Intermath | Workshop Support
 Lesson Plan

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 at-bats. However, when a
player reaches base without getting a hit or an out, it is not included as an
at-bat 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
at-bats (100=120-19-1) 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)?

Introduction/Practice/Exploration

We decided to solve this problem by using Excel spreadsheet.  In column one we put the walks from one to seventy-five.  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, hands-on, other)
Hands-on, computer

Estimated time
Approximately two hours

Resources & Materials