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Gegenzahl: Fraction Input and Number Line Representation

Gegenzahl: Fraction Input and Number Line Representation
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2024-12-16 19:45
In collections Gegenzahl und Betrag einer rationalen Zahl
The Gegenzahl example demonstrates converting fractions to positions on a number line. Key math concepts include absolute value, number line representation, and fraction conversion. Construction involves using Textfield for input, Polygon for drawing the number line, Shuffle for random point arrangement, Distance for measuring distances, and Circle for drawing circles. Suitable for middle school s

GeoGebra Commands & Parameters

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  4. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {6, 4, 8, 10, 3, 7, 4, 9, 5, 7, 3, 8, 4, 8, 3, 5, 1, 8, 2, 0, 9, 4, 9, 1, 2, 2, 6, 8, 8, 10, 5, 1, 0, 3, 8, 8, 2, 10, 0, 6, 4, 3, 9, 8, 5, 2, 8, 7, 5, 8, 2, 6, 4, 8, 3, 3, 8, 3, 1, 6, 5, 6, 1, 6, 1, 1, 8, 10, 10, 1, 10, 8, 9, 3, 7, 3, 0, 9, 10, 4, 0, 9, 9, 5, 0, 3, 8, 1, 0, 4, 10, 9, 3, 6, 2, 2, 2, 8, 0, 4}
  5. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  6. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {0, 0, 0, 6, 4, 5, 1, 9, 2, 9, 1, 7, 0, 7, 7, 0, 7, 2, 3, 1, 10, 1, 2, 3, 7, 4, 3, 10, 5, 4, 0, 10, 7, 6, 9, 0, 7, 0, 3, 0, 6, 8, 7, 4, 0, 7, 0, 8, 2, 7, 7, 9, 0, 7, 10, 0, 10, 3, 3, 5, 8, 2, 8, 5, 10, 7, 4, 9, 8, 4, 4, 3, 8, 9, 0, 10, 7, 5, 7, 6, 9, 5, 6, 3, 4, 0, 3, 10, 7, 4, 10, 1, 2, 1, 10, 2, 1, 9, 3, 9}
  7. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  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. Shuffle(1…10) → ExNumList, {6, 4, 8, 9, 2, 5, 7, 3, 1, 10}
  15. Length(ExNumList) → questionCountMax
  16. Shuffle({1, 2, 3}) → NumListModMid, {3, 1, 2}
  17. If(questionCount ≤ 3, 1, 2) → metaprogression
  18. If(metaprogression ≟ 1, NumListModStart(questionCount), NumListModMid(modindex)) → mod
  19. Shuffle(Sequence[i, i, 1, If[mod ≟ 1, 1, mod ≟ 2, 3, 2]]) → SubGroupList, {1}
  20. If(mod ≟ 1, 15, 1 + 7 / 8, mod ≟ 2 ∧ subgroup ≟ 1, 7.5, mod ≟ 2 ∧ subgroup ≟ 2, 3, mod ≟ 2 ∧ subgroup ≟ 3, 1.5, mod ≟ 3 ∧ subgroup ≟ 1, 1.5) → grenze
  21. Sequence(GeradePLinks + ((Length[Segment[GeradePLinks, GeradePRechts]] * i / 30), 0), i, 0, 30) → GeradePoints
  22. Sequence(Segment[GeradePoints(i) + (0, dyStriche), GeradePoints(i) + (0, (-dyStriche))], i, 1, 31) → l2
  23. Segment(GeradePLinks + (-0.3, 0), GeradePRechts + (0.3, 0)) → g
  24. Shuffle(Sequence[i, i, -15, 15]) → NumListGanzeRaw, {-14, -10, 7, -7, 6, -12, -6, 4, -2, 13, 3, -1, -9, -13, 9, 5, 15, 12, 1, 11, 14, -5, -8, 8, 0, 2, -11, -15, -3, -4, 10}
