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面积大小比较：更大、更小还是相等？

面积大小比较：更大、更小还是相等？
几何画板及绘图内容加载中，请稍等……
2022-07-25 17:07
所属专题 Wiederholung: Längen- und Flächenmaße Wiederholung: Flächen- und Raummaße
本范例通过GeoGebra互动练习，让学生比较不同图形的面积大小。核心数学概念是面积的比较与测量，涉及使用Polygon命令绘制多边形、Point命令创建顶点、Sequence命令生成图形序列、Midpoint命令找中点，并结合If条件判断和Shuffle命令实现题目的随机排列。学生在练习中需要判断两个图形的面积是大于、小于还是等于关系，适合5-6年级学生掌握面积概念和测量技能。

GeoGebra 命令及参数

  1. Shuffle({3, 4, 15, 13, 14, 1, 5, 9, 10, 11, 12, 2, 8, 6, 7}) → NosCase, {8, 13, 9, 12, 5, 11, 4, 3, 7, 1, 14, 15, 10, 2, 6}
  2. Shuffle(Sequence[Random[1, 49], i, 1, 100]) → randomNosForY, {13, 26, 8, 20, 49, 31, 48, 16, 42, 49, 17, 1, 30, 23, 29, 26, 4, 35, 12, 16, 34, 34, 44, 3, 13, 27, 5, 18, 15, 8, 15, 34, 46, 44, 16, 30, 33, 7, 38, 45, 44, 38, 9, 3, 16, 27, 40, 23, 38, 5, 29, 41, 47, 12, 19, 5, 20, 30, 10, 48, 36, 5, 32, 12, 3, 10, 40, 13, 34, 35, 19, 31, 29, 29, 46, 18, 44, 18, 47, 32, 7, 13, 25, 22, 11, 19, 37, 27, 49, 27, 25, 30, 37, 33, 27, 36, 27, 15, 9, 7}
  3. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  4. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  5. Shuffle(Sequence[Random[50, 99], i, 1, 100]) → randomNosForX, {62, 88, 57, 59, 89, 96, 72, 78, 94, 58, 88, 91, 81, 64, 65, 83, 88, 73, 68, 54, 70, 67, 53, 90, 67, 97, 63, 75, 64, 53, 70, 56, 62, 99, 94, 56, 82, 88, 76, 93, 88, 68, 70, 81, 98, 79, 81, 77, 82, 84, 54, 69, 73, 63, 75, 65, 97, 58, 74, 73, 71, 69, 59, 87, 90, 98, 73, 86, 93, 94, 76, 92, 88, 54, 52, 51, 77, 65, 79, 74, 68, 98, 80, 52, 96, 75, 75, 77, 53, 91, 77, 89, 54, 55, 50, 68, 52, 62, 67, 59}
  6. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  7. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  8. Shuffle(Sequence[Random[2, 10], i, 1, 100]) → randomNosForK, {2, 6, 9, 5, 7, 4, 4, 2, 6, 6, 10, 2, 5, 7, 4, 3, 3, 7, 7, 7, 5, 3, 7, 9, 7, 2, 6, 8, 6, 4, 10, 8, 5, 2, 2, 8, 4, 5, 9, 10, 7, 9, 4, 10, 8, 3, 8, 2, 2, 9, 8, 8, 10, 4, 9, 9, 5, 3, 7, 2, 7, 10, 8, 2, 3, 4, 8, 9, 5, 6, 5, 6, 4, 5, 10, 9, 3, 2, 6, 10, 10, 6, 2, 6, 9, 7, 2, 7, 2, 4, 10, 8, 6, 4, 7, 7, 8, 7, 5, 10}
  9. Append(true, Sequence[If[randomNosForK(i) ≟ randomNosForK(i - 1), false, true], i, 2, 100]) → stayK
  10. IndexOf(true, checkboxes) → SelectedCheckbox
  11. Point(Line[F11, Vector[(0, 0), (0, -1.2)]]) → F21
  12. Shuffle(Sequence[Random[1, 3], i, 1, 100]) → randomNosPositionAnswerCorrect, {2, 1, 1, 1, 2, 2, 2, 2, 1, 3, 3, 1, 3, 1, 3, 2, 1, 3, 2, 3, 2, 3, 2, 3, 3, 3, 2, 3, 2, 3, 3, 3, 1, 1, 1, 2, 1, 2, 2, 1, 3, 1, 2, 1, 1, 1, 1, 2, 3, 2, 1, 3, 2, 3, 1, 2, 3, 2, 2, 3, 3, 1, 1, 1, 1, 1, 3, 2, 3, 1, 1, 1, 2, 2, 2, 1, 3, 2, 3, 3, 1, 1, 3, 2, 2, 2, 3, 3, 3, 2, 1, 1, 3, 2, 3, 2, 1, 2, 3, 3}
