What a Point in a Scatter Plot Means

5 min

Teacher Prep
Setup
1 minute quiet think time followed by a whole-class discussion.

Narrative

In this activity, students examine a scatter plot showing weight and fuel efficiency of cars. Students can show their understanding of what data graphed as points means and become familiar with the context of fuel efficiency.

This activity uses the Co-Craft Questions math language routine to advance reading and writing as students make sense of a context and practice generating mathematical questions.

Launch

Arrange students in groups of 2. Use Co-Craft Questions to orient students to the context and elicit possible mathematical questions.

Display the problem stem, table, and scatter plot. Give students 1–2 minutes to write a list of mathematical questions that could be asked about the situation before comparing questions with a partner.

Student Task

What questions do you have about these data?

car weight
(kg)		 fuel efficiency (mpg)
A 1,549 25
B 1,610 20
C 1,737 21
D 1,777 20
E 1,486 23
F 1,962 16
G 2,384 16
H 1,957 19
I 2,212 16
J 1,115 29
K 2,068 18
L 1,663 19
M 2,216 18
N 1,432 25
O 1,987 18
P 1,580 26
Q 1,234 30
R 1,656 23

A scatterplot.
A scatterplot with 20 data points. The horizontal axis is labeled “weight, in kilograms” and the numbers 1,000 through 2,500, in increments of 250, are indicated. The vertical axis is labeled “fuel efficiency, in miles per gallon” and the numbers 14 through 32, in increments of 2, are indicated. The graph shows the trend of the 20 data points moving linearly downward and to the right. The approximate coordinates of 11 selected data points are as follows: 1,130 comma 28. 1,240 comma 30. 1,400 comma 25. 1,490 comma 23. 1,550 comma 25. 1,590 comma 26. 1,650 comma 19. 1,740 comma 21. 1,775 comma 20. 1,950 comma 19. 2,200 comma 16.

Sample Response

Sample response:

  • Are the weight and fuel efficiency of cars related?
  • What is fuel efficiency?
  • Which point represents car A?
Activity Synthesis (Teacher Notes)

Invite several partners to share one question with the class and record responses. Ask the class to make comparisons among the shared questions and their own. Ask, “What do these questions have in common? How are they different?” Listen for and amplify language related to the learning goal, such as finding individual cars in the scatter plot or noticing a pattern in the data.

If necessary, explain a bit about fuel efficiency so that students understand this measurement. Fuel efficiency is a measure of the average distance a car will travel using a certain amount of gas. Commonly this is measured in miles per gallon. For example, a car that has a fuel efficiency of 25 miles per gallon (mpg) should be able to drive approximately 25 miles while using up a gallon of gas. Many factors can influence fuel efficiency, including the way an engine is engineered (to produce more power, an engine may use more gasoline), driving conditions (more frequent stopping and starting or driving up and down hills will use fuel less efficiently), and what accessories are being used (air conditioning requires energy from burning fuel that is not used for actually driving the car).

Standards
Building On
  • 5.G.2·Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
  • 5.G.A.2·Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

15 min

15 min