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Modeling Division as a Fraction

Modeling Division as a Fraction
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2022-11-21 19:18
Geometric ConstructionGraphing
This example demonstrates how division can be represented as fractions using pie charts. It helps students connect division operations with fractional concepts. Key mathematical ideas include fraction representation, division, and graphical visualization. Construction involves GeoGebra commands like Circle, Vector, Translate, and Sequence. Suitable for elementary students in grades 4-5 for mathematical exploration and classroom use.

GeoGebra Commands & Parameters

  1. Circle(C1, rCfr) → c
  2. Circle(C2, rCfr) → d
  3. Vector(C1, C2) → cTra
  4. Translate(C2, cTra) → C3
  5. Translate(C3, cTra) → C4
  6. Circle(C3, rCfr) → e
  7. Circle(C4, rCfr) → f
  8. Translate(C4, cTra) → C5
  9. Circle(C5, rCfr) → g
  10. Sequence(Rotate[A, ((2 * pi / b) * k), C1], k, 1, b) → settCfr1
  11. If(a ≟ 5, (1.5, 0), (x(C1), 0)) → CT1'
  12. CircleSector(C1, settCfr1(2), settCfr1(1)) → sect1gr
  13. CircleSector(C1, settCfr1(1), settCfr1(2)) → sect1pi
  14. CircleSector(C1, settCfr1(2), settCfr1(3)) → sect1ch
  15. Translate(sect1gr, cTra) → sect2gr
  16. Translate(sect1gr, Vector[(2 * cTra)]) → sect3gr
  17. Translate(sect1gr, Vector[(3 * cTra)]) → sect4gr
  18. Translate(sect1gr, Vector[(4 * cTra)]) → sect5gr
  19. Translate(sect1pi, cTra) → sect2pi
  20. Translate(sect1pi, Vector[(2 * cTra)]) → sect3pi
  21. Translate(sect1pi, Vector[(3 * cTra)]) → sect4pi
  22. Translate(sect1pi, Vector[(4 * cTra)]) → sect5pi
  23. Translate(sect1ch, cTra) → sect2ch
  24. Translate(sect1ch, Vector[(2 * cTra)]) → sect3ch
  25. Translate(sect1ch, Vector[(3 * cTra)]) → sect4ch
  26. Translate(sect1ch, Vector[(4 * cTra)]) → sect5ch
  27. Vector(C1, CT1') → toq2c1
  28. Vector(C2, CT2') → toq2c2
  29. Vector(C3, CT3') → toq2c3
  30. Vector(C4, CT4') → toq2c4
  31. Vector(C5, CT5') → toq2c5
  32. Take({sect1ch, sect2ch, sect3ch, sect4ch, sect5ch}, 1, a) → allSecCh
  33. Take({sect1gr, sect2gr, sect3gr, sect4gr, sect5gr}, 1, a) → allSecGr
  34. Zip(Translate[p, Vector[q]], p, allSecPink, Vector[q], If[1 ≤ aniSli ≤ 2, (allq2Vec * (aniSli - 1)), 2 < aniSli ≤ 3, allq2Vec]) → allTraPink
  35. Zip(Translate[p, Vector[q]], p, allOutlinesPink, Vector[q], If[1 ≤ aniSli ≤ 2, (allq2Vec * (aniSli - 1)), 2 < aniSli ≤ 3, allq2Vec]) → allTraOutPink
  36. SelectedIndex(ddMenu) → is
  37. If(a ≟ 5, allOutlinesGr, a ≟ 4, {allOutlinesGr(2), allOutlinesGr(3), allOutlinesGr(4), allOutlinesGr(5)}, a ≟ 3, {allOutlinesGr(2), allOutlinesGr(3), allOutlinesGr(4)}, a ≟ 2, {allOutlinesGr(2), allOutlinesGr(4)}, {allOutlinesGr(3)}) → allOutlinesGrDisplay
  38. If(a ≟ 5, allSecPink, a ≟ 4, {allSecPink(2), allSecPink(3), allSecPink(4), allSecPink(5)}, a ≟ 3, {allSecPink(2), allSecPink(3), allSecPink(4)}, a ≟ 2, {allSecPink(2), allSecPink(4)}, {allSecPink(3)}) → allSecPinkDisplay
