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体育场馆改造数学练习：比例与代数应用

体育场馆改造数学练习：比例与代数应用
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2023-10-18 22:17
所属专题 Wiederholung: Direkte und Indirekte Proportionalität Indirekte Proportionalität
该范例演示了通过几何图形和代数方法分析体育场馆改造的比例关系。核心数学概念包括直接与间接比例、代数方程求解以及解决方案的比较与验证。作图要点涉及使用GeoGebra命令如If、Join、Polygon等构建图形，并设置输入框和验证按钮。适合小学五年级至六年级学生，用于练习比例和代数应用，辅助理解几何与代数之间的联系。

GeoGebra 命令及参数

  1. If(step ≟ 5, End1, H0) → H1
  2. Join(Sequence[Shuffle[Sequence[1, maxexnum]], m, 1, floor(110 / maxexnum)]) → listExNums
  3. Textfield(input1) → InputBox1
  4. Textfield(input2) → InputBox2
  5. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  6. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {1, 4, 5, 1, 5, 3, 9, 5, 10, 5, 9, 8, 2, 2, 5, 9, 1, 6, 10, 0, 9, 0, 5, 5, 2, 8, 2, 3, 6, 0, 3, 5, 8, 0, 0, 8, 7, 7, 5, 5, 5, 9, 3, 8, 2, 2, 7, 3, 2, 2, 0, 1, 1, 9, 9, 2, 3, 4, 2, 7, 4, 7, 2, 5, 10, 5, 4, 3, 1, 0, 9, 9, 10, 2, 9, 2, 0, 2, 7, 1, 8, 10, 0, 8, 0, 9, 9, 1, 2, 2, 9, 3, 3, 4, 9, 0, 1, 5, 3, 8}
  7. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {0, 9, 8, 0, 6, 9, 5, 10, 3, 10, 9, 2, 3, 3, 3, 1, 3, 8, 3, 4, 0, 6, 2, 5, 10, 6, 6, 9, 3, 7, 2, 2, 6, 3, 6, 7, 6, 2, 10, 6, 9, 5, 3, 1, 3, 6, 2, 7, 5, 8, 10, 10, 0, 3, 4, 10, 2, 0, 4, 1, 2, 5, 8, 2, 3, 10, 7, 9, 7, 10, 9, 8, 8, 3, 0, 8, 8, 10, 7, 1, 4, 8, 3, 8, 4, 10, 7, 8, 6, 3, 8, 8, 0, 4, 6, 9, 2, 9, 4, 0}
  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. SpeechBubbleRight(A_{2}, 6.38, 0.9) → Vieleck1
  15. Point(Line[Midpoint[B_{2}, B1], xAxis]) → C_{2}
  16. CircleArc(C_{2}, B_{2}, B1) → c
  17. CircleArc(D1 + Vector[C_{2}, B_{2}], D1, D_{2}) → d
  18. If(step ≟ 2, S, O) → J1_{2}
  19. Point(Line[H0, xAxis]) → H2_{1}
  20. If(step ≟ 5, End2, Z0) → Z1
  21. If(step ≟ 5, End3, J1_{2}) → J1
  22. Point(Line[A, xAxis]) → B
  23. Point(Line[A, xAxis]) → C
  24. Point(Line[D, xAxis]) → Da
  25. Point(Line[D, xAxis]) → Db
  26. Point(Line[D, xAxis]) → Dc