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用质因数分解表示合数：探索数学中的乘法原理

用质因数分解表示合数：探索数学中的乘法原理
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2022-12-27 23:09
几何作图
这个范例演示了如何将合数分解为质因数的乘积，展示了质数在乘法中的基础作用。核心数学概念是质因数分解和数的分解。作图要点包括使用GeoGebra命令如PrimeFactors、IsPrime等来生成质因数列表，并可视化分解过程。适合小学四年级到五年级的学生，用于巩固数感和分解因数技能。

GeoGebra 命令及参数

  1. KeepIf(Mod[selectedNum, jj] ≟ 0, jj, Sequence[selectedNum]) → factorsAll
  2. If(¬Defined[selectedNum], {}, If[active1, {"$\math{1 \times 1 }\;$"}, Zip[(((("$\math{" * Text[kk]) * " \times ") * Text[selectedNum / kk]) * "\; }$"), kk, factorsAll]]) → dropDown
  3. SelectedIndex(dropDown) → Options
  4. If(Length[selectedNums] ≤ 1, {1}, Take[selectedNums, 1, Length[selectedNums] - 1]) → selectedNums'
  5. If(countQuestion ≤ 30, Product[Take[selectedNums, 1, Length[selectedNums] - 1]], Element[factorsAll, Options]) → firstFact
  6. Sequence("×", kk, 1, Length[selectedNums] - 1) → times
  7. Flatten({Sequence[{Element[selectedNums', kk], Element[times, kk]}, kk, 1, Length[times] - 1], Last[selectedNums']}) → product'
  8. If(countQuestion ≤ 30, TableText[Flatten[RemoveUndefined[{If[Length[selectedNums'] ≥ 2, product', Length[selectedNums'] ≟ 1, Last[selectedNums'], {}], If[Length[selectedNums'] ≥ 2, "="], If[Length[selectedNums'] ≥ 2, Text[Product[selectedNums']]]}]], "lh"], Text[Element[factorsAll, Options]]) → ProductText'
  9. Corner(5) → AppSize
  10. Flatten(Sequence[Sequence[(kk * horizontalSeparation), kk, 1, 30 / rows], jj, 1, rows]) → xCoordinates
  11. Flatten(Sequence[Sequence[8.4 - (anim * 0.5) - (kk * verticalSeparation), jj, 1, 30 / rows], kk, 0, rows]) → yCoordinates
  12. Zip((jj, kk), jj, xCoordinates, kk, yCoordinates) → textsPositions
  13. Text((("\ovalbox{" * A10) * "}"), Element[textsPositions, A10], true, true, 0, 0) → B10
  14. Text((("\ovalbox{" * A11) * "}"), Element[textsPositions, A11], true, true, 0, 0) → B11
  15. Text((("\ovalbox{" * A12) * "}"), Element[textsPositions, A12], true, true, 0, 0) → B12
  16. Text((("\ovalbox{" * A13) * "}"), Element[textsPositions, A13], true, true, 0, 0) → B13
  17. Text((("\ovalbox{" * A14) * "}"), Element[textsPositions, A14], true, true, 0, 0) → B14
  18. Text((("\ovalbox{" * A15) * "}"), Element[textsPositions, A15], true, true, 0, 0) → B15
  19. Text((("\ovalbox{" * A16) * "}"), Element[textsPositions, A16], true, true, 0, 0) → B16
  20. Text((("\ovalbox{" * A17) * "}"), Element[textsPositions, A17], true, true, 0, 0) → B17
  21. Text((("\ovalbox{" * A18) * "}"), Element[textsPositions, A18], true, true, 0, 0) → B18
  22. Text((("\ovalbox{" * A19) * "}"), Element[textsPositions, A19], true, true, 0, 0) → B19
  23. Text((("\ovalbox{" * A20) * "}"), Element[textsPositions, A20], true, true, 0, 0) → B20
  24. Text((("\ovalbox{" * A21) * "}"), Element[textsPositions, A21], true, true, 0, 0) → B21
  25. Text((("\ovalbox{" * A22) * "}"), Element[textsPositions, A22], true, true, 0, 0) → B22
  26. Text((("\ovalbox{" * A23) * "}"), Element[textsPositions, A23], true, true, 0, 0) → B23
  27. Text((("\ovalbox{" * A24) * "}"), Element[textsPositions, A24], true, true, 0, 0) → B24
