MA19.MM.19

Mathematics (2019) Grade(s): 09-12 - Mathematical Modeling

MA19.MM.19
Construct a sampling distribution for a random event or random sample.

Unpacked Content

Knowledge

Students know:

The circumference of any circle is 2πr and therefore, the circumference of a unit circle is 2π.

Skills

Students are able to:

Translate between arc length and central angle measures in circles.

Understanding

Students understand that:

Radians measure angles as a ratio of the arc length to the radius.
The unit circle has a circumference of 2π which aids in sense making for angle measure as revolutions (one whole revolution measures 2π radians) regardless of radius.
Use of the unit circle gives a one-to-one ratio between arc length and the measure of the central angle, putting the angle in direct proportion to the arc length, and that the circle can then be divided up to find the radian measure of other angles.

Vocabulary

Radian measure
Constant of proportionality
Unit circle
Intercepted arc

COS Examples

Examples: How many times do we expect a fair coin to come up heads“ in 100 flips and on average how far away from this expected value do we expect to be on a specific set of flips? What do we expect to be the average height for a random sample of students in a local high school given the mean and standard deviation of the heights of all students in the high school?“

MA19.MM.19 Construct a sampling distribution for a random event or random sample.