By David Reid
1.
Remind the class of the definition of theoretical
probability: the number of successful events possible divided by the
total number of possible events. To
check ask:
a.
what is the theoretical probability of rolling 5 on a
dice (1/6),
b.
what is the theoretical probability of rolling and odd
number on a dice (3/6 or 1/2),
c.
what is the theoretical probability of rolling 7 on a
dice (0/6).
2.
Ask what is the theoretical probability of someone
being born in January. Encourage discussion. Possible answers are “About 1/12” (discuss
whether it is exactly 1/12; are all months equally likely?); “about 31/365” (Is
this exact? Are all years 365 days
long? Are all days equally likely?)
3.
Collect data from the class on birth month.
a.
Display as both a bar chart and a line chart (and for
grade 6 a circle chart).
b.
Discuss advantages and disadvantages of each type of
display.
4.
Have the class calculate, based on the data displayed,
the experimental probability of being born in each month (If needed remind them
that experimental probability is the number of successful events observed
divided by the total number of observed events.
5.
Discuss what they would do to get experimental results
that were closer to the theoretical values (Use a larger sample).
6.
Have each person calculate their age in days. Include yourself.
a.
Assemble this data into a sorted list.
b.
Ask them what the average age is in the class.
c.
Discuss the difference between the mean and the
median.
d.
Discuss the effect of removing the outlier (you).
e.
Ask if mode would be useful for this data.
7.
Ask them what the average birth month is. Suggest coding the moths with numbers. Does the mean mean anything? What about the median? What about the mode?
Grade 4
F1- recognize and use a
variety of methods for the collection and organization of data
F3- read and interpret
bar graphs, line graphs, pictographs, and stem-and-leaf plots
F5- construct bar
graphs, pictographs, and stem-and-leaf plots
F7- describe data,
using the mean
F8- explore real-world
issues of interest to students and for which data collection is necessary to
determine an answer
G1- predict
probabilities as either close to 0, near 1, or near ½
G2- cite examples of
everyday events with very high or very low probabilities
G3- predict whether
one simple outcome is more or less likely than another
G4- use fractions to
describe experimental probabilities
Grade 5
F2- use pictographs
and bar graphs to display and interpret data
F4- create and
interpret line graphs
F6- recognize and
explain the effect of certain changes in data on the mean of that data
F7- explore relevant
issues for which data collection assists in reaching conclusions
G1- conduct simple
experiments to determine probabilities
G2- Determine simple
theoretical probabilities and use fractions to describe them
Grade 6
F1- choose and
evaluate appropriate samples for data collection
F4- use bar graphs,
double bar graphs and stem-and-leaf plots to display data
F5- use circle graphs
to represent data proportionally
F7- make inferences
from data displays
F8- demonstrate an
understanding of the differences among mean, median, and mode
F9- explore relevant
issues for which data collection assists in reaching conclusions
G1- conduct simple
simulations to determine probabilities
G2- evaluate the
reliability of sampling results
G3- analyze simple
probabilistic claims
G4- determine
theoretical probabilities