Baseball stars Alex Rodriguez, Nomar Garciaparra,
and Derek Jeter (left to right) are ready to help you learn about the mean,
median, and mode.


Introduction
Students will use statistics
from baseball players to learn about the mean, median, and mode.
Subject: Math
Topic: Mean, Median, & Mode
Grade Level: 5th & 6th
Student Lesson name and URL:
http://ctap295.ctaponline.org/~gstewart/student
Standards Addressed
California
Mathematics Academic Content Standards
Grade Level: Fifth
Number Sense
Statistics, Data Analysis and Probability
Mathematical Reasoning
California
Language Art Content Standards
Grade Level: Fifth
Reading Comprehension (Focus on Informational Materials)
Structural Features of Informational Materials
Research and Technology
Fifth Grade Math
(5) Number
Sense: Students perform calculations and solve problems involving
addition, subtraction, and simple multiplication and division of fractions
and decimals.
2.1 Add, subtract, multiply, and divide with decimals; add with negative
integers; subtract positive integers from negative integers; and verify
the reasonableness of the results.
2.2 Demonstrate proficiency with division, including division with
positive decimals and long division with multidigit divisors.
(5) Statistics,
Data Analysis and Probability: Students display, analyze, compare
and interpret different data sets, including data sets of different sizes.
1.1 Know the concepts of mean, median, and mode; compute and compare
simple examples to show that they may differ.
(5) Mathematical
Reasoning: Students make decisions about how to approach problems.
1.1 Analyze problems by identifying relationships, discriminating
relevant from irrelevant information, sequencing and prioritizing information,
and observing patterns.
Fifth Grade Language Arts
(5) Reading Comprehension
(Focus on Informational Materials):
Students read and understand
gradelevelappropriate material. By grade eight, students read one million
words annually, including online information. In grade five, students make
progress toward this goal.
(5) Structural Features
of Informational Materials
2.1 Understand how text features (e.g., format, graphics, sequence,
diagrams, illustrations, charts, maps) make information accessible and
usable.
2.2 Analyze text which is organized in sequential or chronological
order.
(5) Research and Technology
1.3 Use organizational features of printed text (e.g., citations,
end notes, bibliographic references) to locate relevant information.
Instructional Objectives
1. Students will use addition, subtraction, multiplication, and division
of integers to calculate the mean, median, and mode for given sets of data.
2. Students will use mathematical reasoning to discriminate between
relevant and irrelevant information.
3. Students will use links and searches to locate relevant information.
Student Activities
Introductory
Activity
1. Each student will take a pretest to determine their knowledge
about mean, median, and mode. Teachers can print out the pretest
for students or have them take it online. If students take the test
online then the website will grade the test as the student completes each
problem. Following completion of the test, students can print out
a page indicating the number of problems that they got correct out of ten.
2. The teacher and students will work together on an M&M's project
introducing the mean, median, and mode. Each student will be given
a snack size package of M&M's. Students will divide their M&M's
into colors and tally the number of M&M's for each color. The
class will work together to make a chart listing the number of pieces that
each student has for each color. Depending on the amount of available
time and how well students understand the concepts, teachers may choose
to
do one color, several colors, or all the colors. The teacher will
introduce the concepts of mean, median, and mode. The mean, or average,
is the sum of the items divided by the number of items. The median
is the middle number when the items are arranged from least to greatest.
If there are two middle numbers, the median is the mean of the two middle
numbers. The mode is the number that occurs most often. Data
may have more than one mode or no mode at all. The class will work
together to determine what the mean, median, and mode are for different
colored M&M's.
Enabling
Activities)
1. The teacher and students will review the concepts of mean, median,
and mode.
2. Students will use baseball statistics from specific players to
practice calculating the mean, median, and mode. When using any of
the links on this website, remember to click "back" if you wish to return
to this website. I would highly suggest having students bookmark
this website in order to facilitate efficient web navigation. This
website has links to statistics for twelve different professional baseball
players. The players have been divided into three groups of four.
Each group contains three batters and one pitcher. The setup is ideal
for one day of guided practice, one day for group practice, and one day
of individual practice. However, the lesson can be shortened or lengthened
depending on the individual needs of students. The statistics screen
includes a three year average of statistics and a career long average of
statistics. These can be used to practice and double check students'
calculation skills. The instructions listed below have students calculating
mean, median, and mode over four, five, and six year spans. This
is just a suggestion, and can be modified to meet the needs of the teacher
and the students. It is highly recommended that the current season
not be included in the calculation of statistics.
Day 1 (guided practice)  Students will work with Alex Rodriguez, Nomar
Garciaparra, Derek Jeter, and Pedro Martinez (pitcher). For each
batter, students will calculate the mean, median, and mode for stolen bases
(SB's) over the past four years. Students will name the batter who
has averaged the most steals during the last four years. Next, students
will look at Pedro Martinez and find the mean, median, and mode for losses
(L) during the previous four years.
Day 2 (group work)  Students will work with Mark McGwire, Ken Griffey
Jr., Ivan Rodriguez, and Randy Johnson (pitcher). For each batter,
students will calculate the mean, median, and mode for home runs (HR's)
over the past five years. Students will name the batter who has averaged
the most home runs during the last five years. Next, students will
look at Randy Johnson and find the mean, median, and mode for strikeouts
(SO) during the previous five years.
