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Demonstration and Explanation of Absolute Value

Demonstration and Explanation of Absolute Value
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2024-12-16 19:46
In collections Gegenzahl und Betrag einer rationalen Zahl
This example demonstrates how to input fractions and explain the geometric meaning of absolute value in GeoGebra. The core math concepts include absolute value, distance on the number line, and integer operations. It uses commands and objects like Textfield, Shuffle, If, Sequence, Distance, Point, Polygon, Element, Append, Remove, Length, Segment, Circle, and Text for interactive visualization. Su

GeoGebra Commands & Parameters

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Shuffle({1, 2, 3}) → NumListModMid, {3, 2, 1}
  4. If(questionCount ≤ 3, 1, 2) → metaprogression
  5. If(metaprogression ≟ 1, NumListModStart(questionCount), NumListModMid(modindex)) → mod
  6. Shuffle(Sequence[i, i, 1, If[mod ≟ 1, 1, mod ≟ 2, 3, 2]]) → SubGroupList, {1}
  7. 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
  8. Sequence(GeradePLinks + ((Length[Segment[GeradePLinks, GeradePRechts]] * i / 30), 0), i, 0, 30) → GeradePoints
  9. Shuffle(Sequence[i, i, -15, 15]) → NumListGanzeRaw, {-10, -8, 3, -1, 15, -6, -4, -2, -3, 2, 12, -5, 6, -14, -9, 0, -13, 1, 5, 10, 14, -11, 8, 4, 13, -15, 9, -7, 7, -12, 11}
  10. Shuffle(Sequence[(0.5 * i), i, -15, 15]) → NumListDezi1Raw, {1.5, -1.5, 4.5, -5, -7, -0.5, -2, -7.5, 1, 0, 6, -6, 6.5, 7.5, 2, 5.5, 7, 4, -3, 5, 2.5, 3.5, -1, -5.5, -3.5, 0.5, 3, -6.5, -4, -4.5, -2.5}
  11. Shuffle(Sequence[(0.2 * i), i, -15, 15]) → NumListDezi2Raw, {-1.6, 1, 0.2, 0.8, 2.2, 1.4000000000000001, -3, -1.8, -0.6000000000000001, 0.6000000000000001, -2.2, -1.4000000000000001, 2, -2.8000000000000003, 3, 1.6, -1.2000000000000002, -2.6, 2.4000000000000004, -0.2, 1.8, 2.6, 0, -2, -0.8, 1.2000000000000002, -1, -2.4000000000000004, -0.4, 2.8000000000000003, 0.4}
  12. Shuffle(Sequence[(i * 0.1), i, -15, 15]) → NumListDezi3Raw, {-1.1, -1, -1.4000000000000001, -0.4, 0.4, 0.5, -0.2, 1.2000000000000002, -1.3, 0.8, -0.9, 0.30000000000000004, -0.6000000000000001, -0.1, 0.6000000000000001, 1, -1.2000000000000002, -0.5, 1.3, -0.30000000000000004, 1.1, -0.8, 0.1, 0, 0.2, -1.5, 0.7000000000000001, 1.4000000000000001, -0.7000000000000001, 1.5, 0.9}
  13. Shuffle({2, 5, 10}) → NumListFracNenner1, {5, 10, 2}
  14. Shuffle({2, 4, 8}) → NumListFracNenner2, {4, 2, 8}
  15. If(subgroup ≟ 1, NumListFracNenner1(1), NumListFracNenner2(1)) → nenner
  16. Shuffle(Sequence[i, i, (-floor((nenner * 1.5))), floor((nenner * 1.5))]) → NumListFracZaehlerRaw, {2, 6, -3, 0, -4, 3, 5, 4, 7, 1, -6, -5, -2, -7, -1}
  17. Shuffle({-1, 1}) → VorzeichenShuffle, {-1, 1}
  18. 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
  19. Distance(GeradePoints(1), GeradePoints(2)) → distP
  20. Point(GeradePointsAbove) → HintPunkt
  21. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  22. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {8, 9, 3, 9, 10, 8, 3, 2, 5, 6, 6, 7, 10, 7, 5, 8, 3, 10, 3, 8, 4, 5, 7, 9, 8, 8, 7, 3, 5, 3, 3, 7, 3, 8, 8, 2, 10, 8, 4, 0, 6, 8, 0, 5, 2, 0, 3, 0, 0, 2, 1, 1, 2, 0, 3, 10, 7, 1, 2, 3, 10, 10, 2, 5, 6, 5, 10, 3, 5, 0, 1, 3, 8, 1, 5, 4, 10, 7, 2, 2, 4, 3, 8, 1, 8, 2, 0, 4, 9, 8, 4, 4, 6, 9, 1, 4, 1, 8, 4, 2}
  23. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  24. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {6, 6, 4, 10, 10, 0, 10, 10, 5, 7, 2, 10, 6, 9, 1, 1, 2, 4, 9, 8, 8, 8, 8, 6, 10, 9, 6, 4, 9, 1, 7, 1, 7, 10, 10, 10, 5, 8, 6, 4, 3, 1, 0, 7, 9, 3, 7, 3, 1, 9, 9, 8, 6, 7, 8, 4, 4, 6, 5, 10, 8, 9, 2, 0, 8, 5, 9, 5, 6, 8, 8, 1, 1, 2, 7, 0, 9, 5, 3, 3, 9, 9, 2, 1, 3, 4, 3, 3, 0, 9, 4, 8, 5, 7, 5, 2, 1, 9, 1, 9}
  25. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  26. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  27. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  28. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  29. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  30. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  31. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  32. Shuffle(1…10) → ExNumList, {9, 10, 8, 3, 1, 2, 4, 7, 6, 5}
  33. Length(ExNumList) → questionCountMax
  34. Sequence(Segment[GeradePoints(i) + (0, dyStriche), GeradePoints(i) + (0, (-dyStriche))], i, 1, 31) → l2
  35. Segment(GeradePLinks + (-0.3, 0), GeradePRechts + (0.3, 0)) → g
  36. Circle(SolMark, toleranz) → solCirc
  37. Text(solutionText, SolMark + (0, (dyBesch * 1.5)), false, true, 0, 0) → SolText
  38. Text(AngabeHelper, C, false, true, -1, 0) → AngabeMaster
  39. Segment(E, xPos) → h
  40. Mod(questionCount, 2) → b
  41. Segment(NullPunkt, D) → i
  42. Segment(E, HintPunkt) → f
  43. Text(correctText1, F, false, true, 0, 0) → correctText2
  44. Segment(xPos + (0, dyAbove) + (0, 0.4), NullPunkt + (0, dyAbove) + (0, 0.4)) → solSec
  45. Text(Text1, Midpoint[E, D] + (0, 1), false, true, 0, 0) → Text6
  46. Segment((x(HintPunkt), y(xPos)), HintPunkt) → j
  47. Distance(HintPunkt, xPos) → d
  48. Text(NumTxtMaster, xPos + (0, (2.3 * dyAbove)), false, true, 0, 0) → Text9
  49. Text(ZMHelper, HintPunkt + (0, 0.5), false, true, 0, 0) → Text7
  50. Text(ZMHelper, HintPunkt + (0.5, 0.5), false, true, 0, 0) → Text10
  51. Text(ZMHelper, HintPunkt + (-0.5, 0.5), false, true, 0, 0) → Text11
  52. Text(NumTxtMaster, xPos + (0, If[showZM, (2.3 * dyAbove), 1 + (0.6 * dyAbove)]), false, true, 0, 0) → Text2