Date: 10/25/11
Grade Level: 8
Text: Pre-Algebra by Larson, Bowell, Kanold, and Stiff
Chapter 6: Section 6.7 Probability and Odds
Objectives/Enduring Understandings:
1) Students will be able to define probability.
2) Students will be able to identify geometric shapes on dartboard.
3) Students will be able to compute probability of dart hitting a section of the given
dartboard.
4) Students will be able to apply their knowledge of probability and apply it to a created
performance task.
5) Students will gain understanding that the data they collect, organize, and display will
influence the interpretation of the data collected.
NCTM Standards:
Understand and apply basic concepts of probability.
understand the concepts of sample space and probability distribution and construct sample
•
spaces and distributions in simple cases;
• use simulations to construct empirical probability distributions;
• compute and interpret the expected value of random variables in simple cases;
• understand the concepts of conditional probability and independent events;
• understand how to compute the probability of a compound event.
Materials and Handouts:
1) Darts and Dartboard
2) Review of definition of probability and probability equation worksheet
3) Probability Chart Worksheets: In Class Activity and Performance Task Activity
4) Baseball Pitches Worksheet
Assessment:
 Students will be receiving feedback during class of how well they apply the concept
of probability to the in class activity by the teacher and peers in the classroom.
 Students will be given a performance task to complete to apply what they have
learned about probability in class. A score guide will be provided. The assignment
is worth 45 points and will be counted towards their project grades.
In Class Activity:
The students will be reviewing the concept of probability with an in class activity
using a dartboard and darts provided by the instructor. The students will throw darts at
the dartboard and indicate what triangle the darts fall into for a total of 6 rounds. They will
indicate their findings on the worksheet provided. They will then calculate the probability
of hitting each triangle with a dart and indicate their findings on the worksheet provided.
Next the students will indicate which area of the dartboard had the greatest probability to
be hit by the darts on the answer line provided on the worksheet. Teacher feedback will be
given to the students as the activity is being completed. The teacher and peers completing
the activity will also answer student questions.
Essential Questions to Ask the Students After the Activity:
1) Why do they think data is collected and analyzed?
2) How do people use data to predict relevant events in their lives?
3) How can predictions be made based on the data you collected?
Performance Task:
The CFS baseball team has had a record year so far in the season. They say the
pitcher has a system down of pitches and has the most strikes in a game to date. Your
mission is to apply your knowledge of probability to the sport of baseball. You will attend
one of the CFS baseball games and collect data based on what pitches are thrown during
the game. Your task is to analyze the probability that certain pitches used during the game
will earn the pitcher a strike. Use the data spreadsheet provided to indicate your data
findings and the baseball pitch worksheet to identify what pitches are being used for all
nine innings. Indicate the probability of a strike for each pitch thrown on the spreadsheet
provided. Conclude from your findings what the probability is that the pitcher will have to
use a certain pitch tactic to gain the most strikes in a game. When you have completed your
worksheet, answer two of the guiding questions provided and use the data you collected or
collect more data if needed, to support your answer. Your answers will be graded by the
grading rubric provided with the assignment.
Guiding Questions:
1) Is there a correlation or connection between the probabilities of the pitch to create
strikes compared to how many strikes are in the inning?
2) Will the probability of creating the strikes change if the pitcher uses the same
throws and throws over different parts of the strike zone? Will the probability still
have a correlation or connection to the pitches thrown? Why or why not?
3) Using the data collected, how could the pitcher change his probability of strikeouts
for pitches thrown during the game?
Accommodations for Students with Disabilities:
1) Limit the amount of pitches to identify to three out of the twelve.
2) If the student is visually challenged, have them work with a partner to complete the
data collection.
3) Allow the student to ask questions and break down the performance task into
smaller/more obtainable goals for the individual student to reach. This may mean
creating a different grading rubric to follow for the student.
References:
"Baseball Pitches Illustrated." Lokesh Dhakar. Web. 26 Oct. 2011.
<http://www.lokeshdhakar.com/2007/09/20/baseball-pitches/>.
Larson, Ron, Laurie Boswell, Timothy Kanold, and Lee Stiff. "Chapter 6: 6.7 Probability and
Odds." Pre-Algebra. Evanston: McDougal Littell, 2005. 306-12. Print.
"Rubrics For Teachers | K-12 Math Rubrics and Assessment." Rubrics For Teachers | K-12
Rubrics and Assessment. Teacher Planet. Web. 26 Oct. 2011.
<http://www.rubrics4teachers.com/mathematics.php>.
Smith, Beverly, and Jay Stepelman. "Chapter 6: Assessment." Teaching Secondary Mathematics:
Teaching and Enrighment Units. By Alfred Posamentier. New York: Allyn and Bacon, 2010.
163-65. Print.
Scoring Guide:
5 Points: Assigned performance task worksheet is filled out and performance task
question is answered on worksheet.
20 Points: Guided questions are answered on separate sheet of paper and handed in
with performance task worksheet. The answers to the questions are
answered with data collected on worksheet.
10 Points: Mathematical computations are correctly done to find the probability in the
performance task.
10 Points: Assignment is well written and has been checked for grammatical and
spelling errors.
Review of Probabilities Worksheet
Definition of Probability:
 The likelihood that the even will occur.
 P (event) = Number of Favorable Outcomes
Number of Possible Outcomes
Performance Task Activity
Score Chart:
Baseball Pitch
Four-seam
Fastball
Two-seam
Fastball
Cutter
Splitter
Forkball
Curveball
Slider
Slurve
Screwball
Changeup
Palmball
Circle Changeup
Inning 1
Inning 2
Inning 3
Baseball Pitch
Four-seam
Fastball
Two-seam
Fastball
Cutter
Splitter
Forkball
Curveball
Slider
Slurve
Screwball
Changeup
Palmball
Circle Changeup
Inning 7
Inning 8
Inning 9
Baseball Pitch
Four-seam
Fastball
Two-seam
Fastball
Probability
Calculation
Inning 4
Inning 5
Inning 6
Cutter
Splitter
Forkball
Curveball
Slider
Slurve
Screwball
Changeup
Palmball
Circle Changeup
Answer: _________________________________________________________________________________________________________
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Baseball Pitches:
In Class Activity
Data Sheet for Dartboard:
Score Chart
Triangle
HAE
BEF
GFC
GDH
EIF
GIF
GHI
EIH
Triangle
HAE
BEF
GFC
GDH
EIF
GIF
GHI
EIH
Dart Throw
1
Dart Throw
2
Dart Throw
3
Probability
Calculation
Answer: _________________________________________________
Dart Throw
4
Dart Throw
5
Dart Throw
6
Dartboard Hung on Wall:
A
E
B
I
H
F
D
C
G