PISA-VET launch_El Iza Mohamedou_19 March 2024.pptx
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.