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Comparing Random Quotients by John Ulbright

Comparing Random Quotients by John Ulbright
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2015-05-19 01:35
SequenceCoordinate GeometryProbability & Statistics
This example demonstrates comparing random quotients. Key mathematical concepts include division and probability statistics. Using GeoGebra commands such as Sequence, Intersect, Point, etc., it constructs a series of random quotients and sorts them. Suitable for middle school and above students to learn division and probability statistics.

GeoGebra Commands & Parameters

  1. Sequence(Random[2, 9], i, 1, n) → factor1
  2. Sequence((Element[factor1, i] * Random[2, 9]), i, 1, n) → product
  3. Sequence(Element[product, i] / Element[factor1, i], i, 1, n) → answer
  4. Intersect(xAxis, yAxis) → A
  5. Point(xAxis) → B
  6. Segment(A, B) → a
  7. Sequence(Polygon[A + ((20 / (n - 1) * i), 0), A + (4, 0) + ((20 / (n - 1) * i), 0), 4], i, 0, n - 1) → rects
  8. Vector(C, D) → u
  9. If(IsInRegion[ONE, Element[rects, 1]], 1, (IsInRegion[ONE, Element[rects, 2]] * 2) + (IsInRegion[ONE, Element[rects, 3]] * 3) + (IsInRegion[ONE, Element[rects, 4]] * 4) + (IsInRegion[ONE, Element[rects, 5]] * 5)) → order1
  10. If(IsInRegion[TWO, Element[rects, 1]], 1, (IsInRegion[TWO, Element[rects, 2]] * 2) + (IsInRegion[TWO, Element[rects, 3]] * 3) + (IsInRegion[TWO, Element[rects, 4]] * 4) + (IsInRegion[TWO, Element[rects, 5]] * 5)) → order2
  11. If(IsInRegion[THREE, Element[rects, 1]], 1, (IsInRegion[THREE, Element[rects, 2]] * 2) + (IsInRegion[THREE, Element[rects, 3]] * 3) + (IsInRegion[THREE, Element[rects, 4]] * 4) + (IsInRegion[THREE, Element[rects, 5]] * 5)) → order3
  12. If(IsInRegion[FOUR, Element[rects, 1]], 1, (IsInRegion[FOUR, Element[rects, 2]] * 2) + (IsInRegion[FOUR, Element[rects, 3]] * 3) + (IsInRegion[FOUR, Element[rects, 4]] * 4) + (IsInRegion[FOUR, Element[rects, 5]] * 5)) → order4
  13. If(IsInRegion[FIVE, Element[rects, 1]], 1, (IsInRegion[FIVE, Element[rects, 2]] * 2) + (IsInRegion[FIVE, Element[rects, 3]] * 3) + (IsInRegion[FIVE, Element[rects, 4]] * 4) + (IsInRegion[FIVE, Element[rects, 5]] * 5)) → order5
  14. Remove(First[{order1, order2, order3, order4, order5}, n], {0, 0, 0, 0, 0}) → PlacedAnswers