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Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 8 Unit 3

Linear Relationships

Lesson 6: More Linear Relationships

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Definition--Slope Concepts--Slope Formula Definition--Slope Concepts--Slope Formula Slope Formula

Topic

Slope

Definition

The Slope Formula calculates the rate of change.

Description

The Slope Formula is typically represented as 

This formula is a cornerstone in algebra, enabling students to analyze linear equations effectively.

Slope
Definition--Slope Concepts--Slope Formula Definition--Slope Concepts--Slope Formula Slope Formula

Topic

Slope

Definition

The Slope Formula calculates the rate of change.

Description

The Slope Formula is typically represented as 

This formula is a cornerstone in algebra, enabling students to analyze linear equations effectively.

Slope
Definition--Slope Concepts--Slope Formula Definition--Slope Concepts--Slope Formula Slope Formula

Topic

Slope

Definition

The Slope Formula calculates the rate of change.

Description

The Slope Formula is typically represented as 

This formula is a cornerstone in algebra, enabling students to analyze linear equations effectively.

Slope
Definition--Slope Concepts--Slope-Intercept Form Definition--Slope Concepts--Slope-Intercept Form Slope-Intercept Form

Topic

Slope

Definition

The slope-intercept form is an equation of a straight line represented as y = m x + b, where m is the slope and b is the y-intercept.

Description

The slope-intercept form is a fundamental concept in algebra, providing a straightforward way to graph linear equations. It is widely used in various fields, from economics to physics, to model linear relationships and predict outcomes based on given data. Understanding this form is crucial for students as it lays the foundation for more complex mathematical concepts and real-world applications.

Slope-Intercept Form
Definition--Slope Concepts--Slope-Intercept Form Definition--Slope Concepts--Slope-Intercept Form Slope-Intercept Form

Topic

Slope

Definition

The slope-intercept form is an equation of a straight line represented as y = m x + b, where m is the slope and b is the y-intercept.

Description

The slope-intercept form is a fundamental concept in algebra, providing a straightforward way to graph linear equations. It is widely used in various fields, from economics to physics, to model linear relationships and predict outcomes based on given data. Understanding this form is crucial for students as it lays the foundation for more complex mathematical concepts and real-world applications.

Slope-Intercept Form
Definition--Slope Concepts--Slope-Intercept Form Definition--Slope Concepts--Slope-Intercept Form Slope-Intercept Form

Topic

Slope

Definition

The slope-intercept form is an equation of a straight line represented as y = m x + b, where m is the slope and b is the y-intercept.

Description

The slope-intercept form is a fundamental concept in algebra, providing a straightforward way to graph linear equations. It is widely used in various fields, from economics to physics, to model linear relationships and predict outcomes based on given data. Understanding this form is crucial for students as it lays the foundation for more complex mathematical concepts and real-world applications.

Slope-Intercept Form
Definition--Slope Concepts--Slopes of Parallel Lines Definition--Slope Concepts--Slopes of Parallel Lines Slopes of Parallel Lines

Topic

Slope

Definition

Parallel lines are lines in the same plane that never meet; they have equal slopes.

Description

Understanding the slopes of parallel lines is essential in geometry and algebra, as it helps in identifying and proving parallelism in shapes and graphs. This concept is applied in various fields, including architecture and engineering, where maintaining parallelism is crucial for structural integrity and design. In mathematics education, this concept aids in developing logical reasoning and problem-solving skills.

Slope
Definition--Slope Concepts--Slopes of Parallel Lines Definition--Slope Concepts--Slopes of Parallel Lines Slopes of Parallel Lines

Topic

Slope

Definition

Parallel lines are lines in the same plane that never meet; they have equal slopes.

Description

Understanding the slopes of parallel lines is essential in geometry and algebra, as it helps in identifying and proving parallelism in shapes and graphs. This concept is applied in various fields, including architecture and engineering, where maintaining parallelism is crucial for structural integrity and design. In mathematics education, this concept aids in developing logical reasoning and problem-solving skills.

Slope
Definition--Slope Concepts--Slopes of Parallel Lines Definition--Slope Concepts--Slopes of Parallel Lines Slopes of Parallel Lines

Topic

Slope

Definition

Parallel lines are lines in the same plane that never meet; they have equal slopes.

Description

Understanding the slopes of parallel lines is essential in geometry and algebra, as it helps in identifying and proving parallelism in shapes and graphs. This concept is applied in various fields, including architecture and engineering, where maintaining parallelism is crucial for structural integrity and design. In mathematics education, this concept aids in developing logical reasoning and problem-solving skills.

