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Statistics and Probability for Middle-School Math Teachers: Addressing the Common Core Teacher Notes Statistical Questions Logistics This lesson is intended for students in Grade 6 as an introductory lesson into the concept of statistical variability. This lesson is written for class sizes larger than 18 students. For smaller class sizes, students may need to generate multiple questions for a valid data set. Materials: 1 – 3” x 24” tag board sentence strip per student 1 – marker per student (Optional) colored sentence strips for headings (Optional) magnetic tape to adhere strips to whiteboard Time: This lesson should be completed in one 45 – minute class period. Objectives/Standards The objectives of this lesson are to: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. CCSS.Math.Content.6.SP.1 Formulate questions that can be answered with data and make sense of practical problems by turning them into statistical investigations. CCSS.Math.Practice.MP1 Interpret variability in terms of the question being asked. References to Common Core are adapted from NGA Center/CCSSO © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. CCSS.Math.Practice.MP2 Introduction For this inquiry, students will generate questions that they are interested in asking their classmates. These questions will be sorted by the teacher into those that are statistical vs. those that are not statistical without revealing why they are being sorted in that manner. Students will look at the characteristics of statistical questions and will determine what makes a question “statistical” in nature, and will use this information to shift a nonstatistical question into one that is statistical. Finally, students will select among the generated questions to develop a method for collecting data to answer the selected statistical question. Activity 1: What makes a question a “statistical” question? This will be the guiding question for this lesson. Provide each student with a sentence strip and a marker. If you have a small class size (<18 students) you may wish to have each student complete two sentence 1 Statistics and Probability for Middle School Teachers: Addressing the Common Core Professional Learning Day; February 28, 2014 1 Statistics and Probability for Middle-School Math Teachers: Addressing the Common Core Teacher Notes strips. Pose the following prompt to your students: Write one question that you would like to ask members of this class. If students ask for clarification on what “the teacher” would like them to ask, tell them that their question is entirely up to them (but should be appropriate to ask in a classroom setting). As students complete their questions, direct them to bring them to the teacher. Questions will be sorted by whether or not they are statistical in nature. For example, if a student writes, “How tall is Johnny?” it would not be considered statistical in nature since the question does not anticipate variability in Johnny’s age. There is a deterministic answer to the question. However, if the question is worded, “How tall are the students in my class?” then it would be considered statistical because there is anticipated variability in the heights of the students within the class. Similarly, if a student asks, “Do students in this class have more dogs than cats?” we would not consider this a statistical question since we can find the total number of dogs and the total number of cats students own and take the higher value to get a single absolute answer. In contrast, asking, “What pets do students in this class prefer?” introduces variability. We are looking for the mode of a data set that can have multiple categories (dog, cat, fish, gerbil, ferret, etc.) and each student in the class could give a different response. What pets do students in this class prefer? In general, a statistical question is one in which the population is specified, variable answers are anticipated, and the question asks for interesting information. Many times, students will write questions which can be answered with only two choices: yes or no. Often, these questions can be reworded to introduce more variability in the answer responses. However, we also do not want to ask questions with too much variability or the data can become meaningless. For initial student questions, sort them into two categories: Statistical Questions Non-Statistical Questions 2 Statistics and Probability for Middle School Teachers: Addressing the Common Core Professional Learning Day; February 28, 2014 Statistics and Probability for Middle-School Math Teachers: Addressing the Common Core Teacher Notes At first, do not place the headings at the top of the columns. Post the responses on a whiteboard using magnetic tape, or tape sentence strips to a sheet of butcher paper. Teacher-written “seed” questions may be included among the student questions. Form student teams of three to four students. Ask student teams to look at the questions on the left and compare them to the questions on the right. Discuss with their teams what they notice. If students are having difficulty, direct them to look at a question on the left (statistical) and write down what responses students in the class might choose. Also have them do the same for a question on the right (non-statistical). Have each team share their observations of the sorted questions. A discussion of variability as the “number of possible answer choices you have” can lead students to realize that if their question can only be answered one way, then it is not a statistical question. Answers need to vary among the students in the class to provide data that has variability. At this point, introduce the headings “Statistical Questions” and “NonStatistical Questions” to the students. Tell students statistical questions: Specify populations and measurements of interest. Anticipate answers based on data that vary. As a whole class, go down the list of statistical questions and discuss why each one of the questions categorized under the heading “Statistical Questions” meets the criteria of a statistical question. Then, have each team choose one “Non-Statistical Question”. Be sure to have several non-statistical questions ready if students did not self-generate enough for each team to have a question. Their task will be to determine why a question was categorized as non-statistical and to reword the question to make it a statistical question. Allow time for student teams to discuss their response and re-write the new question on the back of the original question’s sentence strip. Each student team will present to the class: The original question and why it was non-statistical. The new question and why it is now a statistical question. Following a team’s presentation, other groups will be asked if they agree or disagree with the new question’s wording. If a group disagrees, they will provide a reason for the disagreement. A whole-class discussion will then be facilitated by the teacher to reach consensus on how the question should be categorized. 