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Special Powers

Special Powers
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2024-10-02 20:26
Coordinate GeometryGeometric Construction
In collections Rechnen mit Potenzen
This example demonstrates the calculation of special powers through multiple-choice and open-ended questions. Key mathematical concepts include the rules of power operations. Various GeoGebra commands such as Textfield, Sequence, Join, etc., are used. Suitable for 7-8th grade students to learn the rules of power operations.

GeoGebra Commands & Parameters

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Textfield(input3) → InputBox3
  4. Textfield(input4) → InputBox4
  5. SpeechBubbleRight(A, 11, 1.8) → Speech1
  6. Sequence(B + ((dfx * i), 0), i, 0, size, 1) → Layer1Points
  7. Sequence(D + ((dfx * i), 0), i, 0, size, 1) → Layer3Points
  8. Sequence(C + ((dfx * i), 0), i, 0, size, 1) → Layer2Points
  9. Join({{Segment[C, Layer2Points(Length[Layer2Points])], Segment[B, Layer1Points(Length[Layer1Points])]}, Sequence[Segment[Layer1Points(i), Layer2Points(i)], i, 1, Length[Layer1Points], 1]}) → Kanten1
  10. Translate(Layer1Points, (Length[Vector[B, Layer1Points(2)] / 2], -0.2)) → BogenUntenStartEndList
  11. Translate(Layer1Points, (Length[Vector[B, Layer1Points(2)]], -0.2 - Length[Vector[B, Layer1Points(2)] / 2])) → BogenUntenMidList
  12. Join({{Segment[C, Layer2Points(Length[Layer2Points])], Segment[D, Layer3Points(Length[Layer3Points])]}, Sequence[Segment[Layer3Points(i), Layer2Points(i)], i, 1, Length[Layer1Points], 1]}) → Kanten2
  13. Textfield(input5) → InputBox5
  14. Textfield(inputText) → Eingabefeld1
  15. SpeechBubbleRight(A, 8.4, 1.8) → Speech2
  16. Translate(Layer3Points, (Length[Vector[B, Layer1Points(2)] / 2], 0.2)) → BogenObenStartEndList
  17. Translate(Layer3Points, (Length[Vector[B, Layer1Points(2)]], 0.2 + Length[Vector[B, Layer1Points(2)] / 2])) → BogenObenMidList
  18. Text(Div2Text, BogenObenMidList(4) + (0, 0.5), false, true, 0, 0) → Text12
  19. Text(Div2Text, BogenObenMidList(3) + (0, 0.5), false, true, 0, 0) → Text13
  20. Text(Div2Text, BogenObenMidList(1) + (0, 0.5), false, true, 0, 0) → Text15
  21. Text(Div2Text, BogenObenMidList(2) + (0, 0.5), false, true, 0, 0) → Text14
  22. Textfield(input6) → InputBox6
  23. Sequence(Text[Mult2Text, BogenUntenMidList(i) + (0, -0.25), false, true, 0, 0], i, 1, 4, 1) → Mult2Besch
  24. SpeechBubbleRight(A, 8.4, 1.8) → Vieleck1
  25. If(step < 8, 8 - step - 1, 0) → inputsol
  26. Sequence(CircumcircleArc[BogenUntenStartEndList(i), BogenUntenMidList(i) + (-0.3, 0), BogenUntenStartEndList(i + 1) + (-0.3, 0)], i, 1, 4, 1) → Mult2Bogen
  27. Sequence(BogenUntenStartEndList(i) + (-0.3, 0), i, 2, 5, 1) → Mult2Pfeile
  28. CircumcircleArc(BogenObenStartEndList(5), BogenObenMidList(4), BogenObenStartEndList(4) + (0.3, 0)) → BogenOben1
  29. CircumcircleArc(BogenObenStartEndList(4), BogenObenMidList(3), BogenObenStartEndList(3) + (0.3, 0)) → BogenOben2
  30. CircumcircleArc(BogenObenStartEndList(3), BogenObenMidList(2), BogenObenStartEndList(2) + (0.3, 0)) → BogenOben3
  31. CircumcircleArc(BogenObenStartEndList(2), BogenObenMidList(1), BogenObenStartEndList(1) + (0.3, 0)) → BogenOben4

AI Drawing Prompt Reference

On a coordinate plane, place several input boxes for a multi-choice style task. Construct three related layers of equally spaced points by drawing a bottom layer and a middle layer, then connect adjacent points on each layer to form boundary segments. Build a second (upper) point layer with its own adjacent connections, and between the upper and middle layers connect corresponding points to create continuous slanted edges. Using the endpoints of each adjacent pair, draw four circular arcs on the lower boundary and four circular arcs on the upper boundary, with the arc middle points guided by the chosen point-layer positions. Add four small labels near the upper arcs and include right-side speech bubbles to prompt the student to apply the power-operation rules.
The prompt above was compiled from the original drawing commands and is for reference only.