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长度单位配对与换算（2级）

长度单位配对与换算（2级）
几何画板及绘图内容加载中，请稍等……
2021-09-27 22:44
数列不等式几何作图滑块动画
所属专题 Wiederholung: Längen- und Flächenmaße
该范例通过交互题目让学生把不同长度单位（如毫米、厘米、分米、米、千米）正确对应，并检验换算结果是否匹配，从而理解长度量的单位体系。核心数学概念包括长度单位的量纲与换算关系、单位前缀（k、m、dm、cm、mm）、以及基于比例的度量换算。作图与交互要点：利用 GeoGebra 的 Sequence 与随机选择机制生成题目所需的数值（如 randomNos1~4、vals1/vals、count），再用条件逻辑 If、Shuffle 随机化单位与题目元素的呈现顺序；通过 Midpoint、Polygon 与 Textfield/文本对象生成带有问题与选项的图形界面（如 questionElement、answerElement、text7~9 等）；同时将答案索引与正确性判断结合（如 unitInd、correctInd、numSepText8、answerCorrect），并用列表与比较类信息确定单位大小关系（如 listSmallerOrEqual、listBiggerOrEqual，配合 unit/units）。适合5-6年级学生用于课堂测量换算练习或巩固长度单位理解，也可作为几何测量单元的随堂互动练习。

