MathPlotAI Logo MathPlotAI

Compute an increased base value using a change factor (multiple equivalent metho

Compute an increased base value using a change factor (multiple equivalent metho
Loading the math board and drawing, please wait…
2023-04-26 15:17
FunctionGeometric ConstructionSlider AnimationGraphing
In collections Prozentrechnung: Vermehrung und Verminderung
This GeoGebra lesson demonstrates how to calculate the new value G+ after a base quantity G is increased by p%, and how to judge which multiple-choice methods are equivalent. It centers on percentage change, the change factor (1 ± p/100), and the relationship between G and the increased value G+. The construction uses a sequence of geometric/text elements to present inputs and evaluate answers: commands and mechanisms from the construction summary include Sequence, Point, Textfield for creating labeled points and displaying values; If for checking user inputs against correct0/correct1/… and providing feedback; CircleArc and Segment for visualizing the proportional/percentage structure; Keep to preserve selected objects; Zip to package outputs. Additional controls such as sizefaktor/sizeall/height manage scaling and step progression (step/maxstep), while UI elements (btnLos, btnNext, btnBack, showBtn) support interactive practice. Suitable for Grades 7–8, for strengthening percent word problems, change-factor interpretation, and reasoning about equivalent solution strategies.

GeoGebra Commands & Parameters

  1. Sequence(O3 + (m * (length / 150, 0)), m, 0, 150) → listPointsO3AllSmall
  2. Sequence(O3 + (m * (length / parts, 0)), m, 0, parts) → listPointsO3All
  3. Point(listPointsO3AllSmall) → P3
  4. Sequence(O1 + (sizefaktor * Vector[O1, O2]) + (0, height / 2) + (m * (size / 20, 0)), m, 0, (20 * (1 - sizefaktor))) → l1
  5. Point(l1) → P
  6. Point(Line[O1, yAxis]) → Q1
  7. Textfield(input1) → Eingabefeld1
  8. Textfield(input2) → Eingabefeld2
  9. If(input3, A, B) → Pchosen
  10. CircleArc(Midpoint[A1, A2] + (arrowdepth, 0), A1, A2) → e
  11. CircleArc(Midpoint[A3, A4] + ((-arrowdepth), 0), A4, A3) → c
  12. CircleArc(Midpoint[B3, B4] + ((-arrowdepth), 0), B4, B3) → d
  13. CircleArc(Midpoint[B1, B2] + (arrowdepth, 0), B1, B2) → f
  14. Textfield(input5) → Eingabefeld5
  15. Textfield(input6) → Eingabefeld6
  16. Point(Line[O3, yAxis]) → O4
  17. Sequence(O4 + (m * (length / parts, 0)), m, 0, parts) → listPointsO4All
  18. KeepIf(x(M) ≤ Max[x(listPointsO3AllSmall(101)), x(P3)], M, listPointsO3All) → listPointsO3
  19. Zip(Segment[M, M - (0, height)], M, listPointsO3) → listLinesO3
  20. KeepIf(x(M) ≤ Max[x(listPointsO3All(21)), x(P3)], M, listPointsO4All) → listPointsO4
  21. Zip(Segment[M, M - (0, height)], M, listPointsO4) → listLinesO4
  22. Segment(P3, (x(P3), y(O4) - height)) → g
  23. Sequence(Text["\textsf\small{" + ((10 * m)) + (("%" * "}")), ((m * length / ((0.5 * parts))) + x(O3), y(O3)), true, true, -0, 1], m, 1, (0.5 * parts)) → listTextAll
  24. Sequence(Text["\textsf{" + ((16 * m)) + (("kg" * "}")), ((m * length / ((0.5 * parts))) + x(O4), y(O4) - height - 0.83), true, true, -0, 1], m, 1, (0.5 * parts)) → listTextAllB
  25. Textfield(input0) → Eingabefeld0
  26. KeepIf((10 * IndexOf[M, listTextAll]) + 2 ≤ Max[102, IndexOf[P3, listPointsO3AllSmall]], M, listTextAll) → listTextShow
  27. KeepIf((10 * IndexOf[M, listTextAllB]) + 2 ≤ Max[102, IndexOf[P3, listPointsO3AllSmall]], M, listTextAllB) → listTextShowB

AI Drawing Prompt Reference

Create a visual representation of percentage change. Include a base value and a change factor controlled by a slider, with geometric shapes and text to display the new value after the base value is increased. Use different methods to verify the results are consistent. The graphic should feature multiple points, line segments, arcs, and text to illustrate the change process and outcomes, with interactive elements for user input and answer checking.
The prompt above was compiled from the original drawing commands and is for reference only.