乘除运算对不等式的影响

乘除运算对不等式的影响
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2015-09-18 18:01
①本范例演示乘除运算对两量间不等式关系的影响;②涉及核心数学概念:不等式性质、乘除运算规则;③作图要点:运用了Function, Point, If, Textfield, Sequence, CircumcircleArc, RandomElement, Random, Sum等GeoGebra命令与对象;④适合初中及以上学生,用于理解不等式在乘除运算下的变化规律。

GeoGebra 命令及参数

  1. Function(ticksize / 4, lowerbound - 0.5, upperbound + 0.5) → abovenumline
  2. Point(abovenumline) → A_d
  3. If(p_{boolean} ≟ true, Random[lowerbound + 5, upperbound - 5], x(A_d)) → x_A
  4. Textfield(ticksize) → inputBox3
  5. Textfield(lowerbound) → inputBox1
  6. Textfield(upperbound) → inputBox2
  7. Function(0, lowerbound - 0.5, upperbound + 0.5) → numline
  8. Sequence((i, 0), i, lowerbound, upperbound, 1) → listTicks
  9. Sequence(Text[i, (i - ticksize / 5, -0.95)], i, lowerbound, upperbound, ticksize) → ListxaxisNumbers
  10. Point(abovenumline) → B_d
  11. If(p_{boolean} ≟ true, Random[lowerbound + 5, upperbound - 5], x(B_d)) → x_B
  12. Textfield(k) → inputBox4
  13. If(SelectedIndex[ListOperation] > 2, 1 / k^(2), 1) → reciprolk
  14. CircumcircleArc(A, M_{A'A}, A') → c
  15. CircumcircleArc(B, M_{B'B}, B') → d
  16. Textfield(k) → InputBoxFactor
  17. If(k > 0, "No", "Yes") → InequalityChange
  18. If(SelectedElement[ListUserAnswerInequalityChange] ≟ InequalityChange, true, false) → CorrectAnswertoInequality
  19. If(x(A) > x(B), 3, 2) → Num1Greater
  20. RandomElement({-3, 2, -1, 3, -2, 2}) → kRandom
  21. If(x(A') > x(B'), 3, 2) → Num1newGreater
  22. Random(2, 3) → OpNumRandom
  23. If(x(A) < 0, floor(lg(abs(x(A)))) + 3, If[x(A) ≟ 0, 1, floor(lg(abs(x(A)))) + 1]) → n_{Aspace}
  24. If(x(B) < 0, floor(lg(abs(x(B)))) + 2, floor(lg(abs(x(B)))) + 1) → n_{Bspace}
  25. Sum(Sequence[{"\;"}, i, 1, 5 - n_{Aspace}]) → listspaceA
  26. If(SelectedIndex[listInput10thLine1] ≟ 2 ∧ k > 0 ∨ SelectedIndex[listInput10thLine1] ≟ 3 ∧ k < 0, true, false) → correctconclusion