积极 AI Logo 积极 AI

数直线上的数比较与排序

数直线上的数比较与排序
几何画板及绘图内容加载中，请稍等……
2022-03-30 16:22
所属专题 Ordnen und Vergleichen von rationalen Zahlen
本例通过GeoGebra数直线交互模型，演示自然数、小数及分数的大小比较与大小排序现象。学生需通过数直线定位判断数值大小，理解数值位置与大小的关系。作图利用Polygon、Sequence、Point、If、Segment、Intersect等GeoGebra命令生成可拖动的数直线与随机数点，适合5-6年级数感与有理数单元，培养数感与符号推理能力。

GeoGebra 命令及参数

  1. Polygon(A_1, D_1, C_1, B_1) → Voben, a_1, d_1, c_1, b_1
  2. Element(l2, Mod[questionCount, 100] + 1) → numY
  3. Element(l1, Mod[questionCount, 100] + 1) → numX
  4. Sequence((i, 0), i, 0, 1, 0.1) → LupenPunkte
  5. Point(LupenPunkteV) → L
  6. Point(f) → E
  7. Point(f) → F
  8. Polygon(E_1, G_1, F_1, Z) → Vunten, e_1, g_1, f_1, z_1
  9. If(numY ≟ 0.14 ∧ L ≟ LupenPunkteV(2) ∧ Help1 ∈ Vunten ∧ 0.43 - 0.01 < x(Help1) < 0.43 + 0.01 ∨ numY ≟ 0.21 ∧ L ≟ LupenPunkteV(3) ∧ Help1 ∈ Vunten ∧ 0.21 - 0.01 < x(Help1) < 0.21 + 0.01 ∨ numY ≟ 0.23 ∧ L ≟ LupenPunkteV(3) ∧ Help1 ∈ Vunten ∧ 0.36 - 0.01 < x(Help1) < 0.36 + 0.01 ∨ numY ≟ 0.37 ∧ L ≟ LupenPunkteV(4) ∧ Help1 ∈ Vunten ∧ 0.65 - 0.01 < x(Help1) < 0.65 + 0.01 ∨ numY ≟ 0.38 ∧ L ≟ LupenPunkteV(4) ∧ Help1 ∈ Vunten ∧ 0.72 - 0.01 < x(Help1) < 0.72 + 0.01 ∨ numY ≟ 0.41 ∧ L ≟ LupenPunkteV(5) ∧ Help1 ∈ Vunten ∧ 0.21 - 0.01 < x(Help1) < 0.21 + 0.01 ∨ numY ≟ 0.49 ∧ L ≟ LupenPunkteV(5) ∧ Help1 ∈ Vunten ∧ 0.87 - 0.01 < x(Help1) < 0.87 + 0.01 ∨ numY ≟ 0.52 ∧ L ≟ LupenPunkteV(6) ∧ Help1 ∈ Vunten ∧ 0.28 - 0.01 < x(Help1) < 0.28 + 0.01 ∨ numY ≟ 0.69 ∧ L ≟ LupenPunkteV(7) ∧ Help1 ∈ Vunten ∧ 0.87 - 0.01 < x(Help1) < 0.87 + 0.01 ∨ numY ≟ 0.77 ∧ L ≟ LupenPunkteV(8) ∧ Help1 ∈ Vunten ∧ 0.65 - 0.01 < x(Help1) < 0.65 + 0.01 ∨ numY ≟ 0.73 ∧ L ≟ LupenPunkteV(8) ∧ Help1 ∈ Vunten ∧ 0.36 - 0.01 < x(Help1) < 0.36 + 0.01 ∨ numY ≟ 0.83 ∧ L ≟ LupenPunkteV(9) ∧ Help1 ∈ Vunten ∧ 0.36 - 0.01 < x(Help1) < 0.36 + 0.01 ∨ numY ≟ 0.92 ∧ L ≟ LupenPunkteV(10) ∧ Help1 ∈ Vunten ∧ 0.28 - 0.01 < x(Help1) < 0.28 + 0.01, true, false) → correctUntenY