GeoGebra 命令及参数

  1. Sequence(Random[0, 1], i, 1, 100) → randomNos4, {1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0}
  2. Sequence(Random[21, 7800000], i, 1, 100) → randomNos2, {5926484, 4183619, 4137953, 5812736, 7496660, 7252599, 6164369, 129410, 1723706, 6086519, 4118023, 1640647, 2136562, 4362710, 5425609, 1589727, 2508144, 246538, 388669, 493387, 2577782, 6904337, 529408, 6554176, 6495693, 5871825, 3136459, 6346921, 6190451, 2193553, 3635394, 6640591, 6119474, 426584, 37228, 3448651, 7607990, 2768743, 1775341, 1361289, 4574165, 1481507, 4584239, 4549068, 3425768, 2143013, 6305592, 733973, 6889863, 601007, 7076081, 7197585, 1685550, 5604432, 726075, 3989680, 3944731, 849660, 4957416, 4452260, 1042863, 4255418, 365689, 2220812, 5637124, 4333519, 1953711, 1446434, 7067993, 3626603, 6900525, 771623, 7718046, 1906370, 4429679, 2083430, 4195036, 5599350, 2992280, 5608254, 2430793, 973233, 4041267, 2209850, 1433809, 1335827, 150769, 3244024, 540044, 2565016, 6822904, 5213671, 3480016, 1001907, 563403, 1973539, 5023943, 3519171, 1664485, 6628461}
  3. Element(randomNos2, Mod[count, 100] + 1) → valMM
  4. NumberSeparationComma(valMM) → valMM1
  5. NumberSeparationComma(valCM) → valCM1
  6. NumberSeparationComma(valDM) → valDM1
  7. NumberSeparationComma(valM) → valM1
  8. NumberSeparationComma(valKM) → valKM1
  9. Sequence(Random[1, Length[units]], i, 1, 100) → randomNos1, {4, 4, 3, 2, 5, 3, 3, 4, 2, 4, 2, 4, 2, 2, 4, 4, 3, 2, 2, 3, 2, 4, 5, 2, 3, 3, 1, 1, 2, 1, 5, 2, 4, 4, 2, 3, 2, 4, 3, 1, 2, 3, 3, 2, 1, 2, 3, 1, 3, 1, 1, 1, 5, 4, 4, 3, 3, 4, 4, 2, 2, 5, 3, 3, 2, 4, 5, 5, 4, 5, 1, 2, 3, 1, 2, 2, 3, 4, 4, 5, 1, 4, 4, 5, 4, 1, 5, 2, 5, 1, 4, 3, 5, 3, 3, 3, 4, 5, 4, 3}
  10. If(unitInd ≟ 1, Random[1, 2], If[unitInd ≟ 2, Random[1, 3], If[unitInd ≟ 3, Random[2, 4], If[unitInd ≟ 4, Random[3, 5], If[unitInd ≟ 5, Random[4, 5]]]]]) → correctInd
  11. If(correctInd > unitInd, 1, If[correctInd ≟ unitInd, 2, If[correctInd < unitInd, 3]]) → version
  12. Shuffle(Flatten[Sequence[Sequence["\textsf{\fcolorbox{#000}{#fff}{" + (Element[vals1, i]) + " " + (Element[units, j]) + "}}", j, 1, If[version ≟ 2, i, If[version ≟ 1, i - 1, If[version ≟ 3 ∧ i ≟ 5, 5, i + 1]]]], i, If[version ≟ 1, 2, 1], 5]]) → listSmallerOrEqual, {"\textsf{\fcolorbox{#000}{#fff}{1 775,341 mm}}", "\textsf{\fcolorbox{#000}{#fff}{1 775 341 mm}}", "\textsf{\fcolorbox{#000}{#fff}{17 753,41 mm}}", "\textsf{\fcolorbox{#000}{#fff}{177 534,1 dm}}", "\textsf{\fcolorbox{#000}{#fff}{1,775341 km}}", "\textsf{\fcolorbox{#000}{#fff}{1 775,341 m}}", "\textsf{\fcolorbox{#000}{#fff}{1,775341 dm}}", "\textsf{\fcolorbox{#000}{#fff}{17 753,41 cm}}", "\textsf{\fcolorbox{#000}{#fff}{17 753,41 dm}}", "\textsf{\fcolorbox{#000}{#fff}{1 775,341 cm}}", "\textsf{\fcolorbox{#000}{#fff}{1 775 341 cm}}", "\textsf{\fcolorbox{#000}{#fff}{1,775341 cm}}", "\textsf{\fcolorbox{#000}{#fff}{17 753,41 m}}", "\textsf{\fcolorbox{#000}{#fff}{1 775,341 dm}}", "\textsf{\fcolorbox{#000}{#fff}{177 534,1 cm}}", "\textsf{\fcolorbox{#000}{#fff}{1 775,341 km}}", "\textsf{\fcolorbox{#000}{#fff}{1,775341 m}}", "\textsf{\fcolorbox{#000}{#fff}{177 534,1 mm}}", "\textsf{\fcolorbox{#000}{#fff}{1,775341 mm}}"}
  13. Shuffle(Flatten[Sequence[Sequence["\textsf{\fcolorbox{#000}{#fff}{" + (Element[vals1, i]) + " " + (Element[units, j]) + "}}", j, If[version ≟ 2, i, If[version ≟ 3, i + 1, If[version ≟ 1 ∧ i ≟ 1, 1, i - 1]]], 5], i, 1, If[version ≟ 3, 4, 5]]]) → listBiggerOrEqual, {"\textsf{\fcolorbox{#000}{#fff}{17 753,41 km}}", "\textsf{\fcolorbox{#000}{#fff}{177 534,1 m}}", "\textsf{\fcolorbox{#000}{#fff}{1 775 341 dm}}", "\textsf{\fcolorbox{#000}{#fff}{177 534,1 km}}", "\textsf{\fcolorbox{#000}{#fff}{1 775,341 km}}", "\textsf{\fcolorbox{#000}{#fff}{1 775 341 cm}}", "\textsf{\fcolorbox{#000}{#fff}{1 775 341 km}}", "\textsf{\fcolorbox{#000}{#fff}{17 753,41 m}}", "\textsf{\fcolorbox{#000}{#fff}{1 775 341 m}}", "\textsf{\fcolorbox{#000}{#fff}{177 534,1 dm}}"}
  14. Sequence(RandomElement[(1…5) \ {randomNos1(i)}], i, 1, 100) → randomNos3, {2, 2, 5, 5, 1, 1, 1, 1, 4, 1, 5, 1, 4, 1, 1, 3, 4, 4, 4, 2, 3, 2, 3, 4, 2, 2, 2, 3, 1, 5, 1, 5, 5, 2, 4, 1, 4, 2, 4, 5, 3, 2, 1, 5, 5, 5, 5, 4, 4, 3, 2, 3, 2, 2, 2, 5, 1, 2, 2, 1, 3, 3, 1, 5, 4, 3, 3, 4, 2, 2, 2, 5, 2, 4, 1, 5, 4, 2, 5, 1, 4, 3, 3, 3, 2, 3, 3, 4, 2, 4, 5, 1, 1, 5, 2, 1, 5, 4, 5, 1}
  15. NumberSeparationComma(If[type ≟ 0, vals(correctInd) / 10, (vals(correctInd) * 10)]) → numSepAnswerCorrect
  16. NumberSeparationComma(If[type ≟ 0, (vals(correctInd) * 10), vals(correctInd) / 10]) → numSepText8
  17. Midpoint(Corner[answerCorrect, 1], Corner[answerCorrect, 3]) → M1
  18. Midpoint(Corner[text9, 1], Corner[text9, 3]) → M8
  19. Midpoint(Corner[text8, 1], Corner[text8, 3]) → M7
  20. Midpoint(Corner[text7, 1], Corner[text7, 3]) → M6
  21. Midpoint(Corner[text6, 1], Corner[text6, 3]) → M5
  22. Midpoint(Corner[text5, 1], Corner[text5, 3]) → M4
  23. Midpoint(Corner[text4, 1], Corner[text4, 3]) → M3
  24. Midpoint(Corner[text3, 1], Corner[text3, 3]) → M2
  25. Polygon(C, D, E, F) → box, c, d, e, f
  26. Textfield(aInput) → InputBox1
  27. Textfield(bInput) → InputBox2
