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Open Middle: Surface Area and Percent for Rectangular Prisms

Open Middle: Surface Area and Percent for Rectangular Prisms
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2021-03-05 00:01
FunctionSolid GeometryGeometric ConstructionGraphing
This Open Middle example guides learners to reason about and compute the surface area of a rectangular prism, then connect the numerical result to percentages (or ratios). The key mathematical ideas are solid-geometry surface area, proportional/percent conversions from area-like quantities, and conditional reasoning implemented via piecewise logic. Construction uses GeoGebra commands Polygon and Segment to build the prism’s faces and edges, and If to switch or activate expressions/logic under different conditions. The model is organized with polygon objects (e.g., poly0, poly3, poly7) and geometric points/segments (e.g., K_1, A0–A9, B, C, H, P, E, G) alongside variable/function handles (e.g., f, g, h, i, j, k, l, m, n) that represent the surface-area and percent relationships. Suitable for middle/high school solid geometry lessons, inquiry-based classrooms, and differentiated practice.

GeoGebra Commands & Parameters

  1. Polygon(A0, B, 4) → poly0, f, g, h, i, A, C
  2. Polygon(A3, H, 4) → poly3, j, k, l, m, E, G
  3. Polygon(A7, P, 4) → poly7, n, p, q, r, I, K
  4. Polygon(A1, D, 4) → poly1, s, t, a, b, M, O
  5. Polygon(A6, N, 4) → poly6, c, d, e, f_1, Q, S
  6. Polygon(A2, K_1, 4) → poly2, k_1, l_1, m_1, n_1, W, Z
  7. Polygon(A8, A8 + (2, 0), 4) → poly8, g_1, h_1, i_1, j_1, U, V
  8. Polygon(A9, T, 4) → poly9, p_1, q_1, r_1, s_1, A_1, B_1
  9. Polygon(A4, J, 4) → poly4, t_1, a_1, b_1, c_1, C_1, D_1
  10. Polygon(A5, L, 4) → poly5, d_1, e_1, f_2, g_2, E_1, F_1
  11. Polygon(G_1, H_1, 4) → poly10, h_2, i_2, j_2, k_2, I_1, J_1
  12. Polygon(G_2, H_2, 4) → poly11, h_3, i_3, j_3, k_3, I_2, J_2
  13. Polygon(G_3, H_3, 4) → poly12, h_4, i_4, j_4, k_4, I_3, J_3
  14. Polygon(G_4, H_4, 4) → poly13, h_5, i_5, j_5, k_5, I_4, J_4
  15. Polygon(G_5, H_5, 4) → poly14, h_6, i_6, j_6, k_6, I_5, J_5
  16. Polygon(G_6, H_6, 4) → poly15, h_7, i_7, j_7, k_7, I_6, J_6
  17. Polygon(G_7, H_7, 4) → poly16, h_8, i_8, j_8, k_8, I_7, J_7
  18. Polygon(G_8, H_8, 4) → poly17, h_9, i_9, j_9, k_9, I_8, J_8
  19. Polygon(G_9, H_9, 4) → poly18, h_{10}, i_{10}, j_{10}, k_{10}, I_9, J_9
  20. Polygon(G_{10}, H_{10}, 4) → poly19, h_{11}, i_{11}, j_{11}, k_{11}, I_{10}, J_{10}
  21. Polygon(Q_1, R_1, S_1, T_1) → q1, l_2, m_2, n_2, p_2
  22. Segment(Q_1, R_1) → q_2
  23. Segment(R_1, S_1) → r_2
  24. Segment(S_1, T_1) → s_2
  25. Segment(T_1, Q_1) → t_2
  26. Polygon(U_1, V_1, W_1, Z_1) → q2, u_1, v_1, w_1, z_1
  27. Segment(U_1, V_1) → a_2
  28. Segment(V_1, W_1) → b_2
  29. Segment(W_1, Z_1) → c_2
  30. Segment(Z_1, U_1) → d_2
  31. Polygon(A_2, B_2, C_2, D_2) → q3, e_2, f_3, g_3, l_3
  32. Segment(A_2, B_2) → m_3
  33. Segment(B_2, C_2) → n_3
  34. Segment(C_2, D_2) → p_3
  35. Segment(D_2, A_2) → q_3
  36. If(c1 ≟ true, "true", "false") → text8
  37. If(c2 ≟ true, "true", "false") → text9
  38. If(c3 ≟ true, "true", "false") → text10

AI Drawing Prompt Reference

Create a 3D rectangular prism net composed of multiple colored rectangular faces, each labeled with its area. Surround the prism with several small square grids representing percentages or ratios. The layout should clearly show the surface area calculation of the six faces and the conversion between area and percentage. Include multiple rectangles and line segments forming the solid geometry model, with conditional text labels displaying 'true' or 'false' to reflect logical relationships.
The prompt above was compiled from the original drawing commands and is for reference only.