  10. If(numX ≟ 0.13 ∧ L ≟ LupenPunkteV(2) ∧ Help ∈ Vunten ∧ 0.36 - 0.01 < x(Help) < 0.36 + 0.01 ∨ numX ≟ 0.2 ∧ L ≟ LupenPunkteV(3) ∧ Help ∈ Vunten ∧ 0.14 - 0.01 < x(Help) < 0.14 + 0.01 ∨ numX ≟ 0.22 ∧ L ≟ LupenPunkteV(3) ∧ Help ∈ Vunten ∧ 0.28 - 0.01 < x(Help) < 0.28 + 0.01 ∨ numX ≟ 0.32 ∧ L ≟ LupenPunkteV(4) ∧ Help ∈ Vunten ∧ 0.28 - 0.01 < x(Help) < 0.28 + 0.01 ∨ numX ≟ 0.39 ∧ L ≟ LupenPunkteV(4) ∧ Help ∈ Vunten ∧ 0.79 - 0.01 < x(Help) < 0.79 + 0.01 ∨ numX ≟ 0.44 ∧ L ≟ LupenPunkteV(5) ∧ Help ∈ Vunten ∧ 0.43 - 0.01 < x(Help) < 0.43 + 0.01 ∨ numX ≟ 0.4 ∧ L ≟ LupenPunkteV(5) ∧ Help ∈ Vunten ∧ 0.14 - 0.01 < x(Help) < 0.14 + 0.01 ∨ numX ≟ 0.53 ∧ L ≟ LupenPunkteV(6) ∧ Help ∈ Vunten ∧ 0.36 - 0.01 < x(Help) < 0.36 + 0.01 ∨ numX ≟ 0.67 ∧ L ≟ LupenPunkteV(7) ∧ Help ∈ Vunten ∧ 0.65 - 0.01 < x(Help) < 0.65 + 0.01 ∨ numX ≟ 0.78 ∧ L ≟ LupenPunkteV(8) ∧ Help ∈ Vunten ∧ 0.72 - 0.01 < x(Help) < 0.72 + 0.01 ∨ numX ≟ 0.79 ∧ L ≟ LupenPunkteV(8) ∧ Help ∈ Vunten ∧ 0.79 - 0.01 < x(Help) < 0.79 + 0.01 ∨ numX ≟ 0.87 ∧ L ≟ LupenPunkteV(9) ∧ Help ∈ Vunten ∧ 0.65 - 0.01 < x(Help) < 0.65 + 0.01 ∨ numX ≟ 0.98 ∧ L ≟ LupenPunkteV(10) ∧ Help ∈ Vunten ∧ 0.72 - 0.01 < x(Help) < 0.72 + 0.01, true, false) → correctUntenX
  11. Shuffle(l1) → randomNosForX, {0.44, 0.53, 0.87, 0.39, 0.78, 0.98, 0.79, 0.13, 0.67, 0.32, 0.2, 0.22, 0.4}
  12. Shuffle(l2) → randomNosForY, {0.14, 0.38, 0.21, 0.69, 0.23, 0.92, 0.73, 0.52, 0.37, 0.49, 0.41, 0.83, 0.77}
  13. Sequence(Segment[(i, 0.01), (i, -0.01)], i, 0, 1, 0.1) → Streifen1
  14. Sequence(E + ((i - 1) * (F - E) / 10), i, 1, 11) → Streifen2Punkte
  15. Sequence(Text[i + "", (i - 0.013, -0.035)], i, 0, 1, 0.1) → Steifen1Text
  16. Sequence(Text[(xCounter + (0.1 * i)) / 10 + "", Element[Streifen2Punkte, i + 1] + (-0.02, -0.047)], i, 1, 9) → Streifen2Text
