NCTM 2012 Presentation 3

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This is the third of the presentations we gave at the TI booth at NCTM 2012 in Philly.

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NCTM 2012 Presentation 3

  1. 1. 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.
  2. 2. Algebra & Geometry Resources for the TN-Nspire DVD Library, Algebra Applications.
  3. 3. Algebra & Geometry Resources for the TN-Nspire DVD Library, Geometry Applications.
  4. 4. 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.
  5. 5. Algebra & Geometry Resources for the TN-Nspire This illustration gives a sense of the size and scale of the Titanic.
  6. 6. Algebra & Geometry Resources for the TN-Nspire To better understand how a ship of this size can float, we explore the concept of density.
  7. 7. 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.
  8. 8. 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.
  9. 9. 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.
  10. 10. 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.
  11. 11. Algebra & Geometry Resources for the TN-Nspire A triangular prism provides a reasonable estimate of this folume.
  12. 12. Algebra & Geometry Resources for the TN-Nspire This is the net for a triangular prism.
  13. 13. Algebra & Geometry Resources for the TN-Nspire Given the dimensions shown, the volume of the triangular prism is found using this formula.
  14. 14. 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.
  15. 15. 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.”
  16. 16. 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.
  17. 17. Algebra & Geometry Resources for the TN-Nspire Create a “volume” variable and calculate the volume of the triangular prism. Then calculate the density.
  18. 18. 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).
  19. 19. Algebra & Geometry Resources for the TN-Nspire When the Titanic struck the iceberg a number of punctures caused water to flow into the hull.
  20. 20. 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.
  21. 21. 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.
  22. 22. 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.
  23. 23. 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.
  24. 24. 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.

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