1.1: Which One Doesn’t Belong?: Types of Data (5 minutes)
This is the first Which One Doesn't Belong routine in the course. In this routine, students are presented with four figures, diagrams, graphs, or expressions with the prompt “Which one doesn’t belong?” Typically, each of the four options “doesn’t belong” for a different reason, and the similarities and differences are mathematically significant. Students are prompted to explain their rationale for deciding that one option doesn’t belong and given opportunities to make their rationale more precise.
This warm-up prompts students to compare four survey questions. It gives students a reason to use language precisely (MP6) and gives you the opportunity to hear how they use terminology and talk about characteristics of the items in comparison to one another.
Arrange students in groups of 2–4. Display the survey questions for all to see. Give students 1 minute of quiet think time and then time to share their thinking with their small group. In their small groups, tell each student to share their reasoning why a particular item does not belong and together find at least one reason each item doesn't belong.
Which one doesn’t belong?
Question A: How many potato chips are in this bag of chips?
Question B: What is the typical number of chips in a bag of chips?
Question C: What type of chips are these?
Question D: What type of chips do students in this class prefer?
Ask each group to share one reason why a particular item does not belong. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which one does not belong, attend to students’ explanations and ensure the reasons given are correct. During the discussion, ask students to explain the meaning of any terminology they use, such as numerical data, categorical data, or average. Also, press students on unsubstantiated claims.
1.2: Representing Data About You and Your Classmates (25 minutes)
In this activity, each group of 4 students is assigned three questions. One of the three they are assigned is a non-statistical question, one would generate numerical data, and one would generate categorical data. Groups also generate a fourth question of their own that can be answered with data. First, the group comes up with four survey questions that they can ask their classmates to collect data about their four questions of interest. Then, they collect data from their classmates by asking the survey questions. Finally, they summarize their results to answer the four questions of interest and reflect on the nature of the different questions they attempted to answer.
In a later lesson, students will represent the distribution of data collected in this activity graphically. If they record the data in their workbooks, it will be easy to retrieve later. If students record data some other way, be sure your method allows them to easily retrieve the data later.
Arrange students in groups of 4. Assign each group one of the following sets of three questions.
- On average, how many letters are in the family (last) names for students in this class?
- Which month has the most birthdays from the class?
- How many periods (or blocks) have there been before this math class?
- On average, what is the furthest, in miles, that each student in this class has ever been from home?
- Would the class rather have a snow day or a field trip day?
- In what year was the 13th Amendment ratified?
- About how long did it take students in this class to get to school this morning?
- Which combination does the class prefer: peanut butter and banana or strawberry and banana?
- What is the lightest element from the periodic table?
- On average, how many movies in the theater did each student in the class watch this summer?
- Does the class prefer to write on paper with or without lines?
- How many seats are in the classroom?
Give students 2 minutes to write a question of their own that could be answered using data from the class. After giving students time to discuss the questions in their groups, pause for a whole group discussion.
Give students an example of the types of questions they should be asking their classmates. “For example, if you are assigned the question, ‘Which month has the most birthdays from the class?’ you might ask your classmates, ‘In what month is your birthday?’”
Supports accessibility for: Language
Your teacher will assign you a set of 3 questions.
- Write another question of your own that will require data collected from the class to answer.
- For each of the 4 questions, write a survey question that will help you collect data from the class that can be analyzed to answer the questions.
- Ask the 4 survey questions to 15 classmates and record their responses to collect data.
- After collecting the data return to your group.
- What is the question of your own that will require data collected from the class to answer?
- What are the 4 survey questions you will ask your classmates?
- Summarize the data for each question in a sentence or two and share the results with your group.
- With your group, decide what the responses for question number 1 have in common. Then do the same for questions numbered 2 and 3.
- Does the question you wrote fit best with the questions from number 1, 2, or 3? Explain your reasoning.
|responder’s name||question 1 response||question 2 response||question 3 response||my question response|
Are you ready for more?
Find a news article that uses numerical data to discuss a statistical question.
Find a news article that uses categorical data to discuss a statistical question.
Students may confuse statistical questions with survey questions. Explain that the set of three questions are statistical questions that can be answered using the survey questions. For example, students may think they should ask each of their classmates for the average distance they have traveled from home. However, students can ask each classmate "What is the furthest distance you have traveled from home?" and colletively use the answers to this survey question to answer the statistical question about the average distance their classmates have travelled from home.
Share all of the questions numbered 1 from each set. Ask students to summarize what responses to these questions might have in common. (In order to answer them, you collect responses that are numbers.)
Repeat for the questions from number 2 and 3. (In order to answer questions from number 2, you collect responses that are descriptive words or characteristics. The questions from number 3 only have one possible answer, and don’t have any variability in the responses.)
Tell students that we call data collected by questions in number 1 numerical data, data collected by questions in number 2 categorical data, and the questions in number 3 are non-statistical questions, because there will be no variability in the responses. Questions in number 1 and 2 are called statistical questions since they require collection of data and there is anticipated variability in the responses.
Supports accessibility for: Memory; Language
To promote student understanding of the differences between statistical and non-statistical questions and classifying data as numerical or categorical, ask:
- “What makes a question statistical?” (There is variability in the data collected.)
- “What is an example of a non-statistical question?” (What value for \(x\) makes the equation \(x + 5 = 7\) true?)
- “What is an example of a statistical question that we have not used in class?” (On average, how many people eat breakfast every day?)
- “What type data is collected to answer the statistical question, ‘Would the class rather have pizza or donuts?’” (Categorical)
- “What is an example of a statistical question that results in numerical data?” (What is the typical surface area of styrofoam pellets?)
To help prepare students for the next lesson, ask:
- “What are some different ways to represent data graphically?” (Bar graphs, dot plots, box plots, pie charts, and histograms.)
1.3: Cool-down - Categorizing Questions (5 minutes)
Cool-downs for this lesson are available at one of our IM Certified Partners
Student Lesson Summary
Statistics is about using data to solve problems or make decisions. There are two types of data:
- Numerical data are expressed using a number. For example, to answer the question “How tall are the students in this class?” you would measure the height of each student which would result in numerical data.
- Categorical data are expressed using characteristics. For example, to answer the question “What brand of phones do people use?” you would survey several people and their answers result in categorical data.
The question that you ask determines the type of data that you collect and whether or not there is variability in the data collected. In earlier grades, you learned that there is variability in a data set if all of the values in the data set are not the same. These are examples of statistical questions because they are answered by collecting data that has variability:
- “What is the average class size at this school?” would produce numerical data with some variability.
- “What are the favorite colors of students in this class?” would produce categorical data with some variability.
These are examples non-statistical questions because they are answered by collecting data that does not vary:
- “How many students are on the roster for this class?” would produce numerical data that does not vary. There is only one value in the data set, so there is no variability.
- “What color is this marker?” would produce categorical data that does not vary. There is only one value in the data set, so there is no variability.