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NCTM 2012 Presentation 3
Algebra & Geometry Resources for the TN-Nspire




    Media4Math includes a variety of free
    and premium resources, including
    short video tutorials on the Nspire,
    Math in the News, and other tutorials.
Algebra & Geometry Resources for the TN-Nspire




    DVD Library, Algebra Applications.
Algebra & Geometry Resources for the TN-Nspire




    DVD Library, Geometry Applications.
Algebra & Geometry Resources for the TN-Nspire




 This presentation on the Titanic comes from
 the Geometry Applications: Area and Volume
 and includes algebra and geometry
 connections.
Algebra & Geometry Resources for the TN-Nspire




    This illustration gives a sense of the
    size and scale of the Titanic.
Algebra & Geometry Resources for the TN-Nspire




    To better understand how a ship of
    this size can float, we explore the
    concept of density.
Algebra & Geometry Resources for the TN-Nspire




    By definition the density of water is 1
    (in units of gm/cm3). A density less
    than 1 causes an object to float;
    greater than 1 and the object sinks.
Algebra & Geometry Resources for the TN-Nspire




    As a simple example, look at a cube
    of length s and mass M. Its density is
    M/s3.
Algebra & Geometry Resources for the TN-Nspire




    This is a rational function. Given
    different values of M, the cube will
    float based on where its graph is
    relative to y = 1, the red line.
Algebra & Geometry Resources for the TN-Nspire




    We can estimate the volume of the
    Titanic by looking at the shape of the
    hull and main body of the ship.
Algebra & Geometry Resources for the TN-Nspire




    A triangular prism provides a
    reasonable estimate of this folume.
Algebra & Geometry Resources for the TN-Nspire




    This is the net for a triangular prism.
Algebra & Geometry Resources for the TN-Nspire




    Given the dimensions shown, the
    volume of the triangular prism is
    found using this formula.
Algebra & Geometry Resources for the TN-Nspire




    These are the dimensions for the
    Titanic. The linear dimensions are for
    the “rectancular prism” section and
    the displacement is the mass of the
    ship.
Algebra & Geometry Resources for the TN-Nspire




    On the Nspire, create a Calculator
    Window and assign the values for
    mass to a variable called “mass.”
Algebra & Geometry Resources for the TN-Nspire




    Make sure the units for mass are are
    gm. You can operate on the “mass”
    variable and reassign the result to
    the same variable.
Algebra & Geometry Resources for the TN-Nspire




    Create a “volume” variable and
    calculate the volume of the triangular
    prism. Then calculate the density.
Algebra & Geometry Resources for the TN-Nspire




    The estimated density of the Titanic
    is less than 1 (and probably a bit
    higher due to the triangular prism
    volume).
Algebra & Geometry Resources for the TN-Nspire




    When the Titanic struck the iceberg a
    number of punctures caused water to
    flow into the hull.
Algebra & Geometry Resources for the TN-Nspire




    When a ship takes on water, the loss
    in volume is immediately converted
    to mass. This leads to a quick
    increase in density.
Algebra & Geometry Resources for the TN-Nspire




    This density expression shows that
    as the volume decreases, the mass
    increases. The variable x is the
    percent of volume lost.
Algebra & Geometry Resources for the TN-Nspire




    This graph shows that when about
    58% of the hull is filled with water, it
    will sink. But this overestimates the
    volume of the hull.
Algebra & Geometry Resources for the TN-Nspire




    This graph scales the volume down
    and gets us to a more accurate
    estimate of when the ship will sink.
Algebra & Geometry Resources for the TN-Nspire




    The Titanic had 16 watertight
    compartments. When it struck the
    iceberg, 5 (possibly 6) of them were
    punctured.
NCTM 2012 Presentation 3

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NCTM 2012 Presentation 3

  • 2. Algebra & Geometry Resources for the TN-Nspire Media4Math includes a variety of free and premium resources, including short video tutorials on the Nspire, Math in the News, and other tutorials.
  • 3. Algebra & Geometry Resources for the TN-Nspire DVD Library, Algebra Applications.
  • 4. Algebra & Geometry Resources for the TN-Nspire DVD Library, Geometry Applications.
  • 5. Algebra & Geometry Resources for the TN-Nspire This presentation on the Titanic comes from the Geometry Applications: Area and Volume and includes algebra and geometry connections.
  • 6. Algebra & Geometry Resources for the TN-Nspire This illustration gives a sense of the size and scale of the Titanic.
  • 7. Algebra & Geometry Resources for the TN-Nspire To better understand how a ship of this size can float, we explore the concept of density.
  • 8. Algebra & Geometry Resources for the TN-Nspire By definition the density of water is 1 (in units of gm/cm3). A density less than 1 causes an object to float; greater than 1 and the object sinks.
  • 9. Algebra & Geometry Resources for the TN-Nspire As a simple example, look at a cube of length s and mass M. Its density is M/s3.
  • 10. Algebra & Geometry Resources for the TN-Nspire This is a rational function. Given different values of M, the cube will float based on where its graph is relative to y = 1, the red line.
  • 11. Algebra & Geometry Resources for the TN-Nspire We can estimate the volume of the Titanic by looking at the shape of the hull and main body of the ship.
  • 12. Algebra & Geometry Resources for the TN-Nspire A triangular prism provides a reasonable estimate of this folume.
  • 13. Algebra & Geometry Resources for the TN-Nspire This is the net for a triangular prism.
  • 14. Algebra & Geometry Resources for the TN-Nspire Given the dimensions shown, the volume of the triangular prism is found using this formula.
  • 15. Algebra & Geometry Resources for the TN-Nspire These are the dimensions for the Titanic. The linear dimensions are for the “rectancular prism” section and the displacement is the mass of the ship.
  • 16. Algebra & Geometry Resources for the TN-Nspire On the Nspire, create a Calculator Window and assign the values for mass to a variable called “mass.”
  • 17. Algebra & Geometry Resources for the TN-Nspire Make sure the units for mass are are gm. You can operate on the “mass” variable and reassign the result to the same variable.
  • 18. Algebra & Geometry Resources for the TN-Nspire Create a “volume” variable and calculate the volume of the triangular prism. Then calculate the density.
  • 19. Algebra & Geometry Resources for the TN-Nspire The estimated density of the Titanic is less than 1 (and probably a bit higher due to the triangular prism volume).
  • 20. Algebra & Geometry Resources for the TN-Nspire When the Titanic struck the iceberg a number of punctures caused water to flow into the hull.
  • 21. Algebra & Geometry Resources for the TN-Nspire When a ship takes on water, the loss in volume is immediately converted to mass. This leads to a quick increase in density.
  • 22. Algebra & Geometry Resources for the TN-Nspire This density expression shows that as the volume decreases, the mass increases. The variable x is the percent of volume lost.
  • 23. Algebra & Geometry Resources for the TN-Nspire This graph shows that when about 58% of the hull is filled with water, it will sink. But this overestimates the volume of the hull.
  • 24. Algebra & Geometry Resources for the TN-Nspire This graph scales the volume down and gets us to a more accurate estimate of when the ship will sink.
  • 25. Algebra & Geometry Resources for the TN-Nspire The Titanic had 16 watertight compartments. When it struck the iceberg, 5 (possibly 6) of them were punctured.