MathPlotAI Logo MathPlotAI

Balance Beam Equations

Balance Beam Equations
Loading the math board and drawing, please wait…
2014-02-06 06:06
FunctionCoordinate GeometryGeometric Construction
In collections Numeracy Practice
This example uses a balance beam model to help students understand equations. Key mathematical concepts include the principle of equation balance. The construction uses GeoGebra commands such as Element, Polygon, OrthogonalLine, etc. Suitable for middle school and above students to learn about equation balance.

GeoGebra Commands & Parameters

  1. Element(LeftSideUnitList, ProblemPicker) → LeftUnitFromList
  2. Element(RightSideUnitList, ProblemPicker) → RightUnitFromList
  3. Element(RightSideXList, ProblemPicker) → RightXFromList
  4. Element(LeftSideXList, ProblemPicker) → LeftXFromList
  5. Polygon(FulcrumBottomLeft, FulcrumTop, FulcrumBottomRight) → poly1, fulcrumbottomright, fulcrumbottomleft, fulcrumtop
  6. OrthogonalLine(A_11, fulcrumtop) → b_2
  7. Point(b_2) → RightUnit5
  8. OrthogonalLine(A_12, fulcrumtop) → a_2
  9. Point(a_2) → RightUnit4
  10. OrthogonalLine(A_13, fulcrumtop) → t_1
  11. Point(t_1) → RightUnit3
  12. OrthogonalLine(A_14, fulcrumtop) → s_1
  13. Point(s_1) → RightUnit2
  14. OrthogonalLine(A_15, fulcrumtop) → r_1
  15. Point(r_1) → RightUnit1
  16. Sum({(y(RightUnit1) > ExpressionLowerLimit) ∧ (y(RightUnit1) < ExpressionUpperLimit), (y(RightUnit2) > ExpressionLowerLimit) ∧ (y(RightUnit2) < ExpressionUpperLimit), (y(RightUnit3) > ExpressionLowerLimit) ∧ (y(RightUnit3) < ExpressionUpperLimit), (y(RightUnit4) > ExpressionLowerLimit) ∧ (y(RightUnit4) < ExpressionUpperLimit), (y(RightUnit5) > ExpressionLowerLimit) ∧ (y(RightUnit5) < ExpressionUpperLimit)}) → SumRightSideUnit
  17. OrthogonalLine(A_20, fulcrumtop) → q_1
  18. Point(q_1) → LeftUnit1
  19. OrthogonalLine(A_19, fulcrumtop) → p_1
  20. Point(p_1) → LeftUnit2
  21. OrthogonalLine(A_18, fulcrumtop) → n_1
  22. Point(n_1) → LeftUnit3
  23. OrthogonalLine(A_17, fulcrumtop) → m_1
  24. Point(m_1) → LeftUnit4
  25. OrthogonalLine(A_16, fulcrumtop) → l_1
  26. Point(l_1) → LeftUnit5
  27. Sum({(y(LeftUnit1) > ExpressionLowerLimit) ∧ (y(LeftUnit1) < ExpressionUpperLimit), (y(LeftUnit2) > ExpressionLowerLimit) ∧ (y(LeftUnit2) < ExpressionUpperLimit), (y(LeftUnit3) > ExpressionLowerLimit) ∧ (y(LeftUnit3) < ExpressionUpperLimit), (y(LeftUnit4) > ExpressionLowerLimit) ∧ (y(LeftUnit4) < ExpressionUpperLimit), (y(LeftUnit5) > ExpressionLowerLimit) ∧ (y(LeftUnit5) < ExpressionUpperLimit)}) → SumLeftSideUnit
  28. OrthogonalLine(A_6, fulcrumtop) → k_1
  29. Point(k_1) → RightX5
  30. OrthogonalLine(A_7, fulcrumtop) → j_1
  31. Point(j_1) → RightX4
  32. OrthogonalLine(A_8, fulcrumtop) → g_1
  33. Point(g_1) → RightX3
  34. OrthogonalLine(A_9, fulcrumtop) → c_1
  35. Point(c_1) → RightX2
  36. OrthogonalLine(A_10, fulcrumtop) → b_1
  37. Point(b_1) → RightX1
  38. Sum({(y(RightX1) > ExpressionLowerLimit) ∧ (y(RightX1) < ExpressionUpperLimit), (y(RightX2) > ExpressionLowerLimit) ∧ (y(RightX2) < ExpressionUpperLimit), (y(RightX3) > ExpressionLowerLimit) ∧ (y(RightX3) < ExpressionUpperLimit), (y(RightX4) > ExpressionLowerLimit) ∧ (y(RightX4) < ExpressionUpperLimit), (y(RightX5) > ExpressionLowerLimit) ∧ (y(RightX5) < ExpressionUpperLimit)}) → SumRightSideX
