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Solving Equations with Inverse Operations

Solving Equations with Inverse Operations
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2024-08-01 16:53
Inequality
In collections Gleichungen lösen mit Umkehroperationen
This example demonstrates how to use inverse operations to solve linear equations. Students can adjust the variable values to observe the changes in the equation and learn how to use inverse operations to solve the equation. The key mathematical concepts involved are linear equations, inverse operations, and algebraic operations. The construction points include using GeoGebra's Shuffle, Join, Insert, etc. commands to build the equation and solve the equation process. Suitable for middle school math, especially for 5-6 grade students.

GeoGebra Commands & Parameters

  1. Shuffle(1…6) → Type1List, {3, 6, 4, 5, 1, 2}
  2. Shuffle(7…12) → Type2List, {10, 9, 8, 11, 7, 12}
  3. Shuffle(19…24) → Type4List, {24, 20, 19, 23, 21, 22}
  4. Join({{3}, Shuffle[{1, 2, 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({{18}, Shuffle[13…17]}) → Type3List
  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 / 5) + 1], k, 1, 24) → Reihenfolge
  13. Join({Sequence[3, k, 1, 12], Sequence[4, k, 1, 12]}) → TaskSignList1
  14. SelectedIndex(dropdown1) → indexdd1
  15. Sequence(If[TaskSignList1(k) ≟ 1, 2, TaskSignList1(k) ≟ 2, 1, TaskSignList1(k) ≟ 3, 4, TaskSignList1(k) ≟ 4, 3], k, 1, 24) → UTaskSignList1
  16. Sequence(ParseToNumber[((((Text[Number1List(k)] * "") * Element[SignList, TaskSignList1(k)]) * "") * Text[Number2List(k)])], k, 1, 24) → Number3List
  17. Join({Sequence[1, k, 1, 6], Sequence[2, k, 1, 6], Sequence[1, k, 1, 6], Sequence[2, k, 1, 6]}) → TaskSignList2
  18. SelectedIndex(dropdown3) → indexdd3
  19. Sequence(If[TaskSignList2(k) ≟ 1, 2, TaskSignList2(k) ≟ 2, 1, TaskSignList2(k) ≟ 3, 4, TaskSignList2(k) ≟ 4, 3], k, 1, 24) → UTaskSignList2
  20. Textfield(input4) → InputBox4
  21. Textfield(input3) → InputBox3
  22. Textfield(input2) → InputBox2
  23. Textfield(input1) → InputBox1
  24. Shuffle(1…numberOfQuestions) → randomQuestions, {6, 8, 22, 13, 5, 16, 2, 9, 7, 1, 3, 24, 15, 21, 23, 19, 4, 10, 12, 20, 18, 14, 11, 17}
  25. Textfield(input) → inputBox
  26. Element(randomQuestions, Mod[questionCount - 1, Length[randomQuestions]] + 1) → randomQuestion
  27. Element(SignTextList, TaskSignList1(question)) → txtSign
  28. Midpoint(Corner[txt02, 3], Corner[txt02, 2] + (3.5, 0.05)) → PosSeg2
  29. Segment(PosSeg2, PosSeg2 + (segLength, 0)) → seg2
  30. Sequence(ParseToNumber[((((Text[Number3List(k)] * "") * Element[SignList, TaskSignList2(k)]) * "") * Text[Number4List(k)])], k, 1, 24) → Number5List
  31. Invert(pixMat) → invPixMat
  32. SelectedIndex(dropdown2) → indexdd2
  33. Segment(PosSegSol, PosSegSol + (segLength / 2, 0)) → segSol
  34. Text((((("\textsf{" * SignTextList(UTaskSignList1(question))) * " ") * ReplaceAll[Text[number2], ".", ","]) * "}"), Midpoint[segSol], false, true, 0, 1) → txtSolution3
  35. Segment(PosSeg1, PosSeg1 + (segLength, 0)) → seg1
  36. Text((((("\textsf{" * SignTextList(TaskSignList1(question))) * " ") * ReplaceAll[Text[number2], ".", ","]) * "}"), Midpoint[seg1], false, true, 0, 1) → txt03
  37. Segment(PosSeg21, PosSeg21 + (segLength, 0)) → seg21
  38. Segment(PosSeg11, PosSeg11 + (segLength, 0)) → seg11
  39. Text((((("\textsf{" * SignTextList(TaskSignList2(question))) * " ") * ReplaceAll[Text[number4], ".", ","]) * "}"), Midpoint[seg11], false, true, 0, 1) → txt06
  40. Segment(PosSegSol2, PosSegSol2 + (segLength / 2, 0)) → segSol2
  41. Text((((("\textsf{" * SignTextList(UTaskSignList2(question))) * " ") * ReplaceAll[Text[number4], ".", ","]) * "}"), Midpoint[segSol2], false, true, 0, 1) → txtSolution4
  42. SelectedIndex(dropdown4) → indexdd4
  43. Text(txtSolution6, Midpoint[Corner[txtSolution2, 1], Corner[txtSolution2, 2]] + (0, -1.35), false, true, 0, 0) → txtSolution7

AI Drawing Prompt Reference

Draw a process of solving linear equations with six steps. First, generate six random numbers, then create two linear equations based on these numbers. Next, use inverse operations to solve the equations step by step, showing each step on the graph. Finally, display the final solution of the equation.
The prompt above was compiled from the original drawing commands and is for reference only.