Unit 5, Lesson 21
Describing Trends in Scatter Plots
Accelerated 7
21.1
Warm-up
Which Three Go Together: Scatter Plots
Instructional Routines
Which Three Go Together?Materials
NoneActivity Narrative
This warm-up prompts students to compare four scatter plots. It gives students a reason to use language precisely (MP6). It gives the teacher an opportunity to hear how students use terminology and talk about characteristics of the items in comparison to one another.
It also introduces students to positive and negative associations by comparing scatter plots with best-fit lines.
Launch
Arrange students in groups of 2–4. Display the scatter plots for all to see. Give students 1 minute of quiet think time and ask them to indicate when they have noticed 3 plots that go together and can explain why. Next, tell students to share their response with their group, and then together find as many sets of three as they can.
Activity
NoneWhich three go together? Why do they go together?
Student Response
Activity Synthesis
Invite each group to share one reason why a particular set of 3 go together. Record and display the responses for all to see. After each response, ask the class if they agree or disagree. Since there is no single correct answer to the question of which three go together, attend to students’ explanations and ensure the reasons given are correct.
During the discussion, ask students to explain the meaning of any terminology they use, such as “trend,” “model,” or “variable.” Also, press students on unsubstantiated claims.
During the discussion, introduce new vocabulary:
- A positive association is a relationship between 2 quantities where one tends to increase as the other increases.
- A negative association is a relationship between 2 quantities where one tends to decrease as the other increases.
Lesson Synthesis
Display the scatter plot for all to see.
A scatterplot. Horizontal, from 10 to 50, by fives, labeled initial battery life (hours). Vertical, from 10 to 45, by fives, labeled later battery life (hours). Line drawn, trend linearly upward and right with 20 data points above and below line.
To highlight the main ideas from today's lesson about associations and trend lines, ask:
- “How would you describe the relationship between the later battery life and initial battery life?” (There is a positive association. Or, as the initial battery life increases, the later battery life tends to increase.)
- “How can we tell if a line is a good fit for the data in a scatter plot?” (It goes through the middle of the data, the sign of the slope matches the sign of the association, or the points are as close as possible to the line.)
Student Lesson Summary
When a linear function fits data well, we say there is a “linear association” between the variables. For example, the relationship between height and weight for 25 dogs with the linear function whose graph is shown in the scatter plot.
We say there is a positive association between dog height and dog weight because knowledge about one variable helps predict the other variable, and when one variable increases, the other tends to increase as well.
What do you think the association between the weight of a car and its fuel efficiency is?
We say that there is a negative association between fuel efficiency and weight of a car because knowledge about one variable helps predict the other variable, and when one variable increases, the other tends to decrease.
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