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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.