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Equivalent Expressions GeoGebra Demo

Equivalent Expressions GeoGebra Demo
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2019-01-19 02:52
FunctionProbability & StatisticsGeometric Construction
This example dynamically demonstrates the concept of equivalent expressions using GeoGebra, involving core math concepts like algebraic operations, conditional probability, isosceles triangles, and parallelograms. It leverages commands such as Sequence, Join, LaTeX, Element, Zip, and Text, along with objects like tileWidthShorter and tileHeight. Ideal for high school mathematics education, combining algebraic manipulation with geometric visualization.

GeoGebra Commands & Parameters

  1. Sequence((-8 + tileWidthLong + 1 + tileWidthShort + 1, j), j, 3, 3 - (3 * tileHeight), (-(1 + tileHeight))) → fixedFrames3
  2. Sequence((-8 + tileWidthLong + 1, j), j, 3, 3 - (3 * tileHeight), (-(1 + tileHeight))) → fixedFrames2
  3. Sequence((-8, j), j, 3, 3 - (3 * tileHeight), (-(1 + tileHeight))) → fixedFrames1
  4. Sequence(Polygon[{tableAnchor + (col1Width, 0 - (rowHeight * i)), tableAnchor + (col1Width + col2Width, 0 - (rowHeight * i)), tableAnchor + (col1Width + col2Width, 0 - (rowHeight * i) - rowHeight), tableAnchor + (col1Width, ((-rowHeight) * i) - rowHeight)}], i, 0, lastRow - 1) → tableCol2
  5. Join({fixedFrames1, fixedFrames2, fixedFrames3}) → fixedFrameAnchors
  6. LaTeX(UnicodeToLetter[10003]) → cmark
  7. LaTeX(UnicodeToLetter[10007]) → xmark
  8. Sequence(Polygon[{tableAnchor + (0, 0 - (rowHeight * i)), tableAnchor + (col1Width, 0 - (rowHeight * i)), tableAnchor + (col1Width, 0 - (rowHeight * i) - rowHeight), tableAnchor + (0, ((-rowHeight) * i) - rowHeight)}], i, 0, lastRow - 1) → tableCol1
  9. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  10. Join({Zip[Polygon[A, A + (tileWidthLong, 0), A + (tileWidthLong, (-tileHeight)), A + (0, (-tileHeight))], A, fixedFrames1], Zip[Polygon[A, A + (tileWidthShort, 0), A + (tileWidthShort, (-tileHeight)), A + (0, (-tileHeight))], A, fixedFrames2], Zip[Polygon[A, A + (tileWidthShorter, 0), A + (tileWidthShorter, (-tileHeight)), A + (0, (-tileHeight))], A, fixedFrames3]}) → frames
  11. Element(frames, 1) → frame1
  12. Element(frames, 2) → frame2
  13. Element(frames, 3) → frame3
  14. Element(frames, 4) → frame4
  15. Element(frames, 5) → frame5
  16. Element(frames, 6) → frame6
  17. Element(frames, 7) → frame7
  18. Element(frames, 8) → frame8
  19. Element(frames, 9) → frame9
  20. Element(cells, 1) → cell1
  21. Element(cells, 2) → cell2
  22. Element(cells, 3) → cell3
  23. Element(cells, 4) → cell4
  24. Element(cells, 5) → cell5
  25. Element(cells, activeCell) → highlightedCell
  26. Element(tableCol1, 1) → col1HeaderCell
  27. Element(tableCol2, 1) → col2HeaderCell
  28. Zip(A ≟ B, A, itemsInCells, B, {7, 2, 3, 6, 1}) → cellsCorrect
  29. Zip(Text[If[A, cmark, ""], Vertex[B, 2] + symbolOffset], A, cellsCorrect, B, cells) → cmarkList
  30. Zip(Text[If[¬A, xmark, ""], Vertex[B, 2] + symbolOffset], A, cellsCorrect, B, cells) → xmarkList
  31. Text("... is equivalent to this expression", tableAnchor + (0.25 + col1Width, ((-rowHeight)) / 1.75)) → col2Header
  32. Text("This expression ...", tableAnchor + (0.25, ((-rowHeight)) / 1.75)) → col1Header
  33. LaTeX("\text{You found the equivalent expressions.}") → feedback
  34. Element(frames, activeTile) → highlightedTile
  35. Text("(1-x)(x-3)^2", tableAnchor + (0.25, ((-rowHeight) * 5) - 0.3), true, true) → expression5
  36. Text("x^3+3x^2+3x+1", tableAnchor + (0.25, ((-rowHeight) * 4) - 0.3), true, true) → expression4
  37. Text("(x+y+3)^2", tableAnchor + (0.25, ((-rowHeight) * 3) - 0.3), true, true) → expression3
  38. Text("(x+3)(-3x-11)", tableAnchor + (0.25, ((-rowHeight) * 2) - 0.3), true, true) → expression2
  39. Text("x^2-16x+64", tableAnchor + (0.25, (-rowHeight) - 0.3), true, true) → expression1