  25. Shuffle(Sequence[(0.5 * i), i, -15, 15]) → NumListDezi1Raw, {-2.5, 4.5, 4, 6.5, 2, -5, 7.5, -4, 3, 1.5, -2, 6, 7, 2.5, -5.5, 1, -1, -3, -4.5, -0.5, 0.5, -1.5, 0, 5.5, 5, -7.5, -6, -3.5, -6.5, 3.5, -7}
  26. Shuffle(Sequence[(0.2 * i), i, -15, 15]) → NumListDezi2Raw, {-1.2000000000000002, 1.8, -0.6000000000000001, -1.8, 2.6, 1, -2.8000000000000003, -0.4, 1.6, -0.2, 3, -3, -0.8, 2.2, 0.2, -1.6, 1.2000000000000002, 2.4000000000000004, 0.8, 2, -2.6, 0.4, -2.4000000000000004, 0, 0.6000000000000001, -2.2, -1, 1.4000000000000001, -1.4000000000000001, 2.8000000000000003, -2}
  27. Shuffle(Sequence[(i * 0.1), i, -15, 15]) → NumListDezi3Raw, {-1, -1.5, 0, -1.2000000000000002, 0.7000000000000001, 1.3, 1, -0.2, 1.2000000000000002, -1.1, 0.1, 0.9, 1.4000000000000001, 0.4, -0.7000000000000001, -0.4, 0.2, -1.4000000000000001, -0.9, -0.6000000000000001, 0.5, 0.30000000000000004, 1.1, -0.5, 0.8, -0.8, -0.1, 1.5, -1.3, -0.30000000000000004, 0.6000000000000001}
  28. Shuffle({2, 5, 10}) → NumListFracNenner1, {5, 2, 10}
  29. Shuffle({2, 4, 8}) → NumListFracNenner2, {8, 4, 2}
  30. If(subgroup ≟ 1, NumListFracNenner1(1), NumListFracNenner2(1)) → nenner
  31. Shuffle(Sequence[i, i, (-floor((nenner * 1.5))), floor((nenner * 1.5))]) → NumListFracZaehlerRaw, {-1, 5, 4, -5, -3, 0, -7, 7, 6, -2, -4, -6, 2, 3, 1}
  32. Shuffle({-1, 1}) → VorzeichenShuffle, {1, -1}
  33. If(mod ≟ 1, (vorzeichen * abs(NumListGanze(1))), mod ≟ 2 ∧ subgroup ≟ 1, (vorzeichen * abs(NumListDezi1(1))), mod ≟ 2 ∧ subgroup ≟ 2, (vorzeichen * abs(NumListDezi2(1))), mod ≟ 2 ∧ subgroup ≟ 3, (vorzeichen * abs(NumListDezi3(1))), mod ≟ 3, (vorzeichen * abs(zaehler / nenner))) → xvalue
  34. Distance(GeradePoints(1), GeradePoints(2)) → distP
  35. Circle(SolMark, toleranz) → solCirc
  36. Sequence(C + ((Length[Segment[GeradePLinks, GeradePRechts]] * i / 30), 0), i, 0, 30) → SoloStartGerade
  37. Join({SoloStartGerade, GeradePoints}) → InputPunktList
  38. Point(InputPunktList) → InputPunkt
  39. IsInRegion(InputPunkt, solCirc) → correct1
  40. Text(solutionText, SolMark + (0, (dyBesch * 1.5)), false, true, 0, 0) → SolText
  41. Text(NumTxtMaster, xPos + (0, (1.7 * dyBesch)), false, true, 0, 0) → Text2
  42. Segment(D, D + ((-dArrow), 0)) → f
  43. Polygon(InputPunkt, InputPunkt + (1, 1), 2) → Vieleck1, h_{1}, i_{1}
  44. Polygon(InputPunkt + (sizeVR, sizeVR), InputPunkt + (sizeVR, (-sizeVR)), InputPunkt + ((-sizeVR), (-sizeVR)), InputPunkt + ((-sizeVR), sizeVR)) → v1, h, i, j, k
  45. Text(NumTxtMasterGegen, SolMark + (0, (3.5 * dyBesch)), false, true, 0, 0) → Text9
  46. Text(solutionText, E, false, true, 0, 0) → SolTextZuWeitLinks
  47. If(¬zuweitlinks, (-0.6, 1), (-0.3, 1)) → F