  13. Element(randomNosPositionAnswerCorrect, Mod[questionCount, 100] + 1) → numPositionAnswerCorrect
  14. Shuffle(Sequence[Random[2, 10], i, 1, 100]) → randomNosForA, {9, 9, 4, 10, 6, 2, 6, 5, 9, 6, 7, 3, 9, 9, 9, 6, 7, 9, 3, 5, 9, 6, 8, 2, 7, 9, 4, 2, 5, 6, 9, 4, 2, 6, 4, 2, 10, 7, 10, 4, 10, 6, 10, 4, 3, 5, 4, 9, 7, 7, 5, 3, 8, 6, 10, 3, 8, 2, 7, 6, 6, 2, 5, 3, 2, 6, 5, 10, 9, 4, 2, 6, 2, 7, 3, 10, 6, 9, 2, 2, 8, 6, 2, 8, 5, 8, 9, 5, 9, 4, 6, 7, 9, 6, 5, 2, 10, 5, 5, 6}
  15. Append(true, Sequence[If[randomNosForA(i) ≟ randomNosForA(i - 1), false, true], i, 2, 100]) → stayA
  16. Remove(Sequence[If[stayA(i), randomNosForA(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForAwithoutRepeat
  17. Element(randomNosForAwithoutRepeat, Mod[questionCount, 100] + 1) → numA
  18. Remove(Sequence[If[stayK(i), randomNosForK(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForKwithoutRepeat
  19. Element(randomNosForKwithoutRepeat, Mod[questionCount, 100] + 1) → numK
  20. Zip((a * k), a, randomNosForAwithoutRepeat, k, randomNosForKwithoutRepeat) → randomNosForZ
  21. Textfield(aInput) → InputBox1
  22. Textfield(bInput) → InputBox2
  23. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
  24. Sequence(RandomElement[Remove[Sequence[3], {randomNosPositionAnswerCorrect(i)}]], i, 1, 100) → randomNosPositionAnswerWrong1, {3, 3, 3, 2, 1, 1, 1, 1, 3, 2, 1, 2, 2, 3, 2, 1, 3, 1, 3, 1, 3, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 3, 1, 3, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 3, 3, 1, 1, 2, 3, 3, 1, 3, 1, 2, 1, 2, 3, 2, 2, 2, 1, 1, 2, 3, 3, 2, 3, 1, 1, 2, 1, 1, 2, 1, 3, 3, 1, 1, 3, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 3, 2, 1, 1, 2}
  25. Sequence(RandomElement[Remove[Remove[Sequence[3], {randomNosPositionAnswerCorrect(i)}], {randomNosPositionAnswerWrong1(i)}]], i, 1, 100) → randomNosPositionAnswerWrong2, {1, 2, 2, 3, 3, 3, 3, 3, 2, 1, 2, 3, 1, 2, 1, 3, 2, 2, 1, 2, 1, 2, 3, 1, 2, 1, 3, 1, 3, 2, 1, 2, 3, 3, 3, 3, 2, 3, 1, 3, 2, 3, 3, 3, 3, 3, 3, 3, 1, 1, 2, 2, 3, 1, 2, 1, 2, 1, 3, 1, 2, 3, 2, 3, 3, 3, 2, 3, 1, 2, 2, 3, 1, 3, 3, 3, 2, 3, 1, 2, 2, 2, 2, 3, 1, 3, 2, 2, 1, 3, 3, 3, 2, 3, 2, 1, 3, 3, 2, 1}
