9-12
In this lesson, students analyze the fairness of certain games by
examining the probabilities of the outcomes. The explorations provide
opportunities to predict results, play the games, and calculate
probabilities. Students should have had prior experiences with simple
probability investigations, including flipping coins, drawing items
from a set, and making tree diagrams. They should understand that the
probability of an event is the ratio of the number of successful
outcomes to the number of possible outcomes. This lesson was adapted
from "Activities: Explorations with Chance," which appeared in the
April 1992 issue of the
Mathematics Teacher. 6-8, 9-12
Students model linear data in a variety of settings that range from car repair costs to sports to medicine. Students work to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit.
6-8, 9-12
This activity demonstrates the Birthday Paradox, using it as a springboard into a unit on probability. Students use a graphing calculator to run a Monte Carlo simulation with the birthday paradox and perform a graphical analysis of the birthday-problem function. This lesson was adapted from an article, written by Matthew Whitney, which appeared in the April 2001 edition of
Mathematics Teacher.
9-12
This activity allows students to look for functions within a given set
of data. After analyzing the data, the student should be able to
determine a type of function that represents the data. This lesson plan
is adapted from an article by Jill Stevens that originally appeared in
the September 1993 issue of the
Mathematics Teacher.
6-8, 9-12
This lesson plan presents a classic game-show scenario. A student picks
one of three doors in the hopes of winning the prize. The host, who
knows the door behind which the prize is hidden, opens one of the two
remaining doors. When no prize is revealed, the host asks if the
student wishes to "stick or switch." Which choice gives you the best
chance to win? The approach in this activity runs from guesses to
experiments to computer simulations to theoretical models. This lesson
was adapted from an article written by J. Michael Shaughnessy and
Thomas Dick, which appeared in the April 1991 issue of the
Mathematics Teacher.
9-12
In this lesson, students interpret the meaning of the slope and
y-intercept of the graph of real-life data. By examining the graphical representation of the data, students relate the slope and
y-intercept
of the least squares regression line to the real-life data. They also
interpret the correlation coefficient of the resulting least squares
regression line.
9-12
This lesson is similar to Lesson One: Traveling Distances; however,
this lesson is designed so students examine real-life data that
illustrates a negative slope. Students interpret the meaning of the
negative slope and
y-intercept of the graph of the real-life
data. By examining the graphical representation of the data, students
relate the slope and
y-intercept of the least squares
regression line to the real-life data. They also interpret the
correlation coefficient of the least squares regression line.
9-12
This lesson is designed to allow students to select their own real-life
data to plot and interpret. Interpreting the meaning of the slope and
y-intercept
of their least squares regression lines will help reinforce the
concepts introduced in Lessons One and Two of this Unit Plan. The
students are then given the opportunity to display their work.
9-12
This lesson is designed to allow students to view the work of other
students in the class and to explain their own work. Some teachers may
be tempted to skip this step in the Unit Plan, but it is very important
that students be given the opportunity to verbalize what the
mathematics means that they performed in Lesson Three.
9-12
In this lesson, students plot data about automobile mileage and interpret the meaning of the slope and
y-intercept
in the resulting equation for the least squares regression line. By
examining the graphical representation of the data, students analyze
the meaning of the slope and
y-intercept of the line and
interpret them in the context of the real-life application. Students
also make decisions about the age and mileage of automobiles based on
the equation of the least squares regression line.
