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Solving Simple Equations with Inverse Operations

Solving Simple Equations with Inverse Operations
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2024-07-30 16:37
Inequality
In collections Gleichungen lösen mit Umkehroperationen
This example demonstrates how to use inverse operations to solve simple linear equations. It involves the core mathematical concept of inverse operations and linear equations. The construction points include: using Shuffle, Join, Insert, etc. GeoGebra commands to generate random linear equations, using Invert command to solve the equation, using Textfield and Element commands to display the result. It is suitable for middle school mathematics education, especially for solving linear equations.

GeoGebra Commands & Parameters

  1. Shuffle(1…6) → Type1List, {3, 4, 1, 6, 5, 2}
  2. Shuffle(13…18) → Type3List, {17, 13, 14, 16, 18, 15}
  3. Shuffle(19…24) → Type4List, {23, 24, 19, 22, 20, 21}
  4. Join({{2}, Shuffle[{1, 3, 4}]}) → Round1
  5. Insert(Last[Round1], Shuffle[Take[Round1, 1, 3]], RandomElement[2…4]) → Round2
  6. Insert(Last[Round2], Shuffle[Take[Round2, 1, 3]], RandomElement[2…4]) → Round3
  7. Insert(Last[Round3], Shuffle[Take[Round3, 1, 3]], RandomElement[2…4]) → Round4
  8. Insert(Last[Round4], Shuffle[Take[Round4, 1, 3]], RandomElement[2…4]) → Round5
  9. Insert(Last[Round5], Shuffle[Take[Round5, 1, 3]], RandomElement[2…4]) → Round6
  10. Join({{8}, Shuffle[{7, 9, 10, 11, 12}]}) → Type2List
  11. Join({Round1, Round2, Round3, Round4, Round5, Round6}) → TypeList
  12. Sequence(Element[If[TypeList(k) ≟ 1, Type1List, TypeList(k) ≟ 2, Type2List, TypeList(k) ≟ 3, Type3List, Type4List], floor(k / 4.1) + 1], k, 1, 24) → Reihenfolge
  13. SelectedIndex(dropdown1) → indexdd1
  14. Textfield(input1) → InputBox1
  15. Sequence(If[TaskSignList(k) ≟ 1, 2, TaskSignList(k) ≟ 2, 1, TaskSignList(k) ≟ 3, 4, TaskSignList(k) ≟ 4, 3], k, 1, 24) → UTaskSignList
  16. Textfield(input2) → InputBox2
  17. Shuffle(1…numberOfQuestions) → randomQuestions, {17, 19, 3, 6, 1, 4, 13, 15, 14, 5, 11, 10, 9, 16, 20, 24, 22, 8, 23, 18, 12, 21, 7, 2}
  18. Textfield(input) → inputBox
  19. Element(randomQuestions, Mod[questionCount - 1, Length[randomQuestions]] + 1) → randomQuestion
  20. Sequence(ParseToNumber[((((Text[Number1List(k)] * "") * Element[SignList, TaskSignList(k)]) * "") * Text[Number2List(k)])], k, 1, 24) → Number3List
  21. Element(SignTextList, TaskSignList(question)) → txtSign
  22. Midpoint(Corner[txt02, 3], Corner[txt02, 2] + (3.5, 0.05)) → PosSeg
  23. Segment(PosSeg, PosSeg + (segLength, 0)) → seg
  24. Invert(pixMat) → invPixMat
  25. SelectedIndex(dropdown2) → indexdd2
  26. Segment(PosSegSol, PosSegSol + (segLength, 0)) → segSol
  27. Text((((("\textsf{" * SignTextList(UTaskSignList(question))) * " ") * ReplaceAll[Text[number2], ".", ","]) * "}"), Midpoint[segSol], false, true, 0, 1) → txtSolution3
  28. Segment(PosSeg1, PosSeg1 + (segLength, 0)) → seg1
  29. Text((((("\textsf{" * SignTextList(TaskSignList(question))) * " ") * ReplaceAll[Text[number2], ".", ","]) * "}"), Midpoint[seg1], false, true, 0, 1) → txt03
  30. Text(txtSolution4, Midpoint[segSol] + (0.25, -1), false, true, 0, 0) → txtSolution5

AI Drawing Prompt Reference

Draw a series of linear equation solving process, including randomly generated equations, the process of solving equations using inverse operations, and text boxes to display the results. First, generate random number lists, then create equations through insertion and combination operations, and finally use inverse operations to solve the equations and display the solving process and results in the graph.
The prompt above was compiled from the original drawing commands and is for reference only.