# 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.)
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 suggest 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.
MA.912.DP.2.AP.1
For two sets of numerical univariate data, calculate and compare the mean, median and range, then select the shape of the data from given graphs.
MA.912.DP.2.AP.5
Match a scatter plot that represents bivariate numerical data with its residual plot.

## 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

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

Type: Formative Assessment

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

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

A MEANingful Discussion about Central Tendency:

Using relatable scenarios, this lesson explores the mean and median of a data set and how an outlier affects each measure differently.

Type: Lesson Plan

Students will explore voter turnout data for three gubernatorial elections before and after the passage of the 19th amendment. They will fit linear functions to the data and compute predicted values for raw and percentage of voter turnout. Students will draw some conclusions concerning the relationship between eligible voters and voter turnout, including possible causes behind the fluctuation in voter participation in this integrated lesson

Type: Lesson Plan

Students will explore voter turnout data for three gubernatorial general elections before and after the passage of the 19th Amendment. They will interpret the correlation of raw voter turnout vs. eligible population using a scatterplot, determine its direction by analyzing the slope and informally determine its strength by analyzing the residuals. Students will draw some conclusions and discuss what a correlation means and how it differs from causation in the context of elections in this integrated lesson.

Type: Lesson Plan

Spreading the Vote - Part 2:

Students will explore voter turnout data for three gubernatorial general elections before and after the passage of the 19th Amendment. They will interpret the correlation of eligible population vs. percentage of voter turnout using a scatterplot, determine its direction by analyzing the slope and informally determine its strength by analyzing the residuals. Students will draw some conclusions and discuss what a correlation means and how it differs from causation in the context of elections in this integrated lesson.

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

Show Me the Money! Selecting Student Athletes for Scholarships:

In this Model Eliciting Activity, MEA, students will use data to decide the ideal candidate for a college scholarship by computing the mean and the standard deviation. The student will present the data using the normal distribution and make recommendations based on the findings. Students will recognize that not all data can be presented in this format.

Model-Eliciting-Activities, MEAs, allow students to critically analyze data sets, compare information, and require students to explain their thinking and reasoning. While there is no one correct answer in an MEA, students should work to explain their thinking clearly and rationally. Therefore, teachers should ask probing questions and provide feedback to help students develop a coherent, data-as-evidence-based approach within this learning experience.

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

How Hot Is It?:

This lesson allows the students to connect the science of cricket chirps to mathematics. In this lesson, students will collect real data using the CD "Myths and Science of Cricket Chirps" (or use supplied data), display the data in a graph, and then find and use the mathematical model that fits their data.

Type: Lesson Plan

Analyzing Box Plots:

This lesson is designed for students to demonstrate their knowledge of box plots.

• Students will need to create four box plots from given data.
• Students will need to analyze the data displayed on the box plots by comparing similarities and differences.
• Students will work with a partner to complete the displays and the follow-up questions.

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

Texting and Standard Deviation:

This lesson uses texting to teach statistics. In the lesson, students will calculate the mean, median, and standard deviation. They will create a normal distribution using the mean and standard deviation and estimate population percentages. They will construct and interpret dot plots based on the data they collected. Students will also use similarities and differences in shape, center, and spread to determine who is better at texting, boys, or girls.

Type: Lesson Plan

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

Height vs. Shoe Size:

This resource provides an introductory lesson on Correlation, the Correlation Coefficient, and Correlation vs. Causation. The lesson is structured around collecting data from a survey at the beginning of class to be used in creating scatter plots and analyzing them using technology. Students engage in discussion activities that challenge their thoughts on linked variables in the media.

Type: Lesson Plan

Heart Rate and Exercise: Is there a correlation?:

Students will use supplied heart rate data to determine if heart rate and the amount of time spent exercising each week are correlated. Students will use GeoGebra to create scatter plots and lines of fit for the data and examine the correlation. Students will gather evidence to support or refute statistical statements made about correlation. The lesson provides easy to follow steps for using GeoGebra, a free online application, to generate a correlation coefficient for two given variables.

Type: Lesson Plan

Span the Distance Glider - Correlation Coefficient:

This lesson will provide students with an opportunity to collect and analyze bivariate data and use technology to create scatter plots, lines of best fit, and determine the correlation strength of the data being compared. Students will have a hands on inquire based lesson that allows them to create gliders to analyze data. This lesson is an application of skills acquired in a bivariate unit of study.

Type: Lesson Plan

Comparing Standard Deviation:

Students will predict and compare standard deviation from a dot plot. Each data set is very different, with a small variation vs. a larger variation. The students are asked to interpret the standard deviation after calculating the range and mean of the each data set.

