nctm 2012 presentation 3

Algebra & Geometry Resources for the TI-Nspire

NCTM 2012WWW.MEDIA4MATH.COM

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.

DVD Library, Algebra Applications.

DVD Library, Geometry Applications.

This presentation on the Titanic comes from the Geometry Applications: Area and Volume and includes algebra and geometry connections.

This illustration gives a sense of the size and scale of the Titanic.

To better understand how a ship of this size can float, we explore the concept of density.

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.

As a simple example, look at a cube of length s and mass M. Its density is M/s3.

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.

We can estimate the volume of the Titanic by looking at the shape of the hull and main body of the ship.

A triangular prism provides a reasonable estimate of this folume.

This is the net for a triangular prism.

Given the dimensions shown, the volume of the triangular prism is found using this formula.

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.

On the Nspire, create a Calculator Window and assign the values for mass to a variable called “mass.”

Make sure the units for mass are are gm. You can operate on the “mass” variable and reassign the result to the same variable.

Create a “volume” variable and calculate the volume of the triangular prism. Then calculate the density.

The estimated density of the Titanic is less than 1 (and probably a bit higher due to the triangular prism volume).

When the Titanic struck the iceberg a number of punctures caused water to flow into the hull.

When a ship takes on water, the loss in volume is immediately converted to mass. This leads to a quick increase in density.

This density expression shows that as the volume decreases, the mass increases. The variable x is the percent of volume lost.

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.

This graph scales the volume down and gets us to a more accurate estimate of when the ship will sink.

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

Algebra & Geometry Resources for the TI-Nspire

NCTM 2012WWW.MEDIA4MATH.COM

nctm 2012 presentation 3

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