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Comparing Rational Numbers with the Number Line

Comparing Rational Numbers with the Number Line
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2025-06-04 17:40
In collections Ordnen und Vergleichen von rationalen Zahlen
This example demonstrates the relationship between rational numbers and their representation on the number line. Key mathematical concepts include comparing rational numbers, the correspondence between points on the number line and rational numbers, and using coordinates to represent rational numbers. Construction involves using GeoGebra commands for number line creation, point marking, text annot

GeoGebra Commands & Parameters

  1. Sequence(-2.5 + (k * 0.1), k, 0, 50) → AllNumbers, {-2.5, -2.4, -2.3, -2.2, -2.1, -2, -1.9, -1.7999999999999998, -1.7, -1.6, -1.5, -1.4, -1.2999999999999998, -1.2, -1.0999999999999999, -1, -0.8999999999999999, -0.7999999999999998, -0.7, -0.5999999999999999, -0.5, -0.3999999999999999, -0.2999999999999998, -0.19999999999999973, -0.09999999999999964, 0, 0.10000000000000009, 0.20000000000000018, 0.30000000000000027, 0.40000000000000036, 0.5, 0.6000000000000001, 0.7000000000000002, 0.8000000000000003, 0.9000000000000004, 1, 1.1, 1.2000000000000002, 1.3000000000000003, 1.4000000000000004, 1.5, 1.6000000000000005, 1.7000000000000002, 1.7999999999999998, 1.9000000000000004, 2, 2.1000000000000005, 2.2, 2.3000000000000007, 2.4000000000000004, 2.5}
  2. Sequence(RandomElement[Join[{AllNumbers, KeepIf[a < 0, a, AllNumbers]}]], i, 1, 100) → randomNumbers1, {-0.8999999999999999, 0.7000000000000002, 1.2000000000000002, 0.7000000000000002, -2.2, -2.2, -1.2, -1.7999999999999998, -0.7999999999999998, -0.5, 2.2, -0.5999999999999999, -1, -0.7, -0.3999999999999999, -0.2999999999999998, 0.40000000000000036, 2, 1.2000000000000002, 2.4000000000000004, -0.09999999999999964, 1.7000000000000002, 1, 2.2, 0.9000000000000004, -0.5999999999999999, -1.9, -0.7999999999999998, -2.3, 1.1, 0.30000000000000027, -1.7999999999999998, 2.4000000000000004, -2.4, -0.19999999999999973, -1.9, -2.3, -0.19999999999999973, -2.3, -1.2, -0.5999999999999999, -1.9, 1.1, -1.2, -0.7, -2.5, 2.4000000000000004, -2.3, -1, -0.7999999999999998, -0.5999999999999999, -1.6, -1.0999999999999999, 2.2, 1.1, -1.5, -0.09999999999999964, -0.7999999999999998, -1.0999999999999999, -1.6, 2.3000000000000007, -2.1, 0.40000000000000036, -2.2, -1.7999999999999998, -2.2, 2.5, 1.7999999999999998, -1.6, -1.9, 1.1, 1, -0.7999999999999998, -1.6, -1.2, 0.8000000000000003, -2.1, 0.8000000000000003, -2.3, -2.1, -0.3999999999999999, 1.7999999999999998, 1.9000000000000004, -1, -0.7999999999999998, -1.7999999999999998, 0.7000000000000002, 2.3000000000000007, -0.19999999999999973, -1.0999999999999999, -1.7999999999999998, -0.5999999999999999, -0.7999999999999998, -2, -0.3999999999999999, 2.4000000000000004, -1.7999999999999998, -2.1, -1.4, -0.09999999999999964}
