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Equivalent Fractions: Choose Coarser/Finer Subdivisions and Identify Equivalent

Equivalent Fractions: Choose Coarser/Finer Subdivisions and Identify Equivalent
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2022-08-10 19:14
PolygonSequenceTransformationGeometric Construction
In collections Bruchzahlen: Erweitern und Kürzen
This GeoGebra worksheet presents three multiple‑choice questions on equivalent fractions. Students are shown a geometric whole divided into equal parts and must select the representation that is a coarser subdivision, then the one that is a finer subdivision, and finally identify a fraction equivalent to the given one. The core mathematical idea is equivalence of fractions (expanding and simplifying) and its visual representation. The construction uses the commands Rotate, Reverse, Sequence, Segment, Translate, LaTeX, Textfield and If to generate the shapes, animate rotations, produce lists of segments, translate them conditionally, and display feedback text. Designed for grade 5‑6 learners to develop number sense and fraction operation skills.

GeoGebra Commands & Parameters

  1. Rotate(ML, (-abs(β - 180°)), P2) → A
  2. Rotate(ML, abs(180° - α), P1) → B
  3. Reverse(Sequence[Translate[B, Vector[(i * (dxStück, 0))]], i, 0, 4]) → Top
  4. Sequence(Translate[A, Vector[(i * (dxStück, 0))]], i, 0, 4) → Bottom
  5. Reverse(Translate[Left, ((4 * dxStück), 0)]) → Right
  6. Sequence(Translate[{Segment[B, P1], Segment[P1, ML], Segment[ML, P2], Segment[P2, A]}, Vector[(i * (dxStück, 0))]], i, 1, 3) → m3
  7. Segment(ML, ML + ((4 * dxStück), 0)) → f
  8. Sequence(Translate[{Segment[P1, ML], Segment[ML, P2]}, Vector[(i * (dxStück, 0))]], i, 1, 3) → m4
  9. Translate(quadrat01, (dxStück, 0)) → quadrat02
  10. Translate(quadrat02, (dxStück, 0)) → quadrat03
  11. Translate(quadrat03, (dxStück, 0)) → quadrat04
  12. Translate(quadrat05, (dxStück, 0)) → quadrat06
  13. Translate(quadrat05, ((2 * dxStück), 0)) → quadrat07
  14. Translate(quadrat05, ((3 * dxStück), 0)) → quadrat08
  15. LaTeX(page, true, true) → Text4
  16. Textfield(input1) → InputBox1
  17. Textfield(input2) → InputBox2
  18. If(page ≟ 2, counter > 0 ∧ showBruchText, page ≟ 3, animationEnded, page ≟ 4, correctPage3, page ≟ 5, correctPage5, true) → fixed
  19. Segment(D, E) → h
  20. If(page ≟ 2 ∧ (¬showBruchText), true) → fixedSquares

AI Drawing Prompt Reference

Draw a whole divided into equal parts, containing multiple polygons and segments. The graph includes two polygons, one with a coarser subdivision and the other with a finer subdivision. There is also a segment representing the equivalent fraction between the two polygons. The graph also includes some squares and segments to represent the equivalence relationship of fractions. Ask the user to choose the coarser subdivision, finer subdivision, and an equivalent fraction.
The prompt above was compiled from the original drawing commands and is for reference only.