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Comparing Fractions by Lew W. S.

Comparing Fractions by Lew W. S.
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2019-03-17 20:10
Coordinate GeometryGeometric Construction
This activity allows students to explore the concept of equivalent fractions visually, particularly when the denominators or numerators are the same. Using GeoGebra commands such as Circle, Point, LCM, Sequence, Midpoint, If, Vector, Translate, GCD, and Textfield, students can gain a deeper understanding of fraction properties. Suitable for students from upper elementary to middle school.

GeoGebra Commands & Parameters

  1. Circle(A_1, r) → c
  2. Point(c) → B
  3. Circle(A_2, r) → d
  4. LCM(denominator_1, denominator_2) → equivalentdenominator
  5. Sequence(Segment[A_2, Rotate[C_2, r°, A_2]], r, 0, 360, 360 / denominator_2) → PIEALL_2
  6. Sequence(Segment[A_2, Rotate[C_2, r°, A_2]], r, 0, 360, 360 / equivalentdenominator) → PIEALL_{2E}
  7. Sequence(CircleSector[A_2, Rotate[C_2, ((-r) - 360 / equivalentdenominator)°, A_2], Rotate[C_2, ((-r))°, A_2]], r, 0, (360 / equivalentdenominator * numerator_{2E}) - 360 / equivalentdenominator, 360 / equivalentdenominator) → PIESECTION_{2E}
  8. Midpoint(A_1, A_2) → A_{mid}
  9. Circle(A_1, r) → PIESECTION_{1whole}
  10. Circle(A_2, r) → PIESECTION_{2whole}
  11. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / denominator_2)°, A_2]], r, 0, (360 / denominator_2 * numerator_2) - 360 / denominator_2, 360 / denominator_2) → PIESECTION_{2subtract}
  12. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / equivalentdenominator)°, A_2]], r, 0, (360 / equivalentdenominator * numerator_{2E}) - 360 / equivalentdenominator, 360 / equivalentdenominator) → PIESECTION_{2Esubtract}
  13. If(ShiftCircleLeftRight ≟ (2.5 * r), 1, 0) → trigger
  14. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / equivalentdenominator)°, A_2]], r, (numerator_{2E} * 360 / equivalentdenominator), (360 / equivalentdenominator * (numerator_{1E} - 1)), 360 / equivalentdenominator) → PIESECTION_{finalsubtract1}
  15. Vector(A_2, A_{2end1}) → u
  16. Translate(PIESECTION_{finalsubtract1}, Vector[(DetachPie * u)]) → PIESECTION_{finalsubtract2}
  17. Vector(A_2, A_{2end2}) → v
  18. Circle(A_2, r) → PIESECTION_{whole1}
  19. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / equivalentdenominator)°, A_2]], r, ((equivalentdenominator - numerator_{2E}) * 360 / equivalentdenominator), (360 / equivalentdenominator * (mixednumerator + equivalentdenominator - numerator_{2E} - 1)), 360 / equivalentdenominator) → PIESECTION_{part1}
  20. Circle(A_2, r) → PIESECTION_{whole2}
  21. Translate(PIESECTION_{whole2}, Vector[(DetachPie * v)]) → PIESECTION_{whole2v}
  22. Translate(PIESECTION_{part1}, Vector[(DetachPie * v)]) → PIESECTION_{part2}
  23. Translate(PIESECTION_{whole1}, Vector[(DetachPie * u)]) → PIESECTION_{whole1u}
  24. If(subtractfractions, "Subtraction of Fractions", "Addition of Fractions") → textTitle
  25. GCD(equivalentnumerator, equivalentdenominator) → ResultGCD
  26. GCD(abs(equivalentnumerator_{subtract}), equivalentdenominator) → ResultGCD_{subtract}
  27. If(abs(equivalentnumerator) < equivalentdenominator, If[ResultGCD ≟ 1, (4.5 * r), (3.5 * r)], If[ResultGCD ≟ 1, 0, (-2 * r)]) → x_{textEquivalentsign3}
  28. If(ResultGCD ≟ 1, (-0.25 * r), If[equivalentnumerator < equivalentdenominator, (5 * r), (-0.25 * r)]) → x_{textposition2}
  29. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / equivalentdenominator)°, A_2]], r, (numerator_{1E} * 360 / equivalentdenominator), (360 / equivalentdenominator * (numerator_{2E} - 1)), 360 / equivalentdenominator) → PIESECTION_{negativefinalsubtract1}
  30. Vector(A_2, A_{2end3}) → w
  31. Translate(PIESECTION_{negativefinalsubtract1}, Vector[(DetachPie * v)]) → PIESECTION_{negativefinalsubtract2}
  32. Textfield(numerator_1) → InputBox1
  33. Textfield(denominator_1) → InputBox2
  34. Textfield(numerator_2) → InputBox3
  35. Textfield(denominator_2) → InputBox4
  36. If(¬subtractfractions, " + ", " − ") → addsign2
  37. Sequence(CircleSector[A_2, Rotate[C_2, ((-r) - 360 / denominator_2)°, A_2], Rotate[C_2, ((-r))°, A_2]], r, 0, (360 / denominator_2 * numerator_2) - 360 / denominator_2, 360 / denominator_2) → PIESECTION_2
  38. Sequence(CircleSector[A_2, Rotate[C_2, r°, A_2], Rotate[C_2, (r + 360 / denominator_2)°, A_2]], r, 0, (360 / denominator_2 * numerator_2) - 360 / denominator_2, 360 / denominator_2) → PIESECTION_{2Compare}
  39. LCM(numerator_1, numerator_2) → equivalentnumerator_{compare}
  40. Sequence(Segment[A_1, Rotate[C_1, r°, A_1]], r, 0, 360, 360 / equivalentdenominator) → PIEALL_{1E}
  41. Sequence(Segment[A_1, Rotate[C_1, r°, A_1]], r, 360 / denominator_1, 360, 360 / denominator_1) → PIEALL_1
  42. Sequence(CircleSector[A_1, Rotate[C_1, r°, A_1], Rotate[C_1, (r + 360 / denominator_1)°, A_1]], r, 0, (360 / denominator_1 * numerator_1) - 360 / denominator_1, 360 / denominator_1) → PIESECTION_1
  43. Sequence(CircleSector[A_1, Rotate[C_1, r°, A_1], Rotate[C_1, (r + 360 / equivalentdenominator)°, A_1]], r, 0, (360 / equivalentdenominator * numerator_{1E}) - 360 / equivalentdenominator, 360 / equivalentdenominator) → PIESECTION_{1E}
  44. Sequence(Segment[A_2, Rotate[C_2, r°, A_2]], r, 0, 360, 360 / denominator_{2Ecompare}) → PIEALL_{2samenumerator}
  45. Sequence(Segment[A_1, Rotate[C_1, r°, A_1]], r, 0, 360, 360 / denominator_{1Ecompare}) → PIEALL_{1samenumerator}