# MA.8.DP.1.2

Given a scatter plot within a real-world context, describe patterns of association.

### Clarifications

Clarification 1: Descriptions include outliers; positive or negative association; linear or nonlinear association; strong or weak association.
General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Data Analysis and Probability
Status: State Board Approved

## Benchmark Instructional Guide

• Association
• Outlier
• Scatter Plot

### Vertical Alignment

Previous Benchmarks

Next Benchmarks

### Purpose and Instructional Strategies

In grades 6 and 7, students described and interpreted, quantitatively and qualitatively, both numerical and categorical univariate data. In grade 8, students encounter bivariate data, and they use scatter plots to determine whether there is any association between the variables. In Algebra 1, students will continue working with scatter plots to display association, but expand their knowledge to consider association in bivariate categorical data, displayed with frequency tables.
• Instruction includes students communicating the relationships between two variables. Students should analyze scatter plots to determine the type and degree of association.

• Outliers in scatter plots are different than outliers in box plots. There is no special rule determining if a data point is an outlier in a scatter plot. Instead, students need to consider why the outlier does not fit the pattern. Students should examine if outliers are valid or represent a recording or measurement error. Students should identify outliers and clusters and give possible reasons for their existence (MTR.4.1, MTR.7.1).
• Instruction includes opportunities to discuss the effects of changing the data slightly and how the changes impact the scatter plots (MTR.4.1).

### Common Misconceptions or Errors

• Students may invert positive and negative correlations.
• Students may incorrectly assume that associations can only have one descriptor.
• For example, students may only say that the correlation is a positive association instead of describing it as a strong, positive linear association.
• Students may misinterpret an outlier and why it may occur in a set of data.

### Strategies to Support Tiered Instruction

• Teacher provides clear examples of associations of scatter plots (representing both strong and weak associations). Teacher facilitates discussion about whether each association is positive or negative.

• Teacher provides examples of different outliers and discusses with students why this occurred. Creating this dialogue will help students begin to understand how outliers can be used differently depending on the type of data collected, and what the data is intended for.
• Instruction includes co-creating a graphic organizer to include examples of different patterns to association. Categories include trends in association (positive, negative, no), strength of association (strong, weak) and pattern of association (linear or nonlinear).

The graphs below shows the test scores of the students in Dexter's class. The first graph shows the relationship between test scores and the amount of time the students spent studying, and the second graph shows the relationship between test scores and shoe size.

• Part A. Describe and explain the pattern of association for each of the graphs.
• Part B. If you were to add an outlier to the first graph, describe the data point and what it would mean in context.

Population density measures are approximations of the number of people per square unit of area. The following scatter plot represents data from each of the 50 states comparing population (in millions) to land area (in 10,000 square miles) in 2012.

• Part A. Describe the type and degree of association between population and land area.
• Part B. Discuss with a partner possible interpretations of your answer to Part A. Do you think this would hold true for other countries?

### Instructional Items

Instructional Item 1
The scatter plot below compares middle school students' scores on the Epworth Sleepiness Scale (ESS) to their scores on a recent math test. The Epworth Sleepiness Scale measures excessive daytime sleepiness with zero being least sleepy. Describe the type and degree of association between scores on the Epworth Sleepiness Scale and scores on the math test.

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

## 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))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.8.DP.1.AP.2: Given a scatter plot, identify whether the patterns of association are no association, positive association, negative association, linear or nonlinear.

## Related Resources

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

## Formative Assessments

Sleepy Statistics:

Students are given a scatter plot in a real-world context and asked to describe the association between the variables.

Type: Formative Assessment

Population Density:

Students are given a scatterplot in a real-world context and asked to describe the association between the variables.

Type: Formative Assessment

Infectious Statistics:

Students are given a scatterplot in a real-world context and asked to describe the association between the variables.

Type: Formative Assessment

Cheesy Statistics:

Students are given a scatterplot in a real-world context and asked to describe the association between the variables.

Type: Formative Assessment

Bungee Cord Data:

Students are asked to construct a scatterplot corresponding to a given set of data.

Type: Formative Assessment

## Lesson Plans

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Clean Up, Collect Data, and Conserve the Environment!:

Students will participate in collecting trash either on campus or another location. They will compare the distance traveled and the weight of the trash bag collected. Students will explore the use of mean and median in finding the ratios of the data set. They will discuss the use of mean and median in finding the relationship between the independent and dependent variables. Students will examine their scatter plot and determine if any patterns of association exist. They will compare their data to a coastal cleanup report. Finally, students will use the data to help determine interventions at the local, state and national level regarding environmental issues.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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?

Type: Lesson Plan

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.

Type: Lesson Plan

Students will gather and use data to calculate a line of fit and the correlation coefficient with their classmates' height and hand size. They will use their line of fit to make approximations.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Star Scatter Plots:

In this lesson, students plot temperature and luminosity data from a provided star table to create a scatter plot. They will analyze the data to sequence the colors of stars from hottest to coolest and to describe the relationship between temperature and luminosity. This lesson does not address differentiation between absolute and apparent magnitude.

