MAFS.912.S-ID.3.7Archived Standard

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

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 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 with 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

This review lesson relates graphical and algebraic representations of bivariate data by giving students opportunities to 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.

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

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 best fit equation and interpret 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 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 their line of best 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

In this lesson, students will interpret and analyze data to create a scatter plot and line of best fit. Students will make predictions for the number of views of a video for any given number of weeks on the charts.

The lesson provides suggestions for finding the line of best fit using different technologies to graph, GeoGebra free online software, Excel spreadsheets, and graphing calculators. Teachers can determine which technology will best suit their class or incorporate all three as part of the lesson.

Type: Lesson Plan

In this lesson students will interpret the meaning of slope and y-intercept in a wide variety of examples of "real world" situations that are modeled by linear functions.

Type: Lesson Plan

This lesson will be using real world examples to help explain the meaning of slope and y-intercept of a linear model in the context of data. Literacy will also be infused during the independent practice portion of the lesson. A PowerPoint is included for guidance throughout the whole lesson and to provide visual representation for students. There are guided notes available as well to provide assistance in note-taking for students.

Type: Lesson Plan

This lesson allows students to use real-world data to construct and interpret scatter plots using technology. Students will create a scatter plot with a line of best fit and a function. They describe the relationship of bi-variate data. They recognize and interpret the slope and y-intercept of the line of best fit within the context of the data.

Type: Lesson Plan

This lesson consists of using data to make scatter plots, interpret slope and the y-intercept and to make predictions about the line of best fit using the slope intercept form.

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 show student's understanding of slope being a rate of change and the y-intercept the value of y when x is zero. They 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

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

After activating prior knowledge and presentation of new skills, students will be collecting and evaluating data to interpret the line of best fit and y-intercept in order to develop an equation in point-slope form to represent the data.

Type: Lesson Plan

This lesson provides students with opportunities to examine the slope and y-intercept of a line of best fit using scatterplots. Students will gain a deeper conceptual understanding of slope and y-intercept based on real world data. Students will graph scatterplots and draw a line of best fit. Then, students will use the line to interpret the slope and y-intercept with regard to the data. Students will also make predictions using the graph and the equation of the data.

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 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

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

The purpose of this task is to assess ability to interpret the slope and intercept of the least squares regression line 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.

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

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