The purpose of this Warm-up is to practice the skill of estimating a reasonable answer based on experience and known information, and also to help students develop a deeper understanding of the meaning of standard units of measurement. It gives students a low-stakes opportunity to share a mathematical claim and the thinking behind it (MP3). Asking, “Does this make sense?” is a component of making sense of problems (MP1), and making an estimate or a range of reasonable answers with incomplete information is part of modeling with mathematics (MP4).

The goal of this discussion is for students to analyze the reasonableness and accuracy of their estimates.

Ask a few students to share their estimates and their reasoning. If a student is reluctant to commit to an estimate, ask for a range of values. Display these responses for all to see in an ordered list or on a number line. Add the least and greatest estimates to the display by asking, “Is anyone’s estimate less than _____? Is anyone’s estimate greater than _____?” If time allows, ask students, “After this discussion, does anyone want to revise their estimate?”

Then reveal the actual value (294.75 minutes), and add it to the display. 

Encourage students to think about and discuss the accuracy of their estimates and the estimates that are displayed by asking questions, such as:

• “Is the actual value inside the range of values?”
• “Is it toward the middle?” 
• “How variable are the estimates?”
• “What are the sources of error?”

Consider developing a method to record a snapshot of the estimates and the actual value so that students can track their progress as estimators over time.

Students practice conceptualizing the distribution shapes of situations. In this activity, emphasis should be placed on students’ justification for their matches as they construct viable arguments (MP3). Students reason abstractly and quantitatively (MP2) when they connect distribution shapes to situations.

In this activity, students extend their thinking about distribution shapes to using the shape to justify making a decision from a set of representations. In previous lessons, students matched distribution shapes to situations. Students practice applying the situations when they choose a representation and are able to remove the others. This activity prepares students to compare specific measures of several distribution shapes in a later lesson.