Content Area: Math

 

Index: 4.4B Grade 12 CPI 2

 

Standard: 4.4 - Data Analysis, Probability, and Discrete Mathematics

 

Strand: B - Probability

 

Cumulative Progress Indicator: 2 - The student will use concepts and formulas of area to calculate geometric probabilities.

 

Grade: 12

 

Sample Activities:

 

·        Students determine the area of an irregular closed figure drawn on a large sheet of paper using the Monte Carlo method: Each person in the group drops a handful of pennies over their shoulder (without looking) onto the paper containing the figure. They count the number of coins on the paper (total shots) and the number within the figure (hits). They thus produce the ratio of hits to total shots and multiply this fraction by this area of the paper to estimate the area of the figure.

 

·        Students work through the On the Boardwalk lesson that is described in the Introduction to the Framework. In this lesson they explore the probability that a quarter thrown onto a rectangular grid will land entirely within one of the squares on the grid, and then discuss how changing the size of the squares will affect the probability.

 

·        A point P inside a square is selected at random and is used to form a triangle with vertices A and B of the square. Students determine the probability that the triangle is acute using a simulation and a theoretical calculation.