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Partial Products Multiplication Demo by Duane Habecker

Partial Products Multiplication Demo by Duane Habecker
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2018-02-20 13:45
Solid Geometry
This example demonstrates the concept of partial products in multiplication through bar charts and area models, providing a visual and geometric interpretation. Key math concepts include multiplication, bar charts/graphs, area calculation, ratios, cuboids, and geometric transformations. It is constructed using GeoGebra commands like Textfield, Segment, Point, Flatten, Sequence, Polygon, Line, Centroid, and Midpoint. Suitable for middle school mathematics education to help students understand the decomposition of multiplication operations and their geometric significance.

GeoGebra Commands & Parameters

  1. Textfield(factor1number) → Factor1
  2. Textfield(factor2number) → Factor2
  3. Segment((x(A) - a, y(A)), (x(A) - a, y(A) - factor1number)) → f
  4. Segment((x(A), y(A) + a), (x(A) + factor2number, y(A) + a)) → g
  5. Point(f) → B
  6. Point(g) → C
  7. Flatten(Sequence[Sequence[(x(A) + j, y(A) - i), j, 0, factor2number], i, 0, factor1number]) → DotsArray
  8. Sequence(Segment[Element[DotsArray, i], Element[DotsArray, ((factor2number + 1) * factor1number) + i]], i, 0, factor2number + 1, 1) → GridVertical
  9. Sequence(Segment[Element[DotsArray, ((factor2number + 1) * i) + 1], Element[DotsArray, ((factor2number + 1) * i) + factor2number + 1]], i, 0, factor1number, 1) → GridHorizontal
  10. Polygon(A, D, F, E) → q1, a_1, d, f_1, e
  11. Line(E, F) → h
  12. Line(D, F) → i
  13. Polygon(D, G, H, F) → q2, d_1, g_1, h_1, f_2
  14. Polygon(F, H, I, K) → q3, f_3, h_2, i_1, k
  15. Polygon(E, F, K, J) → q4, e_1, f_4, k_1, j
  16. Centroid(q1) → M
  17. Centroid(q4) → N
  18. Centroid(q2) → O
  19. Centroid(q3) → P
  20. Midpoint(g) → Q
  21. Midpoint(f) → R