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 Election Project: Predicting Outcomes using Statistics
 Subject:Mathematics (Algebra/Statistics) Grade Level: 8-11 Description: This unit teaches students about the basics of statistics using data from student opinions on everyday topics. These lessons are framed as practice for learning the math skills the students will need to predict the winner of the next U.S. presidential election. These predictions are based on students' use of measurements of central tendency and box-and-whisker plots to analyze surveyed responses about opinions on major election issues. How it Works: Days 1-2: Intro to Election Project. This portion of the unit provides a context for the study of measurements of central tendency, dispersion, and their graphic representation. It is connected to real life and therefore frames the usefulness of the math that students are about to learn. This piece may be done in conjunction with another discipline (e.g., social studies) as an interdisciplinary project, in advisory, or in the Math class. Days 3-7 focus on math skills and are not strictly dependent on the context of the elections. If completing the election project is not feasible for you, these days address Standards 1-3, but not 4 (see below), which appears most clearly in the election project. Days 8+: Completing the election project and/or other assessments. All materials (packets) for these are included, as well as an overview of tips in facilitating completion of the project, although detailed daily lesson plans are not. The amount of time and guidance to be given to your students for this process will depend on their level of language and familiarity with such project. Final Project/Product: Create a book of “U.S. Presidential Election-2008” data, analysis, predictions, and conclusions and/or a learning log. Overall Value: This project addresses key NYS Mathematics standard, provides a connection to real-life issue, and offers opportunities to critique usefulness of Math in real life (see its advantages and limitations) and nterdisciplinary work (Social Studies, English, Science). English Language Learners: In addition to points addressed in “Overall Value” and “Tips for the Teacher “, there is a built-in focus on vocabulary, visuals, and on modeling vs. explaining that teachers unfamiliar with teaching ELLs sometimes overlook. Tips for the Teacher: Leave pictures, labels, and flip charts with essential questions and key vocabulary around the room throughout the unit. Constantly point to them in conversations with students (one on one or large group). Slowly, kindly, push students to use this vocabulary (Example: One campaign issue is “sick people”…that is completely correct. What is another way to say that in English? Look on this chart (point)…repeat after me) Be very attentive to organization, particularly in the surveying, field trip, and data compilation phases of the project. Be sure every adult involved clearly know his or her role and that students do not throw out any data collection surveys or compilation pages (even if they think they don't need them anymore!) until the end of the project. Best way to ensure this: provide systems for students to store information (folders, file cabinets, etc.).
 Students categorize data as qualitative or quantitative. Grade: High School Subject: Integrated Algebra/Statistics Students compare and contrast the appropriateness of different measures of central tendency for a given data set. Grade: High School Subject: Integrated Algebra/Statistics Students construct a histogram, cumulative frequency histogram, and box-and-whisker plot, given a set of data. Grade: High School Subject: Integrated Algebra/Statistics Students identify and describe sources of bias and its effect, drawing conclusions from data. Grade: High School Subject: Integrated Algebra/Statistics Student understand how the five statistical summary (minimum, maximum, and the three quartiles) is used to construct a box-and-whisker plot). Grade: High School Subject: Integrated Algebra/Statistics Students analyze and interpret a frequency distribution table or histogram, a cumulative frequency distribution table or histogram, or a box-and-whisker plot. Grade: High School Subject: Integrated Algebra/Statistics

 Day 1: Introduction to Election Project: Who will win in 2008?

 Day 2: How can we measure and talk about the opinions of different groups?