  17. Sequence(Segment[Element[Streifen2Punkte, i] + (0, 0.007), Element[Streifen2Punkte, i] + (0, -0.007)], i, 0, 11) → Streifen2
  18. Sequence(Segment[(i, 0.003), (i, -0.003)], i, 0, 1, 0.01) → Streifen1_2
  19. Segment(E + (0, 0.02), E + (0, -0.02)) → g
  20. Segment(F + (0, 0.02), F + (0, -0.02)) → h
  21. Sequence(Segment[E + ((i - 1) * (F - E) / 10) + (0, 0.007), E + ((i - 1) * (F - E) / 10) + (0, -0.007)], i, -5, 16) → Streifen2_2
  22. Sequence(Segment[E + ((i - 1) * (F - E) / 10) + (0, 0.003), E + ((i - 1) * (F - E) / 10) + (0, -0.003)], i, -5, 16, 0.1) → Streifen2_3
  23. Polygon(P, Q, R, S) → v2, p_1, q, r, s
  24. Polygon(T, U, V, W) → v3, t, u, v, w
  25. Sequence(Mod[floor(numY100 / 10^(i)), 10], i, 0, 1) → DigitsZahl2
  26. Sequence(Mod[floor(numX100 / 10^(i)), 10], i, 0, 1) → DigitsZahl1
  27. If(numY ≟ 0.14 ∧ L ≟ LupenPunkteV(2) ∧ Help ∈ Vunten ∧ 0.43 - 0.01 < x(Help) < 0.43 + 0.01 ∨ numY ≟ 0.21 ∧ L ≟ LupenPunkteV(2) ∧ Help ∈ Vunten ∧ 0.21 - 0.01 < x(Help) < 0.21 + 0.01 ∨ numY ≟ 0.23 ∧ L ≟ LupenPunkteV(3) ∧ Help ∈ Vunten ∧ 0.36 - 0.01 < x(Help) < 0.36 + 0.01 ∨ numY ≟ 0.37 ∧ L ≟ LupenPunkteV(4) ∧ Help ∈ Vunten ∧ 0.65 - 0.01 < x(Help) < 0.65 + 0.01 ∨ numY ≟ 0.38 ∧ L ≟ LupenPunkteV(4) ∧ Help ∈ Vunten ∧ 0.72 - 0.01 < x(Help) < 0.72 + 0.01 ∨ numY ≟ 0.41 ∧ L ≟ LupenPunkteV(5) ∧ Help ∈ Vunten ∧ 0.21 - 0.01 < x(Help) < 0.21 + 0.01 ∨ numY ≟ 0.49 ∧ L ≟ LupenPunkteV(5) ∧ Help ∈ Vunten ∧ 0.87 - 0.01 < x(Help) < 0.87 + 0.01 ∨ numY ≟ 0.52 ∧ L ≟ LupenPunkteV(6) ∧ Help ∈ Vunten ∧ 0.28 - 0.01 < x(Help) < 0.28 + 0.01 ∨ numY ≟ 0.69 ∧ L ≟ LupenPunkteV(7) ∧ Help ∈ Vunten ∧ 0.87 - 0.01 < x(Help) < 0.87 + 0.01 ∨ numY ≟ 0.77 ∧ L ≟ LupenPunkteV(8) ∧ Help ∈ Vunten ∧ 0.65 - 0.01 < x(Help) < 0.65 + 0.01 ∨ numY ≟ 0.73 ∧ L ≟ LupenPunkteV(8) ∧ Help ∈ Vunten ∧ 0.36 - 0.01 < x(Help) < 0.36 + 0.01 ∨ numY ≟ 0.83 ∧ L ≟ LupenPunkteV(9) ∧ Help ∈ Vunten ∧ 0.36 - 0.01 < x(Help) < 0.36 + 0.01 ∨ numY ≟ 0.92 ∧ L ≟ LupenPunkteV(10) ∧ Help ∈ Vunten ∧ 0.28 - 0.01 < x(Help) < 0.28 + 0.01, true, false) → b
