Title
Let's Play Ball
Topic
Number Concepts
Ratios, Proportions, Percents
In baseball and softball, a hit means the batter makes contact with the ball
and makes it safely to a base. A player's batting average represents the
ratio of the number of hits over the number of atbats. However, when a
player reaches base without getting a hit or an out, it is not included as an
atbat in the player's average. For example, a player who goes to the
plate 120 times, has 30 hits, 19 walks, and 1 hit by pitch, would have 100
atbats (100=120191) and a batting average of 30/100 = 0.300
because it represents the player's ability to get a hit after putting the ball
in play.
At the end of the season, a player has an average of exactly 0.336, and
had exactly one walk for every three hits. Assuming the player was never
hit by a pitch, how many plate appearances did the player have (including
walks)?
Grade levels
Grades 6 to 8
Introduction/Practice/Exploration
We decided to solve this problem by using Excel spreadsheet. In column
one we put the walks from one to seventyfive. In column two we did the
hits based on the formula =3*A2. In column three we figured the times at
plate by using the formula =B1/0.336. We came to the conclusion that for
every fourteen walks every column would have integers which would equal the
0.336 batting average we were seeking. We found a pattern of plus 14 for
walks, plus 42 for hits, and plus 125 for at plate appearances. We decided
that a major league player can play 160 games and average four times at bat
every game. With this information we decided the most logical answer for
the solution to the problem was : 56 walks, 168 hits, and 500 times at
plate for an average of 0.336.
After exploring with Excel we graphed the data as shown below.
The results are shown here:
Lesson Type (lab, demo, worksheet, handson, other)
Handson, computer
Estimated time
Approximately two hours
Resources & Materials
Excel Spreadsheet
NCTM Process Standard(s)
(may be more than one. Standard(s) need to appear here, not just reference number)
Author & Contact
Peggy Reigle
preigle@athensacademy.org
