积极 AI Logo 积极 AI

Rechentrick: Nullen und Nachkommastellen

Rechentrick: Nullen und Nachkommastellen
几何画板及绘图内容加载中，请稍等……
2025-11-26 03:48
所属专题 Quadratzahlen und Quadratwurzeln
该范例演示了如何通过几何图形理解小数和进位概念。核心数学概念包括实数、小数点位置和几何作图。作图要点涉及使用GeoGebra命令如Flatten、If、Sequence等来构造图形。适合小学高年级或初中数学教学，用于直观理解小数概念。

GeoGebra 命令及参数

  1. Flatten(Flatten[Sequence[Shuffle[1…12], k, 1, 100]]) → questionTypeSpezial
  2. If(level ≤ 1, Flatten[Sequence[Shuffle[1…2], k, 1, 100]], Flatten[Sequence[If[Mod[questionTypeSpezial(k), 2] ≟ 1, {1}, {2}], k, 1, 100]]) → listQuestionType
  3. Flatten(Sequence[Shuffle[1…9], k, 1, 100]) → listNumbers1
  4. Flatten(Sequence[Shuffle[1…12], k, 1, 100]) → listNumbers2
  5. If(type ≟ 1, If[level ≟ 1, listNumbers1(counter), listNumbers2(counter)], If[level ≟ 1, (listNumbers1(counter))^(2), (listNumbers2(counter))^(2)]) → number3
  6. If(type ≟ 1, number3^(2), sqrt(number3)) → solution3
  7. If(level ≤ 1, Flatten[Sequence[Shuffle[1…2], k, 1, 100]], Flatten[Sequence[If[questionTypeSpezial(k) ≤ 6, {1}, {2}], k, 1, 100]]) → listExampleType
  8. If(type ≟ 1, number2^(2), sqrt(number2)) → solution2
  9. If(example ≟ 1, (number2 * If[type ≟ 1, 10, 100]), If[type ≟ 1, number2 / 10, number2 / 100]) → number1
  10. If(type ≟ 1, number1^(2), sqrt(number1)) → solution1
  11. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {2, 1, 1, 1, 2, 6, 6, 2, 8, 4}
  12. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  13. Textfield(input) → inputBox
  14. Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, 0, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, 0, RasterMaxY / RasterStepXY]}) → RasterStrecken
  15. Join({Sequence[Text[UnicodeToLetter[65 + k], Midpoint[Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY)), Corner[4] + (RasterPixMat * (((k + 1) * RasterStepXY), RasterMaxY))], false, true, 0, -1], k, 0, RasterMaxX / RasterStepXY - 1], Sequence[Text[("" * k), Midpoint[Corner[4] + (RasterPixMat * (RasterMaxX, ((k - 1) * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], false, true, 1, 0], k, 1, RasterMaxY / RasterStepXY]}) → RasterBeschriftung
  16. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte
  17. Translate(imgChilliRot1, Vector[(1 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliRot2
  18. Textfield(input1) → A3inputBox1
  19. Textfield(input2) → A2inputBox2
  20. Textfield(input3) → A1inputBox3
  21. Polygon(pWhiteBoxLU, pWhiteBoxRU, pWhiteBoxRO, pWhiteBoxLO) → qWhiteBox, segWhite_{3}, segWhite_{2}, segWhite_{4}, segWhite_{1}
  22. Polygon(HintLO, HintRO, HintRU, HintLU) → hintBox, segHint_{1}, segHint, segHint_{2}, segHint_{3}
  23. Segment(pPfeilO_{1}, pPfeilU_{1}) → segPfeil_{1}
  24. Segment(pPfeilO_{2}, pPfeilU_{2}) → segPfeil_{2}
  25. If(type ≟ 1, number1 ≥ 100 ∨ number1 ≟ 10 ∨ number2 ≥ 100 ∨ number2 ≟ 10 ∨ number3 ≥ 100 ∨ number3 ≟ 10, solution1 ≟ 10 ∨ solution2 ≟ 10 ∨ solution3 ≟ 10 ∨ solution1 ≥ 20 ∨ solution2 ≥ 20 ∨ solution3 ≥ 20) → showHint1
  26. If(showHint1 ∧ showHint2, (x(PosHint1) + 1, y(PosHint1) - 2.3), PosHint1 + (1, 0)) → PosHint2
  27. Segment(pPfeilO_{3}, pPfeilU_{3}) → segPfeil_{3}
  28. Segment(pPfeilO_{4}, pPfeilU_{4}) → segPfeil_{4}
  29. Polygon(HintLO_{1}, HintRO_{1}, HintRU_{1}, HintLU_{1}) → hintBox_{1}, segHint_{4}, segHint_{5}, segHint_{6}, segHint_{7}
  30. Segment(pPfeilO_{9}, pPfeilU_{9}) → segPfeil_{6}
  31. Segment(pPfeilO_{8}, pPfeilU_{8}) → segPfeil_{7}
  32. Segment(pPfeilO_{7}, pPfeilU_{7}) → segPfeil_{8}
  33. Segment(pPfeilO_{6}, pPfeilU_{6}) → segPfeil_{9}
  34. Segment(PWaumL_1, PWarumR_1) → warum_1
  35. Segment(PWaumL_{2}, PWarumR_{2}) → warum_{2}
  36. Segment(PWaumL_{3}, PWarumR_{3}) → warum_{3}
  37. Segment(PWaumL_{4}, PWarumR_{4}) → warum_{4}
  38. Segment(PWaumL_{5}, PWarumR_{5}) → warum_{5}
  39. Segment(PWaumL_{8}, PWarumR_{8}) → warum_{8}
  40. Segment(PWaumL_{9}, PWarumR_{9}) → warum_{7}
  41. Segment(PWaumL_{11}, PWarumR_{11}) → warum_{9}
  42. Segment(PWaumL_{12}, PWarumR_{12}) → warum_{10}
  43. Segment(PWaumL_{13}, PWarumR_{13}) → warum_{11}
  44. Segment(PWaumL_{14}, PWarumR_{14}) → warum_{12}
  45. Segment(PWaumL_{18}, PWarumR_{18}) → warum_{15}
  46. Segment(PWaumL_{20}, PWarumR_{20}) → warum_{13}
  47. Segment(PWaumL_{19}, PWarumR_{19}) → warum_{14}
  48. Segment(PWaumL_{16}, PWarumR_{16}) → warum_{17}
  49. Segment(PWaumL_{15}, PWarumR_{15}) → warum_{18}
  50. Segment(PWaumL_{17}, PWarumR_{17}) → warum_{16}
  51. Segment(PWaumL_{10} + (0.02, 0), PWarumR_{10}) → warum_{6}