Subject:  Math
Topic:  Mean, Median, & Mode
Grade Level:  5th & 6th
Student Lesson name and URL:
http://ctap295.ctaponline.org/~gstewart/student

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 grade-level-appropriate 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 pre-test to determine their knowledge about mean, median, and mode.  Teachers can print out the pre-test 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 post-test to determine their knowledge about mean, median, and mode.  Teachers can print out the pre-test 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 post-test.
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 post-test than the pre-test.  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 pre-test/post-test, and a number of 
quizzes made by other teachers.  Have students use the "pre-test" or "post-test" 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 post-test.  Otherwise, they will have access to the post-test. 
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 pre-test -- This is what the test will appear like if students take the test online.  This link will take you directly to the test.  The pre-test 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 Pre-Test". 
printable version of pre-test & 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 post-test -- This is what the test will appear like if students take the test online.  This link will take you directly to the test.  The post-test 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 Post-Test". 
printable version of post-test & key -- This link will allow you to print a copy of the test, as well as the answer key.