MAFS.912.S-ID.2.6Archived Standard

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

Type: Formative Assessment

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

Type: Formative Assessment

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

Students are given a set of data and are asked to use technology to create a scatter plot and write a function that fits the data set.

Type: Formative Assessment

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

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

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

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

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

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

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

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

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

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 arm length. Using technology the students will explore in-depth how to perform a least square regression as a procedure for determining the line of best fit.

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

The students are asked to create a scatter plot of Bennie's height, determine an equation of best fit, calculate residuals and create a residual plot. The students are then asked to use the residual plot to determine if a linear model is the best predictor of the data.

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 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

This lesson examines the differences between quantitative and qualitative data and guides students through displaying quantitative data on a scatter plot and then separating the data into qualitative categories to be displayed and interpreted in a two-way frequency table.

Type: Lesson Plan

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

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

This lesson unit is intended to help you assess how well students understand the notion of correlation. In particular this unit aims to identify and help students who have difficulty in understanding correlation as the degree of fit between two variables, making a mathematical model of a situation, testing and improving the model, communicating their reasoning clearly and evaluating alternative models of the situation.

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

Students will model molecular motion with everyday materials (shaker bottles) then associate their model/actions to the phase transitions of water while graphing its heat curve from data collected during a structured inquiry lab.

Type: Lesson Plan

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

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

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

Statistical analysis played an essential role in using microgravity sensors to determine location of caves in Wakulla County.

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

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

Type: Perspectives Video: Professional/Enthusiast

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

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

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

Students in a first Algebra course model the relationship between two variables by fitting functions to data. The focus of this tutorial is on (1) using technology to create a scatterplot of data and calculate the equation of the least squares regression line and (2) informally assessing the fit of a function fitted to data by calculating, graphing, and analyzing residuals.

Type: Professional Development

Students will first measure and plot the total mass vs liquid volume in a graduated cylinder. They will then use slope and the mathematical formula for the plot to determine the density of the liquid, the density of a solid added to the liquid, and the mass of the graduated cylinder.

Type: Teaching Idea

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

In a variety of fields, functions are used to mathematically model bivariate data in order to describe, understand, and make predictions about the relationship between two variables. The focus of this tutorial is on (1) teaching students how to model the relationships between two variables with linear and exponential functions and (2) using models to make predictions about values of variables.

Type: Tutorial

Type: Unit/Lesson Sequence

Khan Academy tutorial video that demonstrates with real-world data the use of Excel spreadsheet to fit a line to data and make predictions using that line.

Type: Video/Audio/Animation

Using this virtual manipulative, students are able to graph a function and a set of ordered pairs on the same coordinate plane. The constants, coefficients, and exponents can be adjusted using slider bars, so the student can explore the affect on the graph as the function parameters are changed. Students can also examine the deviation of the data from the function. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the java applet.

Type: Virtual Manipulative

This is an online graphing utility that can be used to create box plots, bubble graphs, scatterplots, histograms, and stem-and-leaf plots.

Type: Virtual Manipulative