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迷宫寻路

迷宫寻路
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2023-07-26 20:45
所属专题 Wiederholung: Direkte und Indirekte Proportionalität Direkte Proportionalität
本范例演示如何在迷宫中寻找从起点到终点的路径。涉及的核心数学概念包括路径规划、逻辑推理和空间想象。构造要点：使用了Shuffle, Element, Flatten, If, Length, Sequence, IsInRegion, Textfield, Text, Point, Segment等GeoGebra命令和对象来创建迷宫网格、随机生成路径、判断路径有效性并交互式展示结果。适合小学5-6年级学生，用于培养逻辑思维和数学应用能力。

GeoGebra 命令及参数

  1. Shuffle(Sequence[10]) → randomNumbers, {3, 6, 8, 7, 5, 10, 2, 9, 4, 1}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Element(allSolutionsCalculated, randomNumber) → expectedSolutionValue
  4. Element(Element[allSolutionsSplitted, randomNumber], 1) → expectedSolutionGanze
  5. Element(Element[allSolutionsSplitted, randomNumber], 3) → expectedSolutionNenner
  6. Element(Element[allSolutionsSplitted, randomNumber], 2) → expectedSolutionZaehler
  7. Flatten({labyrinthW01, labyrinthW02, labyrinthW03, labyrinthW04}) → labyrinthWaagrecht
  8. Flatten({labyrinthS01, labyrinthS02, labyrinthS03, labyrinthS04}) → labyrinthSenkrecht
  9. Flatten({labyrinthSenkrecht, labyrinthWaagrecht}) → labyrinth
  10. If(randomNumber ∈ {1, 2, 3, 4, 5, 10}, inputno, inputyes) → correct
  11. Length(randomNumbers) → numberOfQuestions
  12. Sequence(Polygon[Element[questionsPositions, i], Element[questionsPositions, i] + sizeWaagrecht, Element[questionsPositions, i] + sizeWaagrecht + sizeSenkrecht, Element[questionsPositions, i] + sizeSenkrecht], i, 1, Length[questionsPositions]) → questionsRectangles
  13. IsInRegion(A, Element[questionsRectangles, actualQuestionNeeded]) → showQuestion
  14. Textfield(studentAnswer01) → inputBox01
  15. Textfield(studentAnswer02) → inputBox02
  16. Textfield(studentAnswer03) → inputBox03
  17. Text("\textsf{" + (ReplaceAll[Element[allTasks, randomNumber], "-", "\\minus"]) + "}", txtTaskPosition, true, true, -1, 0) → txtTask
  18. If((¬needGanze) ∧ needBruch, 5.25, 5.95) → startPositionBruchXValue
  19. Point(Line[B, xAxis]) → B2
  20. Segment(C, D) → f
  21. Segment(E, F) → g