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Graphing Indirect Proportion in Coordinates: Visual Judgment Practice

Graphing Indirect Proportion in Coordinates: Visual Judgment Practice
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2023-10-18 22:18
In collections Wiederholung: Direkte und Indirekte Proportionalität Indirekte Proportionalität
This GeoGebra example demonstrates how an indirect proportion (inverse proportionality) relationship appears on a coordinate graph, guiding students to judge whether statements are true by comparing graph behavior with the underlying numerical rule. The key mathematics includes indirect proportionality, the invariant product of variables, and distinguishing direct vs. indirect proportionality in r

GeoGebra Commands & Parameters

  1. Join(Sequence[Join[{{5}, Shuffle[Sequence[1, maxexnum - 1]]}], m, 1, floor(110 / maxexnum)]) → listExNums
  2. SelectedIndex(DropDown2) → input7
  3. SelectedIndex(DropDown1) → input6
  4. If(exnum ≟ 1, selected1, If[exnum ≟ 2, selected2, selected3]) → selected
  5. Transpose(Join[Sequence[{Shuffle[{1, 2, 3}]}, m, 1, 100]]) → listPos
  6. Textfield(input1) → InputBox1
  7. Textfield(input2) → InputBox2
  8. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  9. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {2, 2, 1, 0, 2, 10, 2, 7, 9, 3, 1, 10, 0, 7, 10, 1, 0, 2, 6, 3, 6, 7, 9, 7, 3, 6, 7, 0, 1, 0, 3, 5, 7, 1, 0, 3, 6, 4, 1, 4, 2, 8, 5, 9, 4, 7, 8, 0, 7, 1, 2, 10, 10, 9, 8, 1, 10, 10, 6, 8, 10, 10, 2, 7, 3, 7, 3, 6, 5, 3, 4, 1, 10, 1, 0, 10, 5, 10, 9, 10, 5, 9, 7, 0, 8, 8, 10, 7, 5, 0, 2, 1, 8, 10, 10, 9, 2, 5, 4, 2}
  10. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  11. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {3, 10, 3, 3, 10, 9, 3, 2, 2, 0, 1, 7, 6, 9, 4, 8, 5, 5, 1, 8, 10, 7, 3, 0, 9, 7, 0, 10, 0, 4, 8, 9, 4, 9, 9, 3, 4, 1, 4, 3, 8, 3, 10, 7, 1, 8, 1, 0, 8, 5, 6, 3, 3, 4, 9, 6, 1, 5, 10, 5, 9, 10, 2, 4, 3, 8, 4, 4, 6, 0, 4, 0, 1, 0, 4, 6, 4, 6, 7, 10, 2, 0, 1, 1, 2, 2, 4, 2, 8, 9, 9, 7, 7, 5, 9, 4, 3, 2, 1, 7}
  12. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  13. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  14. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  15. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  16. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  17. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  18. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  19. SpeechBubbleRight(A, 5.5, 0.55) → Vieleck1
  20. Element({B1, B2, B3}, selected) → B
  21. SpeechBubbleRight(C, 7.1, 1.25) → Vieleck2
  22. Segment(D, D + (scale * (coordwidth, 0))) → f
  23. Segment(D, D + (scale * (0, coordheight))) → g
  24. Sequence(D + ((m * scale) * (coordwidth / 13, 0)), m, 0, 13, 1) → pointsx
  25. Sequence(D + ((m * scale) * (0, coordheight / 13)), m, 0, 13, 1) → pointsy
  26. Sequence(Text[(("\textsf{" * ReplaceAll["" + ((m * 2)) + "", ".", ","]) * "}"), (x(D) - 0.45, (((2 * m) * scale) * coordheight / 13) + y(D) - 0.33), true, true, -0, 1], m, 1, 6) → texty
  27. Sequence(Text["\textsf{" + ((2 * m)) + "}", ((((2 * m) * scale) * coordwidth / 13) + x(D), y(D) - 0.75), true, true, -0, 1], m, 0, 6) → textx
  28. Flatten(Sequence[Sequence[D + (m * ((scale * coordwidth / 13), 0)) + (j * (0, (scale * coordwidth / 13))), m, 0, coordwidth + 4], j, 0, coordheight + 4]) → coordpoints
  29. Translate(Sequence[((coordsize * m), (coordsize * 24 / m)), m, 2, 12], D) → points
  30. Textfield(input3) → InputBox3
  31. Textfield(input4) → InputBox4
  32. Textfield(input5) → InputBox5
  33. Sequence(E + (0.795 * (0, (-m))), m, -1, 4) → l4
  34. SpeechBubbleRight(G, 8, 0.9) → Vieleck3
  35. If(exnum ≟ 5, N2, N1) → N
  36. If(exnum ≟ 5, O2, O1) → O
  37. Zip(Segment[P - (0, lineheight), P + (0, lineheight)], P, KeepIf[IndexOf[m, pointsx] < 14, m, pointsx]) → linesx
  38. Zip(Segment[P - (lineheight, 0), P + (lineheight, 0)], P, KeepIf[IndexOf[m, pointsy] < 14, m, pointsy]) → linesy
  39. Textfield(input0) → InputBox0