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百分比增加与减少基准值计算练习

百分比增加与减少基准值计算练习
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2023-04-26 16:12
函数最值优化不等式
所属专题 Prozentrechnung: Vermehrung und Verminderung
本范例是一个交互式的百分比计算练习程序，通过随机生成题目帮助学生掌握基准值的增加（Vermehrte Grundwerte）和减少（Verminderte Grundwerte）计算。核心数学概念包括：理解变化因子（Änderungsfaktor）的概念，掌握单步及多步百分比问题的求解方法。程序使用Shuffle和Element命令随机抽取题目，通过Textfield创建输入框接收学生答案，利用If和Defined命令进行答案验证，并配置btnValidate按钮、btnTryAgain重试按钮和btnNew新题按钮实现完整的练习反馈流程。适合7-8年级学生复习和巩固百分比计算知识，也可用于课堂即时测评。

GeoGebra 命令及参数

  1. Join({Join[{firstEx, Shuffle[Sequence[1, 12] \ firstEx]}], Join[Sequence[Shuffle[Sequence[1, maxexnum]], m, 1, floor(110 / maxexnum)]]}) → listExNums
  2. Textfield(input1) → InputBox1
  3. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  4. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {8, 6, 9, 6, 4, 0, 2, 3, 6, 8, 7, 8, 3, 0, 4, 7, 7, 3, 1, 10, 1, 4, 1, 8, 2, 10, 9, 0, 0, 3, 3, 6, 3, 10, 3, 0, 4, 6, 0, 9, 7, 6, 2, 6, 3, 2, 5, 7, 6, 9, 2, 10, 4, 7, 0, 0, 3, 3, 1, 6, 1, 2, 3, 6, 7, 7, 10, 1, 1, 8, 6, 2, 9, 0, 4, 9, 9, 3, 0, 10, 10, 6, 9, 8, 0, 8, 9, 7, 0, 10, 6, 6, 4, 9, 8, 2, 0, 7, 9, 9}
  5. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  6. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {8, 4, 2, 3, 0, 1, 1, 5, 3, 0, 8, 7, 4, 4, 1, 4, 7, 3, 7, 7, 10, 8, 6, 10, 10, 6, 2, 7, 7, 7, 9, 10, 8, 7, 7, 6, 6, 3, 10, 6, 1, 2, 10, 1, 8, 0, 3, 8, 7, 8, 0, 8, 10, 0, 7, 8, 10, 5, 8, 9, 3, 6, 6, 6, 1, 9, 3, 5, 7, 2, 7, 3, 8, 8, 7, 3, 5, 2, 6, 7, 6, 6, 7, 4, 0, 8, 6, 4, 9, 8, 9, 4, 3, 0, 0, 1, 9, 9, 8, 8}
  7. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  8. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  9. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  10. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  11. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  12. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  13. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  14. Defined(input1) → fixed
  15. NumberSeparationComma(numA) → Text39
  16. Textfield(input3) → InputBox3
  17. Textfield(input4) → InputBox4
  18. Textfield(input5) → InputBox5
  19. Textfield(input2) → InputBox2
  20. Semicircle(B1 + (0, circleheight), B1) → c
  21. Semicircle(B1 + (0, (2 * circleheight) - 0.2), B1 + (0, circleheight - 0.2)) → d
  22. Semicircle(B1 + (circlewidth, 0), B1 + (circlewidth, circleheight)) → e
  23. Semicircle(B1 + (circlewidth, circleheight - 0.2), B1 + (circlewidth, (2 * circleheight) - 0.2)) → f
  24. Textfield(input6) → InputBox6
  25. Textfield(input7) → InputBox7
  26. If(opt2, input3 ≟ solopt2, input3 ≟ solopt1) → correct3
  27. Point(Line[P0, xAxis]) → P1
  28. Point(Line[P0, xAxis]) → P2
  29. Point(Line[P0, xAxis]) → P3
  30. Point(Line[P0, xAxis]) → P4
  31. Point(Line[P0, xAxis]) → P5
  32. Point(Line[P0, xAxis]) → P6
  33. Point(Line[P0, xAxis]) → P7
  34. Point(Line[P0, xAxis]) → P8
  35. Point(Line[P0, xAxis]) → P9
  36. Point(Line[P0, xAxis]) → P10
  37. Point(Line[P0, xAxis]) → P11
  38. Point(Line[P0, xAxis]) → P12
  39. Element({P1, P2, P3, P4, P5, P6, P7, P8, P9, P10, P11, P12}, exnum) → P
  40. Point(Line[E0, xAxis]) → E1
  41. Point(Line[E0, xAxis]) → E2
  42. Point(Line[E0, xAxis]) → E3
  43. Point(Line[E0, xAxis]) → E4
  44. Point(Line[E0, xAxis]) → E5
  45. Point(Line[E0, xAxis]) → E6
  46. Point(Line[E0, xAxis]) → E7
  47. Point(Line[E0, xAxis]) → E8
  48. Point(Line[E0, xAxis]) → E9
  49. Point(Line[E0, xAxis]) → E10
  50. Point(Line[E0, xAxis]) → E11
  51. Point(Line[E0, xAxis]) → E12
  52. Element({E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12}, exnum) → E

AI 绘图提示语参考

绘制一个练习用的矩形区域作为画布背景，矩形由四个角点围成，并在其内部预留一处水平线穿过的基准位置。再在同一基准点附近做一套“半圆轮廓”装饰：以一个左侧起点为圆心的上半圆，同时在下方再放一个偏移的上半圆组合，整体形成类似左右对称的弧形框架；再在矩形右侧对应位置放置两段竖向半圆弧，使弧形上下与半径略有缩短。最后在矩形上方与弧形附近加入多处可输入的文本框区域，并在弧形框架边界上标出可供生成的多个落在水平线上的点，用于后续连线或标注。
以上提示语为根据原始绘图命令整理而来，仅供参考。