Slope
Definition--Slope Concepts--Slopes of Perpendicular Lines Definition--Slope Concepts--Slopes of Perpendicular Lines Slopes of Perpendicular Lines

Topic

Slope

Definition

Perpendicular lines intersect at a right angle, and their slopes are negative reciprocals of each other.

Description

The concept of perpendicular slopes is vital in geometry, as it helps in determining the orthogonality of lines. This principle is used in various applications, such as designing perpendicular intersections in roadways and creating right-angle joints in construction. In education, it enhances students' understanding of geometric properties and their ability to solve related problems.

Slope
Definition--Slope Concepts--Slopes of Perpendicular Lines Definition--Slope Concepts--Slopes of Perpendicular Lines Slopes of Perpendicular Lines

Topic

Slope

Definition

Perpendicular lines intersect at a right angle, and their slopes are negative reciprocals of each other.

Description

The concept of perpendicular slopes is vital in geometry, as it helps in determining the orthogonality of lines. This principle is used in various applications, such as designing perpendicular intersections in roadways and creating right-angle joints in construction. In education, it enhances students' understanding of geometric properties and their ability to solve related problems.

Slope
Definition--Slope Concepts--Slopes of Perpendicular Lines Definition--Slope Concepts--Slopes of Perpendicular Lines Slopes of Perpendicular Lines

Topic

Slope

Definition

Perpendicular lines intersect at a right angle, and their slopes are negative reciprocals of each other.

Description

The concept of perpendicular slopes is vital in geometry, as it helps in determining the orthogonality of lines. This principle is used in various applications, such as designing perpendicular intersections in roadways and creating right-angle joints in construction. In education, it enhances students' understanding of geometric properties and their ability to solve related problems.

Slope
Definition--Slope Concepts--Steepness Definition--Slope Concepts--Steepness Steepness

Topic

Slope

Definition

Steepness is a measure of how steep a line is, typically calculated as the absolute value of the slope.

Description

Steepness is a key concept in understanding the inclination of lines and surfaces. It is commonly used in fields like geology and civil engineering to assess the gradient of terrains and structures. In math education, learning about steepness helps students grasp the concept of slope and its practical implications, enhancing their analytical skills and understanding of real-world phenomena.

Slope
Definition--Slope Concepts--Steepness Definition--Slope Concepts--Steepness Steepness

Topic

Slope

Definition

Steepness is a measure of how steep a line is, typically calculated as the absolute value of the slope.

Description

Steepness is a key concept in understanding the inclination of lines and surfaces. It is commonly used in fields like geology and civil engineering to assess the gradient of terrains and structures. In math education, learning about steepness helps students grasp the concept of slope and its practical implications, enhancing their analytical skills and understanding of real-world phenomena.

Slope
Definition--Slope Concepts--Steepness Definition--Slope Concepts--Steepness Steepness

Topic

Slope

Definition

Steepness is a measure of how steep a line is, typically calculated as the absolute value of the slope.

Description

Steepness is a key concept in understanding the inclination of lines and surfaces. It is commonly used in fields like geology and civil engineering to assess the gradient of terrains and structures. In math education, learning about steepness helps students grasp the concept of slope and its practical implications, enhancing their analytical skills and understanding of real-world phenomena.

Slope
Definition--Slope Concepts--The Rise Over the Run Definition--Slope Concepts--The Rise Over the Run The Rise Over the Run

Topic

Slope

Definition

The rise over the run describes the change in y over the change in x in a linear relationship.

Description

The concept of "rise over run" is foundational in understanding how to calculate the slope of a line. It is used in various disciplines, such as physics and economics, to model relationships and predict trends. In education, mastering this concept is crucial for students as it forms the basis for graphing linear equations and understanding the behavior of lines in a coordinate plane.

Slope
Definition--Slope Concepts--The Rise Over the Run Definition--Slope Concepts--The Rise Over the Run The Rise Over the Run

Topic

Slope

Definition

The rise over the run describes the change in y over the change in x in a linear relationship.

Description

The concept of "rise over run" is foundational in understanding how to calculate the slope of a line. It is used in various disciplines, such as physics and economics, to model relationships and predict trends. In education, mastering this concept is crucial for students as it forms the basis for graphing linear equations and understanding the behavior of lines in a coordinate plane.

Slope
Definition--Slope Concepts--The Rise Over the Run Definition--Slope Concepts--The Rise Over the Run The Rise Over the Run

Topic

Slope

Definition

The rise over the run describes the change in y over the change in x in a linear relationship.

