Lesson 2

This warm-up prompts students to compare four questions. It gives students a reason to use language precisely (MP6) and provides the opportunity to talk about characteristics of the items in comparison to one another. Monitor for students who mention numerical and categorical data as well as those who refer to the variability of the data to determine whether the question is statistical.

Arrange students in groups of 2–4. Display the questions for all to see. Give students 1 minute of quiet think time and then time to share their thinking with their small group.

Record and display the responses for all to see. There is no single correct answer to the questions, so 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 survey study, statistical question, observational study, or experimental study. Also, press students on unsubstantiated claims.

Here are some questions for discussion.

• “What is a statistical question?” (A question that requires data to be collected and in which variation is expected in the data collected.)
• “What is the difference between an observational study and an experimental study?” (In an observational study, you collect the data without influencing things directly to answer your question. In an experimental study, you directly influence things and collect data to answer your question.)
• “What makes a survey a special type of observational study?” (In a survey, you ask people questions and their responses are the data. In other observational studies, the researcher observes people and the information they record about the observations becomes the data.)

In this activity, students take turns with a partner recognizing the purposes of and differences among sample surveys, experiments, and observational studies. Students trade roles explaining their thinking and listening, providing opportunities to explain their reasoning and critique the reasoning of others (MP3).

Arrange students in groups of 2. Tell students that, for each question, one partner determines if a survey, observational study, or experimental study would be the best way to collect data to answer the question. The partner’s job is to listen and make sure they agree. If they don’t agree, the partners discuss until they come to an agreement. For the next question, the students swap roles. If necessary, demonstrate this protocol before students start working.

Display the statements for all to see.

• Surveys are sets of questions given to people to seek their responses.
• Observational studies collect data without influencing things directly.
• Experimental studies collect data by directly influencing something to determine how another thing is changed.

Some students may be confused about when to use an experiment or observational study. Ask students to recall the definition of the studies and point out that experiments require dividing the subjects into 2 groups and directly influencing one of the groups.

The mathematical purpose of this discussion is for students to recognize the purposes of and differences among sample surveys, experiments, and observational studies. Here are some questions for discussion:

• “How did you determine which type of study would be best for each situation?” (I really had to look at the question of interest and determine what would be needed to answer it. If observations would be enough, then I chose an observational study. If I needed to get people’s opinions, then a survey made sense. Finally, if I wanted to know one variable’s effect on another variable, then I chose an experimental study.)
• “What type of study is most appropriate for measuring one variable’s effect on another variable?” (Experimental)
• “What type of study are you likely to be conducting if you collect information about populations to learn about the population, compare populations, or compare variable influence within a population?” (An observational study)
• “Why is a survey a useful type of study?” (A survey is useful for collecting opinions or thoughts which cannot be measured otherwise. It can also be useful to find out more about the population you are studying by asking questions.)

The mathematical purpose of this activity is for students to recognize the purposes of and differences among sample surveys, experiments, and observational studies, and to apply that knowledge in context. Students also have the chance to discuss how to interpret the results from a survey, including whether a causal relationship is likely present based on the study’s methods.

Tell students that they will be answering questions about a given study and will then design their own study.

The goal of this discussion is to discuss the difference between association and causation, and the reasoning that goes into designing an experimental study. Here are some questions for discussion.

• “The given study showed that people who watch television for at least 2 hours every night have lower energy in the evening than people who do not watch as much television. Is this statement describing an association or causation? Explain your reasoning.” (It is describing an association. Using the survey data, we are able to see that people who watch more television report having less energy in the evening, but we do not know if that is caused by some other factor. Maybe people watch television because they have less energy or something else entirely.)
• “What did you include in your experimental design?” (I included two different groups, I assigned people to the groups at random, I recorded their energy levels at the start of the study, and I recorded the energy of each group at the end of the month.)
• “What are some ways to categorize the different factors that our class included in their experimental design?” (Treatment groups, control groups, time, sample size, pre-test, post-test, random selection, random assignment to groups.)