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Solving Two-Step Equations

Solving Two-Step Equations
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2023-02-28 23:43
FunctionInequalitySlider AnimationGraphing
① This interactive activity demonstrates how to solve two-step linear equations, allowing students to explore multiple solution paths and justify each step. ② Core math concepts include solving linear equations, properties of equality (addition, multiplication, distributive), and logical justification of solution steps. ③ Construction highlights: Uses GeoGebra commands such as Shuffle, Element, If, Text, KeepIf, Corner, and TableText to generate randomized problems and choices; objects like randomSol, randomP1, randomQ1 control problem parameters; colorCancel and colorHL highlight key steps; text objects justif2LessThan, simpText, oppositeText present the solution process. ④ Suitable for middle school (grades 6-8) algebra learning, classroom demonstration, or self-paced practice; includes Spanish translation and is a verified resource.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Create an interactive math activity demonstrating how to solve two-step linear equations. Generate random equations with numeric coefficients and constants, highlight key steps with different colors, and display the solution process along with logical justifications. Present the equations and steps in a table format, suitable for middle school algebra learning.
The prompt above was compiled from the original drawing commands and is for reference only.