Type: Lesson Plan

Close to the Crossbar with Standard Deviation:

The lesson will connect student's prior knowledge of measures of central tendency to standard deviation and variance. Students will learn how to calculate and analyze variance and standard deviation. With a partner, students will collect data from kicking a ball into a goal mark. Students will collect data and find the mean, then calculate standard deviation and variance, and compare the data between boys and girls. They will analyze the data distribution in terms of how many students are within certain numbers of standard deviations from the mean.

Type: Lesson Plan

Bowling for Box Plots:

Students will learn about the effects of an outlier and interpret differences in shape, center, and spread using a bowling activity to gather data. The students will learn to score their games, report their scores, and collectively measure trends and spread by collaborating to create a box plot. They will analyze and compare box plots, and determine how much of an effect an extreme score (outlier) can have on the overall box plot of the data.

Type: Lesson Plan

"What's My Grade" is a lesson that will focus on a sample student's grades to demonstrate how a final grade is calculated as well as explore possible future grades. Students will create the distributions of each grade category using histograms. They will also analyze grades using mean and standard deviation. Students will use statistics to determine data distribution while comparing the center and spread of two or more different data sets.

Type: Lesson Plan

College Freshman Entrance Data:

An introduction to classifying data as normally distributed, skewed left, or skewed right, Technology is used to calculate the mean, median, and standard deviation. Data listing ranking, acceptance rates, average GPA, SAT and ACT scores, and tuition rates from 36 Universities are used.

Type: Lesson Plan

How tall is an 8th grader?:

Ever wonder about the differences in heights between students in grade 8? In this lesson, students will use data they collect to create and analyze multiple box plots using 5-number summaries. Students will make inferences about how height and another category may or may not be related.

Type: Lesson Plan

Plane Statistics:

This lesson starts with an activity to gather data using paper airplanes then progresses to using appropriate statistics to compare the center and spread of the data. Box plots are used in this application lesson of concepts and skills previously acquired.

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

Standard Deviation and the Normal Curve in Kahoot!:

In this three-day lesson, students learn about standard deviation, the normal curve, and how they are applied. Your students will be engaged and learning when they collect and analyze data using a free Kahoot! quiz.

Type: Lesson Plan

Study of Crowd Ratings at Disney:

In this lesson, students develop a strong use of the vocabulary of correlation by investigating crowd ratings at Disney. Students will determine weekly crowd rating regression lines and correlations and discuss what this means for a Disney visit.

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

Picturing the Normal World:

This is an introductory lesson on normally distributed data. Students will calculate the standard deviation and use the Empirical Rule.

Type: Lesson Plan

This resource can be used to teach students how to create and compare box plots. After completing this lesson, students should be able to answer questions in both familiar and unfamiliar situations.

Type: Lesson Plan

The Distance a Coin Will Travel:

This lesson is a hands-on activity that will allow students to collect and display data about how far different coins will travel. The data collected is then used to construct double dot plots and double box plots. This activity helps to facilitate the statistical implications of data collection and the application of central tendency and variability in data collection.

Type: Lesson Plan

Which is Better? Using Data to Make Choices:

Students use technology to analyze measures of center and variability in data. Data displays such as box plots, line plots, and histograms are used. The effects of outliers are taken into consideration when drawing conclusions. Students will cite evidence from the data to support their conclusions.

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

Calculating Residuals and Constructing a Residual Plot with Soccer Seats:

Students will learn all about residuals. The definition, how to calculate them, how to plot and analyze residuals, and how to use them to assess the fit of a linear function. They will do this within the context of comparing the location of a seat in a soccer stadium with its price.

Type: Lesson Plan

How many licks does it take to get to the center?:

Students will create different displays, line plots, histograms, and box plots from data collected about types of lollipops. The data will be analyzed and compared. Students will determine "Which lollipop takes the fewest number of licks to get to the center: a Tootsie Pop, a Blow Pop, or a Dum Dum?"

Type: Lesson Plan

Birthday Party Decisions:

Students will create and compare four different boxplots to determine the best location for a birthday party.

Type: Lesson Plan

Outliers in the Outfield â€“ Dealing With Extreme Data Points:

Students will explore the effects outliers have on the mean and median values using the Major League Baseball (MLB) salary statistics. They will create and compare box plots and analyze measures of center and variability. They will also be given a set of three box plots and asked to identify and compare their measures of center and variablity.

Type: Lesson Plan

In terms of soccer: Nike or Adidas?:

In this lesson, students calculate and interpret the standard deviation for two data sets. They will measure the air pressure for two types of soccer balls. This lesson can be used as a hands-on activity or completed without measuring using sample data.

