Curriculum  /  Math  /  8th Grade  /  Unit 8: Bivariate Data  /  Lesson 4

Bivariate Data

Lesson 4

Math

Unit 8

8th Grade

Lesson 4 of 9

Objective

Informally fit a line to data. Judge the fit of the line and make predictions about the data based on the line.

Common Core Standards

Core Standards

  • 8.SP.A.2 — Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

Foundational Standards

  • 8.F.A.3
  • 8.F.B.4

Criteria for Success

  1. Understand that a line can be drawn through a set of data in a scatter plot to represent a linear trend in the data.
  2. Understand that a best fit line does not go through all or specific data points but rather is as close to as many data points as possible in a scatter plot; there is not one unique line that best fits a data set.
  3. Draw a line through a data set to best represent a trend in the data.
  4. Use a best fit line to make predictions about the data.

Tips for Teachers

In this lesson, students apply their understanding of linear relationships to scatter plots that have linear trends in the data. They realize that by drawing a line to best represent the trend in the data, they can better understand the relationship between the quantities and even make predictions (MP.4). In the next lesson, students write equations for these lines allowing students to analyze the relationships even more.

Lesson Materials

  • Wikisticks or raw spaghetti (1 per student or small group)
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Anchor Problems

25-30 minutes

Problem 1

For each graph shown below, draw a line that best represents the data points in the graph. Describe your thought process in drawing your lines. 

 

Guiding Questions

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Student Response

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Problem 2

The table below includes data from a Midwestern city about the sizes and sale prices of various homes sold in this city in 2013. The scatter plot that represents the table is also shown below.

a.   Describe the relationship you see between the two variables in the scatter plot.

b.   Do you see any clusters or outliers? Explain.

c.   Draw a line to best represent the trend in the data. Explain your strategy for determining where to draw the line.

d.   Use your line to estimate the cost of a house in 2013 that had 3,000 square feet.

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 8 Mathematics > Module 6 > Topic B > Lesson 8 — Example 1

Grade 8 Mathematics > Module 6 > Topic B > Lesson 8 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem 3

This scatter diagram shows the lengths and widths of the eggs of some American birds.

 

a.   What does the graph show about the relationship between the lengths of birds' eggs and their widths?

b.   Another sample of eggs from similar birds has an average length of 35 millimeters. If these bird eggs follow the trend in the scatter plot, about what width would you expect these eggs to have, on average?

c.   Draw a line that best represents the trend in the data.

d.   Explain why, in this case, it is not a good strategy to draw a line of best fit using point E (the farthest point to the right) and point (12, 8) (the farthest point to the left).

Guiding Questions

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Student Response

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References

MARS Summative Assessment Tasks for Middle School Birds' Eggs

Birds' Eggs from the Summative Assessment Tasks for Middle School is made available through the Mathematics Assessment Project under the CC BY-NC-ND 3.0 license. Copyright © 2007-2015 Mathematics Assessment Resource Service, University of Nottingham. Accessed June 21, 2017, 11:01 a.m..

Modified by Fishtank Learning, Inc.

Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

The scatter plot below shows the number of days with ground snow covering greater than 1 inch for different temperatures in a northeast city.

a.   Choose a point in the scatter plot and explain what it means in context of the situation.

b.   Use the line shown in the graph to predict the average number of days with more than 1 inch of snow when the temperature was 23 °F.

c.   Do you think the line shown in the graph is well-fit to the data? Explain your reasoning.

d.   A fellow classmate uses the strategy of drawing a line so that half of the points are above the line and half of the points are below the line. Explain or show how this could result in a line that was not representative of the data.

Student Response

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Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Next

Write equations to represent lines fit to data and make predictions based on the line.

Lesson 5
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Associations in Bivariate Numerical Data

Topic B: Associations in Bivariate Categorical Data

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