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两步方程求解探索

两步方程求解探索
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2023-02-28 23:43
函数不等式滑块动画函数图像
① 本范例通过交互式活动演示如何求解两步线性方程，学生可探索不同的解题路径并验证每一步的合理性。② 核心数学概念包括线性方程的求解、等式性质（加法、乘法、分配律等）以及解题步骤的逻辑论证。③ 作图要点：利用GeoGebra的Shuffle、Element、If、Text、KeepIf、Corner、TableText等命令生成随机题目与选项，通过randomSol、randomP1、randomQ1等对象控制题目参数，并使用colorCancel、colorHL等对象高亮关键步骤，配合justif2LessThan、simpText、oppositeText等文本对象呈现解题过程。④ 适合初中（6-8年级）学生学习代数方程，也可用于教师课堂演示或学生自主练习，支持西班牙语翻译，已通过资源验证。

GeoGebra 命令及参数

  1. Shuffle(Flatten[{Sequence[-15, 15], Sequence[((2 * ii) + 1) / 2, ii, -5, 5], Sequence[((3 * ii) + 1) / 3, ii, -2, 2], Sequence[((3 * ii) + 2) / 3, ii, -2, 2], Sequence[((4 * ii) + 1) / 4, ii, -1, 2], Sequence[((4 * ii) + 3) / 4, ii, -1, 1], Sequence[((5 * ii) + 1) / 5, ii, -1, 1]}]) → randomSol, {-0.5, -0.75, -0.6666666666666666, 11, 4.5, -1.6666666666666667, -15, 5.5, 0.75, 0, -7, -10, 2, -3.5, 8, -8, 3.5, -1.5, 1.5, -9, 0.5, 1.75, 1.25, -4.5, 12, -14, 9, 15, -6, 1, 1.3333333333333333, 2.6666666666666665, 7, 2.25, -3, -0.25, 2.5, 10, 0.6666666666666666, -12, 13, 0.25, -2, 3, -11, 1.2, 2.3333333333333335, -5, 0.3333333333333333, 4, 14, 1.6666666666666667, -0.3333333333333333, -2.5, 6, -1.3333333333333333, -4, 5, -1, -13, -0.8, 0.2}
  2. Element(randomSol, Mod[countQuestion, Length[randomSol]] + 1) → solution
  3. Shuffle(KeepIf[IsInteger[(jj * solution)] ∧ abs((jj * solution)) ≤ 15, jj, Sequence[-10, 10] \ {0, 1}]) → randomP1, {-8, -4, 8, 4}
  4. Element(randomP1, 1) → p1
  5. Shuffle(KeepIf[0 < abs((solution * p1) + qq) ≤ 16, qq, Sequence[-15, 15] \ {0}]) → randomQ1, {-7, -5, 4, 9, -1, 5, 3, -9, -4, -2, 6, -13, 1, -15, -8, 7, 2, 8, -11, -3, 10, -12, -14, -10}
  6. Shuffle(Sequence[-5, 5] \ {0, (-solution)}) → randomQ2, {3, 5, 1, -3, -4, -1, -5, 2, 4, -2}
  7. Shuffle(Sequence[12]) → randomFormat, {1, 5, 12, 4, 3, 6, 9, 7, 11, 2, 10, 8}
  8. If(p1 ≠ -1, (If[n ≟ 6, "\bold{", "{"] * "x}"), "") → A6
  9. Element(randomQ1, 1) → q1
  10. Text(r1) → C2
  11. If(p1 ≠ -1, "=", "") → B6
  12. If(p1 ≟ -1, (("\bold{" * Text[(-r1) + q1]) * "}"), (((((((("\dfrac{" * If[n ≟ 5, (("\bold\textcolor{" * colorHL) * "}{"), ""]) * Text[r1 - q1]) * If[n ≟ 5, "}", ""]) * "}{") * If[4 ≤ n ≤ 5, (("\bold\textcolor{" * colorHL) * "}{"), ""]) * p1) * If[4 ≤ n ≤ 5, "}", ""]) * "}")) → C5
  13. If(p1 ≠ -1, simpText, "") → D6
  14. If(p1 ≟ -1, oppositeText, ((((((("\textsf{" * If[n ≟ 4, (("\bold\textcolor{" * colorHL) * "}{"), ""]) * "Divide") * If[n ≟ 4, "}", ""]) * " both sides of the equation by \(") * If[n ≟ 4, (("\bold\color{" * colorHL) * "}"), ""]) * p1) * "\).}")) → D5
  15. Element(randomQ2, Mod[countQuestion, Length[randomQ2]] + 1) → q2