 Day 3: Measurements of Central Tendency: The Basics of Quantitative Data

 Day 4: Measurements of Central Tendency: Tricky Quantitative Data & Qualitative Data.
 Objectives Students will be able to calculate mode, mean, and median for data sets seeming to have multiple modes or medians. Students will be able to explain how to calculate mode, mean, and median, and explain when it is not possible to do so. Students will be able to identify a data set as qualitative or quantitative. Students will be able to explain the difference between qualitative and quantitative data, and what that means for calculating measurements of central tendency. Materials “The Big Picture” Flip chart--attached “Election Issues” Flip chart Statistics Practice Packet (copies for students)--attached Statistics Practice packet (1 copy on transparencies) and overhead Procedure 1 DO NOW: The following are the ages of the students in my group: 12, 15, 13, 15, 14. 1) What is the mode age of students in my group? 2) What is the median age? 3) What is the mean age? a. Allow time for students to complete, circulating to help strugglers and asking some students to help others. b. If students finish quickly, tell them to start page 8 as you finish helping others. c. Ask three students to present their solutions (2 minutes each). Keywords qualitative, quantitative, mean, median, mode, central, tendency , ascending, descending Procedure 2 Calculating measurements of central tendency: practice a. Explain to students that they have the period to complete pages 7-10. Show them the two sets of data in question (p.7, p.9) and point out that these are answers from last year's class. (Not really--you made them up to have two data items that repeat the most, and an even number of data items, but don't tell them this.) b. READ THROUGH the questions on page 7 with them. Ask if they think they can answer qualitative and quantitative questions, and if they can explain in their own words how to get mean, median & mode. They should say yes! c. WARN THEM…this data is tricky on purpose! Point out that after the question “Show your work” (for the mode on p.8), they are asked “What is the problem?”… SOMETIMES THEY WILL DO EVERYTHING CORRECTLY & THEY WILL COME ACROSS A PROBLEM!. Tell them not to get frustrated. d. If there is no problem, tell them to write NONE. IF there is a problem, tell them to explain the problem and then explain what THEY think they should do to fix the problem. Procedure 3 Allow students the period to work. a. You will need to circulate a lot, helping students when they get to the “problems”, encouraging them not to get frustrated and to write down their ideas. b. Prod them to come up with ideas…(Ex: Do you think there can be 2 modes. Yes or no? What would you do? Write it down!), encouraging them to get others' ideas as well. c. Work with struggling students on basics and discussion challenge (bottom p.8) with more advanced students. d. You may need to give direction on the CONCLUSION at the bottom of p. 10 as students reach that point. Remember--it is okay right now if students are not getting the right answers… Discussion will be tomorrow. Extension Homework: Finish pages 7-10 if you haven't. For struggling or special needs students, you may want to go around individually and adjust their data to avoid the “problems” (2 numbers that repeat the most, 2 number in the middle), to give them practice with the simplest case first (or perhaps only requiring them to do the simplest case, depending on their goals). Assessment Informal observation of their work on pages. 7-10 and their participation in class discussion. Interdisciplinary overlap- Instead of using data from “previous classes,” talk to science or social science teachers to see if there is data related to their class that you can use. This will make the discussion of “WHICH measurement of central tendency is most representative” more interesting & more representative.

 Day 5: Measurements of Central Tendency: Tricky Qualitative Data & Quantitative Data (continued)

 Day 6: Analyzing data using Box & Whisker Plots
 Objectives Given a set of data, students will be able to calculate the 5 numbers of a 5-number summary and identify them by name. Students will be able to construct a box-and-whisker plot. Students will be able to identify for which sets of data it is possible to construct a box-and-whisker plot, for which it is not possible to do so, and explain why. Materials “The Big Picture” Flip chart--attached “Election Issues” Flip chart Statistics Practice Packet (copies for students)--attached Statistics Practice packet (1 copy on transparencies) and overhead Keywords maximum, minimum, quartile Procedure 1 DO NOW: Explain in your own words what you think the following words mean: a) maximum, b) minimum, c) quarter, d) range. a. If you want some information, would you rather look at a list of numbers or a graph? Why? b. Share answers to vocabulary, recording them on the board for later reference. If students bring up the idea of \$0.25 for a quarter, relate this to the percentage of a dollar. c. Try to elicit the fraction representation. d. Discuss question #2. Try to elicit the ideas of information being easier to understand VISUALLY (in picture form), but ONLY if you understand the picture! Procedure 2 Box & Whisker Plot a. Explain: This is a graph that allows us to see how the data is spread out around the median. Advantage: we get more information than just one number. b. Show the students the box & whisker plot on pg. 12. Acknowledge that it looks scary, but that it actually is based on just FIVE numbers (fill in 5 together on overhead). c. Go through each of the 5 numbers, pointing to them on the box & whisker plot, and filling in the chart what they are. (Ex: MINIMUM= the smallest data item, MAXIMUM=the largest data item, MEDIAN=the data item in the middle when we put them all in order.) d. Take a bit more time with the 1st & 3rd quartile. Without defining them, use the place in the chart to do a think aloud and demonstrate how you calculated them. Then ask the students to explain how you got them (1st quartile is the median of the data below the true median. 3rd quartile is the median of the data above the true median). Record the class answer & allow the students to copy notes. Procedure 3 Elicit from students WHY we use the word "quartile". a. Refer back to do now, and quarter meaning 25% or ¼. b. Read through top of page 13 together. Allow students the choice: to begin working on pages 13-14 on their own or to join your group at the front of the room to do page 13 together before finishing page 14 on their own. c. While students are circulating, you will need to help with the frustration of trying to do a box-and-whisker for qualitative data. d. Encourage students to always write out the specific problems they are encountering when they get frustrated (example: How am I supposed to find the maximum, minimum, median, etc of data like “pink, blue…” None of them are bigger or smaller, so I can’t put them in order. Not possible!) Extension Homework: Finish pages 13-14. Possible extension: Include a few more pages on histograms or line plots, particularly to address the need to visually represent qualitative data. Assessment Informally, small group work. Interdisciplinary overlap- Again, speak to other subject teacher to get data relevant to their classes, or at least to get ideas of what kind of data sets you could invent that might simultaneously support student learning in other classes.

