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Comparing Operators with Integers: Add/Subtract and Decide >, <, or =

Comparing Operators with Integers: Add/Subtract and Decide >, <, or =
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2026-02-18 23:14
In collections Addieren und Subtrahieren von ganzen und rationalen Zahlen
This example lets students generate integer add/subtract scenarios and then determine whether the resulting relationship is greater than, less than, or equal. It emphasizes how to infer inequality outcomes from the computed difference and its sign. Key concepts include integer addition and subtraction, difference sign analysis (positive/negative/zero), and inequality comparison operators (>, <, ≥,

GeoGebra Commands & Parameters

  1. Sequence(RandomElement[NumberList], k, 1, 100) → NumberList1, {7, 6, 8, 9, 3, 6, 9, 6, 9, 7, 5, 4, 7, 7, 2, 2, 2, 9, 4, 4, 8, 1, 9, 4, 5, 9, 2, 3, 6, 3, 6, 5, 7, 7, 6, 2, 3, 1, 2, 8, 3, 3, 6, 1, 5, 5, 9, 4, 9, 7, 7, 2, 2, 8, 2, 8, 4, 3, 3, 7, 1, 7, 7, 5, 3, 6, 9, 2, 5, 9, 9, 1, 3, 6, 2, 8, 1, 7, 5, 4, 4, 1, 5, 8, 8, 7, 8, 9, 4, 2, 3, 7, 2, 7, 7, 2, 6, 5, 4, 2}
  2. Sequence(RandomElement[Remove[NumberList, {NumberList1(k)}]], k, 1, 100) → NumberList2, {6, 1, 9, 2, 6, 4, 3, 3, 4, 9, 1, 9, 1, 2, 6, 3, 9, 7, 6, 3, 9, 8, 7, 7, 6, 2, 5, 5, 2, 7, 8, 7, 8, 5, 2, 6, 6, 2, 4, 7, 7, 8, 7, 6, 4, 1, 6, 2, 2, 5, 6, 9, 7, 6, 3, 7, 6, 8, 5, 2, 2, 3, 4, 2, 7, 9, 3, 8, 3, 2, 3, 7, 8, 7, 6, 5, 7, 5, 4, 7, 8, 8, 3, 3, 3, 8, 3, 8, 7, 4, 9, 3, 7, 3, 1, 3, 4, 2, 9, 3}
  3. Sequence(RandomElement[{-1, 1}], k, 1, 100) → SignList11, {1, 1, 1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, 1, -1}
  4. Join(Sequence[Shuffle[{1, 1, -1}], k, 1, 34]) → SameSign
  5. Sequence((SignList11(k) * SameSign(k)), k, 1, 100) → SignList13, {1, -1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1}
  6. Sequence(RandomElement[CasesSign1], k, 1, 100) → SignCase12, {1, 1, 4, 1, 2, 3, 1, 2, 3, 4, 3, 3, 1, 1, 1, 4, 3, 2, 1, 2, 4, 1, 3, 3, 4, 2, 4, 4, 4, 1, 1, 4, 3, 4, 2, 2, 1, 1, 4, 4, 4, 2, 2, 2, 3, 3, 2, 4, 1, 4, 1, 2, 3, 3, 3, 4, 2, 4, 1, 3, 2, 4, 2, 1, 4, 2, 4, 4, 3, 4, 3, 2, 4, 1, 2, 1, 1, 2, 1, 3, 2, 1, 4, 1, 2, 1, 4, 3, 3, 4, 2, 2, 1, 4, 3, 4, 3, 4, 1, 3}
  7. Sequence(RandomElement[Remove[CasesSign1, {SignCase12(k)}]], k, 1, 100) → SignCase14, {2, 3, 3, 3, 1, 2, 3, 4, 1, 1, 2, 1, 2, 2, 4, 3, 2, 4, 3, 3, 2, 4, 4, 1, 3, 4, 3, 3, 3, 4, 3, 1, 2, 2, 3, 1, 2, 2, 3, 3, 2, 3, 3, 3, 1, 4, 4, 2, 3, 2, 2, 4, 1, 2, 1, 1, 3, 1, 2, 4, 1, 3, 3, 2, 3, 1, 1, 2, 4, 2, 2, 4, 3, 2, 1, 3, 4, 1, 3, 1, 4, 4, 2, 4, 3, 3, 3, 4, 4, 3, 1, 1, 3, 3, 2, 3, 2, 1, 2, 2}
  8. Join(Sequence[Shuffle[{1, 1, 2, 2, 3, 3}], k, 1, 17]) → SignList2
  9. Unique(Join[CaseMat21]) → AllCombinations2
  10. If(level ≟ 2 ∧ SignList2(counter) ≟ 2 ∧ Length[AllCombinations2] ≟ 4, 1, SignList2(counter)) → sign2
  11. If(left1 < right1, SelectedIndex[dropdown11] ≟ 2, left1 ≟ right1, SelectedIndex[dropdown11] ≟ 3, SelectedIndex[dropdown11] ≟ 4) → correct1
