Standard #: MA.8.DP.1.3


This document was generated on CPALMS - www.cpalms.org



Given a scatter plot with a linear association, informally fit a straight line.


Clarifications


Clarification 1: Instruction focuses on the connection to linear functions.

Clarification 2: Instruction includes using a variety of tools, including a ruler, to draw a line with approximately the same number of points above and below the line.



General Information

Subject Area: Mathematics (B.E.S.T.)
Grade: 8
Strand: Data Analysis and Probability
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • Association
  • Line of Fit
  • Scatter Plot

 

Vertical Alignment

Previous Benchmarks

Next Benchmarks

 

Purpose and Instructional Strategies

In grades 6 and 7, students created graphical representations for both numerical and categorical univariate data. In grade 8, students encounter bivariate data displayed with scatter plots, and they use their knowledge of graphing lines to determine approximate lines of fit. In Algebra 1, students will continue working with scatter plots and lines of fit to display association, but expand their knowledge to consider association in bivariate categorical data, displayed with frequency tables.
  • Instruction includes the understanding that a straight line can used to display a linear association in a scatter plot. This line allows predictions of other potential data points. Instruction includes students discussing what it means to be above and below the line of fit (MTR.4.1).
  • Instruction includes providing opportunities to look at multiple lines of fit and determine which would be the best model for the scatter plot. The use of manipulatives are a way for students to make adjustments on their informal fit of a line. Students should compare and contrast their models and explain why their models best represent the fit of the data (MTR.4.1).
  • Instruction includes the use of linear models to represent the line of fit. Students should describe the x-intercept and slope in terms of the context within the scatter plot.

 

Common Misconceptions or Errors

  • Students may incorrectly believe the line of fit should go through all the data points. To address this misconception, provide examples to students to show some lines that do go through data points and examples that may go through very few or no data points.
  • Students may incorrectly think the line of fit should go through the first and last data point on the scatter plot. To address this misconception, provide examples to students to show some lines that do not go through the first and last data point.

 

Strategies to Support Tiered Instruction

  • Using digital tools to model graphing a line of fit will provide clarity for misunderstanding that a line of fit needs to either start with the first and end with the last point or go through all points.
  • Teacher provides examples to showing lines of fit that go through data points and examples that may go through very few or no data points.
  • Teacher provides examples to show lines of fit that do not go through the first and last data point.

 

Instructional Tasks

Instructional Task 1 (MTR.6.1, MTR.7.1)
Each graph shows the same set of data and a line that has been fitted to the data.
graph shows the same set of data and a line that has been fitted to the data.
  • Part A. Determine which line, a, b or c, most appropriately fits the data and explain why.
  • Part B. What statistical question could be asked to represent the set of data?

 

Instructional Items

Instructional Item 1
The scatter plot below shows the relationship between the ages and weights of 50 female infants. Draw a line on the scatter plot that fits the data.
scatter plot shows the relationship between the ages and weights of 50 female infants.

Instructional Item 2
A scatter plot is shown in the coordinate plane. Draw a line on the scatter plot that fits the data.
A scatter plot is shown in the coordinate plane.

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.


Related Courses

Course Number1111 Course Title222
1205050: M/J Accelerated Mathematics Grade 7 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1205070: M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812030: Access M/J Grade 8 Pre-Algebra (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))


Related Access Points

Access Point Number Access Point Title
MA.8.DP.1.AP.3 Given a scatter plot with a linear association, use tools to draw or place a line of fit.


Related Resources

Formative Assessments

Name Description
Two Scatterplots

Students are asked to compare two lines fitted to data to determine which fit is better.

Three Scatterplots

Students are asked to informally assess three lines fitted to data to determine which fit is the best.

Line of Good Fit - 2

Students are asked to informally fit a line to model the relationship between two quantitative variables and to assess how well that line fits the data.

Line of Good Fit - 1

Students are asked to informally fit a line to model the relationship between two quantitative variables and to assess how well that line fits the data.

Lesson Plans

Name Description
Why Correlations?