Type: Lesson Plan

This lesson allows students to have a hands-on experience collecting real-world data, creating graphical representations, and analyzing their data. Students will make predictions as to the outcome of the data and compare their predictions to the actual outcome. Students will create and analyze line plots, histograms, and box plots.

Type: Lesson Plan

Comparing Data Using Box Plots:

Students will use box plots to compare two or more sets of data. They will analyze data in context by comparing the box plots of two or more data sets.

Type: Lesson Plan

Digging the Plots:

Students construct box plots and use the measure(s) of center and variability to make comparisons, interpret results, and draw conclusions about two populations.

Type: Lesson Plan

A Walk Down the Lane:

Students will collect data, and create box plots. Students will make predictions about which measurement best describes the spread and center of the data. Students will use this information to make predictions.

Type: Lesson Plan

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.

Type: Lesson Plan

How do we measure success?:

Students will use the normal distribution to estimate population percentages and calculate the values that fall within one, two, and three standard deviations of the mean. Students use statistics and a normal distribution to determine how well a participant performed in a math competition.

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

If The Shoe Fits â€“ A "Normal" Cinderella Story:

Using a normal distribution manipulative and a calculator, students will explore the normal distribution curve to determine the area between each standard deviation from the mean using the empirical rule. Students will use the mean and standard deviation to predict outcomes in real-world situations and finally answer the age old question: What size was Cinderella's glass slipper?

Type: Lesson Plan

The students will compare the effects of outliers on measures of center and spread within dot plots and box plots.

Type: Lesson Plan

Why do I have to have a bedtime?:

This predict, observe, explain lesson that allows students to make predictions based on prior knowledge, observations, discussions, and calculations. Students will receive the opportunity to express themselves and their ideas while explaining what they learned. Students will make a prediction, collect data, and construct a scatter plot. Next, students will calculate the correlation coefficient and use it to describe the strength and magnitude of a relationship.

Type: Lesson Plan

Baking Soda and Vinegar: A statistical approach to a chemical reaction.:

Students experiment with baking soda and vinegar and use statistics to determine which ratio of ingredients creates the most carbon dioxide. This hands-on activity applies the concepts of plot, center, and spread.

Type: Lesson Plan

Should Statistics be Shapely?:

Students will Interpret differences in shape, center, and spread of a variety of data displays, accounting for possible effects of extreme data points.

Students will create a Human Box Plot using their data to master the standard and learning objectives, then complete interactive notes with the classroom teacher, a formative assessment, and later a summative assessment to show mastery.

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

The Cereal Prize Estimation:

How many boxes of cereal would you have to purchase to win all six prizes?

This lesson uses class data collected through simulations to allow students to answer this question. Students simulate purchasing cereal boxes and create a t-confidence interval with their data to determine how many boxes they can expect to buy.

Type: Lesson Plan

Students investigate correlation and causation through the medium of cartoons. Students construct arguments in favor of and against causal relationships between two strongly correlated events and decide which one is more reasonable. Students create cartoons representing the idea that correlation does not imply causation.

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

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

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.

Type: Lesson Plan

Sweet Statistics - A Candy Journey:

Students will sort pieces of candy by color and then calculate statistical information such as mean, median, mode, interquartile range, and standard deviation. They will also create an Excel spreadsheet with the candy data to generate pie charts and column charts. Finally, they will compare experimental data to theoretical data and explain the differences between the two. This is intended to be an exercise for an Algebra 1 class. Students will need at least 2 class periods to sort their candy, make the statistical calculations, and create the charts in Excel.

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

Exploring Box plots:

This lesson involves real-world data situations. Students will use the data to create, explore, and compare the key components of a box plot.

Type: Lesson Plan

The Debate: Who is a Better Baller?:

In this activity the students will use NBA statistics on Lebron James and Tim Duncan who were key players in the 2014 NBA Finals, to calculate, compare, and discuss mean, median, interquartile range, variance, and standard deviation. They will also construct and discuss box plots.

Type: Lesson Plan

Who's Better?--Using Data to Determine:

This lesson is intended for use after students are able to construct data plots (histograms, line plots, box plots). Students are tasked with not only constructing data plots, but also matching data plots to data sets. In the summative assessment, students are given two data sets and asked to select which of three data plots (histogram, line plot, or box plot) would best be used to compare the data. After choosing and constructing their plot, students are then tasked with forming a conclusion based on the plots they have constructed.

Type: Lesson Plan

Burgers to Smoothies.:

Students will create double box plots to compare nutritional data about popular food choices.

