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DrsCavanaugh


MATH APPLICATIONS WITH DIGITALCAMERAS
Your phone's digital camera (or your students') is an excellent tools for enhancing the math classroom.
They can also assist with applications under the current math reform movement,
moving away from isolated problems in a drillandpractice format to one more
rooted in authentic experiences and problem solving.
Digital images can be used to help demonstrate accomplishment
of standards such as National Council for Teachers of Mathematics (NCTM) standards
for Algebra, Geometry and Measurement. For example, you could apply
standards from by having images that allow students to measure and compare sides,
shape and angles by using images as models. The NCTM standards
include the statement that "Similarity also can be related to such realworld
contexts as photographs, models, projections of pictures" which can be an
excellent application of a digital image. NCTM encourages that "Students at all levels should have opportunities to model a wide
variety of phenomena mathematically in ways that are appropriate to their level."
Additionally while interacting with the digital images, students are also meeting
the national technology standard (ISTE) specifying that students use technology tools to
publish and interact with peers, experts and other audiences. Using
digital images can provide documentation for the teacher, and allow for the
creation of more authentic assessment tools and examples.
Use your digital camera to demonstrate perspective by
showing objects situated at different distances, or set up a discrepant
event as displayed in this image where a known larger object appears
smaller than a comparative known smaller object. 
Chicago IL, Field Museum')" _wpro_href="javascript:makePopUpWin('images/descrepant.jpg','Discrepant event image caused by background reference',241,234,'Discrepant event image caused by background reference,<br> Chicago IL, Field Museum')" class="">

Scale and measurements: Use your camera to capture
objects at the same distance to calculate the height of an unknown object
or to calculate the volume of an object. Geometric shapes are shown here with
the lighthouses as cylinder and conic sections. 
Mayport Florida')" _wpro_href="javascript:makePopUpWin('images/lighthouse.jpg','Mayport Lighthouse image',493,200,'Lighthouse  Cylinder Section,<br> Mayport Florida')" class="">
St. Augustine Florida')" _wpro_href="javascript:makePopUpWin('images/st_a_lig.jpg','St. Augustine Lighthouse image',500,309,'Lighthouse  Conic Section,<br> St. Augustine Florida')" class="">

You can enhance through photomanipulation existing
geometric shapes by adding highlights to the images to outline the
shapes. In this image, a picture of the front of a building was
enhanced to show the basic shapes on the building, including the
triangle, rectangle, semicircle, square, and others. 

Show objects that demonstrate structural strength, tension,
and construction using geometry. In these photos a bridge which uses the
basic
structural shape of triangles with the tension wires, but also shows parabolas
in the shape of the bridge. 

Use the digital camera to demonstrate, display, or print
calculator procedures. With today's modern graphing calculators you
can use your digital camera to capture images of the the steps in a
calculation process along with the associated displays from the calculator
screen. The process takes you beyond what you can accomplish with a
calculator overhead LCD repeater or screen capture program on a computer. 

Demonstrate math manipulatives. Using a camera with
live video output, students can participate in problemsolving while
watching the steps on a large screen TV. The images can then be
included in assessment tools, with the advantage of being more
authentic. 

Use digital images to perform scale measurements. With
these images of lizard tracks and a quarter as a scale reference object,
students can calculate the distances between foot prints and then use Alexander's formula (see formula)
to calculate the speed at which the animal
was moving
Alexander's formula for indirect speed measurement
Estimated Speed (meters/second) = (0.25) x (gravitational constant)^{0.5}
x (stride length)^{1.67} x (hip height)^{1.17}
Hip height = about 4 x track length of a single foot print
Stride length = distance from a print until it repeats
Gravitational constant = 9.8 m/s/s 

Images can be used to develop and provide concrete examples of geometric
shapes, symmetry and patterns, such as tessellations. Additionally, digital cameras can be used for math application labs
covering topics such as direct and indirect measurement, manmade and
natural geometry, money and counting, measurement and scale, and the calculations
of speeds and distances.