  28. Text((("\ovalbox{" * A25) * "}"), Element[textsPositions, A25], true, true, 0, 0) → B25
  29. Text((("\ovalbox{" * A26) * "}"), Element[textsPositions, A26], true, true, 0, 0) → B26
  30. Text((("\ovalbox{" * A27) * "}"), Element[textsPositions, A27], true, true, 0, 0) → B27
  31. Text((("\ovalbox{" * A28) * "}"), Element[textsPositions, A28], true, true, 0, 0) → B28
  32. Text((("\ovalbox{" * A29) * "}"), Element[textsPositions, A29], true, true, 0, 0) → B29
  33. Text((("\ovalbox{" * A30) * "}"), Element[textsPositions, A30], true, true, 0, 0) → B30
  34. IsPrime(A1) → C1
  35. IsPrime(A2) → C2
  36. IsPrime(A3) → C3
  37. IsPrime(A4) → C4
  38. IsPrime(A5) → C5
  39. IsPrime(A6) → C6
  40. IsPrime(A7) → C7
  41. IsPrime(A8) → C8
  42. IsPrime(A9) → C9
  43. IsPrime(A10) → C10
  44. IsPrime(A11) → C11
  45. IsPrime(A12) → C12
  46. IsPrime(A13) → C13
  47. IsPrime(A14) → C14
  48. IsPrime(A15) → C15
  49. IsPrime(A16) → C16
  50. IsPrime(A17) → C17
  51. IsPrime(A18) → C18
  52. IsPrime(A19) → C19
  53. IsPrime(A20) → C20
  54. IsPrime(A21) → C21
  55. IsPrime(A22) → C22
  56. IsPrime(A23) → C23
  57. IsPrime(A24) → C24
  58. IsPrime(A25) → C25
  59. IsPrime(A26) → C26
  60. IsPrime(A27) → C27
  61. IsPrime(A28) → C28
  62. IsPrime(A29) → C29
  63. IsPrime(A30) → C30
  64. Zip((((("SetFixed(B" * jj) * ",true, ") * If[kk, "true", "false"]) * ")"), jj, Sequence[30], kk, primesOrNot) → FixNonPrimes
  65. Flatten({Sequence[{Element[selectedNums, kk], Element[times, kk]}, kk, 1, Length[times]], Last[selectedNums]}) → product
  66. Text((("\ovalbox{\hspace{4}" * A1) * "\hspace{5}}"), Element[textsPositions, A1], true, true, 0, 0) → B1
  67. Text((("\ovalbox{\hspace{4}" * A2) * "\hspace{5}}"), Element[textsPositions, A2], true, true, 0, 0) → B2
  68. Text((("\ovalbox{\hspace{4}" * A3) * "\hspace{5}}"), Element[textsPositions, A3], true, true, 0, 0) → B3
  69. Text((("\ovalbox{\hspace{4}" * A4) * "\hspace{5}}"), Element[textsPositions, A4], true, true, 0, 0) → B4
  70. Text((("\ovalbox{\hspace{4}" * A5) * "\hspace{5}}"), Element[textsPositions, A5], true, true, 0, 0) → B5
  71. Text((("\ovalbox{\hspace{4}" * A6) * "\hspace{5}}"), Element[textsPositions, A6], true, true, 0, 0) → B6
  72. Text((("\ovalbox{\hspace{4}" * A7) * "\hspace{5}}"), Element[textsPositions, A7], true, true, 0, 0) → B7
  73. Text((("\ovalbox{\hspace{4}" * A8) * "\hspace{5}}"), Element[textsPositions, A8], true, true, 0, 0) → B8
  74. Text((("\ovalbox{\hspace{4}" * A9) * "\hspace{5}}"), Element[textsPositions, A9], true, true, 0, 0) → B9
  75. If(countQuestion ≤ 30, selectedNums(Length[selectedNums]), selectedNum / Element[factorsAll, Options]) → secondFact
  76. Min(RemoveUndefined[{1, 3.2 / secondFact, 14 / firstFact}]) → sqLength
  77. If(Length[selectedNums] ≥ 2, Sequence[Translate[B, ((0, (-sqLength)) * kk)], kk, 0, secondFact], {(-10, 0), (-10, -10)}) → PointsLeft
  78. If(Length[selectedNums] ≥ 2, Sequence[Translate[B, ((sqLength, 0) * kk)], kk, 0, firstFact], {(-10, 0), (-10, -10)}) → PointsUp
