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Fitting a Line to Data

Classroom Resource Information

Title:

Fitting a Line to Data

URL:

https://aptv.pbslearningmedia.org/resource/our20-math-864/fitting-a-line-to-data/

Content Source:

PBS

Type:

Audio/Video

Overview:

In this video lesson, students' focus becomes more holistic and they begin to see a set of data points as a single thing that can be analyzed, not just a bunch of disconnected points. Students see that sometimes we can model the relationship between two variables with a line (MP4), although they continue to analyze the connections between the scatter plot and the line by comparing individual points. As they see these connections, students begin to see the structure of the scatter plot (MP7) and to use that structure to reason abstractly and quantitatively (MP2).

Content Standard(s):

Mathematics
MA2019 (2019)
Grade: 8

19. Given a scatter plot that suggests a linear association, informally draw a line to fit the data, and assess the model fit by judging the closeness of the data points to the line.

Unpacked Content

Evidence Of Student Attainment:

Students:
Given a variety of scatterplots representing bivariate data,

Determine if the plots suggest a linear relationship.
Informally fit a straight line to the data.
Assess the model fit by judging the closeness of the data points to the line.

Teacher Vocabulary:

Scatter plot
Linear association
Quantitative variable

Knowledge:

Students know:

Patterns found on scatter plots of bivariate data, (linear/non-linear, positive/negative).
Strategies for informally fitting straight lines to bivariate data with a linear relationship.
Methods for finding the distance between two points on a coordinate plane and between a point and a line.

Skills:

Students are able to:

Construct a scatter plot to represent a set of bivariate data.
Use mathematical vocabulary to describe and interpret patterns in bivariate data.
Use logical reasoning and appropriate strategies to draw a straight line to fit data that suggest a linear association.
Use mathematical vocabulary, logical reasoning, and closeness of data points to a line to judge the fit of the line to the data.

Understanding:

Students understand that:

Using different representations and descriptors of a data set can be useful in seeing important features of the situation being investigated.
When visual examination of a scatter plot suggests a linear association in the data, fitting a straight line to the data can aid in interpretation and prediction.

Diverse Learning Needs:

Essential Skills:

Learning Objectives:
M.8.19.1: Define scatter plot, outlier, linear, quantitative, line of best fit, and variable.
M.8.19.2: Analyze scatter plots to determine line of best fit.
M.8.19.3: Explain how to draw informal inferences from data distributions.
M.8.19.4: Recall how to summarize numerical data sets in relation to their context.
M.8.19.5: Recognize the concept of outlier and its relationship to the data distribution.
M.8.19.6: Draw an estimate for a line of best fit.

Prior Knowledge Skills:

Define numerical data set, measure of variation, and measure of center.
Relate the measure of variation, of a data set, with the concept of range.
Relate the measure of the center for a numerical data set with the concept of measure of center.
Define numerical data set, quantitative, measure of center, median, frequency distribution, and attribute.
Compare and contrast the center and variation.
Collect the data.
Organize the data.
Describe how attribute was measured including units of measurement.
Identify the attribute used to create the numerical set.

Mathematics
MA2019 (2019)
Grade: 8
Accelerated

35. Given a scatter plot that suggests a linear association, informally draw a line to fit the data, and assess the model fit by judging the closeness of the data points to the line. [Grade 8, 19]

Unpacked Content

Evidence Of Student Attainment:

Students:
Given a variety of scatterplots representing bivariate data,

Determine if the plots suggest a linear relationship.
Informally fit a straight line to the data.
Assess the model fit by judging the closeness of the data points to the line.

Teacher Vocabulary:

Scatter plot
Linear association
Quantitative variable

Knowledge:

Students know:

Patterns found on scatter plots of bivariate data, (e.g., linear/non-linear, positive/negative).
Strategies for informally fitting straight lines to bivariate data with a linear relationship.
Methods for finding the distance between two points on a coordinate plane and between a point and a line.

Skills:

Students are able to:

Construct a scatter plot to represent a set of bivariate data.
Use mathematical vocabulary to describe and interpret patterns in bivariate data.
Use logical reasoning and appropriate strategies to draw a straight line to fit data that suggest a linear association.
Use mathematical vocabulary, logical reasoning, and closeness of data points to a line to judge the fit of the line to the data.

Understanding:

Students understand that:

Using different representations and descriptors of a data set can be useful in seeing important features of the situation being investigated.
When visual examination of a scatter plot suggests a linear association in the data, fitting a straight line to the data can aid in interpretation and prediction.

Diverse Learning Needs:

Tags:

association, data points, line, scatter plot

License Type:

Public Domain
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses

Accessibility

Video resources: includes closed captioning or subtitles

Comments

Support materials are available for this lesson.

This resource provided by:

Author:

Kristy Lacks

ALEX Classroom Resource

Fitting a Line to Data