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Comparing Fractions and Finding Midpoints

Comparing Fractions and Finding Midpoints
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2023-11-29 21:38
SequenceCoordinate GeometryGeometric ConstructionSlider Animation
In collections Ordnen und Vergleichen von Bruchzahlen
This example demonstrates how to compare two fractions and find the midpoint fraction between them using GeoGebra. Key math concepts include fraction comparison, midpoint calculation, and rational number concepts. GeoGebra commands used in the construction summary are: Sequence, Circle, Textfield, SpeechBubbleLeft, Midpoint, Point, Segment, Join, Polygon, IsInRegion, If, Text. Suitable for upper elementary grades (5-6) to teach and practice fraction comparison and rational number concepts.

GeoGebra Commands & Parameters

  1. Sequence(Zentrum - ((Vector[ZSR, ZSL] * 1) * masterzoom / 80) - ((Vector[ZSR, ZSL] * i) * masterzoom / 10), i, 0, 1) → U2Rechts
  2. Sequence(Zentrum + ((Vector[ZSR, ZSL] * 7) * masterzoom / 80) + ((Vector[ZSR, ZSL] * i) * masterzoom / 10), i, 0, 6) → U2Links
  3. Sequence(Zentrum - ((Vector[ZSR, ZSL] * 1) * masterzoom / 80) - ((Vector[ZSR, ZSL] * i) * masterzoom / 5), i, 0, 1) → U1Rechts
  4. Sequence(Zentrum + ((Vector[ZSR, ZSL] * 15) * masterzoom / 80) + ((Vector[ZSR, ZSL] * i) * masterzoom / 5), i, 0, 3) → U1Links
  5. Circle(U1Rechts(1), 0.3) → B2Goal
  6. Circle(U1Links(2), 0.3) → B1Goal
  7. Textfield(input1) → InputBox1
  8. Textfield(input2) → InputBox2
  9. Textfield(input3) → InputBox3
  10. Textfield(input4) → InputBox4
  11. SpeechBubbleLeft(SpeechA1, 9, 3) → Step1Speech
  12. SpeechBubbleLeft(SpeechSpecial, 10.5, 2.4) → Step2Speech
  13. SpeechBubbleLeft(SpeechA2, 12, 1.5) → Step3Speech
  14. Midpoint(U1Links(1), U1Rechts(1)) → MPetrol1
  15. Circle(MPetrol1, 2.8) → Petrol1
  16. SpeechBubbleLeft(SpeechA4, 12, 2.5) → Step4Speech
  17. Point(StaengelPunkte) → ZoomPunkt
  18. Segment(StaengelStart, StaengelEnd) → Staengel
  19. SpeechBubbleLeft(SpeechA5, 11, 3) → Step5Speech
  20. Midpoint(U2Links(1), U2Rechts(1)) → MPetrol2
  21. Circle(MPetrol2, 2.8) → Petrol2
  22. SpeechBubbleLeft(SpeechA7, 11, 3) → Step7Speech
  23. Textfield(input5) → InputBox5
  24. Textfield(input6) → InputBox6
  25. SpeechBubbleLeft(SpeechA8, 11, 3) → Step8Speech
  26. SpeechBubbleLeft(SpeechA9, 11.5, 2.2) → Step9Speech
  27. Segment(ZSL, ZSR) → h
  28. Sequence(Zentrum + ((Vector[ZSR, ZSL] * 3) * masterzoom / 80) + ((Vector[ZSR, ZSL] * i) * masterzoom / 20), i, 0, 14) → U3Links
  29. Sequence(Zentrum - ((Vector[ZSR, ZSL] * 1) * masterzoom / 80) - ((Vector[ZSR, ZSL] * i) * masterzoom / 20), i, 0, 3) → U3Rechts
  30. Sequence(Zentrum + (Vector[ZSR, ZSL] * masterzoom / 80) + ((Vector[ZSR, ZSL] * i) * masterzoom / 40), i, 0, 30) → U4Links
  31. Sequence(Zentrum - ((Vector[ZSR, ZSL] * 1) * masterzoom / 80) - ((Vector[ZSR, ZSL] * i) * masterzoom / 40), i, 0, 7) → U4Rechts
  32. Sequence(Zentrum + ((Vector[ZSR, ZSL] * i) * masterzoom / 80), i, 0, 10) → U5Links
  33. Sequence(Zentrum - ((Vector[ZSR, ZSL] * i) * masterzoom / 80), i, 0, 7) → U5Rechts
  34. Join({Sequence[Segment[U1Links(i) + (0, 0.15), U1Links(i) + (0, -0.15)], i, 1, 5], Sequence[Segment[U1Rechts(i) + (0, 0.15), U1Rechts(i) + (0, -0.15)], i, 1, 5]}) → U1Strecken
  35. Join({Sequence[Segment[U2Links(i) + (0, 0.15), U2Links(i) + (0, -0.15)], i, 1, 5], Sequence[Segment[U2Rechts(i) + (0, 0.15), U2Rechts(i) + (0, -0.15)], i, 1, 5]}) → U2Strecken