  26. Shuffle(Sequence[Random[1, 15], i, 1, 100]) → randomNosCase, {13, 10, 4, 6, 6, 1, 13, 8, 9, 5, 5, 12, 2, 1, 7, 12, 8, 3, 5, 8, 15, 12, 4, 3, 12, 1, 3, 1, 14, 2, 11, 12, 15, 13, 5, 1, 14, 2, 13, 14, 10, 10, 11, 14, 14, 3, 2, 5, 15, 7, 2, 2, 5, 1, 8, 8, 13, 2, 15, 13, 9, 8, 12, 3, 10, 4, 2, 8, 7, 12, 14, 7, 15, 3, 2, 12, 6, 14, 6, 6, 14, 14, 8, 12, 3, 8, 7, 4, 3, 14, 1, 14, 9, 9, 11, 12, 4, 14, 4, 10}
  27. Sequence(RandomElement[{-2, -1, 1, 2}], i, 1, 200) → randomNosForNumDeviation1, {-1, 2, -2, -1, -1, 2, -2, 2, -1, 1, -1, -2, 1, 1, -2, 1, -1, -2, 1, -2, 2, -1, -1, 1, -2, -2, -2, 1, -1, 1, 1, -2, -1, -2, -2, 1, 2, -1, 2, -2, -2, 2, -2, -2, 1, 1, -1, 2, 2, -2, 1, 2, 1, -1, -2, -2, -2, -2, -2, -1, 2, 1, -1, 2, 1, 2, -1, 1, 1, 1, -2, 2, 1, -2, -2, 1, 2, 1, -1, -1, -1, 1, -2, 2, -2, 1, 2, -2, -2, 1, -1, 2, -1, 2, 1, -1, 1, -2, -1, 2, 2, 1, -1, 1, -1, 1, -2, -1, -2, -2, -2, -1, 1, -2, -1, 1, 1, 2, -1, -2, 2, -2, -2, 1, -2, 2, -2, 2, -1, -2, -1, 1, 1, 2, -2, -2, 1, -1, -2, 1, 2, -1, -1, -1, -1, -1, -1, -2, 2, 2, -2, 1, -2, 2, -2, -2, 2, -2, 2, -2, 2, -1, 2, 2, -2, -1, -2, 1, -2, -2, 1, -2, -2, 2, -1, -2, 1, 2, 1, 2, 2, 1, -2, -2, -1, -1, -1, -1, 2, -1, -2, 2, -2, 1, -1, 1, -1, 1, -1, 2}
  28. Element(randomNosForNumDeviation1, Mod[questionCount, 100] + 1) → numDeviation1
  29. Zip(RandomElement[{-2, -1, 1, 2} \ {m}], m, randomNosForNumDeviation1) → randomNosForNumDeviation2
  30. Element(randomNosForNumDeviation2, Mod[questionCount, 100] + 1) → numDeviation2
  31. Element(randomNosPositionAnswerWrong1, Mod[questionCount, 100] + 1) → numPositionAnswerWrong1
  32. Element(randomNosPositionAnswerWrong2, Mod[questionCount, 100] + 1) → numPositionAnswerWrong2
  33. Midpoint(PbottomLeftCornerFeedback, PbottomRightCornerFeedback) → PbottomMiddle
  34. Append(true, Sequence[If[randomNosCase(i) ≟ randomNosCase(i - 1), false, true], i, 2, 100]) → stayNos
  35. Remove(Sequence[If[stayNos(i), randomNosCase(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosCasewithoutRepeat
  36. If(numPositionAnswerCorrect ≟ 1, true, false) → c1
  37. If(numPositionAnswerCorrect ≟ 2, true, false) → c2
  38. If(numPositionAnswerCorrect ≟ 3, true, false) → c3
  39. Polygon(F11, (x(F13), y(F11)), F13, (x(F11), y(F13))) → q1, f11, j, f13, k
  40. Polygon(F21, (x(F23), y(F21)), F23, (x(F21), y(F23))) → q2, f21, l, f23, m
  41. Polygon(F31, (x(F31), y(F33)), F33, (x(F33), y(F31))) → q3, n, p, q, r

AI 绘图提示语参考

在坐标平面上绘制多个矩形与对比用的点构造图。先给定下方与上方各两组角点：分别形成一个正确矩形的四个顶点（左上、右上、右下、左下），再在另一位置为反馈与题目生成对应点，并用其中两点的中点作为辅助位置。随后把每组顶点连成封闭多边形，得到至少三个多边形区域，其中一个是以指定四点确定的矩形，其余两块由各自的三到四个点对确定的角点组合构成。最后在各图形区域下方标注用于比较的输入框位置，并安排三个答案位置的显示顺序。
以上提示语为根据原始绘图命令整理而来，仅供参考。