Standard 2: Solve problems involving univariate and bivariate numerical data.

General Information
Number: MA.912.DP.2
Title: Solve problems involving univariate and bivariate numerical data.
Type: Standard
Subject: Mathematics (B.E.S.T.)
Grade: 912
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.912.DP.2.AP.4
Fit a linear function to bivariate numerical data that suggests a linear association and interpret the slope and y-intercept of the model.
MA.912.DP.2.AP.6
Given a scatter plot with a line of fit and residuals, determine the strength and direction of the correlation. Interpret strength and direction within a real-world context.
MA.912.DP.2.AP.8
Given a scatter plot, select a quadratic function that fits the data the best.
MA.912.DP.2.AP.9
Given a scatter plot, select an exponential function that fits the data the best. 

Related Resources

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

Formative Assessments

Tuition:

Students are asked to use a linear model to make a prediction about the value of one of the variables.

Type: Formative Assessment

Foot Length:

Students are asked to interpret the line of best fit, slope, and y-intercept of a linear model.

Type: Formative Assessment

Residuals:

Students are asked to compute, graph, and interpret the residuals associated with a line of best fit.

Type: Formative Assessment

How Many Jeans?:

Students are asked to select a measure of center to compare data displayed in dot plots and to justify their choice.

Type: Formative Assessment

Texting During Lunch Histograms:

Students are asked to select measures of center and spread to compare data displayed in histograms and to justify their choices.

Type: Formative Assessment

Texting During Lunch:

Students are asked to select a measure of center to compare data displayed in frequency tables and to justify their choice.

Type: Formative Assessment

Swimming Predictions:

Students are asked to use a linear model to make and interpret predictions in the context of the data.

Type: Formative Assessment

July December Correlation:

Students are asked to compute and interpret the correlation coefficient for a given set of data.

Type: Formative Assessment

How Big Are Feet?:

Students are asked to compute and interpret the correlation coefficient for a given set of data.

Type: Formative Assessment

House Prices:

Students are asked to informally fit a line to model the relationship between two quantitative variables in a scatterplot, write the equation of the line, and use it to make a prediction.

Type: Formative Assessment

Correlation Order:

Students are asked to estimate a correlation coefficient for each of four data sets and then order the coefficients from least to greatest in terms of the strength of relationship.

Type: Formative Assessment

Correlation for Life Expectancy:

Students are asked to compute and interpret the correlation coefficient for a given set of data.

Type: Formative Assessment

Total Points Scored:

Students are given a set of data and are asked to determine how the mean is affected when an outlier is removed.

Type: Formative Assessment

Using Spread to Compare Tree Heights:

Students are asked to compare the spread of two data distributions displayed using box plots.

Type: Formative Assessment

Using Centers to Compare Tree Heights:

Students are asked to compare the centers of two data distributions displayed using box plots.

Type: Formative Assessment

Comparing Distributions:

Students are given two histograms and are asked to describe the differences in shape, center, and spread.

Type: Formative Assessment

Slope for Human Foot Length Model:

Students are asked to interpret the meaning of the slope of the graph of a linear model.

Type: Formative Assessment

Slope for Life Expectancy:

Students are asked to interpret the meaning of the slope of the graph of a linear model.

Type: Formative Assessment

Intercept for Life Expectancy:

Students are asked to interpret the intercept of a linear model of life expectancy data.

Type: Formative Assessment

Probability of Your Next Texting Thread:

Students are asked to find the probability that an outcome of a normally distributed variable is greater than a given value.

Type: Formative Assessment

Range of Texting Thread:

Students are asked to find the probability that an outcome of a normally distributed variable is between a standard deviation level.

Type: Formative Assessment

Label a Normal Curve:

Students are asked to scale and label a normal curve given the mean and standard deviation of a data set with a normal distribution.

Type: Formative Assessment

Area Under the Normal Curve:

Students are asked to find the probability that an outcome of a normally distributed variable is between two given values using both a Standard Normal Distribution Table and technology.

Type: Formative Assessment

Algebra Test Scores:

Students are asked to select a histogram for which it would be appropriate to apply the 68-95-99.7 rule.

Type: Formative Assessment

Bungee Cord Model:

Students are asked to interpret the meaning of the constant term in a linear model.

Type: Formative Assessment

Lesson Plans

What happens to available energy as it moves through an ecosystem?:

This activity is a lab exercise where students look at the passing of water in cups and compare it to the loss of available energy as it moves through an ecosystem. Students will collect data, calculate efficiency, graph the data and respond to reflection questions to connect the data to what happens in an ecosystem. The end of the activity includes a connection to the 10% rule where only 10% of energy from one trophic level is available at the next level.

Type: Lesson Plan

Mass Mole Relationships: A Statistical Approach To Accuracy and Precision:

The lesson is a laboratory-based activity involving measurement, accuracy and precision, stoichiometry and a basic statistical analysis of data using a scatter plot, linear equation, and linear regression (line of best fit). The lesson includes teacher-led discussions with student participation and laboratory-based group activities.

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.

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.

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

Movies Part 2: What’s the Spread?:

Follow Jake along as he relates box plots with other plots and identifies possible outliers in real-world data from surveys of moviegoers' ages in part 2 in this interactive tutorial.

This is part 2 of 2-part series, click HERE to view part 1.

