Lesson 1

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.

Display the image and headlines for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice and wonder with their partner, followed by a whole-class discussion.

Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the image or statement. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information.

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 just having the part of the graph from 1998 to 2012?” (In the whole graph, you 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 just seems to connect the first point in the graph to the last point. This could be misleading since 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 works 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).

Arrange students in groups of 2. Display these 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.

Identify students who sort any of the studies incorrectly.

Some students may have trouble determining whether a study is an experiment or not. Ask students to recall the definition of an experiment. Point out that experiments generally have 2 groups of subjects with only 1 variable changed between the groups.

The purpose of this discussion is for students to classify each study by study type, and to informally critique the design of each study. For previously identified students, ask, “What misconception did you have that caused you to sort one of the studies the way you did?” (I thought the sweetener and fly study was experimental because it seemed like an experiment. I realized it was observational because all the researcher did was observe several different bowls with the same type of liquid in it.)

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 example in which the letter sent home was a survey because the participants had to respond to a question.)
• “What were some reasons that you said some of the studies were good?” (There was random assignment in some of the designs. Some of the questions asked in surveys asked about the facts. Some of the studies had a large sample size.)
• “What were some reasons that you said some of the studies were bad?” (The sample size was small. The questions seemed to lead the people being surveyed to give a particular answer. Some of the experiments did 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 answer the question being asked, and whether you are influencing the results of the study by the way you ask the questions.)
• “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 directly to respond to a set of questions. In a general observational study, the researcher does not need to ask questions of the participants.)