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Open Middle: Surface Area and Percent (Rectangular Prism)

Open Middle: Surface Area and Percent (Rectangular Prism)
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2021-03-05 00:20
PolygonSolid GeometryGeometric Construction
This example demonstrates an open-middle exploration of how surface area of a rectangular prism can be interpreted using percentages and ratios. Students study how changes in a prism’s dimensions or in selected faces translate into “part-to-whole” relationships expressed as percent. Key concepts include solid geometry (surface area of a rectangular prism), ratio and percent interpretation, and reasoning from geometric measures to quantitative comparisons. Construction highlights: GeoGebra’s Polygon and Segment are used to build the face boundaries of the 3D model; multiple polygon objects (e.g., poly0, poly3, poly7) represent different faces; segment-defined point connections (e.g., K_1, A0, A1, …, plus auxiliary points such as B, C, H, P, E, G) define the vertices and edges that determine the geometry; additional diagram/point objects (e.g., pic1–pic9, A2–A9) support precise placement and interactive relationships. Suitable for middle to high school mathematics classes focusing on surface area, proportional reasoning, and percent-based interpretation, as well as classroom inquiry or practice tasks.

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

AI Drawing Prompt Reference

Draw a 3D perspective model of a rectangular prism using several quadrilateral faces. First set up a consistent set of corner points for the prism, then connect appropriate groups of four points to form multiple closed quadrilateral polygons, each representing a different face of the prism (visible sides and additional faces). Ensure the edges between neighboring corners are represented so the prism’s face boundaries match across adjacent polygons. Finally, include additional quadrilateral face outlines in an auxiliary placement and connect their neighboring corner points with straight segments to form complete, closed face regions, producing a clear prism surface partition suitable for surface-area ratio or percent reasoning.
The prompt above was compiled from the original drawing commands and is for reference only.