  16. KeepIf(IsInteger[(jj * solution)], jj, Sequence[15] \ {1}) → randomP2
  17. Element(randomFormat, Mod[countQuestion, Length[randomFormat]] + 1) → format
  18. Corner(5) → AppSize
  19. Text(r2) → C16
  20. Text(r2) → C52
  21. TableText(Take[{{C1, B1, A1, D1}, {C16, B16, A16, D16}, {C17, B17, A17, D17}, {C18, B18, A18, D18}, {C19, B19, A19, D19}, {C20, B20, A20, D20}, {C21, B21, A21, D21}, {C22, B22, A22, D22}}, 1, 1 + Min[n, 7]], "rcll", 10, vspace) → tableFormat9D
  22. TableText(Take[{{A1, B1, C1, D1}, {A16, B16, C16, D16}, {A17, B17, C17, D17}, {A18, B18, C18, D18}, {A19, B19, C19, D19}, {A20, B20, C20, D20}, {A21, B21, C21, D21}, {A22, B22, C22, D22}}, 1, 1 + Min[n, 7]], "rcll", 10, vspace) → tableFormat5D
  23. TableText(Take[{{C1, B1, A1, D1}, {C2, B2, A2, D2}, {C3, B3, A3, D3}, {C4, B4, A4, D4}, {C5, B5, A5, D5}, {C6, B6, A6, D6}}, 1, 1 + Min[n, If[p1 ≟ -1, 4, 5]]], "rcll", 10, vspace) → tableFormat3
  24. TableText(Take[{{A1, B1, C1, D1}, {C9, B9, A9, D9}, {C10, B10, A10, D10}, {C11, B11, A11, D11}, {C12, B12, A12, D12}, {C13, B13, A13, D13}}, 1, 1 + Min[n, If[p1 ≟ -1, 4, 5]]], "rcll", 10, vspace) → tableFormat2
  25. TableText(Take[{{A1, B1, C1, D1}, {A2, B2, C2, D2}, {A3, B3, C3, D3}, {A4, B4, C4, D4}, {A5, B5, C5, D5}, {A6, B6, C6, D6}}, 1, 1 + Min[n, If[p1 ≟ -1, 4, 5]]], "rcll", 10, vspace) → tableFormat1
  26. TableText(Take[{{C1, B1, A1, D1}, {A9, B9, C9, D9}, {A10, B10, C10, D10}, {A11, B11, C11, D11}, {A12, B12, C12, D12}, {A13, B13, C13, D13}}, 1, 1 + Min[n, If[p1 ≟ -1, 4, 5]]], "rcll", 10, vspace) → tableFormat4
  27. TableText(Take[{{A1, B1, C1, D1}, {A25, B25, C25, D25}, {A26, B26, C26, D26}, {A27, B27, C27, D27}, {A28, B28, C28, D28}, {A29, B29, C29, D29}, {A30, B30, C30, D30}, {A31, B31, C31, D31}}, 1, 1 + Min[n, 7]], "rcll", 10, vspace) → tableFormat6D
  28. TableText(Take[{{C1, B1, A1, D1}, {C25, B25, A25, D25}, {C26, B26, A26, D26}, {C27, B27, A27, D27}, {C28, B28, A28, D28}, {C29, B29, A29, D29}, {C30, B30, A30, D30}, {C31, B31, A31, D31}}, 1, 1 + Min[n, 7]], "rcll", 10, vspace) → tableFormat10D
  29. TableText(Take[{{A1, B1, C1, D1}, {A34, B34, C34, D34}, {A35, B35, C35, D35}, {A36, B36, C36, D36}, {A37, B37, C37, D37}, {A38, B38, C38, D38}, {A39, B39, C39, D39}, {A40, B40, C40, D40}}, 1, 1 + Min[7, n]], "rcll", 10, vspace) → tableFormat7D
  30. TableText(Take[{{C1, B1, A1, D1}, {C34, B34, A34, D34}, {C35, B35, A35, D35}, {C36, B36, A36, D36}, {C37, B37, A37, D37}, {C38, B38, A38, D38}, {C39, B39, A39, D39}, {C40, B40, A40, D40}}, 1, 1 + Min[7, n]], "rcll", 10, vspace) → tableFormat11D