  28. Polygon(P4, P2, P1, P3) → correctBlue, p4, p2, p1, p3
  29. Polygon(Q4, Q2, Q1, Q3) → correctRed, q4_{1}, i, j, q3_{1}
  30. Polygon(I_1, K_1, J_1, H_1) → left, i_1, k_1, j_1, k
  31. Polygon(M_1, O_1, N_1, L_1) → right, m_1, o_1, n_1, l_1
  32. Intersect(gl11, Voben) → P_1, Q_1
  33. Intersect(gl1, Voben) → R_1, S_1
  34. Intersect(gl2, Voben) → T_1, U_1
  35. Intersect(gl3, Voben) → V_1, W_1
  36. Intersect(gl4, Voben) → Z_1, A_2
  37. Intersect(gl5, Voben) → B_2, C_2
  38. Intersect(gl6, Voben) → D_2, E_2
  39. Intersect(gl7, Voben) → F_2, G_2
  40. Intersect(gl8, Voben) → H_2, I_2
  41. Intersect(gl9, Voben) → J_2, K_2
  42. Intersect(gl10, Voben) → L_2, M_2
  43. Polygon(R_1, T_1, U_1, S_1) → q1, m, t_1, u_1, n
  44. Polygon(T_1, V_1, W_1, U_1) → q2, c, v_1, w_1, d
  45. Polygon(V_1, Z_1, A_2, W_1) → q3, e, f_2, a_2, g_2
  46. Polygon(Z_1, B_2, C_2, A_2) → q4, h_2, b_2, c_2, i_2
  47. Polygon(B_2, D_2, E_2, C_2) → q5, j_2, d_2, e_2, k_2
  48. Polygon(D_2, F_2, G_2, E_2) → q6, l_2, m_2, n_2, p_2
  49. Polygon(F_2, H_2, I_2, G_2) → q7, q_2, r_2, s_2, t_2
  50. Polygon(H_2, J_2, K_2, I_2) → q10, f_3, g_3, h_3, i_3
  51. Polygon(J_2, L_2, M_2, K_2) → q9, j_3, k_3, l_3, m_3
  52. If(numX ≟ 0.13 ∧ L ≟ LupenPunkteV(2) ∧ Help1 ∈ Vunten ∧ 0.36 - 0.01 < x(Help1) < 0.36 + 0.01 ∨ numX ≟ 0.2 ∧ L ≟ LupenPunkteV(3) ∧ Help1 ∈ Vunten ∧ 0.14 - 0.01 < x(Help1) < 0.14 + 0.01 ∨ numX ≟ 0.22 ∧ L ≟ LupenPunkteV(3) ∧ Help1 ∈ Vunten ∧ 0.28 - 0.01 < x(Help1) < 0.28 + 0.01 ∨ numX ≟ 0.32 ∧ L ≟ LupenPunkteV(4) ∧ Help1 ∈ Vunten ∧ 0.28 - 0.01 < x(Help1) < 0.28 + 0.01 ∨ numX ≟ 0.39 ∧ L ≟ LupenPunkteV(4) ∧ Help1 ∈ Vunten ∧ 0.79 - 0.01 < x(Help1) < 0.79 + 0.01 ∨ numX ≟ 0.44 ∧ L ≟ LupenPunkteV(5) ∧ Help1 ∈ Vunten ∧ 0.43 - 0.01 < x(Help1) < 0.43 + 0.01 ∨ numX ≟ 0.4 ∧ L ≟ LupenPunkteV(5) ∧ Help1 ∈ Vunten ∧ 0.14 - 0.01 < x(Help1) < 0.14 + 0.01 ∨ numX ≟ 0.53 ∧ L ≟ LupenPunkteV(6) ∧ Help1 ∈ Vunten ∧ 0.36 - 0.01 < x(Help1) < 0.36 + 0.01 ∨ numX ≟ 0.67 ∧ L ≟ LupenPunkteV(7) ∧ Help1 ∈ Vunten ∧ 0.65 - 0.01 < x(Help1) < 0.65 + 0.01 ∨ numX ≟ 0.78 ∧ L ≟ LupenPunkteV(8) ∧ Help1 ∈ Vunten ∧ 0.72 - 0.01 < x(Help1) < 0.72 + 0.01 ∨ numX ≟ 0.79 ∧ L ≟ LupenPunkteV(8) ∧ Help1 ∈ Vunten ∧ 0.79 - 0.01 < x(Help1) < 0.79 + 0.01 ∨ numX ≟ 0.87 ∧ L ≟ LupenPunkteV(9) ∧ Help1 ∈ Vunten ∧ 0.65 - 0.01 < x(Help1) < 0.65 + 0.01 ∨ numX ≟ 0.98 ∧ L ≟ LupenPunkteV(10) ∧ Help1 ∈ Vunten ∧ 0.72 - 0.01 < x(Help1) < 0.72 + 0.01, true, false) → thinkingFalseColorsX
  53. If(numY ≟ 0.14 ∧ L ≟ LupenPunkteV(2) ∧ Help ∈ Vunten ∧ 0.43 - 0.01 < x(Help) < 0.43 + 0.01 ∨ numY ≟ 0.21 ∧ L ≟ LupenPunkteV(3) ∧ Help ∈ Vunten ∧ 0.21 - 0.01 < x(Help) < 0.21 + 0.01 ∨ numY ≟ 0.23 ∧ L ≟ LupenPunkteV(3) ∧ Help ∈ Vunten ∧ 0.36 - 0.01 < x(Help) < 0.36 + 0.01 ∨ numY ≟ 0.37 ∧ L ≟ LupenPunkteV(4) ∧ Help ∈ Vunten ∧ 0.65 - 0.01 < x(Help) < 0.65 + 0.01 ∨ numY ≟ 0.38 ∧ L ≟ LupenPunkteV(4) ∧ Help ∈ Vunten ∧ 0.72 - 0.01 < x(Help) < 0.72 + 0.01 ∨ numY ≟ 0.41 ∧ L ≟ LupenPunkteV(5) ∧ Help ∈ Vunten ∧ 0.21 - 0.01 < x(Help) < 0.21 + 0.01 ∨ numY ≟ 0.49 ∧ L ≟ LupenPunkteV(5) ∧ Help ∈ Vunten ∧ 0.87 - 0.01 < x(Help) < 0.87 + 0.01 ∨ numY ≟ 0.52 ∧ L ≟ LupenPunkteV(6) ∧ Help ∈ Vunten ∧ 0.28 - 0.01 < x(Help) < 0.28 + 0.01 ∨ numY ≟ 0.69 ∧ L ≟ LupenPunkteV(7) ∧ Help ∈ Vunten ∧ 0.87 - 0.01 < x(Help) < 0.87 + 0.01 ∨ numY ≟ 0.77 ∧ L ≟ LupenPunkteV(8) ∧ Help ∈ Vunten ∧ 0.65 - 0.01 < x(Help) < 0.65 + 0.01 ∨ numY ≟ 0.73 ∧ L ≟ LupenPunkteV(8) ∧ Help ∈ Vunten ∧ 0.36 - 0.01 < x(Help) < 0.36 + 0.01 ∨ numY ≟ 0.83 ∧ L ≟ LupenPunkteV(9) ∧ Help ∈ Vunten ∧ 0.36 - 0.01 < x(Help) < 0.36 + 0.01 ∨ numY ≟ 0.92 ∧ L ≟ LupenPunkteV(10) ∧ Help ∈ Vunten ∧ 0.28 - 0.01 < x(Help) < 0.28 + 0.01, true, false) → thinkingFalseColorsY