# MAFS.8.SP.1.2Archived Standard

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.
General Information
Subject Area: Mathematics
Domain-Subdomain: Statistics & Probability
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Investigate patterns of association in bivariate data. (Supporting Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes
Test Item Specifications

• Assessment Limits :
Numbers in items must be rational numbers. Trend/association is based on visual inspection. Line of best fit must be informally assessed. Trend/association must be linear.
• Calculator :

Neutral

• Context :

Allowable

Sample Test Items (2)

## Related Courses

This benchmark is part of these courses.
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))
2003030: M/J STEM Physical Science (Specifically in versions: 2015 - 2022, 2022 and beyond (current))
2002200: M/J STEM Environmental Science (Specifically in versions: 2015 - 2022, 2022 and beyond (current))
2001025: M/J STEM Astronomy and Space Science (Specifically in versions: 2015 - 2022, 2022 and beyond (current))
2000025: M/J STEM Life Science (Specifically in versions: 2015 - 2022, 2022 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Formative Assessments

Two Scatterplots:

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

Type: Formative Assessment

Three Scatterplots:

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

Type: Formative Assessment

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.

Type: Formative Assessment

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.

Type: Formative Assessment

## Lesson Plans

The changing climate is an important topic for both scientific analysis and worldly knowledge. This lesson uses data collected by the National Snow and Ice Data Center to create and use mathematical models as a predictive tool and do critical analysis of sea ice loss.

Type: Lesson Plan

Sensoring Data:

In this follow up lesson, students will explore data collection using the weather station sensor and perform statistical analysis of the data. Students will use a scientific method of inquiry to plan an investigation of their own. This activity is meant to allow students to use a variety of skills they have acquired throughout a statistics unit in a personally meaningful way.

Type: Lesson Plan

Shipwrecked Pirates:

In this lesson, students will take the role of shipwrecked pirates. Working in groups, they will have to use the concepts of force, speed, scatter plots, and literal equations to come up with a way of getting one student to a nearby sister island so that they will both have enough food to survive.

Type: Lesson Plan

Sensoring Data:

In this follow up lesson, students will explore data collection using the weather station sensor and perform statistical analysis of the data. Students will use a scientific method of inquiry to plan an investigation of their own. This activity is meant to allow students to use a variety of skills they have acquired throughout a statistics unit in a personally meaningful way.

Type: Lesson Plan

Steel vs. Wooden Roller Coaster Lab:

This lesson is a Follow Up Activity to the Algebra Institute and allows students to apply their skills on analyzing bivariate data. This STEM lesson allows students the opportunity to investigate if there is a linear relationship between a coaster's height and speed. Using technology the students can determine the line of best fit, correlation coefficient and use the line for interpolation. This lesson also uses prior knowledge and has students solve systems of equations graphically to determine which type of coaster is faster.

Type: Lesson Plan

Height Arm Juxtaposition:

This lesson is a Follow Up Activity to the Algebra Institute and allows students to apply their skills on analyzing bivariate data. This STEM lesson allows students the opportunity to investigate if there is a linear relationship between a person's height and arm length. Using technology the students will explore in-depth how to perform a least square regression as a procedure for determining the line of best fit.

Type: Lesson Plan

Height Scatterplot Lab:

This lesson is a Follow Up Activity to the Algebra Institute and allows students to apply their skills on analyzing bivariate data. This STEM lesson allows students the opportunity to investigate if there is a linear relationship between a person's height and foot length. Using technology the students can determine the line of best fit, correlation coefficient and use the line for interpolation.

Type: Lesson Plan

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.

Type: Lesson Plan

Scatter Plots at Arm's Reach:

This lesson is an introductory lesson to scatter plots and line of best fit (trend lines). Students will be using m&m's to represent different associations in scatter plots, and measure each other's height and arm span to create their own bivariate data to analyze. Students will be describing the association of the data, patterns of the data, informally draw a line of best fit (trend line), write the equation of the trend line, interpret the slope and y-intercept, and make predictions.

Type: Lesson Plan

Creating a Linear Model:

Students will analyze data to create scatter plots. They will draw the line of best fit to determine linear models. The teacher will use PowerPoint and activities included to guide the students into finding the line of best fit.

Type: Lesson Plan

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.

Type: Lesson Plan

Scattered Data:

This lesson allows students to use real-life problem-solving skills to construct and interpret scatter plots by generating and recording their own data. Students will investigate patterns between bivariate measurement data. They will model linear associations with a line of best fit.

Type: Lesson Plan

Spaghetti Bridges:

Students use data collection from their spaghetti bridge activity to write linear equations, graph the data, and interpret the data.

Type: Lesson Plan

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.

Type: Lesson Plan

## Original Student Tutorials

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.

Type: Original Student Tutorial

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.

Type: Original Student Tutorial

## Perspectives Video: Professional/Enthusiasts

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.

Type: Perspectives Video: Professional/Enthusiast

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.

Type: Perspectives Video: Professional/Enthusiast

You and Michael:

In this problem solving task, students will test Marcus Vitruvius"s theory that a person"s height is approximately equal to their arm span (wingspan). Students will test this theory via collection, recording, graphing and analysis of data.

