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Division of Powers

Division of Powers
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2024-10-16 17:46
SequenceCoordinate GeometryInequality
In collections Rechnen mit Potenzen
This example demonstrates how to perform division of powers, showing the relationship between fractions and exponents. The core mathematical concepts involved include the definition of exponents, rules of exponent operations, and the relationship between fractions and exponents. The construction points include using GeoGebra's Textfield, Shuffle, If, Join, Polygon, and other commands and objects. Suitable for middle school mathematics education, particularly for students in grades 7-8.

GeoGebra Commands & Parameters

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Shuffle({1, 2, 3}) → ModusList, {2, 3, 1}
  4. If(questionCount ≥ 4, 4, questionCount) → metaprogression
  5. Join({{1}, ModusList}) → ModusMioPlaylist
  6. Shuffle(Sequence[i, i, 1, 19]) → AStartList, {15, 19, 5, 14, 2, 17, 10, 11, 6, 4, 12, 7, 9, 1, 3, 8, 13, 18, 16}
  7. Shuffle(Sequence[i, i, 1, 19]) → BStartList, {3, 1, 9, 18, 19, 6, 10, 2, 15, 14, 5, 11, 8, 17, 7, 12, 13, 16, 4}
  8. Shuffle(Sequence[i, i, 1, 9]) → AMidList, {7, 6, 9, 8, 5, 3, 2, 1, 4}
  9. Shuffle(Sequence[i, i, 1, 9]) → BMidList, {1, 5, 7, 9, 2, 6, 4, 8, 3}
  10. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, rectangleCorrectS3, rectangleCorrectS4, rectangleCorrectS2, rectangleCorrectS1
  11. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {1, 8, 6, 8, 1, 10, 5, 7, 3, 7, 0, 0, 4, 4, 5, 2, 6, 10, 4, 5, 3, 0, 4, 9, 1, 0, 6, 9, 4, 9, 9, 6, 6, 8, 7, 6, 9, 5, 1, 6, 4, 4, 3, 9, 0, 5, 6, 5, 0, 1, 3, 5, 1, 1, 6, 8, 1, 5, 9, 1, 7, 3, 9, 0, 9, 6, 3, 7, 8, 10, 2, 5, 0, 8, 7, 2, 8, 0, 5, 3, 5, 1, 4, 1, 5, 2, 10, 8, 0, 0, 7, 0, 10, 0, 8, 2, 4, 0, 2, 3}
  12. Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
  13. Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {0, 5, 3, 9, 1, 5, 6, 8, 0, 7, 3, 2, 7, 7, 1, 9, 7, 6, 4, 9, 7, 6, 6, 2, 8, 7, 1, 8, 3, 8, 9, 0, 6, 7, 3, 3, 5, 5, 9, 8, 4, 7, 1, 2, 7, 10, 4, 6, 6, 1, 0, 9, 1, 4, 8, 4, 4, 7, 10, 10, 1, 9, 0, 3, 4, 7, 8, 10, 4, 6, 2, 2, 10, 1, 1, 9, 2, 2, 1, 7, 4, 0, 3, 3, 8, 3, 8, 0, 2, 8, 10, 0, 8, 2, 10, 7, 3, 0, 0, 3}
  14. Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
  15. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  16. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  17. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  18. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  19. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  20. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  21. Shuffle(Sequence[i, i, -10, 10] \ {0}) → XGanzzhahlList, {6, -2, -3, 1, 4, 8, 3, 10, -10, 2, 9, -1, -6, -8, -4, 5, 7, -7, -9, -5}
  22. Shuffle(Sequence[i, i, 1, 10]) → XStartList, {8, 9, 4, 2, 10, 1, 5, 7, 3, 6}
  23. Shuffle(Join[{XDezizahlList, XGanzzhahlList}]) → XMidList, {-9, 1, -0.4, -0.8, 3, 5, 3.5, -1.5, 2, 1.1, 3.8, 0.4, 0.7, 0.9, 1.8, 1.2, 10, 4.6, -2, 0.6, 8, -1.3, 0.3, -7, 2.5, 3.6, 4.1, 4, -4, 2.4, 0.2, 2.9, 4.3, -0.1, 2.8, -1.9, 4.5, -0.3, -0.5, -6, 3.3, 3.9, -1.2, 4.4, 1.6, -5, -0.7, 0.1, -0.9, 3.2, -3, 4.8, -8, 1.3, 5, -1.1, 4.9, 4, -1.7, 0.5, 4.7, 1.4, -0.6, 1.5, 3.7, 3, -1.6, 1.7, 2.3, -1, 2.1, -1.8, -0.2, -2, 9, 6, 4.2, -10, 2, -1.4, 3.1, 2.6, 0.8, 7, 2.2, 3.4, -1, 1.9, 2.7, 1}
  24. Text(Text2, E, false, true, -1, 0) → Text6
  25. Text(Text3, F, false, true, -1, 0) → Text7
  26. Midpoint(Corner[Text6, 1], Corner[Text6, 4]) → Pos1
  27. Midpoint(Corner[Text7, 1], Corner[Text7, 3]) → Pos2
  28. Textfield(input3) → InputBox3
  29. Text(Text4, B, false, true, -1, 0) → Text10
  30. Midpoint(Corner[Text10, 1], Corner[Text10, 3]) → Pos3
  31. If(modus ≟ 1, Defined[input1], modus ≟ 2, Defined[input2], Defined[input3]) → fixed
  32. Midpoint(Corner[Text12, 1], Corner[Text12, 3]) → Pos4
  33. Text(Text12, A, false, true, -1, 0) → Text5

AI Drawing Prompt Reference

Create a visual representation of power division, featuring two input boxes for numerical values, with randomly generated sequences and coordinate points forming geometric shapes to illustrate the relationship between fractions and exponents, and geometrically depict the calculation results, showing the rules of exponent operations in a step-by-step manner from input to output.
The prompt above was compiled from the original drawing commands and is for reference only.