How Much Wider is a Smile?
Student Page

Part I: We are going to work with photographs, make some measurements and see by what percentage a mouth can be increased in width.

To look at the photos, open the Java Applet Index page.

Note: It will open in a separate window. Arrange your browser windows so that the applet and the student page can be easily viewed.

Here are some things to notice on the applet:

  • display of x (in pixels)
  • display of y (in pixels)

To get an idea of how this will work, select one of the faces.

Here are some questions to think about:

Looking at the x-coordinates
  1. Click on the left side of the mouth. What value is x?
  2. Click on the right side of the mouth. What value is x?
  3. What is the difference between the two values of x?
Looking at the y-coordinates
  1. Click on left side of the mouth. What value is y?
  2. Click on the right side of the mouth. What value is y?
  3. What is the difference between the two values of y?

To determine the distance in pixels of the resting mouth, should you pay more attention to the change in the x-coordinate or the y-coordinate? Can you explain why?

Measurements:

Now that you have the idea of how to find measurements in pixels. Find the lengths of the resting mouth and the smiling mouth for each person.

Part II:

Using the data that we have, let's calculate the percentage increase. Need help in knowing how to do that? Check the Dr. Math links below.

Final Task:

Generalize the method that you used to find the lengths between points located on the face. Write the steps needed to calculate the percentage increase between the resting and smiling mouth.

Extension:

Use your own photograph and see how much wider your smile is!

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Selections from Ask Dr. Math Archives:

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Figuring Percentage of Increase
In 1990, Allen County, Kansas, had 14,385 people. Now, in 2001, it contains 14,905 people. How do I calculate the increase, using a percentage?

Percent of Increase
I need to figure out a percent increase: the figure in 1995 was 50,000 and the estimated figure for 2000 is 325,000.

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