  39. OrthogonalLine(A_5, fulcrumtop) → t
  40. Point(t) → LeftX5
  41. OrthogonalLine(A_4, fulcrumtop) → s
  42. Point(s) → LeftX4
  43. OrthogonalLine(A_3, fulcrumtop) → r
  44. Point(r) → LeftX3
  45. OrthogonalLine(A_2, fulcrumtop) → q
  46. Point(q) → LeftX2
  47. OrthogonalLine(A_1, fulcrumtop) → p
  48. Point(p) → LeftX1
  49. Sum({(y(LeftX1) > ExpressionLowerLimit) ∧ (y(LeftX1) < ExpressionUpperLimit), (y(LeftX2) > ExpressionLowerLimit) ∧ (y(LeftX2) < ExpressionUpperLimit), (y(LeftX3) > ExpressionLowerLimit) ∧ (y(LeftX3) < ExpressionUpperLimit), (y(LeftX4) > ExpressionLowerLimit) ∧ (y(LeftX4) < ExpressionUpperLimit), (y(LeftX5) > ExpressionLowerLimit) ∧ (y(LeftX5) < ExpressionUpperLimit)}) → SumLeftSideX
  50. If(BeamLeftTotal > BeamRightTotal, -1, If[BeamLeftTotal ≟ BeamRightTotal, 0, 1]) → BeamLeftYValue
  51. Segment(BeamLeft, BeamRight) → a
  52. Line(BeamLeft, BeamRight) → b
  53. Point(b) → A
  54. Point(b) → B
  55. OrthogonalLine(A, b) → c
  56. OrthogonalLine(BeamLeft, b) → d
  57. OrthogonalLine(BeamRight, a) → e
  58. OrthogonalLine(B, b) → f
  59. Point(c) → C
  60. OrthogonalLine(C, c) → g
  61. Intersect(d, g) → D
  62. Intersect(e, g) → E
  63. Intersect(f, g) → F
  64. Polygon(C, A, BeamLeft, D) → poly2, LeftBasketLeftSide, LeftBasketBottomSide, LeftBasketRightSide, LeftBasketTopSide
  65. Polygon(BeamRight, B, F, E) → poly3, RightBasketBottomSide, RightBasketRightSide, RightBasketTopSide, RightBasketLeftSide
  66. Segment(A, B) → h
  67. Polygon(H, J, M, L) → poly4, h_1, LeftExpressionBottom, m, l
  68. Polygon(N, O, K, I) → poly5, n, RightExpressionBottom, k, i
  69. Point(Circle[FulcrumBottomLeft, -7]) → P
  70. Segment(FulcrumBottomLeft, P) → a_1
  71. OrthogonalLine(A_10, fulcrumtop) → d_1
  72. OrthogonalLine(A_9, fulcrumtop) → e_1
  73. OrthogonalLine(A_9, fulcrumtop) → f_1
  74. OrthogonalLine(A_8, fulcrumtop) → i_1
  75. Sum({(y(LeftX1) > ExpressionLowerLimit) ∧ (y(LeftX1) < ExpressionUpperLimit), (y(LeftX2) > ExpressionLowerLimit) ∧ (y(LeftX2) < ExpressionUpperLimit), (y(LeftX3) > ExpressionLowerLimit) ∧ (y(LeftX3) < ExpressionUpperLimit), (y(LeftX4) > ExpressionLowerLimit) ∧ (y(LeftX4) < ExpressionUpperLimit), (y(LeftX5) > ExpressionLowerLimit) ∧ (y(LeftX5) < ExpressionUpperLimit)}) → LeftSideXTotal
  76. If(BeamLeftYValue ≟ 0, "Equation Balanced!", "Not Balanced") → text7
  77. Element(RightSideXList, 2) → j
  78. Element(RightSideXList, 1) → Test
  79. Segment(S, TRC) → c_2
  80. OrthogonalLine(S, c_2) → d_2
  81. Point(d_2) → T
  82. OrthogonalLine(T, d_2) → e_2
  83. OrthogonalLine(TRC, c_2) → f_2
  84. Intersect(e_2, f_2) → U
  85. Polygon(S, T, U, TRC) → poly6, s_2, t_2, u, trc

AI Drawing Prompt Reference

Draw a balance beam model to illustrate the principle of equation balance. Start with a fulcrum at the top of the beam, then draw multiple units vertically extending from both sides of the fulcrum, representing terms on both sides of an equation. Differentiate the units on the left and right sides with colors or shapes. Ensure the units on both sides are balanced in number, position, and shape. First draw the beam and fulcrum, then add the units, and finally connect corresponding units with dashed lines or arrows to emphasize the balance.
The prompt above was compiled from the original drawing commands and is for reference only.