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Solve Linear Equations with Inverse Operations: Arrow Steps & Error Checking

Solve Linear Equations with Inverse Operations: Arrow Steps & Error Checking
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2024-07-30 21:07
FunctionTransformationInequalityGeometric Construction
In collections Gleichungen lösen mit Umkehroperationen
This GeoGebra lesson demonstrates how to solve linear equations by applying inverse operations step by step, using arrow diagrams to show how each forward transformation can be reversed to reach the correct solution. The key mathematical ideas are linear equation solving, properties of equality, inverse operations for addition/subtraction and multiplication/division, and diagnosing/repairing common mistakes made during equation transformations. Construction highlights from the provided command summary: Sequence and Element are used to generate and manage step/option structure; Textfield and InputBox collect user answers; SelectedIndex controls multiple-choice selections; Segment and PolyLine (arrow/path visuals) illustrate the step-by-step transformation flow; Invert is used to reverse the arrows/operation order; If switches feedback and solution messages based on correctness; validate checks submissions, while variables like attemptCount and questionCount track progress. Suitable for grades ~5–6 and early middle school, as a practice activity, interactive assessment, or guided classroom demonstration.

GeoGebra Commands & Parameters

  1. Sequence(Random[1, 10], i, 1, 10) → randomNumbers, {10, 9, 8, 5, 4, 9, 9, 4, 1, 1}
  2. Element(randomNumbers, Mod[questionCount, Length[randomNumbers]] + 1) → randomNumber
  3. Textfield(input) → inputBox
  4. Textfield(input031) → InputBox031
  5. Textfield(input032) → InputBox032
  6. Textfield(input033) → InputBox033
  7. Textfield(input041) → InputBox041
  8. Textfield(input042) → InputBox042
  9. Textfield(input043) → InputBox043
  10. Textfield(input044) → InputBox044
  11. Textfield(input091) → InputBox091
  12. Textfield(input092) → InputBox092
  13. Textfield(input093) → InputBox093
  14. Textfield(input101) → InputBox101
  15. Textfield(input102) → InputBox102
  16. Textfield(input103) → InputBox103
  17. Textfield(input104) → InputBox104
  18. Textfield(input131) → InputBox131
  19. Textfield(input132) → InputBox132
  20. Textfield(input133) → InputBox133
  21. Textfield(input141) → InputBox141
  22. Textfield(input142) → InputBox142
  23. Textfield(input143) → InputBox143
  24. Textfield(input144) → InputBox144
  25. Textfield(input171) → InputBox171
  26. Textfield(input172) → InputBox172
  27. Textfield(input173) → InputBox173
  28. Textfield(input181) → InputBox181
  29. Textfield(input182) → InputBox182
  30. Textfield(input183) → InputBox183
  31. Textfield(input184) → InputBox184
  32. SelectedIndex(dropdown031) → index031
  33. SelectedIndex(dropdown032) → index032
  34. SelectedIndex(dropdown041) → index041
  35. SelectedIndex(dropdown042) → index042
  36. SelectedIndex(dropdown091) → index091
  37. SelectedIndex(dropdown092) → index092
  38. SelectedIndex(dropdown101) → index101
  39. SelectedIndex(dropdown102) → index102
  40. SelectedIndex(dropdown131) → index131
  41. SelectedIndex(dropdown132) → index132
  42. SelectedIndex(dropdown141) → index141
  43. SelectedIndex(dropdown142) → index142
  44. SelectedIndex(dropdown171) → index171
  45. SelectedIndex(dropdown172) → index172
  46. SelectedIndex(dropdown181) → index181
  47. SelectedIndex(dropdown182) → index182
  48. Segment(PosSeg1, PosSeg1 + (segLength, 0)) → seg1
  49. Segment(PosSeg2, PosSeg2 + (segLength, 0)) → seg2
  50. Invert(pixMat) → invPixMat
  51. Segment(PosSeg3, PosSeg3 + (segLength, 0)) → seg3
  52. Segment(PosSeg4, PosSeg4 + (segLength, 0)) → seg4
  53. Text((("\textsf{" * number3List(Task)) * "}"), Point[seg3, 1] + (0.1, 0.05), false, true, 1, 0) → txtRes1
  54. Segment(PosSegCalc1, PosSegCalc1 + (segLengthCalc, 0)) → segCalc1
  55. Segment(PosSegCalc2, PosSegCalc2 + (segLengthCalc, 0)) → segCalc2
  56. Text((("\textsf{" * number3List(Task)) * "}"), Point[segCalc2, 1] + (0.1, 0.05), false, true, 1, 0) → txtCalc3
