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Elevation Comparison of Two California Cities

Elevation Comparison of Two California Cities
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2015-10-13 23:24
Coordinate GeometryOptimizationInequality
In collections CCSS Support Algebra I Unit 1 CCSS Support Math I Unit 1
This example compares the elevations of two California cities, El Centro and Imperial, using inequalities. Key mathematical concepts include inequalities and elevation. The construction uses Polygon, Segment, Sequence, and other GeoGebra commands. Suitable for middle school mathematics education.

GeoGebra Commands & Parameters

  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