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Graphing Rational Numbers on a Horizontal Line

Graphing Rational Numbers on a Horizontal Line
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2019-05-02 20:58
Geometric Construction
This example demonstrates plotting rational numbers on a horizontal line, illustrating the geometric representation of rational numbers and their probabilistic distribution. Key mathematical concepts include rational number definition, coordinate system application, and random variable generation. Construction involves GeoGebra commands like RandomElement, If, Polygon, etc. Suitable for middle school students learning rational numbers and probability basics, useful as a teaching aid.

GeoGebra Commands & Parameters

  1. RandomElement({2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}) → Cdenom
  2. If(Cdenom ≟ 2, Random[-20, 20, true], If[Cdenom ≟ 3, Random[-30, 30, true], If[Cdenom ≟ 4, Random[-40, 40, true], If[Cdenom ≟ 5, Random[-50, 50, true], If[Cdenom ≟ 6, Random[-60, 60, true], If[Cdenom ≟ 7, Random[-70, 70, true], If[Cdenom ≟ 8, Random[-80, 80, true], If[Cdenom ≟ 9, Random[-90, 90, true], If[Cdenom ≟ 10, Random[-100, 100, true], If[Cdenom ≟ 11, Random[-110, 110, true], If[Cdenom ≟ 12, Random[-120, 120, true]]]]]]]]]]]) → Cnum
  3. Polygon(I, W, V, J) → poly1, i, w, v, j
  4. Polygon(J, V, U, K) → poly2, j_1, v_1, u, k
  5. Polygon(K, U, T, L) → poly3, k_1, u_1, t, l
  6. Polygon(L, T, S, M) → poly4, l_1, t_1, s, m
  7. Segment(H, G) → c
  8. Segment(G, Z) → d
  9. Segment(Z, E) → e
  10. Segment(E, F) → f
  11. FractionText(C) → Cfancy
  12. RandomElement({2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}) → Ddenom
  13. RandomElement({-9, -8, -7, -6, -5, -4, -3, -2, -1, 1, 2, 3, 4, 5, 6, 7, 8, 9}) → Dwhole
  14. Random(1, Ddenom - 1, true) → Dnum
  15. FractionText(Dnum / Ddenom) → Dfancy
  16. If(Dwhole < 0, Dwhole - Dnum / Ddenom, Dwhole + Dnum / Ddenom) → D
  17. Segment(A_1, Aact) → aerr
  18. Segment(B_1, Bact) → berr
  19. Segment(C_1, Cact) → cerr
  20. Segment(D_1, Dact) → derr
  21. Sort({A, B, C, D}) → test
  22. Sort({x(A_1), x(B_1), x(C_1), x(D_1)}) → test2
  23. If(IndexOf[A, Sort[{A, B, C, D}]] ≟ IndexOf[x(A_1), Sort[{x(A_1), x(B_1), x(C_1), x(D_1)}]], 1) → orderA
  24. If(IndexOf[B, Sort[{A, B, C, D}]] ≟ IndexOf[x(B_1), Sort[{x(A_1), x(B_1), x(C_1), x(D_1)}]], 1) → orderB
  25. If(IndexOf[C, Sort[{A, B, C, D}]] ≟ IndexOf[x(C_1), Sort[{x(A_1), x(B_1), x(C_1), x(D_1)}]], 1) → orderC
  26. If(IndexOf[D, Sort[{A, B, C, D}]] ≟ IndexOf[x(D_1), Sort[{x(A_1), x(B_1), x(C_1), x(D_1)}]], 1) → orderD

AI Drawing Prompt Reference

Draw a series of rational number points on a horizontal line. Connect the points with line segments to form a continuous graph. Label each point with a fraction text to show its value. The overall layout should be simple and reflect the geometric representation and probability distribution of rational numbers, suitable for a teaching demonstration.
The prompt above was compiled from the original drawing commands and is for reference only.