  57. Segment(PosSegCalc2 + (0, (-dis2)), PosSegCalc2 + (segLengthCalc, (-dis2))) → segCalc3
  58. Segment(PosSegCalc1 + (0, (-dis2)), PosSegCalc1 + (segLengthCalc, (-dis2))) → segCalc4
  59. Text((("\textsf{" * number3List(Task)) * "}"), Point[segCalc3, 1] + (0.1, 0.05), false, true, 1, 0) → txtCalc5
  60. Text((("\textsf{" * number4List(Task)) * "}"), Midpoint[Point[segCalc4, 1] + (0, 0.1), Point[segCalc3, 0]], false, true, 0, 0) → txtCalc6
  61. PolyLine(PosSB, Corner[txt021, 1] + (-0.1 + 1.75, 0.05), Corner[txt021, 1] + (-0.1, 0.05), Corner[txt021, 4] + (-0.1, 0.05), Corner[txt021, 3] + (0, 0.05), Corner[txt021, 2] + (0, 0), Corner[txt021, 1] + (-0.1 + 2.5, 0.05), PosSB) → sb02
  62. PolyLine(PosSB, Corner[txt061, 1] + (-0.1 + 1.75, 0.05), Corner[txt061, 1] + (-0.1, 0.05), Corner[txt061, 4] + (-0.1, 0.05), Corner[txt061, 3] + (0, 0.05), Corner[txt061, 2] + (0, 0), Corner[txt061, 1] + (-0.1 + 2.5, 0.05), PosSB) → sb06
  63. PolyLine(PosSB, Corner[txt081, 1] + (-0.1 + 1.75, 0.05), Corner[txt081, 1] + (-0.1, 0.05), Corner[txt081, 4] + (-0.1, 0.05), Corner[txt081, 3] + (0, 0.05), Corner[txt081, 2] + (0, 0), Corner[txt081, 1] + (-0.1 + 2.5, 0.05), PosSB) → sb08
  64. PolyLine(PosSB, Corner[txt131, 1] + (-0.1 + 1.75, 0.05), Corner[txt131, 1] + (-0.1, 0.05), Corner[txt131, 4] + (-0.1, 0.05), Corner[txt131, 3] + (0, 0.05), Corner[txt131, 2] + (0, 0), Corner[txt131, 1] + (-0.1 + 2.5, 0.05), PosSB) → sb13
  65. PolyLine(PosSB, Corner[txt171, 1] + (-0.1 + 1.75, 0.05), Corner[txt171, 1] + (-0.1, 0.05), Corner[txt171, 4] + (-0.1, 0.05), Corner[txt171, 3] + (0, 0.05), Corner[txt171, 2] + (0, 0), Corner[txt171, 1] + (-0.1 + 2.5, 0.05), PosSB) → sb17
  66. If(step ≟ 3, correct031 ∧ correctdd032 ∧ correct033, step ≟ 14, correct141 ∧ correctdd141 ∧ correct142 ∧ correct143 ∧ correctdd142 ∧ correct144, step ≟ 17, correctdd171 ∧ correct171 ∧ correctdd172 ∧ correct172 ∧ correct173, step ≟ 18, correct181 ∧ correctdd181 ∧ correct182 ∧ correct183 ∧ correctdd182 ∧ correct184, true, step ≟ 4, correct041 ∧ correctdd041 ∧ correct042 ∧ correct043 ∧ correctdd042 ∧ correct044, step ≟ 9, correctdd091 ∧ correct091 ∧ correctdd092 ∧ correct092 ∧ correct093, step ≟ 10, correct101 ∧ correctdd101 ∧ correct102 ∧ correct103 ∧ correctdd102 ∧ correct104, step ≟ 13, correctdd131 ∧ correct131 ∧ correctdd132 ∧ correct132 ∧ correct133) → clickableBtnNext
  67. PolyLine(PosSB, Corner[txt55, 1] + (-0.1 + 1.75, 0.05), Corner[txt55, 1] + (-0.1, 0.05), Corner[txt55, 4] + (-0.1, 0.05), Corner[txt55, 3] + (0, 0.05), Corner[txt55, 2] + (0, 0), Corner[txt55, 1] + (-0.1 + 2.5, 0.05), PosSB) → sb55
  68. PolyLine(PosSB, Corner[txt071, 1] + (-0.1 + 1.75, 0.05), Corner[txt071, 1] + (-0.1, 0.05), Corner[txt071, 4] + (-0.1, 0.05), Corner[txt071, 3] + (0, 0.05), Corner[txt071, 2] + (0, 0), Corner[txt071, 1] + (-0.1 + 2.5, 0.05), PosSB) → sb07
  69. PolyLine(PosSB, Corner[txt201, 1] + (0.5, -0.1), Corner[txt201, 2] + (0.1, -0.1), Corner[txt201, 3] + (0.1, 0.1), Corner[txt201, 4] + (-0.1, 0.1), Corner[txt201, 1] + (-0.1, -0.1), PosSB) → sb20
  70. Segment(Midpoint[Corner[txt203, 3], Corner[txt203, 2]] + (0.25, 0.04), Midpoint[Corner[txt203, 3], Corner[txt203, 2]] + (0.25, 0.04) + (segLength, 0)) → seg201
  71. Segment(Point[seg201, 0] + (segLength + 0.25, -0.4) + (1.05 + 0.25, 0.4), Point[seg201, 0] + (segLength + 0.25, -0.4) + (1.05 + 0.25, 0.4) + (segLength, 0)) → seg202
  72. Segment(Midpoint[Corner[txt204, 3], Corner[txt204, 2]] + (0.25, 0.04), Midpoint[Corner[txt204, 3], Corner[txt204, 2]] + (0.25, 0.04) + (segLength, 0)) → seg204
  73. Segment(Point[seg204, 0] + (segLength + 0.25, -0.4) + (1.05 + 0.25, 0.4), Point[seg204, 0] + (segLength + 0.25, -0.4) + (1.05 + 0.25, 0.4) + (segLength, 0)) → seg203

AI Drawing Prompt Reference

Create a visual representation for solving linear equations, showing a sequence of random numbers and arrows to illustrate inverse operations step by step. Include text boxes for user input, dropdown menus for selections, and line segments as arrows to guide the transformation flow. Provide feedback messages indicating correctness or errors based on user answers, demonstrating the process of equation solving and error checking.
The prompt above was compiled from the original drawing commands and is for reference only.