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Multiplying Proper Fractions – Area Model Problems (1)

Multiplying Proper Fractions – Area Model Problems (1)
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2016-11-01 23:03
PolygonSequenceGeometric ConstructionSlider Animation
① This interactive GeoGebra example demonstrates the multiplication of proper fractions using dynamic area models, allowing users to explore 15 different fraction multiplication problems via a slider. ② The core mathematical concepts include fraction multiplication, area model representation, part-whole relationships, and the geometric interpretation of multiplying fractions. ③ Construction highlights: the applet uses commands such as Segment, Point, Sequence, Polygon, Element, Max, If, and FractionText to build adjustable rectangular grids, manage problem switching with a slider, and display fraction labels; numList and denomList store numerators and denominators, while H-series objects highlight the overlapping regions. ④ It is suitable for upper elementary to middle school students learning fraction multiplication, as well as for teachers demonstrating the concept in class, fostering a visual and intuitive understanding of why multiplying fractions yields a smaller product.

GeoGebra Commands & Parameters

  1. Segment((0, 3), (4.8, 3)) → e
  2. Point(e) → H15
  3. Point(e) → H14
  4. Point(e) → H13
  5. Point(e) → H12
  6. Point(e) → H11
  7. Point(e) → H10
  8. Point(e) → H9
  9. Point(e) → H8
  10. Point(e) → H7
  11. Point(e) → H6
  12. Point(e) → H5
  13. Point(e) → H4
  14. Point(e) → H3
  15. Point(e) → H2
  16. Point(e) → H1
  17. Element(f2denom, ex) → d
  18. Element(f2num, ex) → c
  19. Element(f1num, ex) → a
  20. Element(f1denom, ex) → b
  21. Max(Sequence[If[Mod[a * c, i] + Mod[b * d, i] ≟ 0, i, -1], i, 1, Min[{a * c, b * d}]]) → Simplified_{GCF}
  22. Sequence(A + t * (B - A), t, 0, 1, 1 / b) → L1
  23. Sequence(C + t * (D - C), t, 0, 1, 1 / b) → L2
  24. Segment(A, B) → c_1
  25. Segment(C, D) → d_1
  26. Sequence(Segment[Element[L1, k], Element[L2, k]], k, 2, b) → L5
  27. Element(dragPoint, ex) → H
  28. Segment(H, E) → f
  29. Segment(E, F) → g
  30. Segment(F, G) → h
  31. Segment(G, H) → i
  32. Segment(D, B) → j
  33. Segment(C, A) → k
  34. Element(L1, a + 1) → T1
  35. Element(L2, a + 1) → T2
  36. Polygon(A, T1, T2, C) → poly1, a_1, t1, t2, c_2
  37. Sequence(E + t * (H - E), t, 0, 1, 1 / d) → L3
  38. Sequence(F + t * (G - F), t, 0, 1, 1 / d) → L4
  39. Sequence(Segment[Element[L3, k], Element[L4, k]], k, 2, d) → L6
  40. Element(L3, c + 1) → T3
  41. Element(L4, c + 1) → T4
  42. Polygon(E, F, T4, T3) → poly2, e_1, f_1, t4, t3
  43. FractionText(Element[f1num, ex] * Element[f2num, ex] / (Element[f1denom, ex] * Element[f2denom, ex])) → simplText
  44. Element(numList, ex) → num
  45. Element(denomList, ex) → denom
  46. Polygon((0, 0), (3 * Element[f1num, ex] / Element[f1denom, ex], 0), (3 * Element[f1num, ex] / Element[f1denom, ex], 3 * Element[f2num, ex] / Element[f2denom, ex]), (0, 3 * Element[f2num, ex] / Element[f2denom, ex])) → overlap, m, n, p, q
  47. If(bl, 0, 1) → black