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Modeling Equations with Balance Models

Modeling Equations with Balance Models
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2019-06-10 07:54
FunctionGeometric Construction
This example demonstrates how changes in variable values affect equations. It involves the core mathematical concepts of equations and their solutions. Using GeoGebra commands such as Line, Circle, Intersect, etc., a balance model of equations is constructed. Suitable for middle school and above students to learn about the concept of equation solutions.

GeoGebra Commands & Parameters

  1. Line(C, A) → f
  2. Circle(B, 2.5) → c
  3. Intersect(c, f, 2) → D
  4. Intersect(c, f, 1) → E
  5. Segment(E, D) → g
  6. OrthogonalLine(D, h) → i
  7. OrthogonalLine(E, h) → j
  8. Circle(D, 0.5) → d
  9. Circle(E, 0.5) → e
  10. Intersect(d, i, 1) → F
  11. Circle(F, 1) → k
  12. Intersect(k, i, 1) → H
  13. LineBisector(F, H) → l
  14. Intersect(i, l) → I
  15. Circle(I, 0.5) → p
  16. Intersect(p, l, 1) → J
  17. Intersect(p, l, 2) → K
  18. Segment(D, F) → m
  19. Segment(F, J) → n
  20. Segment(F, K) → q
  21. Segment(K, H) → r
  22. Segment(J, H) → s
  23. Polygon(F, J, H, K) → q1, f_1, j_1, h_1, k_1
  24. DrawSquare(h, H) → L, M, N, O, q2, t, a, b, g_1, i_1
  25. DrawSquare(h, O) → P, Q, R, S, q3, l_1, m_1, n_1, p_1, q_1
  26. DrawSquare(h, S) → T, U, V, W, q4, r_1, s_1, t_1, a_1, b_1
  27. DrawSquare(h, W) → Z, A_1, B_1, C_1, q5, c_1, d_1, e_1, f_2, g_2
  28. DrawSquare(h, C_1) → D_1, E_1, F_1, G_1, q6, h_2, i_2, j_2, k_2, l_2
  29. DrawSquare(h, G_1) → H_1, I_1, J_1, K_1, q7, m_2, n_2, p_2, q_2, r_2
  30. DrawSquare(h, E) → G, L_1, M_1, N_1, q8, s_2, t_2, a_2, b_2, c_2
  31. Circle(N_1, 1) → d_2
  32. Intersect(d_2, j, 1) → O_1
  33. OrthogonalLine(O_1, j) → e_2
  34. Circle(O_1, answer / 5) → c_3
  35. Intersect(c_3, e_2, 1) → P_1
  36. Intersect(c_3, e_2, 2) → Q_1
  37. OrthogonalLine(P_1, e_2) → f_3
  38. OrthogonalLine(Q_1, e_2) → g_3
  39. Circle(P_1, 2.5) → d_3
  40. Circle(Q_1, 2.5) → e_3
  41. Intersect(d_3, f_3, 2) → R_1
  42. Intersect(e_3, g_3, 2) → S_1
  43. Polygon(Q_1, P_1, R_1, S_1) → q9, h_3, i_3, j_3, k_3
  44. Segment(N_1, O_1) → l_3
  45. LineBisector(S_1, R_1) → m_3
  46. Intersect(m_3, j_3) → T_1
  47. DrawX(B, solution, answer, h, T_1) → q10, n_3, p_3, q_3, r_3, s_3, U_1, V_1