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数感训练（第二级）：有理数的比较与数轴表示

数感训练（第二级）：有理数的比较与数轴表示
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2025-01-21 20:19
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所属专题 Rationale Zahlen & Arbeiten mit der Zahlengerade
① 本范例是一个面向初中生的交互式数感训练工具，通过随机生成有理数（包括整数、小数、分数及正负数）并让学生在数轴上定位或比较大小，直观展示有理数的数值关系。② 核心数学概念是有理数的比较与排序，以及有理数在数轴上的表示，涵盖正负数、小数、分数等不同形式。③ 作图要点：利用GeoGebra的RandomElement、Vector、Segment、Join、Remove、Unique、Element、Polygon、If、Text等命令构建动态题目系统，通过滑块（如maxNums、minNums）控制题目难度，使用随机数生成器（randomNos、numbersGanze、numbers3Dezimal1Neg等）产生不同类别的有理数，并借助按钮（button1）触发新题，通过显示矩形（showrect）和答案显示（showsolution）实现交互反馈，同时统计正确次数（countCorrect）。④ 适合7-8年级学生进行有理数概念巩固与数感训练，也可用于课堂演示或自主练习。

GeoGebra 命令及参数

  1. RandomElement(minNums) → minNum
  2. RandomElement(maxNums) → maxNum
  3. Vector(A + (0.5, 0), B) → u
  4. Segment((10, b), (10, (-b))) → g
  5. Join({{100}, Shuffle[Sequence[Random[5, 95], i, 1, 100]]}) → randomNos
  6. Remove((((minNum * 10) + 1)…0) / 10, numbersGanze) → numbers3Dezimal1Neg
  7. Remove((0…((maxNum * 10) - 1)) / 10, numbersGanze) → numbers4Dezimal1Pos
  8. Remove((((minNum * 100) + 1)…0) / 100, Flatten[{numbersGanze, numbers3Dezimal1Neg}]) → numbers5Dezimal2Neg
  9. Remove((0…((maxNum * 100) - 1)) / 100, Flatten[{numbersGanze, numbers4Dezimal1Pos}]) → numbers6Dezimal2Pos
  10. Unique(Flatten[Zip[Sequence[Sequence[j - i / a, i, 1, a - 1], j, minNum + 1, 0], a, {2, 3, 4, 5, 6, 8, 10}]]) → numbers1BruecheNeg
  11. Unique(Flatten[Zip[Sequence[Sequence[j + i / a, i, 1, a - 1], j, 0, maxNum - 1], a, {2, 3, 4, 5, 6, 8, 10}]]) → numbers2BruechePos
  12. Join(Sequence[Shuffle[{1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 6}], i, 1, 10]) → numbersToTakeWSK
  13. Element(numbersToTakeWSK, Mod[count, Length[numbersToTakeWSK]] + 1) → actualNumberToTakeWSK
  14. Element(numbersAll, actualNumberToTakeWSK) → numbers
  15. RandomElement(numbers) → num
  16. Polygon((Max[0, If[numPos ≥ numZero > numPos - 0.5, numZero, numPos - 0.5]], -0.3), (Min[10, If[numPos < numZero ≤ numPos + 0.5, numZero, numPos + 0.5]], -0.3), (Min[10, If[numPos < numZero ≤ numPos + 0.5, numZero, numPos + 0.5]], 0.3), (Max[0, If[numPos ≥ numZero > numPos - 0.5, numZero, numPos - 0.5]], 0.3)) → q1, h, i, j, k
  17. Segment((0, 0), (0.1, 0)) → P0
  18. Segment((0.1, 0), (0.2, 0)) → P1
  19. Segment((0.2, 0), (0.3, 0)) → P2
  20. Segment((0.3, 0), (0.4, 0)) → P3
  21. Segment((0.4, 0), (0.5, 0)) → P4
  22. Segment((0.5, 0), (0.6, 0)) → P5
  23. Segment((0.6, 0), (0.7, 0)) → P6
  24. Segment((0.7, 0), (0.8, 0)) → P7
  25. Segment((0.8, 0), (0.9, 0)) → P8
  26. Segment((0.9, 0), (1, 0)) → P9
  27. Segment((1, 0), (1.1, 0)) → P10
  28. Segment((1.1, 0), (1.2, 0)) → P11
  29. Segment((1.2, 0), (1.3, 0)) → P12
  30. Segment((1.3, 0), (1.4, 0)) → P13
  31. Segment((1.4, 0), (1.5, 0)) → P14
  32. Segment((1.5, 0), (1.6, 0)) → P15
  33. Segment((1.6, 0), (1.7, 0)) → P16
  34. Segment((1.7, 0), (1.8, 0)) → P17
  35. Segment((1.8, 0), (1.9, 0)) → P18
  36. Segment((1.9, 0), (2, 0)) → P19
  37. Segment((2, 0), (2.1, 0)) → P20
  38. Segment((2.1, 0), (2.2, 0)) → P21
  39. Segment((2.2, 0), (2.3, 0)) → P22
  40. Segment((2.3, 0), (2.4, 0)) → P23
  41. Segment((2.4, 0), (2.5, 0)) → P24
  42. Segment((2.5, 0), (2.6, 0)) → P25
  43. Segment((2.6, 0), (2.7, 0)) → P26
  44. Segment((2.7, 0), (2.8, 0)) → P27
  45. Segment((2.8, 0), (2.9, 0)) → P28
  46. Segment((2.9, 0), (3, 0)) → P29
  47. Segment((3, 0), (3.1, 0)) → P30
