The purpose of this Warm-up is to prepare students for the Information Gap activity that follows. First, students are given a problem with incomplete information. They are prompted to brainstorm what they need to know to solve a problem that involves the masses of elephants. Next, they practice asking for information, explaining the rationale for their request, and persevering if their initial questions are unproductive (MP1). Once students have enough information, they solve the problem.

Tell students that the problem is a part of an Information Gap routine. In the routine, one person has a problem with incomplete information, and another person has data that can help with solving it. Explain that it is the job of the person with the problem to think about what is needed to answer the question, and then to request it from the person with information. 

Tell students that they will try to solve the problem this way as a class to learn the routine. In this round, the students have the problem, and the teacher has the information.

• Ask students, “What specific information do you need to find out whether there is a significant difference?” 
• Select students to ask their questions. Respond to each question with, “Why do you need to know _____?” 
• After students justify their question, answer questions only if the questions can be answered using these data:
  • The distribution of masses for each set of elephants is approximately symmetric.
  • Captive Asian elephants:
    • Mean mass of captive elephants: 3,073 kg
    • Standard deviation of captive elephant masses: 282 kg
    • Median mass of captive elephants: 3,055 kg
    • IQR of captive elephant masses: 399 kg
  • Wild Asian elephants:
    • Mean mass of wild elephants: 2,373 kg
    • Standard deviation of wild elephant masses: 121 kg
    • Median mass of wild elephants: 2,386 kg
    • IQR of wild elephant masses: 163 kg
• If students ask for information that is not on the data card, respond with, “I don’t have that information.”

When students think they have enough information, give them 2 minutes to solve the problem. (There is a significant difference in mass between captive and wild Asian elephants. Because the distributions are symmetric, it makes sense to use the mean and standard deviation masses for the two groups. The difference in means of 700 kilograms is very different, even in light of the standard deviations for the groups.)

Tell students that they will work in small groups and use the routine to solve problems in the next activity.

Math Community

At the end of the Warm-up, display the Math Community Chart. Tell students that norms are expectations that help everyone in the room feel safe, comfortable, and productive doing math together. Using the Math Community Chart, offer an example of how the “Doing Math” actions can be used to create norms. For example, “In the last exercise, many of you said that our math community sounds like ‘sharing ideas.’ A norm that supports that is ‘We listen as others share their ideas.’ For a teacher norm, ‘questioning vs telling’ is very important to me, so a norm to support that is ‘Ask questions first to make sure I understand how someone is thinking.’”

Invite students to reflect on both individual and group actions. Ask, “As we work together in our mathematical community, what norms, or expectations, should we keep in mind?” Give 1–2 minutes of quiet think time and then invite as many students as time allows to share either their own norm suggestion or to “+1” another student’s suggestion. Record student thinking in the student and teacher “Norms” sections on the Math Community Chart. 

Conclude the discussion by telling students that what they made today is only a first draft of math community norms and that they can suggest other additions during the Cool-down. Throughout the year, students will revise, add, or remove norms based on those that are and are not supporting the community. 

This is the first Information Gap activity in the course. In this activity, students compare distributions but do not initially have enough information to do so. To bridge the gap, they need to exchange questions and ideas.

The Information Gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information that they need to solve it. This may take several rounds of discussion if their first requests do not yield the information that they need (MP1). It also allows them to refine the language that they use and to ask increasingly more precise questions until they get the information they need (MP6).

This task is provided for optional, additional practice for understanding variability in context.

The mathematical purpose of this activity is to compare data sets, and to interpret the measures of center and measures of variability in the context of the problem.