NCTM Standards:
Number and Operations:
      Understand numbers and relationships among numbers
      Understand and use ratios and proportions to represent quantitative relationships
Measurement:
      Understand processes of measurement
Geometry:
      Specify locations and describe spatial relationships using coordinate geometry

Objectives:
      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.

Assessment:

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.

Extension:

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 "annie.smile.jpg" in the html code with the name of your other jpeg, for example "john.smile.jpg."

Math Forum Resources

[Problems of the Week]  [T2T]  [Dr. Math]

Selections from Math Forum Problems of the Week:

ElemPoW: Less Pay, More Work, October 13-17, 1997

What percentage increase in hours is necessary to balance a corresponding percentage decrease in wage in order to obtain the same amount of pay?

Selections from Teacher2Teacher Discussions:

Percentage of change

Tips for determining the percentage of change for an investment question.

Selections from Ask Dr. Math Archives:

Percentage Increase in Cost of Eggs

When eggs went from 17 to 39 cents, by what percent did the price increase?

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.