  36. Join({Sequence[Segment[U3Links(i) + (0, 0.15), U3Links(i) + (0, -0.15)], i, 1, 5], Sequence[Segment[U3Rechts(i) + (0, 0.15), U3Rechts(i) + (0, -0.15)], i, 1, 5]}) → U3Strecken
  37. Join({Sequence[Segment[U4Links(i) + (0, 0.15), U4Links(i) + (0, -0.15)], i, 1, 5], Sequence[Segment[U4Rechts(i) + (0, 0.15), U4Rechts(i) + (0, -0.15)], i, 1, 5]}) → U4Strecken
  38. Join({Sequence[Segment[U5Links(i) + (0, 0.15), U5Links(i) + (0, -0.15)], i, 1, 5], Sequence[Segment[U5Rechts(i) + (0, 0.15), U5Rechts(i) + (0, -0.15)], i, 1, 5]}) → U5Strecken
  39. Segment(C, ZSL) → i
  40. Segment(ZSR, D) → j
  41. Segment(U1Links(4) + (0, 0.3), U1Links(4) + (0, -0.3)) → f
  42. Segment(U1Rechts(2) + (0, 0.3), U1Rechts(2) + (0, -0.3)) → g
  43. Polygon({WhiteCheese1E1, WhiteCheese1E2, WhiteCheese2E2, WhiteCheese2E1}) → validatebox
  44. IsInRegion(B1Pos, validatebox) → b1inbox
  45. IsInRegion(B2Pos, validatebox) → b2inbox
  46. IsInRegion(B1Pos, B1Goal) → b1correct
  47. IsInRegion(B2Pos, B2Goal) → b2correct
  48. Midpoint(U, Q) → PlusZoom1
  49. Midpoint(R, Q) → PlusZoom2
  50. Midpoint(S, R) → PlusZoom3
  51. Midpoint(T, S) → PlusZoom4
  52. Join({Sequence[Segment[PlusZoomPunkte(i) + (0, 0.15), PlusZoomPunkte(i) + (0, -0.15)], i, 1, 5], Sequence[Segment[PlusZoomPunkte(i) + (0, 0.15), PlusZoomPunkte(i) + (0, -0.15)], i, 1, 4]}) → PlusZoomStrecken
  53. If(step ≟ 3, 2 / 5, step ≟ 5, 3 / 5, 7 / 10) → grenzelinks
  54. If(step ≟ 3, input1 / input2 ≠ grenzesol ∧ grenzelinks < input1 / input2 < grenzerechts, step ≟ 5, input3 / input4 ≠ grenzesol ∧ grenzelinks < input3 / input4 < grenzerechts, input5 / input6 ≠ grenzesol ∧ grenzelinks < input5 / input6 < grenzerechts) → showhint
  55. If(masterzoom < 1.5, 5, 160, 1.5 ≤ masterzoom < 3, 10, 3 ≤ masterzoom < 6, 20, 6 ≤ masterzoom < 12, 40, 12 ≤ masterzoom < 22, 80) → maxnenner
  56. If(maxnenner ≟ 160, 1, maxnenner ≟ 5, 32, maxnenner ≟ 80, 2, maxnenner ≟ 40, 4, maxnenner ≟ 20, 8, maxnenner ≟ 10, 16) → helperdiv
  57. Text(Dyn35, U1Links(1) + (0, 0.9), false, true, 0, 0) → Text35
  58. Text(Dyn1320, U3Links(3) + (0, 0.9), false, true, 0, 0) → Text37
  59. Text(Dyn710, U2Links(1) + (0, 0.9), false, true, 0, 0) → Text38
  60. Text(Dyn1520, U3Links(1) + (0, 0.9), false, true, 0, 0) → Text39
  61. Text(Dyn45, U1Rechts(1) + (0, 0.9), false, true, 0, 0) → Text40
  62. Text(Dyn2940, U4Links(3) + (0, 0.9), false, true, 0, 0) → Text41
  63. Text(Dyn3140, U4Links(1) + (0, 0.9), false, true, 0, 0) → Text42
  64. Text(Dyn6180, U5Links(3) + (0, 0.9), false, true, 0, 0) → Text43
  65. Text(Dyn6380, U5Links(1) + (0, 0.9), false, true, 0, 0) → Text44

AI Drawing Prompt Reference

Draw a coordinate-plane style diagram with several vertical ruler-like tick columns. Create point sequences at equal spacing along two opposite directions from a shared reference, then connect short offset segments to form a grid of small bars on the left and right sides. Mark two matching answer areas by taking two midpoints between paired points, and drawing circles with the same radius centered at those midpoints. Add multiple text input boxes for the fraction-comparison and midpoint values, plus left-facing speech bubbles to guide the steps. Include a validation polygon region and show the checker regions around the two circle targets.
The prompt above was compiled from the original drawing commands and is for reference only.