Type: Original Student Tutorial

Movies Part 1: What's the Spread?:

Follow Jake as he displays real-world data by creating box plots showing the 5 number summary and compares the spread of the data from surveys of the ages of moviegoers in part 1 of this interactive tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Type: Original Student Tutorial

Perspectives Video: Experts

Tree Rings Research to Inform Land Management Practices:

In this video, fire ecologist Monica Rother describes tree ring research and applications for land management.

Type: Perspectives Video: Expert

Oceanography & Math:

A discussion describing ocean currents studied by a physical oceanographer and how math is involved. 

Type: Perspectives Video: Expert

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

Assessment of Past and Present Rates of Sea Level Change:

In this video, Brad Rosenheim describes how Louisiana sediment cores are used to estimate sea level changes over the last 10,000 years. Video funded by NSF grant #: OCE-1502753.

Type: Perspectives Video: Expert

Analyzing Antarctic Ice Sheet Movement to Understand Sea Level Changes:

In this video, Eugene Domack explains how past Antarctic ice sheet movement rates allow us to understand sea level changes. Video funded by NSF grant #: OCE-1502753.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Statistical Inferences and Confidence Intervals :

Florida State University Counseling Psychologist discusses how he uses confidence intervals to make inferences on college students' experiences on campus based on a sample of students.

Type: Perspectives Video: Expert

Mathematically Exploring the Wakulla Caves:

The tide is high!  How can we statistically prove there is a relationship between the tides on the Gulf Coast and in a fresh water spring 20 miles from each other?

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Statistics and Scientific Data:

Hear this oceanography student float some ideas about how statistics are used in research.

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiasts

Nestle Waters & Statistical Analysis:

Hydrogeologist from Nestle Waters discusses the importance of statistical tests in monitoring sustainability and in maintaining consistent water quality in bottled water.

Type: Perspectives Video: Professional/Enthusiast

Statistical Art: Four Words:

Graphic designer and artist, Drexston Redway infuses statistics into his artwork to show population distribution and overlap of poverty and ethnicity in Tallahassee, FL.

Type: Perspectives Video: Professional/Enthusiast

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.

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.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Linear Regression for Analysis of Sea Anemone Data:

Will Ryan describes how linear regression models contribute towards his research on sea anemones.

Type: Perspectives Video: Professional/Enthusiast

Sampling Strategies for Ecology Research in the Intertidal Zone:

Will Ryan describes methods for collecting multiple random samples of anemones in coastal marine environments.

Type: Perspectives Video: Professional/Enthusiast

Normal? Non-Normal Distributions & Oceanography:

What does it mean to be normally distributed?  What do oceanographers do when the collected data is not normally distributed? 

Type: Perspectives Video: Professional/Enthusiast

Mathematically Modeling Eddy Shedding :

COAPS oceanographer Dmitry Dukhovskoy describes the process used to mathematically model eddy shedding in the Gulf of Mexico.

Type: Perspectives Video: Professional/Enthusiast

Sampling Amphibian Populations to Study Human Impact on Wetlands:

Ecologist Rebecca Means discusses the use of statistical sampling and comparative studies in field biology.

Type: Perspectives Video: Professional/Enthusiast

Winning the Race with Data Logging and Statistics:

Data logging has transformed competitive racing! These SCCA drivers discuss how they use computers to compare multiple sets of data after test runs.

Type: Perspectives Video: Professional/Enthusiast

Residuals and Laboratory Standards:

Laws and regulations that affect the public are being formed based on data from a variety of laboratories. How can we be sure that the laboratories are all standardized?

Type: Perspectives Video: Professional/Enthusiast

Analyzing Wildlife Data Trends with Regression :

Dr. Bill McShea from the Smithsonian Institution discusses how regression analysis helps in his research.

This video was created in collaboration with the Okaloosa County SCIENCE Partnership, including the Smithsonian Institution and Harvard University.

Type: Perspectives Video: Professional/Enthusiast

Revolutionize Wing Design with Equations and Statistics:

Brandon Reese, a PhD candidate in the FAMU-FSU College of Engineering, discusses the significance of both Bernoulli's equation and statistical analysis for the design of a "smart wing."

Type: Perspectives Video: Professional/Enthusiast

Perspectives Video: Teaching Idea

Smile Statistics:

This quantitative measurement and statistics activity will allow you to save face.

Type: Perspectives Video: Teaching Idea

Teaching Idea

An Ecological Field Study with Statistical Analysis of Two Populations:

Students will design an investigation that compares a characteristic of two populations of the same species. Students will collect data in the field and analyze the data using descriptive statistics.

Type: Teaching Idea

Student Resources

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

Original Student Tutorials

Movies Part 2: What’s the Spread?:

Follow Jake along as he relates box plots with other plots and identifies possible outliers in real-world data from surveys of moviegoers' ages in part 2 in this interactive tutorial.

This is part 2 of 2-part series, click HERE to view part 1.

Type: Original Student Tutorial

Movies Part 1: What's the Spread?:

Follow Jake as he displays real-world data by creating box plots showing the 5 number summary and compares the spread of the data from surveys of the ages of moviegoers in part 1 of this interactive tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Type: Original Student Tutorial

Perspectives Video: Expert

Mathematically Exploring the Wakulla Caves:

The tide is high!  How can we statistically prove there is a relationship between the tides on the Gulf Coast and in a fresh water spring 20 miles from each other?

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Parent Resources

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