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Multiple Models for Proper Fractions by EDC Interactive Math

Multiple Models for Proper Fractions by EDC Interactive Math
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2013-06-05 04:34
FunctionGeometric ConstructionGraphing
In collections Fraction worksheets fifth grade fractions
This example demonstrates proper fractions through various models including linear, number line, set, and area representations. Key math concepts involve fraction notation, number line interpretation, set theory, and area calculations. It is constructed using GeoGebra commands like Segment, Point, Circle, Polygon, Vector, Rotate, CircleSector, Sequence, and FractionText. Suitable for elementary and middle school mathematics education to visually understand different representations of proper 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

AI Drawing Prompt Reference

Draw a diagram showing proper fractions with linear, number line, set, and area models. Start by drawing a line segment to represent the numerator, and mark intervals on it for the number line. Then, use a circle and sectors to illustrate the area model, dividing the circle into equal parts based on the denominator and highlighting the numerator portion with different colors. Finally, represent the proper fraction with sets, using hollow circles for the excluded parts and solid circles for the included parts, arranged below the number line.
The prompt above was compiled from the original drawing commands and is for reference only.