# Standard 1: Represent and investigate numerical bivariate data.

General Information
Number: MA.8.DP.1
Title: Represent and investigate numerical bivariate data.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Strand: Data Analysis and Probability

## Related Benchmarks

This cluster includes the following benchmarks.

## Related Access Points

This cluster includes the following access points.

## Access Points

MA.8.DP.1.AP.1
Graph bivariate data using a scatter plot.
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.
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

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

## 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

Aquarium Visitors:

Students are given a set of data and are asked to choose the scale for the axes, graph the data, and explain why they chose the scales they used.

Type: Formative Assessment

Time to Get to School:

Students are asked to describe potentially important variables that can be used in a model to predict the amount of time required to get to school.

Type: Formative Assessment

Rain Damage Model:

Students are asked to describe potentially important variables that can be used in a model to predict the amount of damage caused by a thunderstorm.

Type: Formative Assessment

Bungee Cord Data:

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

Type: Formative Assessment

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

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

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

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

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 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.

Type: Original Student Tutorial

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

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

Scatterplots Part 1: Graphing:

Learn how to graph bivariate data in a scatterplot in this interactive tutorial.

This is part 1 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

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

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

## Teaching Idea

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.

Type: Teaching Idea

## Virtual Manipulative

KidsZone: Create a Graph:

Create bar, line, pie, area, and xy graphs.

Type: Virtual Manipulative

## Student Resources

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

## 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 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.

Type: Original Student Tutorial

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

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

Scatterplots Part 1: Graphing:

Learn how to graph bivariate data in a scatterplot in this interactive tutorial.

This is part 1 in 6-part series. Click below to open the other tutorials in the series.

Type: Original Student Tutorial

## Parent Resources

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