Standard #: MAFS.8.F.2.5 (Archived Standard)

Students are asked to describe the relationship between two quantities in a nonlinear function.

Students are asked to analyze and describe the relationship between two linearly related quantities.

Students are given a verbal description of the relationship between two quantities and are asked to sketch a graph to model the relationship.

Students are given a verbal description of the relationship between two quantities and are asked to sketch a graph to model the relationship.

• Interpret distance-time graphs as if they are pictures of situations rather than abstract representations of them.
• Have difficulty relating speeds to slopes of these graphs.

• Interpret speed as the slope of a linear graph.
• Translate between the equation of a line and its graphical representation.

In this lesson students will categorize a list of stars based on absolute brightness, size, and temperature. Students will analyze astronomical data presented in charts and plot their data on a special graph called a Hertzsprung-Russell Diagram (H-R Diagram). Using this diagram, they must determine the proper classification of individual stars. Using their data analysis, students completing this lesson will develop two short essay responses to a professional client indicating which stars are Main Sequence Stars and which ones are White Dwarfs, Giants, or Supergiants.

This lesson unit is intended to help you assess how well students use algebra in context, and in particular, how well students:

• Explore relationships between variables in everyday situations.
• Find unknown values from known values.
• Find relationships between pairs of unknowns, and express these as tables and graphs.
• Find general relationships between several variables, and express these in different ways by rearranging formulae.

Students construct and calibrate a simple hydrometer using different salt solutions. They then graph their data and determine the density and salinity of an unknown solution using their hydrometer and graphical analysis.

Learn how math models can show why social distancing during a epidemic or pandemic is important in this interactive tutorial.

Cruise along as you discover how to qualitatively describe functions in this interactive tutorial.

Nick Moore discusses his research behind optimizing wing design using inspiration from animals and how they swim and fly.

Download the CPALMS Perspectives video student note taking guide.

Fishery Scientist from Florida State University discusses his new research in deep sea sharks and the unusual behavior that is found when the data is graphed.

Download the CPALMS Perspectives video student note taking guide.

Lofty ideas about kites helped power a kayak from California to Hawaii.

Related Resources:
KROS Pacific Ocean Kayak Journey: GPS Data Set[.XLSX]
KROS Pacific Ocean Kayak Journey: Path Visualization for Google Earth[.KML]

Download the CPALMS Perspectives video student note taking guide.

The purpose of this task is for students to interpret two distance-time graphs in terms of the context of a bicycle race. There are two major mathematical aspects to this: interpreting what a particular point on the graph means in terms of the context and understanding that the "steepness" of the graph tells us something about how fast the bicyclists are moving.

The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.

This is a simple task about interpreting the graph of a function in terms of the relationship between quantities that it represents.

In this task students draw the graphs of two functions from verbal descriptions. Both functions describe the same situation but changing the viewpoint of the observer changes where the function has output value zero. This small twist forces the students to think carefully about the interpretation of the dependent variable. This task could be used in different ways: To generate a class discussion about graphing. As a quick assessment about graphing, for example during a class warm-up. To engage students in small group discussion.

In this task students interpret two graphs that look the same but show very different quantities. The first graph gives information about how fast a car is moving while the second graph gives information about the position of the car. This problem works well to generate a class or small group discussion. Students learn that graphs tell stories and have to be interpreted by carefully thinking about the quantities shown.

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

This resource features two pairs of interactive graphs to help students explore rate of change and linear relationships. "Users can drag a slider on an interactive graph to modify a rate of change (cost per minute for phone use) and learn how modifications in that rate affect the linear graph displaying accumulation (the total cost of calls). In this first part, Constant Cost per Minute, the cost per minute for phone use remains constant over time. In the second part, Changing Cost per Minute, the cost per minute for phone use changes after the first sixty minutes of calls." (from NCTM's Illuminations)

In this tutorial, students will compare linear functions from a graph. Students should have an understanding of slope and rate of change before reviewing this tutorial.

This tutorial shows how to compare linear functions that are presented in both a table and graph. Students should have an understanding of rate of change before viewing this video.

Students will compare linear functions presented in a graph and in a table. Students should have a strong understanding of rate of change before viewing this tutorial.

In this tutorial, you will look at several real-world examples of linear graphs and interpret the relationship between the two variables.

Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed.

In this online tool, students input a function to create a graph where the constants, coefficients, and exponents can be adjusted by slider bars. This tool allows students to explore graphs of functions and how adjusting the numbers in the function affect the graph. Using tabs at the top of the page you can also access 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.

This interactive simulation investigates graphing linear and quadratic equations. Users are given the ability to define and change the coefficients and constants in order to observe resulting changes in the graph(s).

Learn how math models can show why social distancing during a epidemic or pandemic is important in this interactive tutorial.

Cruise along as you discover how to qualitatively describe functions in this interactive tutorial.

The purpose of this task is for students to interpret two distance-time graphs in terms of the context of a bicycle race. There are two major mathematical aspects to this: interpreting what a particular point on the graph means in terms of the context and understanding that the "steepness" of the graph tells us something about how fast the bicyclists are moving.

The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.

This is a simple task about interpreting the graph of a function in terms of the relationship between quantities that it represents.

In this task students draw the graphs of two functions from verbal descriptions. Both functions describe the same situation but changing the viewpoint of the observer changes where the function has output value zero. This small twist forces the students to think carefully about the interpretation of the dependent variable. This task could be used in different ways: To generate a class discussion about graphing. As a quick assessment about graphing, for example during a class warm-up. To engage students in small group discussion.

In this task students interpret two graphs that look the same but show very different quantities. The first graph gives information about how fast a car is moving while the second graph gives information about the position of the car. This problem works well to generate a class or small group discussion. Students learn that graphs tell stories and have to be interpreted by carefully thinking about the quantities shown.

Students can practice answering mathematics questions on a variety of topics. With an account, students can save their work and send it to their teacher when complete.

In this tutorial, students will compare linear functions from a graph. Students should have an understanding of slope and rate of change before reviewing this tutorial.

This tutorial shows how to compare linear functions that are presented in both a table and graph. Students should have an understanding of rate of change before viewing this video.

Students will compare linear functions presented in a graph and in a table. Students should have a strong understanding of rate of change before viewing this tutorial.

In this tutorial, you will look at several real-world examples of linear graphs and interpret the relationship between the two variables.

Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed.

In this online tool, students input a function to create a graph where the constants, coefficients, and exponents can be adjusted by slider bars. This tool allows students to explore graphs of functions and how adjusting the numbers in the function affect the graph. Using tabs at the top of the page you can also access 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.

This interactive simulation investigates graphing linear and quadratic equations. Users are given the ability to define and change the coefficients and constants in order to observe resulting changes in the graph(s).

The purpose of this task is for students to interpret two distance-time graphs in terms of the context of a bicycle race. There are two major mathematical aspects to this: interpreting what a particular point on the graph means in terms of the context and understanding that the "steepness" of the graph tells us something about how fast the bicyclists are moving.

The primary purpose of this task is to elicit common misconceptions that arise when students try to model situations with linear functions. This task, being multiple choice, could also serve as a quick assessment to gauge a class' understanding of modeling with linear functions.

This is a simple task about interpreting the graph of a function in terms of the relationship between quantities that it represents.

In this task students draw the graphs of two functions from verbal descriptions. Both functions describe the same situation but changing the viewpoint of the observer changes where the function has output value zero. This small twist forces the students to think carefully about the interpretation of the dependent variable. This task could be used in different ways: To generate a class discussion about graphing. As a quick assessment about graphing, for example during a class warm-up. To engage students in small group discussion.

In this task students interpret two graphs that look the same but show very different quantities. The first graph gives information about how fast a car is moving while the second graph gives information about the position of the car. This problem works well to generate a class or small group discussion. Students learn that graphs tell stories and have to be interpreted by carefully thinking about the quantities shown.

This resource features two pairs of interactive graphs to help students explore rate of change and linear relationships. "Users can drag a slider on an interactive graph to modify a rate of change (cost per minute for phone use) and learn how modifications in that rate affect the linear graph displaying accumulation (the total cost of calls). In this first part, Constant Cost per Minute, the cost per minute for phone use remains constant over time. In the second part, Changing Cost per Minute, the cost per minute for phone use changes after the first sixty minutes of calls." (from NCTM's Illuminations)

Allows students access to a Cartesian Coordinate System where linear equations can be graphed and details of the line and the slope can be observed.