Students will investigate the relationship of the equation of a normal curve to its graph. They will use a slider to change the values of two parameters, m and s, to investigate their effects on the normal curve, noting in particular that m represents the location of the mean and that s represents the distance from the mean to the curve at the point of inflection.

• Students will identify the three defining characteristics of a normal curve related to shape, center, spread, and area.
• Students will recognize that normal curves form a family whose members share these same characteristics.
• Students will use appropriate tools strategically (CCSS Mathematical Practices).
• Students will model with mathematics (CCSS Mathematical Practices).

• normal curve
• mean
• standard deviation
• point of inflection
• density functions

This lesson involves investigating the relationship of the equation of a normal curve to its graph.
As a result, students will:

• Identify the axis of symmetry as the line x =, the mean of the distribution represented by the normal curve, and the standard deviation as the distance from that line to the point of inflection.
• They will use a slider to change the values of two parameters, m and s to investigate their effects on the normal curve, noting in particular that m represents the location of the mean and that s represents the distance from the mean to the curve at the point of inflection.
• Estimate the area under a normal curve graphed on a coordinate grid and investigate how this area changes as the mean and standard deviation are changed.c