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.
Display the first paragraph of the activity statement for all to see. Ask students to solve the problem. When they recognize that not enough information is given, display the second prompt and ask what they need to know to be able to solve the problem. Display the sentence frame, “Can you tell me . . .,” for all to see, and invite students to use it to frame their information request. Give students 2 minutes of quiet think time.
100 captive Asian and 100 wild Asian elephants are weighed. There is a meaningful difference between the masses of the 2 groups if the measures of center are at least twice as far apart as the measure of variability. Is there a meaningful difference between the masses of these 2 groups of elephants? Explain your reasoning.
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.
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.
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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.
Display the first paragraph of the activity statement for all to see. Ask students to solve the problem. When they recognize that not enough information is given, display the second prompt and ask what they need to know to be able to solve the problem. Display the sentence frame, “Can you tell me . . .,” for all to see, and invite students to use it to frame their information request. Give students 2 minutes of quiet think time.
100 captive Asian and 100 wild Asian elephants are weighed. There is a meaningful difference between the masses of the 2 groups if the measures of center are at least twice as far apart as the measure of variability. Is there a meaningful difference between the masses of these 2 groups of elephants? Explain your reasoning.
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.
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.