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Reduction with Change Factor

Reduction with Change Factor
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2023-04-26 16:09
FunctionCoordinate Geometry
In collections Prozentrechnung: Vermehrung und Verminderung
This example demonstrates the process of reduction using a change factor. Key mathematical concepts include percentage calculation and the application of change factors. Using GeoGebra commands such as Sequence, Join, Shuffle, etc., it dynamically shows the effect of change factors in various scenarios. Suitable for 7-8th grade students for in-depth practice.

GeoGebra Commands & Parameters

  1. Sequence(Random[1, 2], m, 1, 110) → listVermehrung, {1, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1}
  2. Join(Sequence[Shuffle[{1, 1, 1, 2, 3}], i, 1, 9]) → specialCase
  3. Shuffle(Sequence[Random[1, 9], i, 1, 110]) → randomNosForY, {5, 1, 9, 2, 2, 7, 2, 5, 1, 5, 4, 1, 9, 1, 3, 3, 1, 3, 4, 6, 5, 6, 7, 6, 2, 4, 5, 2, 2, 9, 4, 9, 5, 1, 9, 9, 8, 3, 9, 7, 9, 1, 1, 8, 2, 9, 5, 5, 7, 7, 6, 7, 8, 7, 4, 3, 7, 2, 8, 2, 1, 5, 9, 2, 2, 8, 3, 3, 2, 4, 8, 4, 5, 3, 4, 5, 4, 8, 5, 3, 3, 3, 9, 6, 8, 3, 7, 5, 3, 8, 2, 8, 8, 9, 7, 5, 6, 7, 3, 1, 4, 8, 4, 5, 2, 7, 6, 3, 7, 4}
  4. If(case ≟ 3, 0, Element[randomNosForY, Mod[questionCount, 100] + 1]) → numY
  5. Shuffle(Sequence[Random[1, 9], i, 1, 110]) → randomNosForZ, {6, 9, 8, 7, 3, 2, 7, 6, 1, 9, 9, 1, 8, 6, 9, 7, 6, 6, 7, 5, 3, 1, 7, 5, 8, 1, 6, 5, 8, 1, 2, 8, 9, 7, 7, 4, 4, 8, 2, 4, 4, 7, 8, 9, 1, 1, 1, 9, 1, 5, 4, 1, 6, 4, 9, 7, 3, 9, 2, 2, 4, 3, 1, 3, 7, 7, 1, 1, 6, 3, 7, 4, 2, 8, 2, 9, 5, 4, 4, 3, 4, 6, 8, 6, 4, 8, 5, 5, 5, 2, 1, 9, 6, 2, 1, 8, 8, 9, 4, 2, 9, 5, 3, 7, 9, 7, 9, 3, 4, 3}
  6. If(case ≟ 2, 0, randomNosForZ(Mod[questionCount, 100] + 1)) → numZ
  7. Shuffle(Sequence[Random[1, 3], i, 1, 110]) → listPosCorrect, {2, 3, 3, 2, 2, 3, 3, 2, 1, 2, 1, 1, 3, 1, 1, 2, 2, 2, 3, 3, 3, 2, 2, 3, 1, 1, 1, 2, 1, 2, 2, 1, 3, 3, 1, 2, 3, 3, 1, 1, 2, 2, 3, 2, 1, 3, 2, 3, 2, 1, 2, 3, 1, 1, 1, 1, 3, 3, 1, 3, 2, 2, 2, 3, 3, 1, 3, 1, 3, 3, 1, 3, 2, 2, 2, 1, 3, 3, 3, 2, 1, 3, 2, 3, 1, 3, 2, 3, 3, 3, 1, 2, 1, 1, 1, 1, 1, 2, 3, 2, 1, 1, 3, 1, 2, 3, 2, 2, 1, 3}
  8. Sequence(FB0 - (m * (0, sizefb)), m, 0, 2) → listFBpoints
  9. If(a, listFBpoints(1), If[b, listFBpoints(2), listFBpoints(3)]) → FB
  10. Textfield(input1) → InputBox1
  11. Textfield(input2) → InputBox2
  12. Shuffle(Sequence[Random[0, 1], i, 1, 110]) → randomNosForX, {0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1}
  13. Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
  14. Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
  15. Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  16. Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  17. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  18. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  19. Zip(RandomElement[{1, 2, 3} \ {m}], m, listPosCorrect) → listPosWrong1
  20. Zip(RandomElement[{1, 2, 3} \ {m, n}], m, listPosCorrect, n, listPosWrong1) → listPosWrong2
  21. If(posCorrect ≟ 1, TextCorrect, If[posWrong1 ≟ 1, TextWrong1, TextWrong2]) → Text1
  22. If(posCorrect ≟ 2, TextCorrect, If[posWrong1 ≟ 2, TextWrong1, TextWrong2]) → Text2
  23. If(posCorrect ≟ 3, TextCorrect, If[posWrong1 ≟ 3, TextWrong1, TextWrong2]) → Text3

AI Drawing Prompt Reference

Draw a graph showing the process of reduction with change factors, including randomly generated sequences, different colors or markers to indicate changes and special cases, and dynamically display the positions of coordinate points as they change with factors, suitable for 7-8th grade students to understand percentage calculations and the application of change factors.
The prompt above was compiled from the original drawing commands and is for reference only.