This lesson is an introductory lesson to correlation coefficients. Students will engage in research prior to the teacher giving any direct instruction. The teacher will provide instruction on how to find the correlation coefficient by hand and using Excel.

Why Correlations?

This lesson is an introductory lesson to correlation coefficients. Students will engage in research prior to the teacher giving any direct instruction. The teacher will provide instruction on how to find the correlation coefficient by hand and using Excel.

Compacting Cardboard

Students investigate the amount of space that could be saved by flattening cardboard boxes. The analysis includes linear graphs and regression analysis along with discussions of slope and a direct variation phenomenon.

A Day at the Park

In this activity, students investigate a set of bivariate data to determine if there is a relationship between concession sales in the park and temperature. Students will construct a scatter plot, model the relationship with a linear function, write the equation of the function, and use it to make predictions about values of variables.

You Can Plot it! Bivariate Data

Students create scatter plots, calculate a regression equation using technology, and interpret the slope and y-intercept of the equation in the context of the data. This review lesson relates graphical and algebraic representations of bivariate data.

Basketball - it's a tall man's sport - or is it?

The students will use NBA player data to determine if there is a correlation between the height of a basketball player and his free throw percentage. The students will use technology to create scatter plots, find the regression line and calculate the correlation coefficient.

Basketball is a tall man's sport in most regards. Shooting, rebounding, blocking shots - the taller player seems to have the advantage. But is that still true when shooting free throws?

Scatter Plots

This lesson is an introduction to scatterplots and how to use a trend line to make predictions. Students should have some knowledge of graphing bivariate data prior to this lesson.

What Will I Pay?

Who doesn't want to save money? In this lesson, students will learn how a better credit score will save them money. They will use a scatter plot to see the relationship between credit scores and car loan interest rates. They will determine a line of fit equation and interpret the slope and y-intercept to make conclusions about interest and credit scores.

An Introduction to Finding Residuals

Students will calculate the residuals of two-variable data. Teachers are provided with materials to review, present, practice, and assess students for this new topic. This is an introductory lesson and could be used before teaching residual plots.

What does it mean?

This lesson provides the students with scatter plots, lines of best fit and the linear equations to practice interpreting the slope and y-intercept in the context of the problem.

Is My Model Working?

Students will enjoy this project lesson that allows them to choose and collect their own data. They will create a scatter plot and find the line of fit. Next they write interpretations of their slope and y-intercept. Their final challenge is to calculate residuals and conclude whether or not their data is consistent with their linear model.

Fit Your Function

Students will make a scatter plot and then create a line of fit for the data. From their graph, students will make predictions and describe relationships between the variables. Students will make predictions, inquire, and formulate ideas from observations and discussions.

Scatter Plots and Correlations

Students create scatter plots, and lines of fit, and then calculate the correlation coefficient. Students analyze the results and make predictions. This lesson includes step-by-step directions for calculating the correlation coefficient using Excel, GeoGebra, and a TI-84 Plus graphing calculator. Students will make predictions for the number of views of a video for any given number of weeks on the charts.

Cat Got Your Tongue?

This lesson uses real-world examples to practice interpreting the slope and y-intercept of a linear model in the context of data. Students will collect data, graph a scatter plot, and use spaghetti to identify a line of fit. A PowerPoint is included for guidance throughout the lesson and guided notes are also provided for students.

If the line fits, where's it?

In this lesson students learn how to informally determine a "best fit" line for a scatter plot by considering the idea of closeness.

Doggie Data: It's a Dog's Life

Students use real-world data to construct and interpret scatter plots using technology. Students will create a scatter plot with a line of fit and a function. They describe the relationship of bivariate data. They recognize and interpret the slope and y-intercept of the line of fit within the context of the data.

Spaghetti Trend

This lesson consists of using data to make scatter plots, identify the line of fit, write its equation, and then interpret the slope and the y-intercept in context. Students will also use the line of fit to make predictions.

