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Partial Products: 1-Digit × 2-Digit Multiplication Visual

Partial Products: 1-Digit × 2-Digit Multiplication Visual
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2014-10-19 03:23
PolygonVectorFunctionGeometric ConstructionSlider Animation
In collections Arithmetic: Skills & Concepts Arithmetic: Skills & Concepts Arithmetic: Skills & Concepts
① This GeoGebra example demonstrates the partial products method for multiplying a 1-digit number by a 2-digit number, visually breaking the two-digit number into tens and ones. ② The core math concept is the distributive property of multiplication over addition, showing that (10a + b) × c = 10a×c + b×c, which underpins the standard multiplication algorithm. ③ Construction details: The applet uses GeoGebra commands such as Vector, Polygon, Segment, and Random to generate random factors, and creates labeled objects (factor1H, factor1T, factor1U, etc.) for the tens and ones digits. Rectangular regions (e.g., ProductF1HxF2H) represent each partial product as an area, making the multiplication visually intuitive. ④ This resource is suitable for upper elementary students (grades 3–5) learning multi-digit multiplication, and can be used by teachers for classroom demonstrations or by students for independent exploration of how multiplication works.

GeoGebra Commands & Parameters

  1. Vector(Q, R) → u
  2. Vector(S, T) → v
  3. Vector(U, V) → w
  4. Polygon(A, B, H, E) → poly1, a, b, h, e
  5. Polygon(E, H, I, F) → poly2, e_1, h_1, i, f
  6. Polygon(F, I, J, G) → poly3, f_1, i_1, j, g
  7. Polygon(B, C, K, H) → poly4, b_1, c, k, h_2
  8. Polygon(H, K, L, I) → poly5, h_3, k_1, l, i_2
  9. Polygon(I, L, M, J) → poly6, i_3, l_1, m, j_1
  10. Polygon(C, D, N, K) → poly7, c_1, d, n, k_2
  11. Polygon(K, N, O, L) → poly8, k_3, n_1, o, l_2
  12. Polygon(L, O, P, M) → poly9, l_3, o_1, p, m_1
  13. Segment(W, Z) → q
  14. Polygon(B_1, C_1, D_1, E_1) → BoxForAnswer, b_2, c_2, d_1, e_2
  15. Random(11, 99) → random1
  16. Random(1, 9) → random2

AI Drawing Prompt Reference

Draw a graphic showing the multiplication of a one-digit number by a two-digit number. Break the two-digit number into tens and ones, and represent each partial product as a rectangular area. Include a random multiplier and a random two-digit number as inputs. Make the graphic intuitive for upper elementary students (grades 3-5).
The prompt above was compiled from the original drawing commands and is for reference only.