Download Favorite Baseball Teams - Howard County Public School System

HCPSS Worthwhile Math Task
Favorite Baseball Teams
Common Core Standard
S.CP.A.4 Construct and interpret two-way frequency tables of data when two categories are
associated with each object being classified. Use the two-way table as a sample space to decide if
events are independent and to approximate conditional probabilities.
MP1:
MP2:
MP3:
MP4:
Make sense of problems and persevere in solving them.
Reason abstractly and quantitatively.
Construct viable arguments and critique the reasoning of others.
Model with mathematics.
Common Core Geometry, Unit 5
The Task
Statistics students at Jackie Robinson High School want to see if there is a relationship between
students’ favorite American League, East Division baseball team and grade. They polled random
students in the school and found the following information:
Name
Baseball Team Grade
Name
Baseball Team Grade
th
Joanna
Orioles
12
Jackson
Yankees
10th
th
Adira
Red Sox
10
Jeff
Orioles
9th
Michael
Orioles
9th
Katie
Orioles
11th
th
Gary
Orioles
11
Savannah
Yankees
12th
Lisa
Yankees
10th
Byron
Blue Jays
11th
Sana
Orioles
9th
Val
Orioles
9th
th
Maria
Red Sox
12
Hurley
Orioles
9th
Charlotte
Orioles
9th
Amy
Red Sox
11th
th
Marley
Orioles
10
Emily
Orioles
12th
Holly
Red Sox
11th
Brandon
Yankees
9th
th
Rachel
Red Sox
9
Mina
Orioles
10th
Trevon
Orioles
11th
Mei
Yankees
11th
Colin
Orioles
12th
Chase
Yankees
9th
th
Sady
Rays
9
Bennett
Orioles
11th
Mercedes
Orioles
9th
Sully
Red Sox
10th
The class needs your help to organize the information and determine if the event {student likes
the Orioles} is independent from {student is in grade y}. They have already determined that
these events will generate conditional probabilities. Estimate the probability that a randomly
selected student is in the 9th grade given the student likes the Orioles. Do this for each grade and
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
determine whether or not the conditional probabilities include independent events. Support your
answer with logical reasoning and mathematical evidence.
The class has also been asked to extend their probability to the entire school population. If there
are 600 students, what is the probability that a student is in the 11th grade given he/she likes the
Orioles?
Facilitator Notes
1. Divide the students into groups of three or four and give them the task.
2. Instruct students to develop a method for organizing the information given; they will
most likely use a two-way table.
3. Give them rulers, lined paper, and/or graph paper so that they can make their tables and
write their answers.
4. Allow students to work and answer any questions they may have. (Look for evidence of
MP1, MP2, and MP4.)
5. Have the groups display their organization charts and let the students see each others’
papers.
6. Students may present their findings to the class by reading their explanations.
7. This task is best suited for students who have already reviewed S.CP.A.3 and know how
to prove independence within conditional probabilities.
Follow-Up Questions
1. As an answer for the second part question, one student said, “All we have to do is
multiply P(student is in 11th grade | student likes the Orioles) by the total number of
students in the school.” Why is this student incorrect? (Look for evidence of MP3.)
2. Develop a method for polling students in our own school (if it is a middle school we can
use the grades 6th, 7th, and 8th). Implement your strategy to find information for a
sampling of students and answer the same questions as the students from Jackie Robinson
High School. Use the school profiles on the website below to find out how many students
are in your school. Use http://www.hcpss.org/schools/profiles/prof_ms_all.pdf for middle
schools and http://www.hcpss.org/schools/profiles/prof_hs_all.pdf for high schools.
(Look for evidence of MP2.)
Solutions
Sample Solution:
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.
HCPSS Worthwhile Math Task
Follow Up Questions:
1. As an answer for the second part question, one student said, “All we have to do is
multiply P(student is in 11th grade | student likes the Orioles) by the total number of
students in the school.” Why is this student incorrect?
The P(student is in 11th grade | student likes the Orioles) uses the sample space of those
students in the school who only like the Orioles. Therefore, we need to limit our sample
space for the second question accordingly. By only multiplying by 600, we did not
restrict the school’s population to only Orioles’ fans.
2. Develop a method for polling students in our own school (if it is a middle school we can
use the grades 6th, 7th, and 8th). Implement your strategy to find information for a
sampling of students and answer the same questions as the students from Jackie Robinson
High School. Use the school profiles on the websites below to find out how many
students are in your school. Use http://www.hcpss.org/schools/profiles/prof_ms_all.pdf
for middle schools and http://www.hcpss.org/schools/profiles/prof_hs_all.pdf for high
schools.
Answers will vary.
Howard County Public Schools Office of Secondary Mathematics Curricular Projects has
licensed this product under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0
Unported License.