This Math Talk focuses on calculating the mean of a set of numbers. It encourages students to think about symmetry and to rely on the structure of the distribution to mentally solve problems. The strategies elicited here will be helpful later in the lesson when students examine and describe distributions.
To mentally calculate the mean, students need to look for and make use of structure (MP7).
This is the first Math Talk activity in the course. See the Launch for extended instructions for facilitating this activity successfully.
This is the first time students do the Math Talk instructional routine, so it is important to explain how it works before starting.
Explain the Math Talk routine: One problem is displayed at a time. For each problem, students are given a few minutes to quietly think and give a signal when they have an answer and a strategy. The teacher selects students to share different strategies for each problem, and might ask questions like “Who thought about it a different way?” The teacher records students' explanations for all to see. Students might be asked to provide more details about why they decided to approach a problem a certain way. It may not be possible to share every possible strategy for the given limited time, so the teacher may gather only two or three distinctive strategies per problem.
Consider establishing a small, discreet hand signal that students can display to indicate that they have an answer they can support with reasoning. This signal could be a thumbs-up, a certain number of fingers that tells the number of responses they have, or another subtle signal. This is a quick way to see if the students have had enough time to think about the problem. It also keeps students from being distracted or rushed by hands being raised around the class.
Display one problem at a time. Give students quiet think time for each problem, and ask them to give a signal when they have an answer and a strategy. Keep all problems displayed throughout the talk. Follow with a whole-class discussion.
Evaluate the mean of each data set mentally.
Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:
Although all correct methods for solving for the mean are valid, highlight the use of symmetry in the data. In previous lessons, students learned that symmetric distributions have a mean in the center of the data. When symmetry is present, it can be used to quickly discover the mean.
Math Community
After the Warm-up, display the revised Math Community Chart created from student responses in Exercise 3. Tell students that today they are going to monitor for two things:
Provide sticky notes for students to record what they see and hear during the lesson.
If students struggle to use symmetry as a method for finding the mean, consider asking them to find the mean for the values: 1, 2, 3, 4, 5.
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This Math Talk focuses on calculating the mean of a set of numbers. It encourages students to think about symmetry and to rely on the structure of the distribution to mentally solve problems. The strategies elicited here will be helpful later in the lesson when students examine and describe distributions.
To mentally calculate the mean, students need to look for and make use of structure (MP7).
This is the first Math Talk activity in the course. See the Launch for extended instructions for facilitating this activity successfully.
This is the first time students do the Math Talk instructional routine, so it is important to explain how it works before starting.
Explain the Math Talk routine: One problem is displayed at a time. For each problem, students are given a few minutes to quietly think and give a signal when they have an answer and a strategy. The teacher selects students to share different strategies for each problem, and might ask questions like “Who thought about it a different way?” The teacher records students' explanations for all to see. Students might be asked to provide more details about why they decided to approach a problem a certain way. It may not be possible to share every possible strategy for the given limited time, so the teacher may gather only two or three distinctive strategies per problem.
Consider establishing a small, discreet hand signal that students can display to indicate that they have an answer they can support with reasoning. This signal could be a thumbs-up, a certain number of fingers that tells the number of responses they have, or another subtle signal. This is a quick way to see if the students have had enough time to think about the problem. It also keeps students from being distracted or rushed by hands being raised around the class.
Display one problem at a time. Give students quiet think time for each problem, and ask them to give a signal when they have an answer and a strategy. Keep all problems displayed throughout the talk. Follow with a whole-class discussion.
Evaluate the mean of each data set mentally.
Ask students to share their strategies for each problem. Record and display their responses for all to see. To involve more students in the conversation, consider asking:
Although all correct methods for solving for the mean are valid, highlight the use of symmetry in the data. In previous lessons, students learned that symmetric distributions have a mean in the center of the data. When symmetry is present, it can be used to quickly discover the mean.
Math Community
After the Warm-up, display the revised Math Community Chart created from student responses in Exercise 3. Tell students that today they are going to monitor for two things:
Provide sticky notes for students to record what they see and hear during the lesson.
If students struggle to use symmetry as a method for finding the mean, consider asking them to find the mean for the values: 1, 2, 3, 4, 5.