3 Statistics and Probability for Middle School Teachers: Addressing the Common Core Professional Learning Day; February 28, 2014 3 Statistics and Probability for Middle-School Math Teachers: Addressing the Common Core Teacher Notes Activity 2: Sorting question types In the next part of this lesson, have student teams separate into partner teams of 2 students each. Provide each student team a set of unsorted questions and a t-chart of “Statistical Questions” vs. “Non-Statistical Questions” and have students cut out the questions and glue under the appropriate heading. As partner teams complete the activity, provide an answer key for students to compare their answers. If students have made mistakes, encourage them to determine why that particular answer was incorrect and share with the teacher prior to advancing to the next activity. Activity 3: Data Collection Plan Once partner teams have checked their work, provide each team with one “Data Collection Plan” worksheet. For this activity: Student partner teams will select one question from the original student-generated list of “Statistical Questions.” If there are enough questions for each partner team to select one question, remove that question from the board as a team selects it. Otherwise, multiple teams can utilize the same question set. Students will identify the population to whom the question applies as well as what is being measured and the variability that is expected in the answers to the question. Students will determine a strategy to collect the data that is necessary to answer their question. Advise students that they should be specific in how they are going to get the answers to their question but do not lead them to a specific technique. Student partner teams will also brainstorm how they are going to organize their collected data. Activity 3 is an excellent way to prepare students to discuss the concepts of bias in data collection strategies as well as introduce data organization techniques for quantitative data (line plots, histograms, and boxplots) and review categorical data organization tools such as bar graphs. Conclusion This lesson is intended to introduce the idea of variability in data to students through the use of carefully worded statistical questions. Students should leave this lesson with the knowledge that a statistical question will lead to a set of data that will have different values and will set the stage to looking at the data set as a “distribution” which can be described by its center, spread, and overall shape. 4 Statistics and Probability for Middle School Teachers: Addressing the Common Core Professional Learning Day; February 28, 2014 Statistical vs. Non-Statistical Questions Cut out the questions below. Sort them on the T-chart according to whether you and your partner agree it is a “Statistical Question” or a “Non-Statistical Question”. You must agree on where a question belongs before you glue it down into position. Once you are finished, ask your teacher for the answer key to check your work. How many hours a night do you spend on homework? How many text messages do students in our class send in one day? What are the heights of the players on the Chicago Bulls basketball team? Do you like listening to music? How many times did students in our class eat at fast-food restaurants in the last month? How many students in this class turned in their science project on time? How many words are there in the Pledge of Allegiance? How many hours per day do students in this class spend playing video games? How many miles do the teachers in our school travel to work each day? What is your favorite type of soda? What were the weekly cupcake sales at a What color M&M appears most often in local bakery for the past year? 1.69 oz bags of the candy? How many hours did you sleep last night? What is the favorite pizza type of 6thgraders at your school? What is the average number of words on a page in your math textbook? How many times did you eat the school lunch last month? 1 Statistical Questions Student Pages 1 Statistical vs. Non-Statistical Questions Sorting Name: ______________________________ Partner Name: _____________________________ Statistical Questions Non-Statistical Questions 2 Statistical Questions Student Pages 2 Data Collection Plan for Statistical Questions Name: ______________________________ Partner Name: _____________________________ 1. What is the statistical question you are going to ask? 2. What is the population (collection of people, animals, plants or things from which we may collect data) to which your question is referring? 3. What is your question measuring? 4. Describe the variability that you expect in the responses to your question: 5. How are you going to collect the data? 6. How might you organize your collected data? 3 Statistical Questions Student Pages 3 Statistical vs. Non-Statistical Questions ANSWER KEY STATISTICAL QUESTIONS NON-STATISTICAL QUESTIONS How many text messages do students in our class send in one day? How many hours a night do you spend on homework? What are the heights of the players on the Chicago Bulls basketball team? Do you like listening to music? How many times did students in our class eat at fast-food restaurants in the last month? How many students in this class turned in their science project on time? How many hours per day do students in this class spend playing video games? How many words are there in the Pledge of Allegiance? How many miles do the teachers in our school travel to work each day? What is your favorite type of soda? What were the weekly cupcake sales at a How many hours did you sleep last local bakery for the past year? night? What color M&M appears most often in 1.69 oz bags of the candy? How many times did you eat the school lunch last month? What is the favorite pizza type of 6thgraders at your school? What is the average number of words on a page in your math textbook? 4 Statistical Questions Student Pages 4