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Rechentrick: Nullen und Nachkommastellen

Rechentrick: Nullen und Nachkommastellen
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2025-11-26 03:48
In collections Quadratzahlen und Quadratwurzeln
This example demonstrates how to understand decimal places and carrying through geometric diagrams. Key mathematical concepts include real numbers, decimal point placement, and geometric construction. Construction involves GeoGebra commands like Flatten, If, Sequence. Suitable for elementary high school or middle school math teaching to visually understand decimal concepts.

GeoGebra Commands & Parameters

  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}