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加州两城海拔比较

加州两城海拔比较
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2015-10-13 23:24
解析几何最值优化不等式
所属专题 CCSS Support Algebra I Unit 1 CCSS Support Math I Unit 1
本例通过比较加州El Centro和Imperial两城的海拔，使用不等式进行描述。涉及的核心数学概念包括不等式和海拔概念。使用了Polygon, Segment, Sequence等GeoGebra命令进行构造。适合初中数学教学。

GeoGebra 命令及参数

  1. Polygon((1.8, y(Corner[1])), Corner[2], Corner[3], (1.8, y(Corner[4]))) → Mask1, a, b, c, d
  2. Polygon(PT1, PT2, PT3, PT4) → Mask2, b_1, c_1, d_1, e
  3. Segment((0, 0), (0, 1)) → i
  4. Segment(C, B) → f
  5. LaTeX("\text{Write an inequality comparing the elevations of the two cities.}") → text2
  6. LaTeX("\text{Plot the elevations on a number line.}") → text3
  7. LaTeX("\text{representing the two elevations can be seen in comparison with}") → text5
  8. LaTeX("\text{each other.}") → text6
  9. Sequence(Segment[A + (i, 0), A + (i, 0.5)], i, -20, 0) → list1
  10. LaTeX("\text{Write an inequality that compares the elevations of the two cities.}") → text13
  11. LaTeX("\text{lower than El Centro’s elevation.}") → text16
  12. LaTeX("\text{since El Centro’s elevation is higher than Imperial’s elevation.}") → text18
  13. LaTeX("\text{Imperial}") → text23
  14. LaTeX("\text{El Centro}") → text24
  15. LaTeX("\text{Elevation (meters)}") → text25
  16. LaTeX("\text{Elevation (meters)}") → text26
  17. LaTeX("\text{Create a number line from at least\textcolor{#000099}{-20} to \textcolor{#000099}{0} so that the values }") → text4
  18. LaTeX((((("\text{Mark\textcolor{#000099}{" * Elevation1) * "} for the elevation of El Centro and\textcolor{#000099}{") * Elevation2) * "} for Imperial.}")) → text7
  19. LaTeX("\text{Imperial’s elevation is to the left of El Centro’s elevation on the }") → text9
  20. LaTeX("\text{ El Centro has a higher elevation.}") → text12
  21. LaTeX((((("\text{The elevation of El Centro, California, is \textcolor{#000099}{" * Elevation1) * "\;meters}, and the elevation of Imperial, California, is \textcolor{#000099}{") * Elevation2) * " \;meters}.}")) → text1
  22. LaTeX("\text{Decide which city has a lower elevation, and which has a higher elevation.}") → text8
  23. LaTeX("\text{number line, and El Centro’s elevation is to the right of Imperial’s}") → text10
  24. LaTeX("\text{ elevation. This means that Imperial has a lower elevation, and}") → text11
  25. LaTeX("\text{Two inequalities can be written. If the symbol\textcolor{#000099}{<} is used, then the }") → text14
  26. LaTeX((((("\text{inequality would be \textcolor{#000099}{" * Elevation2) * " < ") * Elevation1) * "}, since Imperial’s elevation is}")) → text15
  27. LaTeX((((("\text{If the symbol\textcolor{#000099}{>} is used, then the inequality would be\textcolor{#000099}{ " * Elevation1) * " > ") * Elevation2) * "},}")) → text17
  28. LaTeX("\text{\mathbf{inequality} a mathematical sentence that shows the relationship between quantities}") → text21
  29. LaTeX("\text{that are not equivalent}") → text22
  30. LaTeX((("\text{Imperial's elevation=\textcolor{#0099FF}{" * Elevation2) * "}}")) → text20
  31. LaTeX((("\text{El Centro's elevation=\textcolor{#FF6600}{" * Elevation1) * "}}")) → text19