Before the first period, print out the activity sheets for each group. These
will help you as you explain this activity. You only need one copy of the
Before the third period begins, provide each group with 3 manila
envelopes or sheets of thick paper. They will use these to make Player discs, 4
on each sheet. They will also need a pencil or pen to divide each circle into
Before the fourth period, provide each group with a pencil with a sharp
tip and a paper clip with one end unbent, to serve as a spinner.
Player Statistics Activity Sheet
Batting Order Activity Sheet
Batting Order Answer Key
Game Day Activity Sheet
Baseball Diamond Activity Sheet
Batting Order Overhead
Sample Disc Overhead
Begin the first period with a discussion about baseball and softball.
Ask students if they play either sport. Guide the discussion toward scoring
runs. Explain that runs are scored when a player circles the bases and reaches
home plate. Ask, "How do you determine which team wins?" [The team
that has scored more runs when the game is over wins.] Ask students to explain how
a batter can get on base, and how runners advance on the bases. As you are
doing this, write the ways players can get on base on the board, along with the
common abbreviations; walk W, single 1B, double 2B, triple 3B, home run HR. Be
sure to address how a batter makes an out. There are three common ways that an
out is made:
- A ground out – when a batter hits
the ball on the ground in fair territory (between the first base line and the
third base line) and the team on the field gets the ball to first base before
the runner reaches first base.
- A fly out – when a batter hits a
ball in the air and it is caught by the team on the field before it touches the
- A strike out – when a batter gets
three strikes. A strike occurs when the batter swings and misses, or the batter
does not swing at a "good" pitch in the "strike zone," or
the batter hits a foul ball that is not caught. The third strike has to be a
swing and miss, or a foul tip that the catcher catches, or when the batter is "caught
looking" at a pitch that is in the strike zone.
Next, ask questions about which type of batter usually bats first,
second, third, etc. Guide the discussion toward the following guidelines using
the Batting Order Overhead:
- The first batter is usually
someone who gets on base a lot.
- Players who get on base a lot usually
bat 1st through 5th.
- The 3rd, 4th,
and 5th batters usually have a lot of doubles and home runs.
- The 4th batter usually
has the most home runs on the team.
- You want to avoid having
consecutive batters who do not get on base a lot.
Separate the class into "teams" of 2 or 3 and distribute the
Player Statistics Activity Sheet and
Batting Order Activity Sheet. Have
students name their teams.
Explain to students that they will be using the provided statistics to
select 9 players for their team and determine their team's batting order. Refer
to the overhead to remind students of the criteria for building a batting
order. Ask questions such as, "How do you determine who gets on base a lot?"
to help guide students in making their decisions. As students analyze the
statistics and choose their players, make sure they are filling out their
batting orders in the "Player" column.
By the end of the period, all groups should have their batting orders
filled out. Close the class period with a discussion about each group's batting
order, and which players they chose for 1st batter and 4th
batter. Guide the discussion toward the terms "chance" and
"likely" in order to introduce the concept of probability. Ask
questions such as, "Which of your players is the most likely to get on
Begin the second period by summarizing the activities from the previous
period. Place the Batting Order Overhead on your projector during the
- "Which of your
players is most likely to hit a home run?"[Answers will vary but the
higher the number in the HR column, the more likely the player will hit a
home run. In the Player Statistics Activity Sheet, this would be Chang.]
- "Will the
player hit a home run every time he is up to bat?" [No.]
- "Which of your
players is most likely to get on base?" [Answers will vary depending
on players on a team, but the players with the lowest numbers in the "Outs"
column is most likely to get on base. For example, Martinez is more likely
than Lin to get on base.]
- "How do you
think the guidelines on the overhead help a team score runs?" [By
using each player's statistics as a measure of likelihood of getting hits,
a manager can plan a batting order in which the team has optimal chance of
scoring the most runs.]
Tell students they will start to prepare a visual display for each
player's statistics. Display the Sample Disc Overhead. Explain that there are two steps in this process:
- Determining a
percent for each type of event (single, out, walk, etc.)
- Using the percent to
determine the size of each section on the disc.
Explain that in the next period students will use a percent protractor
to measure the size of each section on the disc. First, they need to calculate
Using the overhead, demonstrate that you first add all of the values to
find the total number of events, which is 50. Then you divide each statistic by
the total to get a decimal, which is converted to a percent by multiplying the decimal by 100 (or moving the decimal 2 places to the right). Briefly discuss the concept of percents: if a
result is 9%, it means "9 per hundred."
Using Marty McSingle's
statistics, the section representing home runs (HR) is calculated by: 2/50 =
0.04 = 4%. Explain that this means you would expect Marty to hit 4 home runs
for every 100 times that he is the batter. Have students take turns calculating
the percents for Marty, and fill in the rest of the bottom row on the overhead
with the calculated percents.
Tell students to
determine all of the percentages for their batters, recording their data on the
Batting Order Activity Sheet.
Students will need guidance as they perform the calculations. Circulate among
the groups to gauge progress. After students have worked on several players, provide
a shortcut – tell them that the total number of events (walks, hits, and outs)
is always 50 for these data, so they can use 50 as the denominator every time.
Ask, "Can anyone tell me a time-saving rule for finding the percent when
the denominator is 50?" [Just double the numerator to find the percent.]
Stress that this rule works because doubling the numerator and denominator creates an equivalent fraction with the denominator being 100.
End the class with a
discussion about the relationship between the percents and the combined part of
the whole that walks, hits, and outs represent. Make a connection between
greater percents and greater likelihood.
