Cluster 3: Interpret linear models. (Algebra 1 - Major Cluster)Archived

Students are asked to interpret a correlation coefficient in context and describe a possible causal relationship.

Type: Formative Assessment

Students are asked to identify all possible causal relationships between two correlated variables.

Type: Formative Assessment

Students are given a statement of association between two variables and are asked to determine if one variable is a cause of the other.

Type: Formative Assessment

Students are given a scenario describing an association between two variables and are asked to determine if one variable is a cause of the other.

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Type: Formative Assessment

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

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

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

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

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

Type: Lesson Plan

This lesson introduces the students to the concepts of correlation and causation, and the difference between the two. The main learning objective is to encourage students to think critically about various possible explanations for a correlation, and to evaluate their plausibility, rather than passively taking presented information on faith. To give students the right tools for such analysis, the lesson covers most common reasons behind a correlation, and different possible types of causation.

Type: Lesson Plan

In this lesson students will determine whether their is a relationship between two variables through a Perspectives Video and real-life examples. Students will learn about confounding variables and investigate why correlation does not imply causation.

Type: Lesson Plan

This is lesson 3 of 3 in the Slope Intercept unit. This lesson introduces similar triangles to explain why slope is the same between any two points on a non-vertical line. In this lesson students perform an activity to determine that slope is constant throughout a line and students will discover the slope for vertical and horizontal lines.

Type: Lesson Plan

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

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

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

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

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

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

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

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

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

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

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

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

Type: Lesson Plan

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

Type: Lesson Plan

This lab exploration provides students with an opportunity to examine the relationship between the amount a linear spring is stretched and the restoring force that acts to return the spring to its rest length. This concept is central to an understanding of elastic potential energy in mechanical systems and has implications in the study of a large array of mechanical and electromagnetic simple harmonic oscillators.

Type: Lesson Plan

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 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

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

Students will interpret the meaning of slope and y-intercept in a wide variety of examples of real-world situations modeled by linear functions.

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

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

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

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

This lesson will not only reinforce students understanding of slope and y-intercept, but will also ensure the students understand how it can be modeled in a real world situation. The focus of this lesson is to emphasize that slope is a rate of change and the y-intercept the value of y when x is zero. Students will be able to read a problem and create a linear equation based upon what they read. They will then make predictions based upon this information.

Type: Lesson Plan

This lesson is on motion of objects. Students will learn what factors affect the speed of an object through experimentation with gumballs rolling down an incline. The students will collect data through experimenting, create graphs from the data, interpret the slope of the graphs and create equations of lines from data points and the graph. They will understand the relationship of speed and velocity and be able to relate the velocity formula to the slope intercept form of the equation of a line.

Type: Lesson Plan

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

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

In this lesson, students will experimentally determine whether an acid/base neutralization reaction is endothermic or exothermic. They will also use their results to identify the limiting reactant at various times in the process and calculate the concentration of one of the reactants.

Type: Lesson Plan

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

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

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

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

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

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

Type: Lesson Plan

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

This is a short unit plan that covers position/time and velocity/time graphs. Students are provided with new material on both topics, will have practice worksheets, and group activities to develop an understanding of motion graphs.

Type: Lesson Plan

The lesson teaches students about an important characteristic of lines: their slope. Slope can be determined either in graphical or algebraic form. Slope can also be described as positive, negative, zero, or undefined. Students get an explanation of when and how these different types of slope occur. Finally, students learn how slope relates to parallel and perpendicular lines. When two lines are parallel, they have the same slope and when they are perpendicular their slopes are negative reciprocals of one another. Prerequisite knowledge: Students must know how to graph points on the Cartesian plane. They must be familiar with the x- and y- axes on the plane in both the positive and negative directions.

Type: Lesson Plan

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.

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

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

Learn what slope is in mathematics and how to calculate it on a graph and with the slope formula in this interactive tutorial.

Type: Original Student Tutorial

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

Type: Perspectives Video: Expert

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

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

Jens Foell discusses the link between correlation and causation in PTSD patients.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Florida State Researcher, Jens Foell, discusses the importance of understanding correlation versus causation when researching personality traits and criminal behavior.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

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

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

Watching this video will cause your critical thinking skills to improve. You might also have a great day, but that's just correlation.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

This is a simple task addressing the distinction between correlation and causation. Students are given information indicating a correlation between two variables, and are asked to reason out whether or not a causation can be inferred.

Type: Problem-Solving Task

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

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

This task would be especially well-suited for instructional purposes. Students will benefit from a class discussion about the slope, y-intercept, x-intercept, and implications of the restricted domain for interpreting more precisely what the equation is modeling.

Type: Problem-Solving Task

This informational text resource is intended to support reading in the content area. Many people are confused about the concept of correlation versus causation. To help demonstrate the misconception in a light and humorous way, this article describes the work of Tyler Vigen. The Harvard student graphs data that are highly correlated but clearly unrelated. The "spurious correlations" help debunk the myth that if there is a correlation, then there is a causal relationship. The article emphasizes that rational human thought is essential to process the relationships and is necessary for studying statistics.

Type: Text Resource

Type: Unit/Lesson Sequence

This session on linear function and slope contains five parts, multiple problems and videos, and interactive activities geared to help students recognize and understand linear relationships, explore slope and dependent and independent variables in graphs of linear relationships, and develop an understanding of rates and how they are related to slopes and equations. Throughout the session, students use spreadsheets to complete the work, and are encouraged to think about the ways technology can aid in teaching and understanding. The solutions for all problems are given, and many allow students to have a hint or tip as they solve. There is even a homework assignment with four problems for students after they have finished all five parts of the session.

Type: Unit/Lesson Sequence

Linear equations can be used to solve many types of real-word problems. In this episode, the water depth of a pool is shown to be a linear function of time and an equation is developed to model its behavior. Unfortunately, ace Algebra student A. V. Geekman ends up in hot water anyway.

Type: Video/Audio/Animation

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

Type: Virtual Manipulative