Day 3 (individual practice)  Students will work with Sammy Sosa, Barry
Bonds, Mike Piazza, and Greg Maddux (pitcher). For each batter, students
will calculate the mean, median, and mode for runs (R) over the past six
years. Students will name the batter who has averaged the most runs
during the last six years. Next, students will look at Greg Maddux
and find the mean, median, and mode for wins (W) during the previous six
years.
Culminating
Activity
1. Each student will be given the baseball cards of two batters and
one pitcher who have links on the website. Another way of doing this
is randomly assigning baseball players to students. Using the information
on the baseball card or from the link, students should determine which
of the two batters is older. For the older player, students will
calculate the mean, median, and mode of runs batted in (RBI's) during the
player's last six years. For the younger player, students will calculate
the mean, median, and mode of doubles (2B's) during the player's last four
years. Next, the student will determine which player averaged more
triples (3B's) during the past five seasons. Finally, the student
will determine the mean, median, and mode games started (GS) for their
pitcher during the previous five seasons.
2. Each student will take a posttest to determine their knowledge
about mean, median, and mode. Teachers can print out the pretest
for students or have them take it online. If students take the test
online then the website will grade the test as the student completes each
problem. Following completion of the test, students can print out
a page indicating the number of problems that they got correct out of ten.
Assessment
Students will be graded on their effort, participation, and performance
on the introductory activity, enabling activities, culminating activity,
and the posttest.
0  Student made no effort
to learn the concepts of mean, median, and mode.
1  Student made little effort
or had little success in learning the concepts of mean, median, and mode.
2  Student had some success
in learning the concepts of mean, median, and mode.
3  Student had good success
in grasping the concepts of mean, median, and mode.
4  Student has obtained
mastery of the concepts of mean, median, and mode.
Results
Due to the fact that my school is still waiting to receive the parent consent
forms for the internet from the district office, I have been unable to
actually teach this lesson. I hope to be able to implement this lesson
next year. I would like to assume that students would score higher
on the posttest than the pretest. It makes sense that students
would show improvement after the concepts of mean, median, and mode have
been taught and reviewed.
Web Resources & Supplementary Materials
Additional
Websites
ESPN Baseball
 The players' baseball statistics and biographies come from athlete searches
done at this site.
Major
League Baseball
 This is the official website of major league baseball.
Upper Deck
Baseball Cards  My website contains
several pictures and photos from this site.
Topps
Baseball Cards
 My website contains several pictures and photos from this site.
Funbrain
Games  This
is a great website with all sorts of fun and educational games.
States
& Capitals Quiz
 This is a quiz for states and capitals. I have found that discussing
the location of
baseball teams
is a great way to review states and capitals, as well as latitude and longitude.
Other
Funbrain Quizzes
 My quiz lab contains the mean, median, and mode pretest/posttest,
and a number of
quizzes made
by other teachers. Have students use the "pretest" or "posttest"
link on the activities student page to take them to the main menu of the
quiz lab. Under student login, students should enter the password
"prefect" and their name. They will then have a selection of quizzes.
It is recommended that you do not let students explore other quizzes until
after they have completed the posttest. Otherwise, they will have
access to the posttest.
Major
League Baseball Team Websites  This website contains links to
team websites for every major league
team. A
great activity is to have students go on a scavenger hunt to find items
such as the cost of a team's
hat, the cost
of a ticket to a game, the score of a particular game, the team's current
record, and much
more. This
teaches students how to navigate a website in order to find specific information.
Introductory
Activity
online
version of pretest  This is what
the test will appear like if students take the test online. This
link will take you directly to the test. The pretest link on the
activities student page will take them to the main menu of the quiz lab.
Under student login, students should enter the password "prefect" and their
name. They will then have a selection of quizzes. Students
should choose "Mean, Median, and Mode PreTest".
printable
version of pretest & key  This
link will allow you to print a copy of the test, as well as the answer
key.
Enabling
Activity
Day 1
Alex
Rodriguez
Nomar
Garciaparra
Derek
Jeter
Pedro
Martinez
Day 2
Mark
McGwire
Ken
Griffey Jr.
Ivan
Rodriguez
Randy
Johnson
Day 3
Sammy
Sosa
Barry
Bonds
Mike
Piazza
Greg
Maddux
Culminating
Activity
online
version of posttest  This is what
the test will appear like if students take the test online. This
link will take you directly to the test. The posttest link on the
activities student page will take them to the main menu of the quiz lab.
Under student login, students should enter the password "prefect" and their
name. They will then have a selection of quizzes. Students
should choose "Mean, Median, and Mode PostTest".
printable
version of posttest & key  This
link will allow you to print a copy of the test, as well as the answer
key.
North Davis Elementary School
555 East
14th St.
Davis,
CA 95616
5307575475
Davis
Joint Unified School District
Gabe Stewart
5th Grade
Teacher
gabrielstewart@hotmail.com
Last Revised:
05/06/2001 