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Rational Number Sets

Rational Number Sets
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2025-01-21 20:18
Coordinate Geometry
In collections Rationale Zahlen & Arbeiten mit der Zahlengerade
This example demonstrates the concept of rational number sets, involving the comparison and ordering of rational numbers, and their representation on the number line. It uses GeoGebra commands such as Join, Sequence, Zip, etc. Suitable for 7-8th grade students.

GeoGebra Commands & Parameters

  1. Join({Sequence[Q0 + (m * (absnotes, 0)), m, 0, 2], {(0, -5), (0, -5), (0, -5)}}) → listPointsNotes
  2. Sequence(Random[1, 1], m, 1, 110) → listCorrect1, {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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}
  3. Zip(RandomElement[{2, 2} \ {m}], m, listCorrect1) → listCorrect2
  4. Flatten(Join[{{7, 15, 8}, Shuffle[(1…15) \ {7, 15, 8}], Sequence[Shuffle[1…15], i, 1, 9]}]) → listExnums
  5. If(listsolhelp ≟ {0, 0, 1}, RandomElement[{{1, 3, 2}, {2, 3, 1}, {3, 2, 1}, {3, 1, 2}}], If[listsolhelp ≟ {0, 1, 1}, RandomElement[{{2, 1, 3}, {2, 3, 1}, {3, 1, 2}, {3, 2, 1}}], {1, 2, 3}]) → listChangedPositions
  6. If(shuffle, IndexOf[1, listChangedPositions], listCorrect1(Mod[questionCount, 100] + 1)) → posC1
  7. If(shuffle, IndexOf[2, listChangedPositions], listCorrect2(Mod[questionCount, 100] + 1)) → posC2
  8. RemoveUndefined({If[selected1, 1], If[selected2, 2], If[selected3, 3]}) → listselected
  9. Zip(RandomElement[{3, 3} \ {m, n}], m, listCorrect1, n, listCorrect2) → listCorrect3
  10. If(shuffle, IndexOf[3, listChangedPositions], listCorrect3(Mod[questionCount, 100] + 1)) → posC3
  11. RemoveUndefined({If[listsolhelp(1) ≟ 1, posC1], If[listsolhelp(2) ≟ 1, posC2], If[listsolhelp(3) ≟ 1, posC3]}) → listsol
  12. Sequence(Random[1, 4], m, 1, 110) → listNote1, {4, 4, 1, 1, 3, 2, 3, 2, 4, 4, 1, 4, 3, 1, 3, 1, 3, 2, 4, 2, 1, 2, 2, 3, 4, 3, 2, 4, 2, 1, 2, 1, 1, 4, 3, 2, 2, 2, 4, 1, 4, 2, 4, 1, 2, 1, 4, 4, 4, 4, 1, 4, 1, 2, 2, 1, 1, 3, 4, 3, 1, 3, 1, 4, 1, 2, 3, 4, 2, 3, 3, 2, 3, 3, 4, 3, 4, 4, 1, 3, 2, 2, 4, 2, 3, 1, 3, 1, 2, 3, 2, 4, 4, 2, 2, 1, 4, 1, 2, 1, 4, 3, 3, 2, 4, 1, 2, 3, 3, 3}
  13. Zip(RandomElement[{5} \ {m}], m, listNote1) → listNote2
  14. Zip(RandomElement[{1, 2, 3, 4} \ {m, n}], m, listNote1, n, listNote2) → listNote3
  15. Zip(RandomElement[{1, 2, 3, 4} \ {m, n, j}], m, listNote1, n, listNote2, j, listNote3) → listNote4
  16. Sequence(P0 + (m * (abstext, 0)), m, 0, 2) → listPointsText
  17. Zip(RandomElement[{1, 2, 3} \ {m, n}], m, listCorrect1, n, listCorrect2) → listWrong3
  18. Textfield(input1) → InputBox1
  19. Textfield(input2) → InputBox2
  20. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  21. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {1, 1, 7, 5, 4, 4, 8, 5, 10, 3, 0, 1, 9, 9, 4, 3, 7, 8, 5, 6, 5, 5, 3, 1, 5, 4, 3, 8, 2, 7, 7, 6, 7, 7, 3, 9, 1, 0, 0, 9, 0, 6, 6, 7, 8, 5, 6, 8, 5, 7, 2, 0, 8, 0, 7, 5, 10, 3, 0, 5, 6, 0, 7, 4, 5, 6, 4, 0, 2, 9, 0, 3, 0, 6, 10, 6, 3, 1, 10, 10, 10, 4, 8, 7, 3, 1, 4, 9, 9, 4, 6, 0, 1, 7, 5, 6, 5, 6, 3, 2}
  22. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {2, 0, 7, 10, 2, 10, 9, 8, 6, 0, 7, 0, 10, 2, 10, 4, 2, 8, 5, 5, 1, 7, 8, 9, 10, 2, 1, 0, 9, 7, 2, 8, 9, 3, 7, 2, 8, 1, 0, 3, 1, 0, 1, 2, 0, 3, 9, 0, 3, 4, 2, 1, 3, 0, 0, 10, 5, 2, 7, 5, 3, 2, 0, 2, 6, 8, 1, 3, 2, 7, 0, 2, 6, 3, 8, 5, 7, 6, 10, 3, 9, 7, 7, 8, 2, 6, 5, 9, 3, 5, 3, 0, 8, 9, 1, 9, 9, 6, 10, 0}
  23. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  24. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  25. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  26. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  27. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  28. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  29. NumberSeparationComma(numX) → Text3
  30. NumberSeparationComma(numY) → Text4
  31. NumberSeparationComma(numZ) → Text5
  32. Zip(RandomElement[{6} \ {m, n, j, l}], m, listNote1, n, listNote2, j, listNote3, l, listNote4) → listNote5
  33. Zip(RandomElement[{1, 2, 3, 4} \ {m, n, j, l, k}], m, listNote5, listNote1, n, listNote2, j, listNote3, l, listNote4, k) → listNote6
  34. Length(listsol) → numSol
  35. Text(numAHelpText, midPointQuestionNumber, true, true, 0, 0) → Text1
  36. Defined(IndexOf[IndexOf[3, listChangedPositions], listselected]) → selectedShuffle3
  37. Defined(IndexOf[IndexOf[2, listChangedPositions], listselected]) → selectedShuffle2
  38. Defined(IndexOf[IndexOf[1, listChangedPositions], listselected]) → selectedShuffle1

AI Drawing Prompt Reference

Display the set of rational numbers in a coordinate system, marking points with different colors and showing their positions on a number line. Randomly generate multiple rational number points and connect them with lines to form a distribution on the number line. Some points are annotated with special symbols, and their order is randomly shuffled to demonstrate the comparison and ordering of rational numbers. Include randomly generated numbers and symbols in the background, along with some auxiliary text explanations.
The prompt above was compiled from the original drawing commands and is for reference only.