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).