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Explore Equivalent Fractions

Explore Equivalent Fractions
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2021-12-16 10:21
This example demonstrates how to find equivalent fractions through transformations. Key mathematical concepts include fractions and equivalence. It uses commands like Sequence, If, Element, Point, Polygon, Textfield, and Corner in GeoGebra. Suitable for high-grade elementary or junior high school students to learn basic concepts of fractions and equivalence.

GeoGebra Commands & Parameters

  1. Sequence(B + ((i * l / q), w), i, 1, p) → list3, {(6, 1.2)}
  2. If(q > 9 ∨ p > 9, true, false) → digit2
  3. If(digit2, (9.1, -2.75), (8, -2.75)) → Q2
  4. If(digit2, (6.8, -2.75), (6, -2.75)) → Q1
  5. If(digit2, (9.1, -1.6), (8, -1.6)) → P2
  6. If(digit2, (6.8, -1.6), (6, -1.6)) → P1
  7. Element(list3, u) → P
  8. Sequence(B + (i * (x(P) - x(B), 0)), i, 1, floor(l / (x(P) - x(B)))) → list4, {(6, -0.5), (12, -0.5)}
  9. Point(list4) → P'
  10. Polygon(B, B + (l, 0), B + (l, w), B + (0, w)) → poly2, a_2, b_2, c_2, d_2
  11. Polygon(A, A + (l, 0), A + (l, w), A + (0, w)) → poly1, a_1, b_1, c_1, d_1
  12. Sequence(Segment[A + ((i * l / q), 0), A + ((i * l / q), w)], i, 1, q - 1) → list1, {1.7000000000000002}
  13. Polygon(A, A + ((p * l / q), 0), A + ((p * l / q), w), A + (0, w)) → poly3, a, b, c, d
  14. Polygon(B, B + ((p1 * l / q1), 0), B + ((p1 * l / q1), w), B + (0, w)) → poly4, f, m, n, e
  15. Sequence(Segment[B + ((i * l / q), 0), B + ((i * l / q), w)], i, 1, q - 1) → list2, {1.7}
  16. Textfield(p) → inputBox1
  17. Textfield(q) → inputBox2
  18. Sequence(Polygon[B + (i * (x(P) - x(B), 0)), B + ((i * (x(P) - x(B))), w), B + (((i - 1) * (x(P) - x(B))), w), B + ((i - 1) * (x(P) - x(B), 0))], i, 1, (x(P') - x(B)) / (x(P) - x(B))) → list5, {10.2}
  19. Sequence(Segment[A + ((i * l / q), 0), A + ((i * l / q), w)], i, 1, q - 1) → list1_1, {1.7000000000000002}
  20. Sequence(Sequence[Segment[B + ((i * l / q) + (j * l / ((q * r))), 0), B + ((i * l / q) + (j * l / ((q * r))), w)], i, 0, q - 1], j, 1, r - 1) → list6, {{1.7, 1.7}}
  21. If(ans1 ≟ (r * p), true, false) → correct1
  22. If(ans2 ≟ (r * q), true, false) → correct2
  23. Polygon(P1, P1 + (1.3, 0), P1 + (1.3, -1), P1 + (0, -1)) → poly5, f_1, g_1, h_1, i_1
  24. Polygon(Q1, Q1 + (1.3, 0), Q1 + (1.3, -1), Q1 + (0, -1)) → poly6, j_1, k_1, l_1, m_1
  25. Polygon(Q2, Q2 + (1.3, 0), Q2 + (1.3, -1), Q2 + (0, -1)) → poly8, s_1, t_1, e_1, f_2
  26. Polygon(P2, P2 + (1.3, 0), P2 + (1.3, -1), P2 + (0, -1)) → poly7, n_1, p_1, q_1, r_1
  27. Corner(text1, 3) → E
  28. If(Length[list4] ≠ 1 ∧ IndexOf[P', list4] ≠ Length[list4], true, false) → arrow
  29. Sequence(Segment[B + (i * (x(P) - x(B), 0)), B + ((i * (x(P) - x(B))), w)], i, 1, (x(P') - x(B)) / (x(P) - x(B)) - 1) → list7, {}
  30. Textfield(input3) → InputBox3
  31. Textfield(input4) → InputBox4
  32. If(ans4 ≟ q / div, true, false) → correct4
  33. If(ans3 ≟ p / div, true, false) → correct3
  34. If(digit2, (6.7, -2.1), (5.9, -2.1)) → H
  35. If(digit2, (8.6, -2.1), (7.8, -2.1)) → I
  36. If(digit2, (6.7, -3.4), (5.9, -3.4)) → J
  37. If(digit2, (8.6, -3.4), (7.8, -3.4)) → K
  38. Polygon(H, H + (1.3, 0), H + (1.3, -1), H + (0, -1)) → poly9, h_2, j, k, g_2
  39. Polygon(J, J + (1.3, 0), J + (1.3, -1), J + (0, -1)) → poly10, j_2, i_2, k_2, l_2
  40. Polygon(I, I + (1.3, 0), I + (1.3, -1), I + (0, -1)) → poly11, i_3, m_2, n_2, p_2
  41. Polygon(K, K + (1.3, 0), K + (1.3, -1), K + (0, -1)) → poly12, k_3, q_2, r_2, s_2
  42. Textfield(input5) → InputBox5
  43. Textfield(input6) → InputBox6
  44. Textfield(input7) → InputBox7
  45. Textfield(input8) → InputBox8
  46. If(ans5 ≟ r, true, false) → correct5
  47. If(ans6 ≟ r, true, false) → correct6
  48. If(ans7 ≟ (r * p), true, false) → correct7
  49. If(ans8 ≟ (r * q), true, false) → correct8
  50. Textfield(input9) → InputBox9
  51. Textfield(input10) → InputBox10
  52. Textfield(input11) → InputBox11
  53. Textfield(input12) → InputBox12
  54. If(ans9 ≟ u, true, false) → correct9
  55. If(ans10 ≟ u, true, false) → correct10
  56. If(ans11 ≟ p / div, true, false) → correct11
  57. If(ans12 ≟ q / div, true, false) → correct12
  58. Textfield(p) → InputBox1
  59. Textfield(q) → InputBox2
  60. Sequence(Segment[B + ((i * l / q1), 0), B + ((i * l / q1), w)], i, 1, q1 - 1) → list2_1, {1.7}

AI Drawing Prompt Reference

Draw a rectangle ABCD with length l and width w. Inside ABCD, draw a rectangle EFGH with length p and width q. Inside EFGH, draw a rectangle IJKL with length p1 and width q1. On rectangle ABCD, draw a point P and then draw a rectangle MNOP with the same width as P. On rectangle EFGH, draw a point Q and then draw a rectangle QRST with the same width as Q. Draw the dividing lines between the rectangles and their proportional relationships. Finally, draw some auxiliary lines and markings to help understand the relationship between the equivalent fractions and the dividing lines.
The prompt above was compiled from the original drawing commands and is for reference only.