Intent

This activity will help students to think of the normal curve in terms of the areas it defines and the probabilities associated with those areas.

Mathematics

In this activity, students will consider the area under the normal curve and begin to develop an intuitive sense of where, for example, two-thirds or three-fourths of the data reside. This lays the groundwork for understanding another important property of standard deviation. In a theoretical normal distribution, about two-thirds of the area falls within one standard deviation on either side of the mean, and about 95 percent of the area falls between two standard deviations on either side of the mean.

Progression

Students will work on this activity individually and then share their results in a class discussion.

Approximate Time

10 minutes for activity (at home or in class)

10 minutes for discussion

Classroom Organization

Individuals, followed by whole-class discussion

Materials

Graph paper or copies of the graphs (optional)

Transparencies of the graphs (optional) [link to BLM pdf of An (AB)Normal Rug, p. 3–4]

Doing the Activity

You might suggest that students trace the five diagrams in this activity onto graph paper or, alternatively, you can distribute copies of them.

Discussing and Debriefing the Activity

Use Question 1 to verify that students understand the idea of area under a curve.

Then turn to Questions 2 and 3. How did you estimate where to draw the vertical lines? You might let students use a transparency of the diagrams to share their estimates of where to draw the lines for each graph. Ask them to explain how they made their estimates.

Key Question

How did you estimate where to draw the vertical lines?