Modeling Linear Relationships:

In this lesson, which is part of a unit on bivariate data and analysis, students use data collected comparing height and arm span and create a scatter plot from the bivariate data. In the first section, How Square Can You Be?, students look at measurement comparisons between the height and arm span of 24 people. The second section, Analyzing the Differences, asks students to look at the data again to answer questions about proportion of height to arm span, such as who is square and who is rectangular. The third section, Using a Scatter Plot, has students analyze the same data on a scatter plot with the line representing Height = Arm Span. There are questions for student to answer independently, but hints are provided.

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Teaching Idea

Birds & Eggs:

In this task, students start by examining a scatter plot about the size of various bird eggs from a collection of measurements. In particular, students are asked to identify a correlation, sketch an approximation for the line of best fit, determine the equation of that line, use the equation of the line and/or the graph to make interpolative predictions, and draw conclusions about the properties of specific eggs by using the graphical presentation of the data.

Type: Teaching Idea

## Tutorial

Scatter Plots:

Scatterplots are used to visualize the relationship between two quantitative variables in a binary relation. As an example, trends in the relationship between the height and weight of a group of people could be graphed and analyzed using a scatter plot.

Type: Tutorial

## Video/Audio/Animations

Trend Lines (Smoking in 1945):

This 5-minute video provides an example of how to solve a problem using a trend line to estimate data through a problem called, "Smoking in 1945."

Type: Video/Audio/Animation

Fitting a Line to Data:

Khan Academy tutorial video that demonstrates with real-world data the use of Excel spreadsheet to fit a line to data and make predictions using that line.

Type: Video/Audio/Animation

## Virtual Manipulatives

Data Flyer:

Using this virtual manipulative, students are able to graph a function and a set of ordered pairs on the same coordinate plane. The constants, coefficients, and exponents can be adjusted using slider bars, so the student can explore the affect on the graph as the function parameters are changed. Students can also examine the deviation of the data from the function. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative

Univariate and Bivariate Data:

This lesson is designed to introduce students to the difference between univariate and bivariate data, and how the two can be represented graphically. This lesson provides links to model discussions and online graphing applets, as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

Type: Virtual Manipulative

Curve Fitting:

With a mouse, students will drag data points (with their error bars) and watch the best-fit polynomial curve form instantly. Students can choose the type of fit: linear, quadratic, cubic, or quartic. Best fit or adjustable fit can be displayed.

Type: Virtual Manipulative

Line of Best Fit:

This manipulative allows the user to enter multiple coordinates on a grid, estimate a line of best fit, and then determine the equation for a line of best fit.

Type: Virtual Manipulative

## STEM Lessons - Model Eliciting Activity

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.

## MFAS Formative Assessments

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.

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.

Three Scatterplots:

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

Two Scatterplots:

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

## Original Student Tutorials Mathematics - Grades 6-8

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.

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.

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

## Original Student Tutorials

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.

Type: Original Student Tutorial

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.

Type: Original Student Tutorial

## Student Center Activity

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

Type: Student Center Activity

## Tutorial

Scatter Plots:

Scatterplots are used to visualize the relationship between two quantitative variables in a binary relation. As an example, trends in the relationship between the height and weight of a group of people could be graphed and analyzed using a scatter plot.

Type: Tutorial

## Video/Audio/Animations

Trend Lines (Smoking in 1945):

This 5-minute video provides an example of how to solve a problem using a trend line to estimate data through a problem called, "Smoking in 1945."

Type: Video/Audio/Animation

Fitting a Line to Data:

Khan Academy tutorial video that demonstrates with real-world data the use of Excel spreadsheet to fit a line to data and make predictions using that line.

Type: Video/Audio/Animation

## Virtual Manipulatives

Data Flyer:

Using this virtual manipulative, students are able to graph a function and a set of ordered pairs on the same coordinate plane. The constants, coefficients, and exponents can be adjusted using slider bars, so the student can explore the affect on the graph as the function parameters are changed. Students can also examine the deviation of the data from the function. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative

Curve Fitting:

With a mouse, students will drag data points (with their error bars) and watch the best-fit polynomial curve form instantly. Students can choose the type of fit: linear, quadratic, cubic, or quartic. Best fit or adjustable fit can be displayed.

Type: Virtual Manipulative

Line of Best Fit:

This manipulative allows the user to enter multiple coordinates on a grid, estimate a line of best fit, and then determine the equation for a line of best fit.

Type: Virtual Manipulative

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

## Teaching Idea

Birds & Eggs:

In this task, students start by examining a scatter plot about the size of various bird eggs from a collection of measurements. In particular, students are asked to identify a correlation, sketch an approximation for the line of best fit, determine the equation of that line, use the equation of the line and/or the graph to make interpolative predictions, and draw conclusions about the properties of specific eggs by using the graphical presentation of the data.

Type: Teaching Idea

## Video/Audio/Animation

Fitting a Line to Data:

Khan Academy tutorial video that demonstrates with real-world data the use of Excel spreadsheet to fit a line to data and make predictions using that line.

Type: Video/Audio/Animation