  28. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
  29. Sequence(Shuffle[Flatten[Sequence[Sequence[G + ((i * dx), (j * dy)), i, 0, 1], j, 0, 3]]], k, 1, 100) → l3, {{(-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 3.066229595924379), (-4.032814719413515, 6.666229595924379)}, {(-4.032814719413515, 6.666229595924379), (-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 4.266229595924379), (-4.032814719413515, 3.066229595924379), (-4.032814719413515, 4.266229595924379)}, {(-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 6.666229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 3.066229595924379)}, {(-4.032814719413515, 3.066229595924379), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 4.266229595924379)}, {(-4.032814719413515, 3.066229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 4.266229595924379)}, {(-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 4.266229595924379), (-4.032814719413515, 3.066229595924379), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 6.666229595924379), (-4.032814719413515, 5.4662295959243785)}, {(-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 4.266229595924379), (-4.032814719413515, 3.066229595924379), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 4.266229595924379)}, {(-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 6.666229595924379), (-4.032814719413515, 3.066229595924379)}, {(-4.032814719413515, 3.066229595924379), (-1.3328147194135145, 4.266229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 6.666229595924379)}, {(-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 4.266229595924379), (-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 4.266229595924379), (-4.032814719413515, 3.066229595924379)}, {(-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 3.066229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 4.266229595924379)}, {(-4.032814719413515, 3.066229595924379), (-4.032814719413515, 6.666229595924379), (-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 6.666229595924379)}, {(-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 3.066229595924379), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 4.266229595924379)}, {(-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 3.066229595924379), (-4.032814719413515, 6.666229595924379), (-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 4.266229595924379)}, {(-4.032814719413515, 3.066229595924379), (-1.3328147194135145, 4.266229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379)}, {(-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 4.266229595924379), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 3.066229595924379)}, {(-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 4.266229595924379), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 3.066229595924379)}, {(-4.032814719413515, 4.266229595924379), (-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 4.266229595924379), (-4.032814719413515, 3.066229595924379)}, {(-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 6.666229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 3.066229595924379)}, {(-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 3.066229595924379), (-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 4.266229595924379), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 6.666229595924379)}, {(-1.3328147194135145, 4.266229595924379), (-4.032814719413515, 3.066229595924379), (-4.032814719413515, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 6.666229595924379), (-4.032814719413515, 5.4662295959243785)}, {(-4.032814719413515, 6.666229595924379), (-4.032814719413515, 4.266229595924379), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 5.4662295959243785), (-4.032814719413515, 3.066229595924379), (-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 4.266229595924379)}, {(-4.032814719413515, 4.266229595924379), (-4.032814719413515, 6.666229595924379), (-4.032814719413515, 5.4662295959243785), (-4.032814719413515, 3.066229595924379), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 6.666229595924379), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 4.266229595924379)}, {(-4.032814719413515, 5.4662295959243785), (-1.3328147194135145, 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5.4662295959243785), (-1.3328147194135145, 5.4662295959243785), (-1.3328147194135145, 3.066229595924379), (-1.3328147194135145, 4.266229595924379)}}
  30. Polygon(Corner[answerCorrect, 1], Corner[answerCorrect, 2], Corner[answerCorrect, 3], Corner[answerCorrect, 4]) → solutionBoxType0, g, h, i, j
  31. Zip(I ∈ box, I, ListM) → inBox

AI 绘图提示语参考

请绘制一个交互式练习，帮助学生正确匹配和验证长度单位，如毫米、厘米、分米、米、千米，以及它们之间的转换关系。展示单位系统的工作原理，以及单位之间的比例关系如何决定正确答案。关键数学概念包括长度测量、基于前缀的单位转换以及通过大小比较单位。图形包含随机生成的题目数据，使用序列和元素/数字处理（例如，randomNos1–4、vals/vals1、count）生成，并使用 Shuffle 随机化顺序。使用 If 逻辑控制题目流程和正确性检查。几何/图形界面元素使用 Midpoint、Polygon 和 Textfield/text 对象构建，例如 questionElement 和 answerElement 使用文本对象（如 text7–9）呈现任务和反馈。通过 indices 和比较结构（例如，unitInd、correctInd、numSepText8、answerCorrect、plus listSmallerOrEqual/listBiggerOrEqual）确定正确性。适合 5–6 年级，既可用于课堂单位转换练习，也可用于加强测量和单位的理解。
以上提示语为根据原始绘图命令整理而来，仅供参考。