  48. Segment((3.1, 0), (3.2, 0)) → P31
  49. Segment((3.2, 0), (3.3, 0)) → P32
  50. Segment((3.3, 0), (3.4, 0)) → P33
  51. Segment((3.4, 0), (3.5, 0)) → P34
  52. Segment((3.5, 0), (3.6, 0)) → P35
  53. Segment((3.6, 0), (3.7, 0)) → P36
  54. Segment((3.7, 0), (3.8, 0)) → P37
  55. Segment((3.8, 0), (3.9, 0)) → P38
  56. Segment((3.9, 0), (4, 0)) → P39
  57. Segment((4, 0), (4.1, 0)) → P40
  58. Segment((4.1, 0), (4.2, 0)) → P41
  59. Segment((4.2, 0), (4.3, 0)) → P42
  60. Segment((4.3, 0), (4.4, 0)) → P43
  61. Segment((4.4, 0), (4.5, 0)) → P44
  62. Segment((4.5, 0), (4.6, 0)) → P45
  63. Segment((4.6, 0), (4.7, 0)) → P46
  64. Segment((4.7, 0), (4.8, 0)) → P47
  65. Segment((4.9, 0), (5, 0)) → P49
  66. Segment((5, 0), (5.1, 0)) → P50
  67. Segment((5.1, 0), (5.2, 0)) → P51
  68. Segment((5.2, 0), (5.3, 0)) → P52
  69. Segment((5.3, 0), (5.4, 0)) → P53
  70. Segment((5.4, 0), (5.5, 0)) → P54
  71. Segment((5.5, 0), (5.6, 0)) → P55
  72. Segment((5.6, 0), (5.7, 0)) → P56
  73. Segment((5.7, 0), (5.8, 0)) → P57
  74. Segment((5.8, 0), (5.9, 0)) → P58
  75. Segment((5.9, 0), (6, 0)) → P59
  76. Segment((6, 0), (6.1, 0)) → P60
  77. Segment((6.1, 0), (6.2, 0)) → P61
  78. Segment((6.2, 0), (6.3, 0)) → P62
  79. Segment((6.3, 0), (6.4, 0)) → P63
  80. Segment((6.4, 0), (6.5, 0)) → P64
  81. Segment((6.5, 0), (6.6, 0)) → P65
  82. Segment((6.6, 0), (6.7, 0)) → P66
  83. Segment((6.7, 0), (6.8, 0)) → P67
  84. Segment((6.8, 0), (6.9, 0)) → P68
  85. Segment((6.9, 0), (7, 0)) → P69
  86. Segment((7, 0), (7.1, 0)) → P70
  87. Segment((7.1, 0), (7.2, 0)) → P71
  88. Segment((7.2, 0), (7.3, 0)) → P72
  89. Segment((7.3, 0), (7.4, 0)) → P73
  90. Segment((7.4, 0), (7.5, 0)) → P74
  91. Segment((7.5, 0), (7.6, 0)) → P75
  92. Segment((7.6, 0), (7.7, 0)) → P76
  93. Segment((7.7, 0), (7.8, 0)) → P77
  94. Segment((7.8, 0), (7.9, 0)) → P78
  95. Segment((7.9, 0), (8, 0)) → P79
  96. Segment((8, 0), (8.1, 0)) → P80
  97. Segment((8.1, 0), (8.2, 0)) → P81
  98. Segment((8.2, 0), (8.3, 0)) → P82
  99. Segment((8.3, 0), (8.4, 0)) → P83
  100. Segment((8.4, 0), (8.5, 0)) → P84
  101. Segment((8.5, 0), (8.6, 0)) → P85
  102. Segment((8.6, 0), (8.7, 0)) → P86
  103. Segment((8.7, 0), (8.8, 0)) → P87
  104. Segment((8.8, 0), (8.9, 0)) → P88
  105. Segment((8.9, 0), (9, 0)) → P89
  106. Segment((9, 0), (9.1, 0)) → P90
  107. Segment((9.1, 0), (9.2, 0)) → P91
  108. Segment((9.2, 0), (9.3, 0)) → P92
  109. Segment((9.3, 0), (9.4, 0)) → P93
  110. Segment((9.4, 0), (9.5, 0)) → P94
  111. Segment((9.5, 0), (9.6, 0)) → P95
  112. Segment((9.6, 0), (9.7, 0)) → P96
  113. Segment((9.7, 0), (9.8, 0)) → P97
  114. Segment((9.8, 0), (9.9, 0)) → P98
  115. Segment((9.9, 0), (10, 0)) → P99
  116. Segment((10, 0), (10.1, 0)) → P100
  117. Segment((4.8, 0), (4.9, 0)) → P48
  118. If(floor(barometer / 2) + 1 ≥ 10, 10, floor(barometer / 2) + 1) → colorIndex
  119. Polygon((-1, -7), (17, -7), (17, 4), (-1, 4)) → canvas, l, m, n, p
  120. Vector(B - (0.5, 0), A) → u1
  121. Segment((0, b), (0, (-b))) → g1
  122. Segment((numZero, a), (numZero, (-a))) → f
  123. Vector((numPos, -0.4), (numPos, 0)) → v
  124. Element(randomNos, Mod[count, Length[randomNos]] + 1) → randomNumUnused
  125. Text("\textsf{" + numText + "}", (numPos - 0.02, -1.0), true, true, 0, 0) → text6

AI 绘图提示语参考

这是一个用于训练有理数概念的数轴图形。数轴上会随机生成整数、小数、分数和带符号的有理数点，这些点代表学习者需要比较或定位的数值。图形中包含一个计数器，用于跟踪正确回答的次数，以及一些交互元素，如提示和反馈按钮，帮助学生理解有理数的比较和排序。构造顺序是：首先绘制数轴，然后根据滑块设置的难度范围生成随机有理数，标记这些点，并显示比较问题，最后更新计数器。
以上提示语为根据原始绘图命令整理而来，仅供参考。