How Much Wider is a Smile?     
by Suzanne Alejandre

Teacher Lesson Plan

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NCTM Standards:
Number and Operations:
      Understand numbers and relationships among numbers
      Understand and use ratios and proportions to represent quantitative relationships

      Understand processes of measurement
      Specify locations and describe spatial relationships using coordinate geometry

      Students use pixel measurements to calculate lengths.
      Students determine the percentage increase from a "resting" to a "smiling" mouth.

Part I:

Students start the activity by opening the Java Applet Index page.

Note: It will open in a separate window. If you are displaying the page for students, arrange your browser windows so that the applet and the directions can be easily viewed. If students are working individually they should be encouraged to do this.

Ask the question:

Can you determine the "pixel" distance between two points?

Prompt students to notice the:

  • display of x (in pixels): How can you calculate how long a line segment is in pixels if you know the x coordinate of both endpoints of that line segment?

  • display of y (in pixels): How can you calculate how long a line segment is in pixels if you know the y coordinate of both endpoints of that line segment?

Students should be aware of the following:

If the line segment is horizontal, pay attention to the x-coordinates. If the line segment is vertical, pay attention to the y-coordinates.

Have the students work through the first example as a class, in groups, pairs or individually.

Part II:

Once students have the technique established, they can continue the activity by finding the measurements for all the photos and calculating the percentage increase.


Ask students to generalize this method and write the steps needed to calculate the percentage increase between the measurements of a person's resting and smiling mouth.


A fun project would be to have the students' photographs instead of strangers' photographs. If you or your students have access to a digital camera, take photographs of the students. Here are the instructions to replace those photos with the ones in the applet.
  1. The pixel dimensions of the photo should be width = 324 by height = 384.
  2. Save the photo as a jpg file.
  3. Make a copy of the "applet.annie2.html" file and replace the name "annie.jpg" in the html code with the name of your jpeg, for example "john.jpg." Similarly, replace the name "" in the html code with the name of your other jpeg, for example ""


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