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Multiple Models for Proper Fractions

Multiple Models for Proper Fractions
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2020-04-23 18:34
FunctionSequenceGeometric Construction
This example demonstrates various representations of proper fractions. It involves key mathematical concepts such as fractions and diagrams. Using GeoGebra commands like Segment, Point, Circle, and Polygon, it dynamically illustrates the geometric meaning of fractions. Suitable for middle school and above students to learn different representations of fractions.

GeoGebra Commands & Parameters

  1. Segment(K_2, K_2 + (1 - num / denom, 0)) → linearModel1SegShift
  2. Point(linearModel1SegShift) → LinearModel1PtL
  3. Circle(R_1, T_1) → Circle_{model}
  4. Point(Circle[R_1, 0.105]) → C_2
  5. Polygon(LinearModel1PtL + (0, -0.03), LinearModel1PtL + (num / denom, -0.03), LinearModel1PtL + (num / denom, 0.03), LinearModel1PtL + (0, 0.03)) → int1, a, b, c, e
  6. Vector(NL_c, NL_l) → u
  7. Vector(NL_c, NL_r) → v
  8. Vector(FP_t, FP) → w
  9. Segment((1, 0.13), (1, 0.17)) → i_2
  10. Segment((0, 0.13), (0, 0.17)) → j_2
  11. Segment(R_1, C_2) → m_2
  12. Rotate(C_2, angle, R_1) → D_2
  13. CircleSector(R_1, C_2, D_2) → r_3
  14. Segment(R_1, D_2) → l_2
  15. Rotate(C_2, (360 / denom)°, R_1) → B_2
  16. Sequence(Segment[Rotate[C_2, ((360 * i / denom))°, R_1], R_1], i, 0, denom) → Angle_{divseq}
  17. Segment(K_2, L_2) → a_2
  18. Vector((0, 0.25), (0.1, 0.25)) → image_{vector}
  19. Sequence(Translate[pic1, Vector[(i * image_{vector})]], i, 0, denom - 1) → Set_{opencat}
  20. Sequence(Translate[pic2, Vector[(i * image_{vector})]], i, 0, num - 1) → Set_{closedcat}
  21. Sequence(Translate[pic3, Vector[(i * image_{vector})]], i, 0, denom - 1) → Set_{openstar}
  22. Sequence(Translate[pic4, Vector[(i * image_{vector})]], i, 0, num - 1) → Set_{closedstar}
  23. Polygon(R_8, F_2, G_2, E_2) → rect_{red}, r_8, f_4, g_4, e_4
  24. Segment(R_8, I_2) → b_2
  25. Segment(E_2, H_2) → n_2
  26. Segment(E_2, M_2) → a_3
  27. Segment(J_2, R_8) → b_3
  28. Polygon((0.045, 0.588), (0.045 + num / ((3 * denom)), 0.588), (0.045 + num / ((3 * denom)), 0.385), (0.045, 0.385)) → areaModel3polyFill, j, k, l, m
  29. Polygon((-0.4493678126189438, 0.486), (-0.0923678126189438, 0.486), (-0.0923678126189438, 0.656), (-0.4493678126189438, 0.656)) → fracBackground, d, f, g, h
  30. Segment(LinearModel1PtL + (0, 0.005), LinearModel1PtR + (0, 0.005)) → linearModel1Line
  31. Sequence(Segment[(i, 0.13), (i, 0.17)], i, 0, 1, 1 / intervalHashMarks) → numLineHashMarks
  32. Sequence(Segment[(i, 0), (i, 0.05)], i, 0, 1, 1 / intervalHashMarks) → linearHashMarks
  33. Sequence(Circle[(0.05 + i, 0.3), 0.045], i, 0, (denom - 1) / 10, 0.1) → setCircleOpen
  34. Sequence(Circle[(0.05 + i, 0.3), 0.04], i, 0, (num - 1) / 10, 0.1) → setCircleShading
  35. Sequence(Segment[(0.045 + i / 11, 0.388), (0.045 + i / 11, 0.588)], i, 0, denom) → Area_{rectdiv}
  36. Sequence(Segment[(0.044 + i / ((3 * denom)), 0.387), (0.044 + i / ((3 * denom)), 0.588)], i, 0, denom) → Area_{rect2}
  37. FractionText(1 / intervalHashMarks) → intervalValue