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

Correlation or Causation: That is the question:

Students will learn how to analyze whether two events/properties demonstrate a correlation or causation or both. They will learn what factors are involved when evaluating whether correlated events demonstrate causation. If two events are claimed to be causal when they are not, they will be able to determine why, and which (if any) causal fallacies are present. At the close of the lesson students will be given situational data and develop a newscast that assumes causation when in fact there is no causal link. Students who are observing will analyze each presentation and determine which (if any) causal fallacy was used (or explain why the newscast is correct in their assumption of causality).

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

Smarter than a Statistician: Correlations and Causation in the Real World!:

Students will learn to distinguish between correlation and causation. They will build their skills by playing two interactive digital games that are included in the lesson. The lesson culminates with a research project that requires students to find and explain the correlation between two real world events.

Type: Lesson Plan

Linear Statistical Models:

In this lesson, students will learn how to analyze data and find the equation of the line of best fit. Students will then find the slope and intercept of the best fit line and interpret the meaning in the context of the data.

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

Is Milk Killing People?:

Students will explore correlation and causation from data through class discussions of real-world examples. They will know positive, negative, strong, and weak correlations. Students make predictions regarding the feasibility of causation by analyzing graphs and scatter plots of data.

Students will participate in an experiment where they will generate and analyze their own data. They will come to conclusion regarding variations in data, correlation and causation. Students are encouraged to explain and justify their responses. The teacher will facilitate discussion of leading question to be geared towards the learning objectives.

During the lesson, students will be assessed by several formative assessments and a summative assessment at the conclusion. The lesson includes a worksheet and data collection sheets.

Type: Lesson Plan

House Hunting!:

In this Model Eliciting Activity, MEA, students will analyze and use factors of various counties to recommend the top 3 to buy for a home given a client’s preferences. Students will use weighted averages, key statistics like median and mean, and correlation to conduct a thorough analysis of the data to justify their recommendations.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

The Best Ballpark:

In this Model Eliciting Activity, MEA, students will apply basic arithmetic and averages to assess and rank the home field advantages of various baseball parks. They will analyze hitting statistics and use weighted averages and composite scores to determine rankings.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

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

Don't Mope Over Slope:

This is an introductory lesson designed to help students have a better understanding of the interpretation of the slope (rate of change) of a graph.

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

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

Analyzing Data with Bell Curves and Measures of Center:

In this lesson, students learn about data sets and will be able to tell if a bell curve represents a normal distribution and explain why a distribution might be skewed. Students will form their own bell curve calculate measures of center and variability based on their data and discuss their findings with the class.

Type: Lesson Plan

The Election Resource:

In this Model Eliciting Activity, MEA, students will analyze sets of data and draw conclusions to justify the top candidates for positions of President, Treasurer, and Secretary of the school's Student Government Association.

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. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx

Type: Lesson Plan

A MEANingful Discussion about Central Tendency:

Using relatable scenarios, this lesson explores the mean and median of a data set and how an outlier affects each measure differently.

Type: Lesson Plan

Hybrid-Electric Vehicles vs. Gasoline-Powered Vehicles:

Students will be comparing hybrid-electric vehicles (HEV) versus gasoline-powered vehicles. They will research the benefits of owning a HEV while also analyzing the cost effectiveness.

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: Whatâ€™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:

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

Type: Perspectives Video: Expert

Oceanography & Math:

<p>A discussion describing ocean&nbsp;currents studied by a physical oceanographer and how math is involved.&nbsp;</p>

Type: Perspectives Video: Expert

Birdsong Series: Statistical Analysis of Birdsong:

<p>Wei&nbsp;Wu discusses his statistical contributions to the Birdsong project which help to quantify&nbsp;the differences in the changes of the zebra finch's song.</p>

Type: Perspectives Video: Expert

Birdsong Series: STEM Team Collaboration :

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

Type: Perspectives Video: Expert

Assessment of Past and Present Rates of Sea Level Change:

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

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.

Type: Perspectives Video: Expert

Statistical Inferences and Confidence Intervals :

<p>Florida State University Counseling Psychologist&nbsp;discusses how he uses confidence intervals to make inferences on college students' experiences on campus based on a sample of students.</p>

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?

Type: Perspectives Video: Expert

Statistics and Scientific Data:

<p>Hear this oceanography student float some ideas about how statistics are used in research.</p>

Type: Perspectives Video: Expert

## Perspectives Video: Professional/Enthusiasts

Nestle Waters & Statistical Analysis:

<p>Hydrogeologist&nbsp;from Nestle Waters discusses the importance&nbsp;of statistical tests in monitoring&nbsp;sustainability and in maintaining consistent&nbsp;water quality in bottled water.</p>

Type: Perspectives Video: Professional/Enthusiast

Statistical Art: Four Words:

<p>Graphic designer and artist,&nbsp;Drexston&nbsp;Redway&nbsp;infuses statistics into his artwork to show population distribution and overlap of poverty and ethnicity in Tallahassee, FL.</p>

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.