  12. If(sign2 ≟ 1, left2 < right2, sign2 ≟ 2, left2 ≟ right2, left2 > right2) → correct2
  13. Sequence(Sample[{1, 2, 3, 4}, 2], k, 1, 100) → PosList3, {{4, 2}, {4, 3}, {1, 2}, {1, 2}, {2, 1}, {3, 4}, {3, 4}, {3, 4}, {3, 2}, {1, 4}, {1, 4}, {1, 2}, {1, 3}, {3, 1}, {2, 3}, {3, 1}, {1, 2}, {2, 4}, {2, 3}, {2, 4}, {2, 3}, {1, 4}, {4, 1}, {3, 1}, {4, 3}, {2, 1}, {2, 3}, {4, 1}, {1, 3}, {1, 3}, {4, 3}, {4, 1}, {1, 2}, {3, 1}, {1, 3}, {1, 3}, {2, 3}, {2, 4}, {2, 1}, {1, 2}, {1, 3}, {4, 1}, {2, 4}, {3, 2}, {4, 1}, {1, 2}, {3, 1}, {3, 4}, {3, 1}, {2, 3}, {2, 3}, {4, 1}, {4, 1}, {2, 4}, {2, 4}, {2, 4}, {2, 4}, {4, 1}, {3, 4}, {2, 4}, {3, 2}, {2, 1}, {1, 2}, {1, 2}, {3, 2}, {2, 3}, {2, 1}, {3, 4}, {1, 4}, {4, 2}, {4, 3}, {2, 4}, {1, 4}, {2, 4}, {3, 4}, {3, 2}, {3, 1}, {2, 4}, {2, 3}, {3, 2}, {3, 2}, {4, 2}, {2, 1}, {4, 2}, {2, 1}, {4, 3}, {3, 4}, {1, 4}, {1, 2}, {4, 2}, {1, 2}, {3, 1}, {1, 2}, {1, 2}, {2, 1}, {1, 2}, {1, 2}, {4, 2}, {2, 1}, {2, 3}}
  14. Min(PosList3(counter)) → pos31
  15. Max(PosList3(counter)) → pos32
  16. If(sign2 ≟ 1, left3 < right3, sign2 ≟ 2, left3 ≟ right3, left3 > right3) → correct3
  17. If(level ≟ 1, correct1, level ≟ 2, correct2, correct3) → correct
  18. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {9, 4, 7, 5, 6, 3, 6, 7, 8, 2}
  19. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  20. Textfield(input) → inputBox
  21. 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
  22. 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
  23. Sequence(Sequence[Corner[4] + (RasterPixMat * ((k * RasterStepXY), (m * RasterStepXY))), k, 0, RasterMaxX / RasterStepXY], m, 0, RasterMaxY / RasterStepXY) → RasterPunkte
  24. Translate(imgChilliGrau1, Vector[(1 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliGrau2
  25. Translate(imgChilliRot1, Vector[(1 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliRot2
  26. Translate(imgChilliRot1, Vector[(2 * Vector[((0.8 * dimChilli), 0)])]) → imgChilliRot3
  27. Textfield(input31) → InputBox31
  28. Textfield(input32) → InputBox32
  29. If(level ≟ 1, SelectedIndex[dropdown11] > 1, level ≟ 2, SelectedIndex[dropdown21] > 1 ∧ SelectedIndex[dropdown22] > 1, Defined[input31] ∧ Defined[input32]) → clickableBtnValidate
  30. Element({"+", "\(-\)"}, If[sign2 ≤ 2, IndexOf[Min[CaseMat21(1)], CaseMat21(1)], IndexOf[Max[CaseMat21(1)], CaseMat21(1)]]) → signSol21
  31. Element({1, -1}, If[sign2 ≤ 2, IndexOf[Min[CaseMat21(1)], CaseMat21(1)], IndexOf[Max[CaseMat21(1)], CaseMat21(1)]]) → fac21
  32. Element({1, -1}, If[sign2 ≥ 2, IndexOf[Min[CaseMat21(2)], CaseMat21(2)], IndexOf[Max[CaseMat21(2)], CaseMat21(2)]]) → fac22
  33. IndexOf({pos31, pos32}, {{1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}}) → Case3
  34. If(CaseRight31 < 0, 2, 8) → exN311
  35. If(CaseRight32 < 0, 2, 8) → exN321
  36. If(CaseRight33 > 0, 8, 2) → exN331
  37. If((CaseRight34 * If[CaseS12 ∈ {1, 2}, 1, -1]) < 0, 2, 8) → exN341
  38. If((CaseRight35 * If[CaseS12 ∈ {1, 2}, 1, -1]) < 0, 2, 8) → exN351
  39. If(CaseLeft36 < 0, 2, 8) → exN361