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Area Model for Distributive Laws

Area Model for Distributive Laws
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2020-02-10 00:07
Coordinate GeometryGeometric Construction
This example demonstrates the distributive law through an area model. Key mathematical concepts include the distributive law and geometric construction. It uses commands such as DynamicCoordinates, Polygon, Point, Segment, Midpoint, Distance, Intersect, If, Vector, Text, etc. Suitable for middle school and above students to learn the distributive law and geometric construction.

GeoGebra Commands & Parameters

  1. DynamicCoordinates(A', If[x(A') < 6, 6, x(A')], If[y(A') < 6, 6, y(A')]) → A
  2. Polygon(A, B, C, D) → q, s1, s2, s4, s3
  3. Point(s3) → V'
  4. Point(s4) → H'
  5. DynamicCoordinates(V', x(V'), floor(y(V'))) → V
  6. DynamicCoordinates(H', floor(x(H')), 0) → H
  7. Segment(H, H_1) → f
  8. Segment(V, V_1) → g
  9. Midpoint(B, V_1) → M1
  10. Midpoint(C, V_1) → M2
  11. Midpoint(B, H_1) → M3
  12. Midpoint(H_1, A) → M4
  13. Distance(B, V_1) → a
  14. Distance(V_1, C) → b
  15. Distance(B, H_1) → c
  16. Distance(H_1, A) → d
  17. Intersect(f, g) → I
  18. Midpoint(C, I) → M6
  19. Midpoint(V_1, H_1) → M5
  20. Midpoint(I, A) → M7
  21. Midpoint(H, V) → M8
  22. Polygon(H_1, B, V_1, I) → q2, h_1, b_1, v_1, i
  23. If(Defined[Intersect[b_1, v_1]], Intersect[b_1, v_1], B) → E
  24. Polygon(I, E, C, H) → q3, i_1, e, c_1, h
  25. If(Defined[Intersect[h_1, i]], Intersect[h_1, i], B) → F
  26. Polygon(A, F, I, V) → q4, a_1, f_1, i_2, v
  27. Polygon(V, I, H, D) → q1, v_2, i_3, h_2, d_1
  28. Vector(J, K) → u
  29. Vector(K, J) → w
  30. Vector(L, M) → j
  31. Vector(M, L) → k
  32. Midpoint(J, K) → M9
  33. Midpoint(L, M) → M10
  34. Segment(J - (0, 0.5), J + (0, 0.5)) → l
  35. Segment(K - (0, 0.5), K + (0, 0.5)) → m
  36. Segment(M - (0.5, 0), M + (0.5, 0)) → n
  37. Segment(L - (0.5, 0), L + (0.5, 0)) → p
  38. Midpoint(C, A) → M0
  39. If(eval, Text[((a + b) * (c + d))], "" + (a + b) + "×" + (c + d) + "") → text11
  40. If(eval, Text[(a * c)], "" + a + "×" + c + "") → text5
  41. If(eval, Text[(b * c)], "" + b + "×" + c + "") → text7
  42. If(eval, Text[(a * d)], "" + a + "×" + d + "") → text6
  43. If(eval, Text[(b * d)], "" + b + "×" + d + "") → text8
  44. Text(((a + b) * (c + d))) → textArea