  39. If(a ≟ 5, allOutlinesCh, a ≟ 4, {allOutlinesCh(2), allOutlinesCh(3), allOutlinesCh(4), allOutlinesCh(5)}, a ≟ 3, {allOutlinesCh(2), allOutlinesCh(3), allOutlinesCh(4)}, a ≟ 2, {allOutlinesCh(2), allOutlinesCh(4)}, {allOutlinesCh(3)}) → allOutlinesChDisplay
  40. If(a ≟ 5, allOutlinesPink, a ≟ 4, {allOutlinesPink(2), allOutlinesPink(3), allOutlinesPink(4), allOutlinesPink(5)}, a ≟ 3, {allOutlinesPink(2), allOutlinesPink(3), allOutlinesPink(4)}, a ≟ 2, {allOutlinesPink(2), allOutlinesPink(4)}, {allOutlinesPink(3)}) → allOutlinesPinkDisplay
  41. If(a ≟ 5, allTraOutPink, a ≟ 4, {allTraOutPink(2), allTraOutPink(3), allTraOutPink(4), allTraOutPink(5)}, a ≟ 3, {allTraOutPink(2), allTraOutPink(3), allTraOutPink(4)}, a ≟ 2, {allTraOutPink(2), allTraOutPink(4)}, {allTraOutPink(3)}) → allTraOutPinkDisplay
  42. If(a ≟ 5, allTraPink, a ≟ 4, {allTraPink(2), allTraPink(3), allTraPink(4), allTraPink(5)}, a ≟ 3, {allTraPink(2), allTraPink(3), allTraPink(4)}, a ≟ 2, {allTraPink(2), allTraPink(4)}, a ≟ 1, {allTraPink(3)}) → allTraPinkDisplay
  43. Translate(sect1pi, Vector[If[1 ≤ aniSli ≤ 2, Vector[(toq2c1 * (aniSli - 1))], 2 < aniSli ≤ 3, toq2c1]]) → tra1pi
  44. Translate(sect2pi, Vector[If[1 ≤ aniSli ≤ 2, Vector[(toq2c2 * (aniSli - 1))], 2 < aniSli ≤ 3, toq2c2]]) → tra2pi
  45. Translate(sect3pi, Vector[If[1 ≤ aniSli ≤ 2, Vector[(toq2c3 * (aniSli - 1))], 2 < aniSli ≤ 3, toq2c3]]) → tra3pi
  46. Translate(sect4pi, Vector[If[1 ≤ aniSli ≤ 2, Vector[(toq2c4 * (aniSli - 1))], 2 < aniSli ≤ 3, toq2c4]]) → tra4pi
  47. Translate(sect5pi, Vector[If[1 ≤ aniSli ≤ 2, Vector[(toq2c5 * (aniSli - 1))], 2 < aniSli ≤ 3, toq2c5]]) → tra5pi
  48. Translate(sect1pi, Vector[If[1 ≤ aniSli ≤ 2, Vector[(toq2c1 * (aniSli - 1))], 2 < aniSli ≤ 3, toq2c1]]) → traOut1pi
  49. Translate(sect2pi, Vector[If[1 ≤ aniSli ≤ 2, Vector[(toq2c2 * (aniSli - 1))], 2 < aniSli ≤ 3, toq2c2]]) → traOut2pi
  50. Translate(sect3pi, Vector[If[1 ≤ aniSli ≤ 2, Vector[(toq2c3 * (aniSli - 1))], 2 < aniSli ≤ 3, toq2c3]]) → traOut3pi
  51. Translate(sect4pi, Vector[If[1 ≤ aniSli ≤ 2, Vector[(toq2c4 * (aniSli - 1))], 2 < aniSli ≤ 3, toq2c4]]) → traOut4pi
  52. Translate(sect5pi, Vector[If[1 ≤ aniSli ≤ 2, Vector[(toq2c5 * (aniSli - 1))], 2 < aniSli ≤ 3, toq2c5]]) → traOut5pi

AI Drawing Prompt Reference

Draw a set of equal-radius circles on the plane using a consistent translation step so multiple circles sit side by side. From the first circle, construct several circular sectors by taking one sector between fixed consecutive angle boundaries and then rotating it around the circle center to create repeated, equal-angle slices. For the same selected sector type, replicate and move those sector pieces to the neighboring circles using the same translation direction and step, so the corresponding angular portions line up across circles. The final image should clearly show division-as-fractions via pie-like partitioned segments that maintain identical angle ranges before and after translation.
The prompt above was compiled from the original drawing commands and is for reference only.