How technology can make my life easier when graphing

Students will use GeoGebra software to explore the concept of correlation coefficient in graphical images of scatter plots. They will also learn about numerical and qualitative aspects of the correlation coefficient, and then do a matching activity to connect all these representations of the correlation coefficient. They will use an interactive program file in GeoGebra to manipulate the points to create a certain correlation coefficient. Step-by-step instructions are included to create the graph in GeoGebra and calculate the r correlation coefficient.

Slope and y-Intercept of a Statistical Model

Students will sketch and interpret the line of fit and then describe the correlation of the data. Students will determine if there’s a correlation between foot size and height by collecting data.

Line of Fit

Students will graph scatterplots and draw a line of fit. Next, students will write an equation for the line and use it to interpret the slope and y-intercept in context. Students will also use the graph and the equation to make predictions.

How Fast Can You Go

Students will apply skills (making a scatter plot, finding Line of Best Fit, finding an equation and predicting the y-value of a point on the line given its x-coordinate) to a fuel efficiency problem and then consider other factors such as color, style, and horsepower when designing a new coupe vehicle.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Why Correlations?

This lesson is an introductory lesson to correlation coefficients. Students will engage in research prior to the teacher giving any direct instruction. The teacher will provide instruction on how to find the correlation coefficient by hand and using Excel.

Constructing and Calibrating a Hydrometer

Students construct and calibrate a simple hydrometer using different salt solutions. They then graph their data and determine the density and salinity of an unknown solution using their hydrometer and graphical analysis.

Scatter plots, spaghetti, and predicting the future

Students will construct a scatter plot from given data. They will identify the correlation, sketch an approximate line of fit, and determine an equation for the line of fit. They will explain the meaning of the slope and y-intercept in the context of the data and use the line of fit to interpolate and extrapolate values.

Original Student Tutorials

Name Description
Scatterplots Part 6: Using Linear Models

Learn how to use the equation of a linear trend line to interpolate and extrapolate bivariate data plotted in a scatterplot. You will see the usefulness of trend lines and how they are used in this interactive tutorial.

This is part 6 in 6-part series. Click below to open the other tutorials in the series.

Scatterplots Part 4: Equation of the Trend Line

Learn how to write the equation of a linear trend line when fitted to bivariate data in a scatterplot in this interactive tutorial.

This is part 4 in 6-part series. Click below to open the other tutorials in the series.

Scatterplots Part 3: Trend Lines

Explore informally fitting a trend line to data graphed in a scatter plot in this interactive online tutorial.

This is part 3 in 6-part series. Click below to open the other tutorials in the series.

Perspectives Video: Professional/Enthusiasts

Name Description
Determining Strengths of Shark Models based on Scatterplots and Regression

Chip Cotton, fishery biologist, discusses his use of mathematical regression modeling and how well the data fits his models based on his deep sea shark research.

Download the CPALMS Perspectives video student note taking guide.

Slope and Deep Sea Sharks

Shark researcher, Chip Cotton, discusses the use of regression lines, slope, and determining the strength of the models he uses in his research.

Download the CPALMS Perspectives video student note taking guide.

Teaching Idea

Name Description
Now That is a Dense Graph

In this activity, the density of ethanol is found by graphical means. In the second part, the density of sodium thiosulfate is found, also by graphical means. The values found are then analyzed statistically.

Student Resources

Original Student Tutorials

Name Description
Scatterplots Part 6: Using Linear Models :

Learn how to use the equation of a linear trend line to interpolate and extrapolate bivariate data plotted in a scatterplot. You will see the usefulness of trend lines and how they are used in this interactive tutorial.

This is part 6 in 6-part series. Click below to open the other tutorials in the series.

Scatterplots Part 4: Equation of the Trend Line:

Learn how to write the equation of a linear trend line when fitted to bivariate data in a scatterplot in this interactive tutorial.

This is part 4 in 6-part series. Click below to open the other tutorials in the series.

Scatterplots Part 3: Trend Lines:

Explore informally fitting a trend line to data graphed in a scatter plot in this interactive online tutorial.

This is part 3 in 6-part series. Click below to open the other tutorials in the series.



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