Median
5 min
Teacher Prep
Setup
Narrative
This Warm-up reinforces students’ understanding about the relationship between the mean absolute deviation (MAD) and the spread of data. In the given scenarios, the number of people attending the two events and their mean age are the same, but the MADs are different. Students are asked to interpret these measures in context and then draw their own dot plot with given conditions.
As students work and discuss, identify several students who drew dot plots that correctly meet the criteria in the second question. Ask students with different dot plots to share during a whole-class discussion.
Students may need more time to make sense of how to generate their own dot plot for the second question. If it is not possible to give students additional time, consider presenting the second question at a different time.
Launch
Arrange students in groups of 2. Give students 1 minute of quiet think time for the first question, and then 2–3 minutes to work on the second question with a partner. Display the following questions for all to see. Ask students to think about and discuss them before drawing their dot plots:
- “How many data points should be on the dot plot?”
- “How would the mean help us place the data points?”
- “How would the MAD help us place the data points?”
- “How should our dot plot compare to the dot plots of Data sets A and B?”
Student Task
-
Here are two dot plots and two stories. Match each story with a dot plot that could represent it. Be prepared to explain your reasoning.
Data set A <p>A dot plot from 10 to 75 by 5’s. Age in years. Labeled data set A, beginning at 10, 5 dots between 15 and 20. 7 dots between 40 and 45. 7 dots between 45 and 50. 1 dot between 55 and 60.</p>Data set B <p>A dot plot from 10 to 75 by 5’s. Age in years. Labeled data set B, beginning at 10, 6 dots between 15 and 20. 2 dots between 30 and 35. 1 dot between 35 and 40. 1 dot on 40. 3 dots between 40 and 45. 3 dots between 45 and 50. 4 dots between 60 and 65.</p>-
Twenty high school students, teachers, and invited guests attend a rehearsal for a high school musical. The mean age is 38.5 years and the MAD is 16.5 years.
- High school soccer team practice is usually watched by supporters of the players. One evening, twenty people watch the team practice. The mean age is 38.5 years and the MAD is 12.7 years.
-
- Another evening, twenty people watch the soccer team practice. The mean age is similar to that from the first evening, but the MAD is greater (about 20 years).
Make a dot plot that could illustrate the distribution of ages in this story.
Sample Response
- Data set A goes with the high-school soccer practice story. Data set B goes with the musical performance story. Sample explanation: The data points in data set B are more spread out, so the MAD for that data set would be larger.
- Sample dot plot:
Activity Synthesis (Teacher Notes)
Invite students to share their response to the first question. Ask a student to explain how they matched one context to its dot plot and another student to explain the second matching context and dot plot. Record and display their responses for all to see. If possible, record their responses directly on the dot plots.
Ask selected students to share their dot plots for the second question and their reasoning. To involve more students in the conversation, consider asking some of the following questions:
- “What was the first piece of information you used to draw your dot plot? Why?”
- “How did you decide where to place your dots?”
- “How is your dot plot the same or different from the one representing the first evening of soccer practice?”
- “Do you agree or disagree with this representation of the context? Why?”
- “Do you have any questions to ask the student who drew the dot plot?”
Standards
- 6.SP.B·Summarize and describe distributions.
- 6.SP.B·Summarize and describe distributions.
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Median
5 min
Teacher Prep
Setup
Narrative
This Warm-up reinforces students’ understanding about the relationship between the mean absolute deviation (MAD) and the spread of data. In the given scenarios, the number of people attending the two events and their mean age are the same, but the MADs are different. Students are asked to interpret these measures in context and then draw their own dot plot with given conditions.
As students work and discuss, identify several students who drew dot plots that correctly meet the criteria in the second question. Ask students with different dot plots to share during a whole-class discussion.
Students may need more time to make sense of how to generate their own dot plot for the second question. If it is not possible to give students additional time, consider presenting the second question at a different time.
Launch
Arrange students in groups of 2. Give students 1 minute of quiet think time for the first question, and then 2–3 minutes to work on the second question with a partner. Display the following questions for all to see. Ask students to think about and discuss them before drawing their dot plots:
- “How many data points should be on the dot plot?”
- “How would the mean help us place the data points?”
- “How would the MAD help us place the data points?”
- “How should our dot plot compare to the dot plots of Data sets A and B?”
Student Task
-
Here are two dot plots and two stories. Match each story with a dot plot that could represent it. Be prepared to explain your reasoning.
Data set A <p>A dot plot from 10 to 75 by 5’s. Age in years. Labeled data set A, beginning at 10, 5 dots between 15 and 20. 7 dots between 40 and 45. 7 dots between 45 and 50. 1 dot between 55 and 60.</p>Data set B <p>A dot plot from 10 to 75 by 5’s. Age in years. Labeled data set B, beginning at 10, 6 dots between 15 and 20. 2 dots between 30 and 35. 1 dot between 35 and 40. 1 dot on 40. 3 dots between 40 and 45. 3 dots between 45 and 50. 4 dots between 60 and 65.</p>-
Twenty high school students, teachers, and invited guests attend a rehearsal for a high school musical. The mean age is 38.5 years and the MAD is 16.5 years.
- High school soccer team practice is usually watched by supporters of the players. One evening, twenty people watch the team practice. The mean age is 38.5 years and the MAD is 12.7 years.
-
- Another evening, twenty people watch the soccer team practice. The mean age is similar to that from the first evening, but the MAD is greater (about 20 years).
Make a dot plot that could illustrate the distribution of ages in this story.
Sample Response
- Data set A goes with the high-school soccer practice story. Data set B goes with the musical performance story. Sample explanation: The data points in data set B are more spread out, so the MAD for that data set would be larger.
- Sample dot plot:
Activity Synthesis (Teacher Notes)
Invite students to share their response to the first question. Ask a student to explain how they matched one context to its dot plot and another student to explain the second matching context and dot plot. Record and display their responses for all to see. If possible, record their responses directly on the dot plots.
Ask selected students to share their dot plots for the second question and their reasoning. To involve more students in the conversation, consider asking some of the following questions:
- “What was the first piece of information you used to draw your dot plot? Why?”
- “How did you decide where to place your dots?”
- “How is your dot plot the same or different from the one representing the first evening of soccer practice?”
- “Do you agree or disagree with this representation of the context? Why?”
- “Do you have any questions to ask the student who drew the dot plot?”
Standards
- 6.SP.B·Summarize and describe distributions.
- 6.SP.B·Summarize and describe distributions.