Type: Lesson Plan

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.

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

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.

Type: Lesson Plan

Scrambled Coefficient:

Students will learn how the correlation coefficient is used to determine the strength of relationships among real data. Students use card sorting to order situations from negative to positive correlations. Students will create a scatter plot and use technology to calculate the line of fit and the correlation coefficient. Students will make a prediction and then use the line of fit and the correlation coefficient to confirm or deny their prediction.

Students will learn how to use the Linear Regression feature of a graphing calculator to determine the line of fit and the correlation coefficient.

The lesson includes the guided card sorting task, a formative assessment, and a summative assessment.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Finding the Hottest Trend:

In this lesson, students will graph a scatter plot and learn how to recognize patterns. The students will learn that correlation may still exist even though the points are not in a perfectly straight line (linear function). Students will be able to identify outliers, describe associations, and justify their reasoning.

Type: Lesson Plan

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.

Type: Lesson Plan

Guess the Celebrities' Heights!:

In this activity, students use scatter plots to compare the estimated and actual heights of familiar celebrities and athletes. They will determine how their answers impact the correlation of their data, including the influence of outliers. Finally, they will compare their correlation to that provided in a scatter plot with a larger data sample.

Type: Lesson Plan

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.

Type: Lesson Plan

## Original Student Tutorials

The Notion of Motion, Part 2 - Position vs Time:

Continue an exploration of kinematics to describe linear motion by focusing on position-time measurements from the motion trial in part 1. In this interactive tutorial, you'll identify position measurements from the spark tape, analyze a scatterplot of the position-time data, calculate and interpret slope on the position-time graph, and make inferences about the dune buggy’s average speed

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

Scatterplots Part 2: Patterns, Associations and Correlations:

Explore the different types of associations that can exist between bivariate data in this interactive tutorial.

This is part 2 in 6-part series. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

## Perspectives Video: Experts

Birdsong Series: Statistical Analysis of Birdsong:

Wei Wu discusses his statistical contributions to the Birdsong project which help to quantify the differences in the changes of the zebra finch's song.

Type: Perspectives Video: Expert

Birdsong Series: STEM Team Collaboration :

Researchers Frank Johnson, Richard Bertram, Wei Wu, and Rick Hyson explore the necessity of scientific and mathematical collaboration in modern neuroscience, as it relates to their NSF research on birdsong.

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiasts

Asymptotic Behavior in Shark Growth Research:

Fishery Scientist from Florida State University discusses his new research in deep sea sharks and the unusual behavior that is found when the data is graphed.

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

Students are asked to examine a scatter plot and then interpret its meaning. Students should identify the form of the relationship (linear, curved, etc.), the direction or correlation (positive or negative), any specific outliers, the strength of the relationship between the two variables, and any other relevant observations.

## MFAS Formative Assessments

Bungee Cord Data:

Students are asked to construct a scatterplot corresponding to a given set of data.

Cheesy Statistics:

Students are given a scatterplot in a real-world context and asked to describe the association between the variables.

Infectious Statistics:

Students are given a scatterplot in a real-world context and asked to describe the association between the variables.

Population Density:

Students are given a scatterplot in a real-world context and asked to describe the association between the variables.

Sleepy Statistics:

Students are given a scatter plot in a real-world context and asked to describe the association between the variables.

## Original Student Tutorials Science - Grades K-8

The Notion of Motion, Part 2 - Position vs Time:

Continue an exploration of kinematics to describe linear motion by focusing on position-time measurements from the motion trial in part 1. In this interactive tutorial, you'll identify position measurements from the spark tape, analyze a scatterplot of the position-time data, calculate and interpret slope on the position-time graph, and make inferences about the dune buggy’s average speed

## Original Student Tutorials Mathematics - Grades 6-8

Scatterplots Part 2: Patterns, Associations and Correlations:

Explore the different types of associations that can exist between bivariate data in this interactive tutorial.

This is part 2 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.

## Student Resources

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

## Original Student Tutorials

The Notion of Motion, Part 2 - Position vs Time:

Continue an exploration of kinematics to describe linear motion by focusing on position-time measurements from the motion trial in part 1. In this interactive tutorial, you'll identify position measurements from the spark tape, analyze a scatterplot of the position-time data, calculate and interpret slope on the position-time graph, and make inferences about the dune buggy’s average speed

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

Scatterplots Part 2: Patterns, Associations and Correlations:

Explore the different types of associations that can exist between bivariate data in this interactive tutorial.

This is part 2 in 6-part series. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

Students are asked to examine a scatter plot and then interpret its meaning. Students should identify the form of the relationship (linear, curved, etc.), the direction or correlation (positive or negative), any specific outliers, the strength of the relationship between the two variables, and any other relevant observations.