  3. Sequence(RandomElement[If[IsInteger[randomNumbers1(i)], Join[{KeepIf[(¬IsInteger[a]) ∧ abs(a - randomNumbers1(i)) > 0.2, a, AllNumbers], KeepIf[a < 0 ∧ (¬IsInteger[a]) ∧ abs(a - randomNumbers1(i)) > 0.2, a, AllNumbers]}], Join[{KeepIf[abs(a - randomNumbers1(i)) > 0.2, a, AllNumbers], KeepIf[a < 0 ∧ abs(a - randomNumbers1(i)) > 0.2, a, AllNumbers]}]]], i, 1, 100) → randomNumbers2, {-0.19999999999999973, -0.7999999999999998, -1.6, -1.0999999999999999, -1.9, -0.7999999999999998, -2.3, 1.9000000000000004, -1.6, -1.7, -1.5, -1, -1.7999999999999998, 0.5, 1.1, -1.6, -1.0999999999999999, -0.2999999999999998, -1.6, 0.9000000000000004, 1.5, -1.2999999999999998, -1.7999999999999998, -1.7, -0.7, 0.6000000000000001, -1.6, -2.2, -1.4, -0.09999999999999964, -1.7999999999999998, 2.2, -0.3999999999999999, -0.5999999999999999, 0.20000000000000018, 1.5, -1.2999999999999998, 2.5, 2.5, -1.5, 1.1, -0.7, -2.4, 1.5, -1, -1.9, -2.5, 0.20000000000000018, -1.5, -2, -1.2999999999999998, -0.5, 0, -1.5, -2.3, -1.0999999999999999, 1.9000000000000004, -1.2999999999999998, 1.3000000000000003, -0.7999999999999998, -0.2999999999999998, -1.5, -1.5, 1.9000000000000004, -0.7999999999999998, -1, -2.5, -1.7, -2.5, -1.4, -1.9, -2.4, -1.7999999999999998, -2, -1.7, 1.4000000000000004, 1.6000000000000005, -0.3999999999999999, 2.3000000000000007, 1.7000000000000002, -2.5, -2.1, 1, -0.19999999999999973, -1.7, 2.3000000000000007, -2.4, -2.4, 1.2000000000000002, -2.1, -0.5, -2.4, 0.40000000000000036, 1.5, 0.40000000000000036, -0.7999999999999998, -2.1, 1.5, 1.3000000000000003, -1.6}
  4. If(questionCount ≟ 1, Min[Element[randomNumbers1, Mod[questionCount, Length[randomNumbers1]] + 1], Element[randomNumbers2, Mod[questionCount, Length[randomNumbers2]] + 1]], Element[randomNumbers1, Mod[questionCount, Length[randomNumbers1]] + 1]) → randomNum1
  5. If(questionCount ≟ 1, Max[Element[randomNumbers1, Mod[questionCount, Length[randomNumbers1]] + 1], Element[randomNumbers2, Mod[questionCount, Length[randomNumbers2]] + 1]], Element[randomNumbers2, Mod[questionCount, Length[randomNumbers2]] + 1]) → randomNum2
  6. If(randomNum1 > randomNum2, 2, If[randomNum1 < randomNum2, 3, If[randomNum1 ≟ randomNum2, 4, 1]]) → solution
  7. Sequence((zahlenstrahlXWert + (zahlenstrahlEinheit * i), zahlenstrahlYWert), i, 0, numDif, 1) → zahlenstrahlPunkteAlle
  8. Point(Join[{{PNum1Start}, zahlenstrahlPunkteAlle}]) → PNum1
  9. Textfield(input) → inputBox
  10. Segment(zahlenstrahlStart - (zahlenstrahlUeberstand, 0), zahlenstrahlEnde + (zahlenstrahlUeberstand, 0)) → zahlenstrahl