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

Linear Regression for Analysis of Sea Anemone Data:

<p>Will Ryan describes how linear regression models contribute towards his research on sea anemones.</p>

Type: Perspectives Video: Professional/Enthusiast

Sampling Strategies for Ecology Research in the Intertidal Zone:

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

Type: Perspectives Video: Professional/Enthusiast

Normal? Non-Normal Distributions & Oceanography:

<p>What does it mean to be normally distributed? &nbsp;What do oceanographers do when the collected data is not normally distributed?&nbsp;</p>

Type: Perspectives Video: Professional/Enthusiast

Mathematically Modeling Eddy Shedding :

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

Type: Perspectives Video: Professional/Enthusiast

Sampling Amphibian Populations to Study Human Impact on Wetlands:

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

Type: Perspectives Video: Professional/Enthusiast

Winning the Race with Data Logging and Statistics:

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

Type: Perspectives Video: Professional/Enthusiast

Residuals and Laboratory Standards:

<p>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?</p>

Type: Perspectives Video: Professional/Enthusiast

Analyzing Wildlife Data Trends with Regression :

<p>Dr. Bill McShea from the Smithsonian Institution discusses how regression analysis helps in his research.</p> <p>This video was created in collaboration with the Okaloosa County SCIENCE Partnership, including the Smithsonian Institution and Harvard University.</p>

Type: Perspectives Video: Professional/Enthusiast

Revolutionize Wing Design with Equations and Statistics:

<p>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."</p>

Type: Perspectives Video: Professional/Enthusiast

## Perspectives Video: Teaching Idea

Smile Statistics:

<p>This quantitative measurement and statistics activity will allow you to save face.</p>

Type: Perspectives Video: Teaching Idea

Speed Trap:

The purpose of this task is to allow students to demonstrate an ability to construct boxplots and to use boxplots as the basis for comparing distributions.

SAT Scores:

This problem solving task challenges students to answer probability questions about SAT scores, using distribution and mean to solve the problem.

Haircut Costs:

This problem could be used as an introductory lesson to introduce group comparisons and to engage students in a question they may find amusing and interesting.

The purpose of this task is to assess ability to interpret the slope and intercept of the line of fit in context.

Coffee and Crime:

This problem solving task asks students to examine the relationship between shops and crimes by using a correlation coefficient. The implications of linking correlation with causation are discussed.

Should We Send Out a Certificate?:

The purpose of this task is to have students complete normal distribution calculations and to use properties of normal distributions to draw conclusions.

Do You Fit in This Car?:

This task requires students to use the normal distribution as a model for a data distribution. Students must use given means and standard deviations to approximate population percentages.

## 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: Whatâ€™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?

Type: Perspectives Video: Expert

Speed Trap:

The purpose of this task is to allow students to demonstrate an ability to construct boxplots and to use boxplots as the basis for comparing distributions.

SAT Scores:

This problem solving task challenges students to answer probability questions about SAT scores, using distribution and mean to solve the problem.

Haircut Costs:

This problem could be used as an introductory lesson to introduce group comparisons and to engage students in a question they may find amusing and interesting.

The purpose of this task is to assess ability to interpret the slope and intercept of the line of fit in context.

Coffee and Crime:

This problem solving task asks students to examine the relationship between shops and crimes by using a correlation coefficient. The implications of linking correlation with causation are discussed.

Should We Send Out a Certificate?:

The purpose of this task is to have students complete normal distribution calculations and to use properties of normal distributions to draw conclusions.

Do You Fit in This Car?:

This task requires students to use the normal distribution as a model for a data distribution. Students must use given means and standard deviations to approximate population percentages.

## Parent Resources

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

Speed Trap:

The purpose of this task is to allow students to demonstrate an ability to construct boxplots and to use boxplots as the basis for comparing distributions.

SAT Scores:

This problem solving task challenges students to answer probability questions about SAT scores, using distribution and mean to solve the problem.

Haircut Costs:

This problem could be used as an introductory lesson to introduce group comparisons and to engage students in a question they may find amusing and interesting.

The purpose of this task is to assess ability to interpret the slope and intercept of the line of fit in context.

Coffee and Crime:

This problem solving task asks students to examine the relationship between shops and crimes by using a correlation coefficient. The implications of linking correlation with causation are discussed.