  31. TableText(Take[{{A1, B1, C1, D1}, {A43, B43, C43, D43}, {A44, B44, C44, D44}, {A45, B45, C45, D45}, {A46, B46, C46, D46}, {A47, B47, C47, D47}, {A48, B48, C48, D48}, {A49, B49, C49, D49}}, 1, 1 + Min[n, 7]], "rcll", 10, vspace) → tableFormat8D
  32. TableText(Take[{{C1, B1, A1, D1}, {C43, B43, A43, D43}, {C44, B44, A44, D44}, {C45, B45, A45, D45}, {C46, B46, A46, D46}, {C47, B47, A47, D47}, {C48, B48, A48, D48}, {C49, B49, A49, D49}}, 1, 1 + Min[n, 7]], "rcll", 10, vspace) → tableFormat12D
  33. TableText(Take[{{A1, B1, C1, D1}, {A52, B52, C52, D52}, {A53, B53, C53, D53}, {A54, B54, C54, D54}, {A55, B55, C55, D55}, {A56, B56, C56, D56}}, 1, 1 + Min[n, 5]], "rcll", 10, vspace) → tableFormat5ND
  34. TableText(Take[{{C1, B1, A1, D1}, {C52, B52, A52, D52}, {C53, B53, A53, D53}, {C54, B54, A54, D54}, {C55, B55, A55, D55}, {C56, B56, A56, D56}}, 1, 1 + Min[n, 5]], "rcll", 10, vspace) → tableFormat9ND
  35. TableText(Take[{{A1, B1, C1, D1}, {A59, B59, C59, D59}, {A60, B60, C60, D60}, {A61, B61, C61, D61}, {A62, B62, C62, D62}, {A63, B63, C63, D63}}, 1, 1 + Min[n, 5]], "rcll", 10, vspace) → tableFormat6ND
  36. TableText(Take[{{C1, B1, A1, D1}, {C59, B59, A59, D59}, {C60, B60, A60, D60}, {C61, B61, A61, D61}, {C62, B62, A62, D62}, {C63, B63, A63, D63}}, 1, 1 + Min[n, 5]], "rcll", 10, vspace) → tableFormat10ND
  37. TableText(Take[{{A1, B1, C1, D1}, {A66, B66, C66, D66}, {A67, B67, C67, D67}, {A68, B68, C68, D68}, {A69, B69, C69, D69}, {A70, B70, C70, D70}}, 1, 1 + Min[n, 5]], "rcll", 10, vspace) → tableFormat7ND
  38. TableText(Take[{{C1, B1, A1, D1}, {C66, B66, A66, D66}, {C67, B67, A67, D67}, {C68, B68, A68, D68}, {C69, B69, A69, D69}, {C70, B70, A70, D70}}, 1, 1 + Min[n, 5]], "rcll", 10, vspace) → tableFormat11ND
  39. TableText(Take[{{A1, B1, C1, D1}, {A73, B73, C73, D73}, {A74, B74, C74, D74}, {A75, B75, C75, D75}, {A76, B76, C76, D76}, {A77, B77, C77, D77}}, 1, 1 + Min[n, 5]], "rcll", 10, vspace) → tableFormat8ND
  40. TableText(Take[{{C1, B1, A1, D1}, {C73, B73, A73, D73}, {C74, B74, A74, D74}, {C75, B75, A75, D75}, {C76, B76, A76, D76}, {C77, B77, A77, D77}}, 1, 1 + Min[n, 5]], "rcll", 10, vspace) → tableFormat12ND
  41. Element(Join[{{tableFormat1, tableFormat2, tableFormat3, tableFormat4}, If[distribute, {tableFormat5D, tableFormat6D, tableFormat7D, tableFormat8D, tableFormat9D, tableFormat10D, tableFormat11D, tableFormat12D}, {tableFormat5ND, tableFormat6ND, tableFormat7ND, tableFormat8ND, tableFormat9ND, tableFormat10ND, tableFormat11ND, tableFormat12ND}]}], format) → text1
  42. If(format ≤ 4, If[p1 ≟ -1, 4, 6], If[distribute, 8, 6]) → maxSL

AI 绘图提示语参考

创建一个交互式数学活动，展示如何解两步线性方程。生成随机方程，包含数字系数和常数项，用不同颜色突出关键步骤，并显示解题过程和逻辑说明。方程以表格形式呈现，包括原始方程、解题步骤和解释，适合中学生对线性方程的学习。
以上提示语为根据原始绘图命令整理而来，仅供参考。