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情境转方程：线性方程与不等式应用

情境转方程：线性方程与不等式应用
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2023-02-24 20:29
函数不等式函数图像
本范例演示如何将实际生活情境逐步转化为数学方程。学生需要根据给定的储蓄问题（现有30美元，目标5周后达到350美元），写出每周需要存款多少的线性方程并求解。核心数学概念包括列方程求解实际问题、线性方程的建立与解法、不等式的应用。作图要点：利用Shuffle命令随机生成不同情境，Sequence命令生成数列，Text命令显示问题文本，Polygon绘制辅助图形，并通过slider实现交互式求解演示。适合6-8年级学生使用，可用于培养代数思维和实际问题建模能力，是练习列方程解应用题的优质互动资源。

GeoGebra 命令及参数

  1. Shuffle(Sequence[3]) → randomSituation, {3, 1, 2}
  2. Corner(5) → AppSize
  3. Shuffle({{1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}}) → randomOrderCB, {{1, 2, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}, {1, 3, 2}, {2, 1, 3}}
  4. Element(randomOrderCB, Mod[example, Length[randomOrderCB]] + 1) → orderCB
  5. Element(randomSituation, Mod[example, Length[randomSituation]] + 1) → situation
  6. Zip((kk, 0), kk, If[situation ≟ 1, {3.2, 2.5, 3}, situation ≟ 2, {1.8, 3, 2}, {1.8, 1.3, 1.3}]) → xcoords
  7. Translate(hGuideline, Vector[(Vector[Corner[4], Corner[1]] / 500 * 16)]) → hGuideline'
  8. Sequence(yFirstCB + (ii * (26 + 16)), ii, 0, 2) → ycoordsCB, {138, 180, 222}
  9. Zip(XX + YY - (0.8, 0), XX, xcoords, YY, ycoords) → departure
  10. Sort(Zip[(kk, -0.5), kk, {If[situation ≟ 1, 7.5, 8], 10.75, 13.25}], {2, 1, 3}) → arrival
  11. Semicircle(A1, D1) → c1
  12. Semicircle(A2, D2) → c2
  13. Semicircle(A3, D3) → c3
  14. Point(c1, anim2) → Panim1
  15. Point(c2, anim1) → Panim2
  16. Point(c3, anim3) → Panim3
  17. Text((("\" * Element[sizes, floor((anim2 * 3)) + 1]) * initialValues(situation)), Panim1, true, true, 1, 1) → animtext1
  18. Text((("\" * Element[sizes, floor((anim1 * 3)) + 1]) * rates(situation)), Panim2, true, true, 1, 1) → animtext2
  19. Text((("\" * Element[sizes, floor((anim3 * 3)) + 1]) * finalvalues(situation)), Panim3, true, true, 1, 1) → animtext3
  20. Polygon({arrival(1), arrival(1) + (wid, 0), arrival(1) + (wid, hei), arrival(1) + (0, hei)}) → q2
  21. Polygon({arrival(2), arrival(2) + (wid, 0), arrival(2) + (wid, hei), arrival(2) + (0, hei)}) → q1
  22. Polygon({arrival(3), arrival(3) + (wid, 0), arrival(3) + (wid, hei), arrival(3) + (0, hei)}) → q3
  23. Text(equation, PointEq, true, true, -1, -1) → equationPos
  24. Polygon({Vertex[q2, 1] + ((-disth), (-distv)), Vertex[q2, 2] + (disth, (-distv)), Vertex[q2, 3] + (disth, distv), Vertex[q2, 4] + ((-disth), distv)}) → q2white
  25. Polygon({Vertex[q2, 1] + ((-2 * disth), (-2 * distv)), Vertex[q2, 2] + ((2 * disth), (-2 * distv)), Vertex[q2, 3] + ((2 * disth), (2 * distv)), Vertex[q2, 4] + ((-2 * disth), (2 * distv))}) → q2Selected
  26. Polygon({Vertex[q1, 1] + ((-disth), (-distv)), Vertex[q1, 2] + (disth, (-distv)), Vertex[q1, 3] + (disth, distv), Vertex[q1, 4] + ((-disth), distv)}) → q1white
  27. Polygon({Vertex[q1, 1] + ((-2 * disth), (-2 * distv)), Vertex[q1, 2] + ((2 * disth), (-2 * distv)), Vertex[q1, 3] + ((2 * disth), (2 * distv)), Vertex[q1, 4] + ((-2 * disth), (2 * distv))}) → q1Selected
  28. Polygon({Vertex[q3, 1] + ((-2 * disth), (-2 * distv)), Vertex[q3, 2] + ((2 * disth), (-2 * distv)), Vertex[q3, 3] + ((2 * disth), (2 * distv)), Vertex[q3, 4] + ((-2 * disth), (2 * distv))}) → q3Selected
  29. Polygon({Vertex[q3, 1] + ((-disth), (-distv)), Vertex[q3, 2] + (disth, (-distv)), Vertex[q3, 3] + (disth, distv), Vertex[q3, 4] + ((-disth), distv)}) → q3white

AI 绘图提示语参考

在画面中创建一个带有三段半圆标记的三列情境图：先放置三个半圆，三者共享相近的基准位置但彼此错开，分别用三个点放在半圆上并加上对应文字，文字内容随三个情境数据在这些点上方动态变化；再在底部形成三个矩形卡片区域并给出三块“白色轮廓+选中轮廓”，让它们与三个底部位置一一对应。整体同时呈现情境文本、速率与终值文本，并用移动的方式展示从起点到终点的对应位置关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。