Begin the third period by reviewing the
information discussed in the previous class. Display the sample
player overhead, and tell the students they will use
the converted percentages to make a visual display such as the one in the
overhead. Use simple examples to show how 50% represents half of a circle, 25%
represents one-fourth of a circle, etc. Tell students that they will be
creating a disc for each player.
Using a compass, have students trace 9 circles on the manila folders or
thick paper you provided. Leave enough room around each circle so that they can
be cut apart and appear as circles on square pieces of paper.
Then, using the statistics for Kelley, demonstrate the use of a percent
protractor to determine the angle for each category.
(Using Kelley will match
data given in the Baseball Probability Activity Sheet 2 Answer Key.) These are
- Draw a radius in the
- Explain that it's
important to begin with the smallest value (2%). Beginning with the
smallest category will ensure that all categories will be represented on
the disc, because these are approximate measures.
- Next, line-up the 0%
mark on the percent protractor, making sure that the protractor is
positioned in the center of the circle.
- Mark the 2% mark,
which corresponds with the calculated size of Kelley's section for home
runs. Draw a radius to this mark, and label the section as "HR."
- Continue through all
types of hits, walks, and outs, using the lowest percentages first. Make the
sections adjacent, and label each section.
- Finally, you will be
left with one last section, for example "singles." Check the
measure of this section to be sure it is close to the calculated percent
value for singles.
Kelley's disc is shown below.
Have the student groups complete a disc for every player the group
selected, and label the discs with the players' names. End the class by having
students share some of their discs. Based on the sizes of certain sections, ask
questions such as, "What is the likelihood of this player making an out? A
home run?" and "On a scale of 0 to 10, where 0 is never happens and 10 is certain to happen, how likely is each event to occur for each player?"
Begin the fourth period by asking students if they have any questions
from the previous period. Tell students that today they will be playing a
baseball game using the player discs they created. Using the player discs, the
small paper squares numbered 1 - 9, the Game Day Batting Order Activity Sheet, and the Baseball Diamond Activity
Sheet, students are ready to "play
ball!" They first need to fill out the names of their players on the Game
Day Batting Order Activity Sheet, which will be used to tally the number of
runs scored. The names should be in the same order as on the Batting Order
Pass out the spinner parts (the pencil and paper clip) to each group. Demonstrate
an "at bat" using the Sample Disc Overhead. The paper clip should be
unbent at one end. Use the pencil point to hold the paper clip in place at the
center of the circle. Spin the paper clip with a flick of a finger, making sure
the spinner spins at least a few times before stopping. If the spinner stops on
the "out" section, it would be recorded with a tally mark as the
first out in Inning 1. If the spinner lands on, for example, on a single (1B),
the square labeled "1" would be placed on first base on the Baseball
Diamond Activity Sheet. This sheet will be used to track the progress of the
batters around the bases.
Explain that the spinner is then spun for Player 2. If a hit occurs,
place the square labeled "2" accordingly. Be sure to use the correct
numbered squares to represent each player's position in the batting order.
Explain to students that to avoid arguments in this simulation, runners
on the bases always move ahead exactly the same number of bases as the number
that corresponds to the hit:
- On an out, all runners stay where
- On a single or a walk, all runners
advance 1 base;
- On a double, all runners advance 2
- On a triple, all runners on base
score (because they advance 3 bases).
- On a home run, all runners score,
including the batter.
For example, suppose Player 1 is on 2nd base, and Player 2 then
hits a double. As a result, Player 1 will advance 2 bases to reach home plate. At
that point, you could tally 1 run for Player 1 using the "RUNS
SCORED" column of the Game Day Batting Order Activity Sheet. You would
also tally 1 run in the first inning on the Baseball Diamond Activity Sheet. Proceed
until three outs are registered, at which point the inning is over. Then add up
the tallies for runs scored for that inning, and record it in the table.
There are two options for the game. You can have each group play a game
of 6 or 9 innings to see how many runs they score. Or, you can have one group
play another group for 6 or 9 innings (in each inning both teams get a turn to
bat until they make three outs). Although there is the possibility that two groups
may have some of the same batters, tell them they are testing their selections
and the order of their batters.
Questions for Students
1. How did you decide on the batting order for your team?
[Answers will vary. Students can share problems they had, such as
having 4 players in a row at the end of the batting order who make a lot of
outs. They also may have had problems with a player like Chang, who gets lots
of hits (suggesting he should be Player 1), but also hits a lot of home runs
(suggesting he should be Player 4).]
2. How did you make use of the percent protractor?
[Answers may vary. Sample answer: I'm not sure how I would have made
the sections of the circle the right size without it. I could have made
sections that were easy, like 50% or 25%. Maybe I could have divided sections
further to make other more difficult sections. For example I could divide a
quarter circle in half to make a section that is about 12%.]
3. Compared to what you expected, were there players you felt were "lucky"
because they got more hits or more home runs than you expected? Be specific in
your answer by using numbers or percents.
[Answers will vary. Sample answer: Kelley got 1 home run in 7 at bats.
You would expect Kelley to get 1 home run in 50 at-bats. I think Kelley was
lucky because she got a home run about 7 times more often than expected.]
4. Did you feel your strategy for making the batting order succeeded? Why
or why not? If you were to play another game, are there any changes you would make to your batting order? Give reasons based on player performance for your change.
[Answers will vary. Students may realize that many trials would be
needed to decide whether one strategy was usually better than another.]
- How did the use of a popular sport affect students' interest in the
- How did
students relate the numerical display of percentage to the use of the segmented
- What various
strategic methods did you observe when students chose their players and the
- How well were the students prepared to convert the data to decimals and percents?
- What parts of the lesson were the most difficult for the students?
- If you were to present this lesson again, what student skills would you want in place to make sure the lesson went smoothly?