Astronomy in the Ice Jack Hansen
Phys 789 Jason Petula
Scott Kelly
Bob Sime
Activity Module
(Probability and Statistics)
Overview:
Abstract
Students will be divided into groups of two, because it is
very difficult for a student to be left out of a group this size.
Each group will determine the mass of 100 pennies. Fifty of
the pennies must be dated before 1980 and fifty of the pennies
must be dated after 2000. After all of the data is collected,
students will share their data with all other groups in the room.
The shared information will be used to conduct comparisons between
the group's data and the classes' data
From the two data tables, each student will construct a stem
& leaf plot. This plot can be used to visualize the bell
curve. From the stem & leaf plot, the following five statistical
points can be determined: lower extreme, lower quartile, median,
upper quartile, and the upper extreme. Finally students will
construct a box-and-whisker plot representing the two populations
of pennies.
Rationale
The rationale of this activity is it allows students an opportunity
to extract statistical information from a data set. Furthermore,
the students can compare their individual data (small data set)
with the class data (large data set) and look for trends or patterns.
Grade Level/Discipline
9-12/any science where two populations need to be compared and
analyzed.
Objectives
Students will extract statistical information from two data sets
so that they can be compared.
Students will synthesize two types of graphs; stem & leaf
and box-and-whisker plots.
Students will analyze stem & leaf plots for bell curve distributions
Connections to Curriculum/Teacher Preparation for Activity:
Standards
Materials List (per group)
1 balance 100 pennies (50 pre-1980/50 post-2000) graph paper
Pre-activity Set-up:
BEFORE STUDENTS ARRIVE: Have pennies divided into two piles
of pre-
1980 and post-2000.
Have students tests grades written on the board
as a data set.
TIMEFRAME: 2 periods/1 block
Teaching Sequence:
Engagement and Exploration:
Students will be introduced to the concept of statistical
analysis by reviewing a data set of their test grades. At the
start of the class, student tests will be handed back and the
teacher will immediately ask the following questions:
What is the median of the data set?
How did your grade compare to the classes' grades?
Should you be concerned? Proud?
Why can't you tell the median immediately? The lowest grade?
The teacher will then instruct the students how to create a stem & leaf plot. Begin with an unsorted plot and end with a sorted stem & leaf plot. Have students discover how the stem & leaf plot visually shows the distribution of data. Next, students will be taught how to determine five statistical points in the following order: lower and upper extreme, median, upper and lower quartiles. From the statistical points have students create a box & whisker plot. Repeat the introduction questions again. Discuss why it is easier for students to now answer them.
Probing Questions:
Where else can this form of statistical analysis be beneficial?
Student Assessment:
Students will receive immediate feedback because the students
plots should be all the same. The idea of the exploration activity
is to introduce how the stem & leaf and box-and-whisker plot
are constructed.
Classroom Components:
Background:
The teachers need to know how to properly construct a stem &
leaf plot and a box-and-whisker plot. It would also be beneficial
if the teacher was comfortable with general statistics, such as
medians and quartiles.
Resources and References:
Statistics for Engineers: http://engineering.uow.edu.au/Courses/Stats/File15104.html
Box Plots: http://shodor.org/interactive/lessons.boxp.html
General Activity Description:
1. Students are to divide themselves into groups of two.
2. Each group is to count out 50 pennies pre-1982 and post-2000.
3. Each group is to create a data table for recording the masses
of the penny groups.
4. Students are to measure and record the masses of the individual
pennies so they have a data set of 100.
5. Each group will create a second data table containing the combined
data from the class.
6. Individual students will create the following plots for their
group data and classroom data:
Unsorted and Sorted Stem & Leaf Plots Box-and-Whiskers Plot
As an enhancement, the teacher can provide students with a set
of pennies dated 1982. These can be massed and plotted.
Analysis:
1.) Can a pennies date be determined by its mass?
2.) Why is there a difference in the mass of the two penny populations?
3.) Why is the classroom data more representative of the population
of all pennies?
4.) What others sciences would benefit from statistically comparing
two or more
populations?
5.) There are three populations of hydrogen: hydrogen (1),
deuterium (2), tritium (3).
The numbers in the parenthesis represent the number of
particles in the nucleus.
The atomic mass of hydrogen is 1.0079. Why is the atomic
mass not a whole
number?