 Day 7: Election Project & Book Construction
 Objectives Students will create their own surveys. Students will complete a field trip during which they survey members of a neighborhood. Students will understand good survey etiquette. Students will understand predictions and outcomes in statistics. Materials “The Big Picture” Flip chart student survey (sample attached) Keywords Procedure 1 Reintroduce the Election Project by focusing students on “The Big Picture” Flip chart. Procedure 2 Create survey with students (see attached sample). a. Be sure to number the opinions (1= strongly oppose, 2-oppose, 3-indifferent, 4-support, 5-strongly support) to facilitate quantitative data analysis. b. Type up, copy, and give each student 20 copies of the survey (created in class or attached). c. Assign them to complete 10 with people in their neighborhood. d. Plan a field trip day (by advisory?). Assign each advisory to a demographically different area of the city. Each student must complete their 10 remaining surveys this day. Procedure 3 Prep for survey field trip day. a. Brainstorm what to do and what not to do when surveying people in a t-chart flip chart (politeness, eye contact, possible phrases to use, always be with a buddy…). b. Choose a student to help you model good survey etiquette and bad survey etiquette (make it humorous-- do everything you shouldn’t). You can do this before doing the brainstorm or after, depending on your kids. c. In conclusion, talk with the class about why it is important to use good survey etiquette (safety, respect, being a good representative of your school. Prepare students for taking the subway (map reading skills!). d. Make sure each student has a demographic group, issue, and a partner. Pairs of partners should be matched up with another pair according to demographic group and issue (e.g., the pair investigating how males feel about keeping abortion legal grouped with the pair investigating how females feel about keeping abortion legal). Procedure 4 Data compilation a. As students are working through pages 6-11 of “Election Project Intro Packet” , give each of them a flip chart paper on which to write their data. This will make their data available to everyone for discussion & for thinking about challenge questions. (See “Election Project Guidelines and Template.) b. Strong classroom management and constant conferencing will be necessary as students work through Election Project Template & Guidelines. c. Be sure to go over rubric with students as they begin this part of the packet. Procedure 5 Be sure to discuss Conclusions, Reflections, and Challenge pieces as a group (pages 10, 11, 12, 15) as a class. a. Interesting reflection and analysis points to try to elicit: • What surprised you most? • Was our prediction correct? Why do you think it was or wasn’t? • How representative was our sample? • Is it possible any of the data was biased? Explain.

Jesseca Long

jrlong9@yahoo.com

Bronx International High School
1110 Boston Rd
Bronx, NY 10456

Jesseca Long is a teacher of Mathematics, French, and ESL. In addition to teaching in the U.S. and Africa, she has worked as a Math coach and teacher trainer, and on facilitating professional development in the areas of Classroom Management, Collaborative Learning, and Language Development in Mathematics. She currently teaches Advanced Algebra & Pre-Calculus to 12th grade students at Bronx International High School.

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