBox(boxWidthHint, boxHeightHintLabel, Element[HintPointsList, 3] + (0, (boxHeightHintLabel + boxHeightHint) / 2)) → Box3HintLabel
  44. centerBox(boxWidthHint, boxHeightHintLabel, Element[HintPointsList, 4] + (0, (boxHeightHintLabel + boxHeightHint) / 2)) → Box4HintLabel
  45. centerBox(boxWidthHint, boxHeightHintLabel, Element[HintPointsList, 5] + (0, (boxHeightHintLabel + boxHeightHint) / 2)) → Box5HintLabel
  46. centerBox(boxWidthHint, boxHeightHintLabel, Element[HintPointsList, 6] + (0, (boxHeightHintLabel + boxHeightHint) / 2)) → Box6HintLabel
  47. centerBox(boxWidthHint, boxHeightHintLabel, Element[HintPointsList, 7] + (0, (boxHeightHintLabel + boxHeightHint) / 2)) → Box7HintLabel
  48. centerBox(boxWidthHint, boxHeightHintLabel, Element[HintPointsList, 8] + (0, (boxHeightHintLabel + boxHeightHint) / 2)) → Box8HintLabel
  49. centerBox(boxWidthHint, boxHeightHintLabel, Element[HintPointsList, 9] + (0, (boxHeightHintLabel + boxHeightHint) / 2)) → Box9HintLabel
  50. centerBox(boxWidthHint, boxHeightHintLabel, Element[HintPointsList, 10] + (0, (boxHeightHintLabel + boxHeightHint) / 2)) → Box10HintLabel
  51. Zip(If[A, "colorPurpleBackground ", "colorWhite"], A, HintClicked) → colorHint
  52. Text(hintNumber) → textHintNumber
  53. RotateText(((("" * "\textsf{") * Element[placeList, 1]) * "}"), pi / 2) → placeLabel1
  54. RotateText(((("" * "\textsf{") * Element[placeList, 2]) * "}"), pi / 2) → placeLabel2
  55. RotateText(((("" * "\textsf{") * Element[placeList, 3]) * "}"), pi / 2) → placeLabel3
  56. RotateText(((("" * "\textsf{") * Element[placeList, 4]) * "}"), pi / 2) → placeLabel4
  57. RotateText(((("" * "\textsf{") * Element[placeList, 5]) * "}"), pi / 2) → placeLabel5
  58. RotateText(((("" * "\textsf{") * Element[placeList, 6]) * "}"), pi / 2) → placeLabel6
  59. RotateText(((("" * "\textsf{") * Element[placeList, 7]) * "}"), pi / 2) → placeLabel7
  60. RotateText(((("" * "\textsf{") * Element[placeList, 8]) * "}"), pi / 2) → placeLabel8
  61. RotateText(((("" * "\textsf{") * Element[placeList, 9]) * "}"), pi / 2) → placeLabel9
  62. RotateText(((("" * "\textsf{") * Element[placeList, 10]) * "}"), pi / 2) → placeLabel10
  63. Zip((((("SetColor(Box" * A) * "Hint,") * B) * ")"), A, digitNum, B, colorHint) → cmdSetColorHint
  64. Zip((((("SetColor(Box" * A) * "HintLabel,") * B) * ")"), A, digitNum, B, colorHint) → cmdSetColorHintLabel
  65. If(decLocation ≟ 1, shift, 0) → s1
  66. If(decLocation ≟ 2, shift, 0) → s2
  67. If(decLocation ≟ 3, shift, 0) → s3
  68. If(decLocation ≟ 4, shift, 0) → s4
  69. If(decLocation ≟ 5, shift, 0) → s5
  70. If(decLocation ≟ 6, shift, 0) → s6
  71. If(decLocation ≟ 7, shift, 0) → s7
  72. If(decLocation ≟ 8, shift, 0) → s8
  73. If(decLocation ≟ 9, shift, 0) → s9
  74. If(decLocation ≟ 10, shift, 0) → s10
  75. Sequence(false, k, 1, 10) → allFalse
  76. Text(If[indexClicked ≟ decLocation ∨ (¬Defined[indexClicked]), "", textExplainationNum], descriptionLoc, true, true, 1, 0) → textExplaination
  77. If(indexClicked ≤ decLocation, indexClicked, decLocation - 1) → startingIndex
  78. Sequence(Element[(("" * placeNum) * ""), k], k, 1, Length[(("" * placeNum) * "")]) → placeNumList
  79. Zip(k + (0, ((-animatePosition) * boxHeightHint)), k, HintPointsList) → lowerPointList
  80. makeBox(lowerPointList(startingIndex) + (((-boxWidthHint)) / 2, boxHeightHint / 2), (boxWidthHint * Length[placeNumList]), boxHeightHint) → positionBox
  81. Zip(Text[(((("\textcolor{" * m) * "}{") * J) * "}"), K + (0.01, 0.01), true, true, 0, 0], m, colorsRainbow, J, digitList, K, Take[HintPointsList, 1, numDigits]) → BoxTextHint
  82. Segment(StartTopPtHint, StartTopPtHint + ((boxWidthHint * numDigits), 0)) → topLine
  83. Translate(topLine, Vector[StartTopPtHint, StartTopPtHint + (0, (-boxHeightHintLabel))]) → midLine
  84. Translate(topLine, Vector[StartTopPtHint, StartTopPtHint + (0, (-boxHeightHint) - boxHeightHintLabel)]) → bottomLine
  85. Sequence(Segment[StartTopPtHint + (k * (boxWidthHint, 0)), StartTopPtHint + ((k * boxWidthHint), (-boxHeightHint) - boxHeightHintLabel)], k, 0, numDigits) → linesVertical
  86. Zip(If[k ≟ "0" ∨ k ≟ ".", colorBlack, colorClicked], k, placeNumList) → colorLowerNums
  87. Zip(Text[(((("\textcolor{" * m) * "}{") * K) * "}"), J, true, true, 0, 0], m, colorLowerNums, K, placeNumList, J, Take[lowerPointList, startingIndex]) → lowerNums
  88. expandCircle(HintPointsList(numDigits), 9 + (7 * pulsing), C1, C3, C5) → pulsingCircle
  89. PointToPixels1(C1, C3, C5, onboardingPt) → onboardingPtPixels

AI 绘图提示语参考

在坐标平面上构造一个用于十进制位值讲解的布局：画出三到五个角点作为界面定位点，并以这些点确定画布大小。用一排等宽的提示框表示从“最高位到千分位”依次排列的十进制位置，包括整数部分与小数点后的十分位、百分位、千分位，并在每个框的上方或内部放置对应的位置文字。再在同一位置为每一位留出可显示的数字占位框，使“十进制点”位置将整数与小数部分分开。整体强调每个框对应的位值含义与相对顺序。
以上提示语为根据原始绘图命令整理而来，仅供参考。