  11. Sequence(numMinimum + i, i, 0, 5, 0.1) → zahlenstrahlWerte, {-2.5, -2.4, -2.3, -2.2, -2.1, -2, -1.9, -1.8, -1.7000000000000002, -1.6, -1.5, -1.4, -1.2999999999999998, -1.1999999999999997, -1.0999999999999996, -0.9999999999999996, -0.8999999999999995, -0.7999999999999994, -0.6999999999999993, -0.5999999999999992, -0.5, -0.3999999999999999, -0.2999999999999998, -0.19999999999999973, -0.09999999999999964, 4.440892098500626E-16, 0.10000000000000053, 0.20000000000000062, 0.3000000000000007, 0.4000000000000008, 0.5, 0.6000000000000001, 0.7000000000000002, 0.8000000000000003, 0.9000000000000004, 1.0000000000000004, 1.1000000000000005, 1.2000000000000006, 1.3000000000000007, 1.4000000000000008, 1.5, 1.5999999999999996, 1.6999999999999993, 1.799999999999999, 1.8999999999999986, 1.9999999999999982, 2.099999999999998, 2.1999999999999975, 2.299999999999997, 2.399999999999997, 2.5}
  12. RemoveUndefined(Sequence[If[Mod[zahlenstrahlWerte(i + 1), 1] ≟ 0 ∨ Mod[zahlenstrahlWerte(i + 1), 1] ≟ 0, (zahlenstrahlXWert + (zahlenstrahlEinheit * i), zahlenstrahlYWert)], i, 0, 50]) → zahlenstrahlPunkte10er
  13. Point(Join[{{PNum2Start}, zahlenstrahlPunkteAlle}]) → PNum2
  14. RemoveUndefined(Sequence[If[Mod[zahlenstrahlWerte(i + 1), 1] ≟ 0 ∨ Mod[zahlenstrahlWerte(i + 1), 1] ≟ 0, zahlenstrahlWerte(i + 1)], i, 0, Length[zahlenstrahlWerte] - 1]) → zahlenstrahlWerte10er
  15. Sequence(Text["\textsf{\(" + (zahlenstrahlWerte10er(i)) + "\)}", zahlenstrahlPunkte10er(i) - (If[zahlenstrahlWerte10er(i) < 0, 0.13, 0], 0.2), true, true, 0, -1], i, 1, Length[zahlenstrahlPunkte10er], 1) → zahlenstrahlBeschriftung
  16. Segment(zahlenstrahlStartSolution - (zahlenstrahlUeberstand, 0), zahlenstrahlEndeSolution + (zahlenstrahlUeberstand, 0)) → zahlenstrahlSolution
  17. Sequence(Text["\textsf{\(" + (zahlenstrahlWerte10er(i)) + "\)}", zahlenstrahlPunkte10er(i) - (If[zahlenstrahlWerte10er(i) < 0, 0.13, 0], 0.2 - verschubZahlenstrahlSolution), true, true, 0, -1], i, 1, Length[zahlenstrahlPunkte10er], 1) → zahlenstrahlBeschriftungSolution
  18. Segment((10, zahlenstrahlYWert - 1.4), (14, zahlenstrahlYWert - 1.4)) → groeßerPfeil
  19. Segment((5, zahlenstrahlYWert - 1.4), (1, zahlenstrahlYWert - 1.4)) → kleinerPfeil
  20. Sequence(Segment[zahlenstrahlPunkteAlle(i) + (0, zahlenstrahlLinienLaenge + If[Mod[zahlenstrahlWerte(i), 1] ∈ {0, 0.5}, 0.1, 0]), zahlenstrahlPunkteAlle(i) - (0, zahlenstrahlLinienLaenge + If[Mod[zahlenstrahlWerte(i), 1] ∈ {0, 0.5}, 0.1, 0])], i, 1, Length[zahlenstrahlPunkteAlle], 1) → zahlenstrahlLinien
  21. Sequence(Segment[zahlenstrahlPunkteAlle(i) + (0, verschubZahlenstrahlSolution + zahlenstrahlLinienLaenge + If[Mod[zahlenstrahlWerte(i), 1] ∈ {0, 0.5}, 0.1, 0]), zahlenstrahlPunkteAlle(i) - (0, (-verschubZahlenstrahlSolution) + zahlenstrahlLinienLaenge + If[Mod[zahlenstrahlWerte(i), 1] ∈ {0, 0.5}, 0.1, 0])], i, 1, Length[zahlenstrahlPunkteAlle], 1) → zahlenstrahlLinienSolution