The purpose of this Warm-up is to elicit the idea that there are different ways to collect and represent data. This will be useful when students examine statistical designs in a later activity. While students may notice and wonder many things about these images, how the data are represented (or misrepresented) is the important discussion point.

Through articulating things they notice and things they wonder about the headlines and graph, students have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.

Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary. If possible, record the relevant reasoning on or near the headline or graph. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and respectfully ask for clarification, point out contradicting information, or voice any disagreement.

Display a wider view of the graph that shows more of the story.

Ask, “How does having the whole graph tell a different story than having just the part of the graph from 2000 to 2012?” (In the whole graph, we can see that the slope of the line is positive over the 112 years represented in the graph, and you could find other 12-year periods in which the slope is negative, positive, or close to zero.) If time allows, follow up by asking, “Does the dashed line appear to be a line of best fit, or is it something else? Explain your reasoning.” (The dashed line does not appear to be a line of best fit. It seems to connect the first point in the graph to the last point. This could be misleading because the line of best fit would have a greater slope than the dashed line, and would be a little lower on the graph.)

Here are some questions for discussion:

• “Why is the dentist headline potentially misleading?” (It does not mention if they recommend other brands as well. For example, dentists might just recommend using any toothpaste at all, and this brand might work just as well as any other brand.)
• “Why is the ruler headline misleading?” (It does not mention what it is that Pythagoras rulers measure better than.)

In this activity, students take turns with a partner classifying studies as surveys, observational studies, or experimental studies, and critiquing the design of the study. Students trade roles explaining their thinking and listening, providing opportunities to explain their reasoning and critique the reasoning of others (MP3). Taking turns classifying studies gives students opportunities to analyze statements and structures closely and make connections (MP2, MP7).

If students have trouble determining whether a study is an experiment or not, consider asking:

• “Recall the definition of an experiment. How does it differ from an observational study?”

• “Experiments generally have two groups of subjects with only one variable changed between the groups. Does that describe either of the study methods you’re considering?”

The purpose of this discussion is for students to classify each study by study type, and to informally critique the design of each study. 

Direct students’ attention to the reference created using Collect and Display. Ask students to share how they classified each study and whether they thought it was good or not. Invite students to borrow language from the display as needed. As they respond, update the reference to include additional phrases.

Here are some questions for discussion:

• “For one of the studies, how did you determine what type of study it was?” (I decided that the missing school study in which the letter is sent home is a survey because the participants had to respond to a question.)
• “What were some reasons that you said some of the studies were better?” (There is random assignment in some of the designs. Some of the questions asked in surveys ask about the facts. Some of the studies have a large sample size.)
• “What were some reasons that you said some of the studies were worse?” (The sample size is small. The questions seem to lead the people being surveyed to give a particular answer. Some of the experiments do not test for what the research question was asking.)
• “What is important to think about when designing a study?” (It is important to think about whether or not the design will lead to an answer to the question being asked, and whether the researcher is influencing the results of the study by the way they ask the questions or collect the data.)
• “How did you determine if a study was observational or experimental?” (I looked for the researcher influencing a variable for the subjects in the study. If this was due to the design of the study, then I knew it was an experiment.)
• “A survey is a specific type of observational study. How did you determine if a situation should be called a survey or observational study?” (In a survey, the researcher asks the participants to respond to a set of questions. In a general observational study, the researcher does not need to ask questions to the participants.)