  79. Translate(PointsLeft, (If[Length[selectedNums] ≥ 2, (sqLength * firstFact), 1], 0)) → PointsRight
  80. Translate(PointsUp, Vector[(0, ((-If[Length[selectedNums] ≥ 2, secondFact, 1]) * sqLength))]) → PointsDown
  81. Polygon({Element[PointsDown, 1], Element[PointsDown, Length[PointsDown]], Element[PointsRight, 1], B}) → q1
  82. Text(secondFact) → labelVSegment
  83. If(Length[selectedNums] ≥ 2, Text[labelVSegment, Midpoint[vSegment], true, true, 1, 0], "") → labelVPositioned_{1}
  84. If(Length[selectedNums] ≥ 2, Text[labelHSegment, Midpoint[hSegment], true, true, 0, -1], "") → labelHPositioned
  85. Sequence((((("SetConditionToShowObject(B" * jj) * ", D") * jj) * ")"), jj, 4, 30) → conditionalVisibForTexts
  86. PrimeFactors(countQuestion) → l1
  87. If(prime ∧ IsPrime[countQuestion], "That's correct!", prime ∧ (¬IsPrime[countQuestion]), ((("Notice that " * l1(1)) * " is a factor of ") * countQuestion), (¬prime) ∧ Product[selectedNums] ≟ countQuestion, "Well done!", (("The product is not equal to " * countQuestion) * ". Keep trying.")) → feedbackText
  88. Translate(B, (0, -5)) → B'
  89. Zip(Segment[AA, BB], AA, PointsLeft, BB, PointsRight) → segmentsH
  90. Zip(Segment[AA, BB], AA, PointsUp, BB, PointsDown) → segmentsV
  91. Translate(PointsRight(1), (0.5, 0)) → A
  92. Translate(PointsRight(Length[PointsRight]), (0.5, 0)) → C
  93. Segment(A, C) → f
  94. Text(("\hspace{5}" * labelVSegment), Midpoint[f], true, true, 1, 0) → labelVPositioned
  95. Translate(PointsLeft(Length[PointsLeft]), (0, -0.5)) → D
  96. Translate(PointsRight(Length[PointsRight]), (0, -0.5)) → E
  97. Segment(D, E) → g
  98. Text(ProductText', Midpoint[g], true, true, 0, -1) → labelHPositoned
  99. TableText(Flatten[{If[Length[selectedNums] ≥ 2, product, Length[selectedNums] ≟ 1, Last[selectedNums], {}], If[Length[selectedNums] ≥ 2, "=", ""], If[Length[selectedNums] ≥ 2, Text[Product[selectedNums]], ""]}], "lh") → ProductText
  100. Polygon(Element[PointsRight, 1], Element[PointsLeft, 1], 4) → poly1
  101. Segment(Translate[PointsLeft(1), (0, -1.5)], Translate[PointsRight(1), (0, -1.5)]) → h
  102. Segment(Translate[PointsRight(1), (0.5, 0)], Translate[PointsRight(1), (0.5, -1)]) → i
  103. Zip((("SetFixed(B" * jj) * ",true, true)"), jj, Sequence[30]) → UnFixAll
  104. Corner(ProductText, 3) → PosUnDo
  105. Text(feedback, B', true, true, 1, 0) → feedbackTextPositioned
  106. Translate(hGuideLine, Vector[(Vector[Corner[4], Corner[1]] / 500 * 16)]) → hGuideLine'
  107. Zip((((("SetColor(B" * jj) * ", ") * If[kk, "colorPrime", "colorInactive"]) * ")"), jj, Sequence[30], kk, primesOrNot) → ColorTheNumbers
  108. Text(ProductText', (0, y(Midpoint[g])), true, true, 1, -1) → labelHPositioned2
  109. Corner(labelHPositoned, 1) → CorLabelH
  110. Zip((((("SetColor(B" * jj) * ", ") * If[jj ≟ 1, "colorBlack", If[kk, "colorPrime", "colorNonPrime"]]) * ")"), jj, Sequence[30], kk, primesOrNot) → ColorTheNumbers2

AI 绘图提示语参考

展示一个复合数如何分解为质因数的乘积，通过可视化过程强调质数在乘法中的基础作用。首先，选择一个复合数，然后将其分解为一系列质因数，并用乘号连接这些质因数，形成一个表达式。在图形中，用圆圈突出显示每个质因数，并按照分解顺序排列，以便清晰地展示质因数分解的过程。
以上提示语为根据原始绘图命令整理而来，仅供参考。