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Multiplying Multi-Digit and 1-Digit Numbers Using Partial Products

Multiplying Multi-Digit and 1-Digit Numbers Using Partial Products
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2023-06-27 15:16
Coordinate GeometrySlider Animation
This example demonstrates how to multiply multi-digit whole numbers by 1-digit whole numbers using partial products and area models. It involves breaking down the multi-digit number into parts, calculating the product of each part step by step, and then adding the results to get the final answer. Key math concepts include the distributive property of multiplication, partial product method, and area models. GeoGebra commands and objects used in the construction include Shuffle, Element, TextToUnicode, SelectedIndex, If, Intersect, Point, Polygon, Sequence, Zip, and Translate. Suitable for upper elementary students learning multiplication of multi-digit numbers, helping them understand the principles and steps of multiplication.

GeoGebra Commands & Parameters

  1. Shuffle(Sequence[t, t, 1, 3]) → allCases, {2, 3, 1}
  2. Element(allCases, Mod[countQuestion, Length[allCases]] + 1) → caseNum
  3. Shuffle(Sequence[t, t, 1, 9]) → allD4, {8, 1, 9, 7, 5, 6, 3, 4, 2}
  4. Element(allD4, Mod[countQuestion, Length[allD4]] + 1) → d4
  5. Shuffle(Sequence[t, t, 1, 9]) → allD2, {9, 5, 3, 7, 6, 2, 4, 8, 1}
  6. Element(allD2, Mod[countQuestion, Length[allD2]] + 1) → d2
  7. Shuffle(Sequence[t, t, 1, 9]) → allD3, {8, 9, 1, 5, 6, 2, 3, 4, 7}
  8. Element(allD3, Mod[countQuestion, Length[allD3]] + 1) → d3
  9. Shuffle(Sequence[t, t, 2, 9]) → allMult, {7, 8, 9, 6, 2, 5, 3, 4}
  10. Element(allMult, Mod[countQuestion, Length[allMult]] + 1) → mult
  11. Shuffle(Sequence[t, t, 0, 9]) → allD1, {6, 2, 0, 8, 5, 4, 9, 7, 1, 3}
  12. Element(allD1, Mod[countQuestion, Length[allD1]] + 1) → d1
  13. TextToUnicode(("" * currentProd)) → uniResult
  14. SelectedIndex(ddMenu) → is
  15. If(caseNum ≟ 1, 217 + 74, caseNum ≟ 2, 255 + 73, 292 + 65) → obj5PosY
  16. Intersect(xAxis, yAxis) → A
  17. Point(xAxis) → B
  18. If(caseNum ≠ 3, A + (0, -1.5), If[caseNum ≟ 3 ∧ currentProd ≥ 10000, A + (-1, -1.5), A + (0, -1.5)]) → recapTextPos
  19. Polygon({A, D, DH, AH}) → rett31
  20. Polygon({D, C, CH, DH}) → rett32
  21. Polygon({C, E, EH, CH}) → rett33
  22. Polygon({E, B, BH, EH}) → rett34
  23. Polygon({A, C, CH, AH}) → rett11
  24. Polygon({C, B, BH, CH}) → rett12
  25. Polygon({A, F, FH, AH}) → rett21
  26. Polygon({F, G, GH, FH}) → rett22
  27. Polygon({G, B, BH, GH}) → rett23
  28. Sequence((k, 7), k, If[caseNum ≟ 1, 3, caseNum ≟ 2, 2, 1], x(B) - x(A), If[caseNum ≟ 1, (0.5 * (x(B) - x(A))), caseNum ≟ 2, (1 / 3 * (x(B) - x(A))), (1 / 4 * (x(B) - x(A)))]) → anchorsUp
  29. Zip(Text[("" * A), B, false, true, 1, 0], A, If[caseNum ≟ 1, allValues1Up, caseNum ≟ 2, allValues2Up, allValues3Up], B, anchorsUp + (-0.15, -0.5)) → allTextsUp
  30. Sequence((k, 3), k, If[caseNum ≟ 1, 3, caseNum ≟ 2, 2, 1], x(B) - x(A), If[caseNum ≟ 1, (0.5 * (x(B) - x(A))), caseNum ≟ 2, (1 / 3 * (x(B) - x(A))), (1 / 4 * (x(B) - x(A)))]) → anchorsIn
  31. Sequence((-14, k), k, If[caseNum ≟ 1, 0, caseNum ≟ 2, -3, -5], 4, If[caseNum ≟ 1, 2, caseNum ≟ 2, 2, 3]) → rightAnchorsVert1
  32. Polygon({A, C, CH, AH}) → rett11Frame
  33. Polygon({C, B, BH, CH}) → rett12Frame
  34. Polygon({A, F, FH, AH}) → rett21Frame
  35. Polygon({F, G, GH, FH}) → rett22Frame
  36. Polygon({G, B, BH, GH}) → rett23Frame
  37. Polygon({A, D, DH, AH}) → rett31Frame
  38. Polygon({D, C, CH, DH}) → rett32Frame
  39. Polygon({C, E, EH, CH}) → rett33Frame
  40. Polygon({E, B, BH, EH}) → rett34Frame
  41. Polygon(C, B, BH, CH) → pulsingObject1, f, g, i, j
  42. Polygon(G, B, BH, GH) → pulsingObject2, k, l, m, n
  43. Polygon(E, B, BH, EH) → pulsingObject3, p, q, r, s
  44. If(caseNum ≟ 1, 260, caseNum ≟ 2, 302, caseNum ≟ 3, 345) → separatBottY
  45. Polygon({R1, R2, R3, R4}) → hlRett11
  46. Translate(R1, Vector[(0, 0), (0, -1)]) → R1'
  47. Translate(R2, Vector[(0, 0), (0, -1)]) → R2'
  48. Translate(R3, Vector[(0, 0), (0, -1)]) → R3'
  49. Translate(R4, Vector[(0, 0), (0, -1)]) → R4'
  50. Polygon({R1 + (0, -1.85), R2 + (0, -1.85), R3 + (0, -1.85), R4 + (0, -1.85)}) → hlRett12
  51. Translate(hlRett11, Vector[(0, 0), (0, -3.65)]) → hlRett23
  52. Translate(hlRett23, Vector[(0, 0), (0, -1.65)]) → hlRett32

AI Drawing Prompt Reference

Draw a multiplication decomposition diagram to show the process of multiplying a multi-digit number by a single-digit number. Start by drawing a rectangle to represent the product of the multiplication. Then, divide the rectangle into smaller rectangles, each representing an intermediate result of the multiplication. For example, if the multi-digit number is 217 and the single-digit number is 74, the rectangle will be divided into two parts, representing the results of 200 multiplied by 74 and 17 multiplied by 74. Finally, label each smaller rectangle with its dimensions and product.
The prompt above was compiled from the original drawing commands and is for reference only.