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Multiplication Algorithm Using Area Model

Multiplication Algorithm Using Area Model
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2016-07-29 02:46
Geometric Construction
This example demonstrates how to multiply multi-digit numbers using the area model, visualized through rectangles. Key math concepts include integer multiplication, area calculation, and geometric modeling. It utilizes GeoGebra commands like Intersect, OrthogonalLine, Polygon, Midpoint, and TableText for construction. Suitable for elementary and middle school students learning multiplication, geometry, and mathematical modeling.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → I
  2. OrthogonalLine(H_1, yAxis) → a
  3. OrthogonalLine(E, yAxis) → b
  4. OrthogonalLine(D, yAxis) → c
  5. OrthogonalLine(C, xAxis) → d
  6. OrthogonalLine(F, xAxis) → e
  7. OrthogonalLine(G, xAxis) → f
  8. Intersect(a, d) → J
  9. Intersect(b, d) → K
  10. Intersect(c, d) → L
  11. Intersect(c, e) → M
  12. Intersect(b, e) → N
  13. Intersect(a, e) → O_1
  14. Intersect(b, f) → P
  15. Intersect(c, f) → Q
  16. Polygon(D, I, C, L) → poly1, d_1, i, c_1, l
  17. Polygon(C, F, M, L) → poly2, c_2, f_1, m, l_1
  18. Polygon(F, G, Q, M) → poly3, f_2, g, q, m_1
  19. Polygon(P, N, M, Q) → poly4, p, n, m_2, q_1
  20. Polygon(N, K, L, M) → poly5, n_1, k, l_2, m_3
  21. Polygon(N, O_1, J, K) → poly6, n_2, o_2, j, k_1
  22. Polygon(K, J, H_1, E) → poly7, k_2, j_1, h_1, e_1
  23. Polygon(K, L, D, E) → poly8, k_3, l_3, d_2, e_2
  24. Intersect(a, f) → R
  25. Polygon(R, P, N, O_1) → poly9, r, p_1, n_3, o_1
  26. Midpoint(j_1) → S
  27. Midpoint(o_2) → T_1
  28. Midpoint(g) → U
  29. Midpoint(o_1) → V
  30. Midpoint(r) → W
  31. Midpoint(q_1) → Z
  32. TableText({{((H * h) * 10000), ((H * t) * 1000), ((H * o) * 100), ((T * h) * 1000), ((T * t) * 100), ((T * o) * 10), ((O * h) * 100), ((O * t) * 10), (O * o), (A * B)}, {"=Hundreds\times hundreds", "=Hundreds\times tens", "=Hundreds\times ones", "=Tens\times hundreds", "=Tens\times tens", "=Tens\times ones", "=Ones\times hundreds", "=Ones\times tens", "=Ones\times ones", "product"}}, "vr") → text1