Description

The concept of "rise over run" is foundational in understanding how to calculate the slope of a line. It is used in various disciplines, such as physics and economics, to model relationships and predict trends. In education, mastering this concept is crucial for students as it forms the basis for graphing linear equations and understanding the behavior of lines in a coordinate plane.

Slope
Definition--Slope Concepts--Undefined Slope Definition--Slope Concepts--Undefined Slope Undefined Slope

Topic

Slope

Definition

Undefined slope occurs when a vertical line is present, meaning there is no change in x.

Description

An undefined slope is a critical concept in mathematics, particularly in graphing. It indicates a vertical line where the change in x is zero, making the slope calculation impossible. This concept is important in various fields, such as computer graphics and data analysis, where vertical lines can represent boundaries or limits. Understanding undefined slopes helps students in identifying and interpreting vertical lines in graphs.

Slope
Definition--Slope Concepts--Undefined Slope Definition--Slope Concepts--Undefined Slope Undefined Slope

Topic

Slope

Definition

Undefined slope occurs when a vertical line is present, meaning there is no change in x.

Description

An undefined slope is a critical concept in mathematics, particularly in graphing. It indicates a vertical line where the change in x is zero, making the slope calculation impossible. This concept is important in various fields, such as computer graphics and data analysis, where vertical lines can represent boundaries or limits. Understanding undefined slopes helps students in identifying and interpreting vertical lines in graphs.

Slope
Definition--Slope Concepts--Undefined Slope Definition--Slope Concepts--Undefined Slope Undefined Slope

Topic

Slope

Definition

Undefined slope occurs when a vertical line is present, meaning there is no change in x.

Description

An undefined slope is a critical concept in mathematics, particularly in graphing. It indicates a vertical line where the change in x is zero, making the slope calculation impossible. This concept is important in various fields, such as computer graphics and data analysis, where vertical lines can represent boundaries or limits. Understanding undefined slopes helps students in identifying and interpreting vertical lines in graphs.

Slope
Definition--Slope Concepts--Zero Slope Definition--Slope Concepts--Zero Slope Zero Slope

Topic

Slope

Definition

Zero slope describes a horizontal line where there is no change in y as x changes.

Description

A zero slope is a key concept in algebra and geometry, representing a horizontal line. It is used in various applications, such as designing flat surfaces and analyzing constant relationships in data. In education, understanding zero slopes helps students in graphing and interpreting horizontal lines, enhancing their ability to analyze linear relationships.

For a complete collection of terms related to Slope click on this link: Slope Collection.

Slope
Definition--Slope Concepts--Zero Slope Definition--Slope Concepts--Zero Slope Zero Slope

Topic

Slope

Definition

Zero slope describes a horizontal line where there is no change in y as x changes.

Description

A zero slope is a key concept in algebra and geometry, representing a horizontal line. It is used in various applications, such as designing flat surfaces and analyzing constant relationships in data. In education, understanding zero slopes helps students in graphing and interpreting horizontal lines, enhancing their ability to analyze linear relationships.

For a complete collection of terms related to Slope click on this link: Slope Collection.

Slope
Definition--Slope Concepts--Zero Slope Definition--Slope Concepts--Zero Slope Zero Slope

Topic

Slope

Definition

Zero slope describes a horizontal line where there is no change in y as x changes.

Description

A zero slope is a key concept in algebra and geometry, representing a horizontal line. It is used in various applications, such as designing flat surfaces and analyzing constant relationships in data. In education, understanding zero slopes helps students in graphing and interpreting horizontal lines, enhancing their ability to analyze linear relationships.

For a complete collection of terms related to Slope click on this link: Slope Collection.

Slope
Desmos Activity: Exploring the Slope Formula Desmos Activity: Exploring the Slope Formula Desmos Activity: Exploring the Slope Formula Click on this link to see the complete collection of Desmos resources.

Use a custom Desmos graphing calculator activity to explore the slope formula. The Desmos activity includes the slope formula equation. Students input the values for the two coordinates. They can also use the provided sliders to input the values. The Desmos interactive will calculate the slope of the line connecting the two points, as well as the graph of the line itself. There is a companion worksheet for this activity, which subscribers can download. The worksheet is a PDF file.

Slope
Desmos Activity: Exploring the Slope Formula Desmos Activity: Exploring the Slope Formula Desmos Activity: Exploring the Slope Formula Click on this link to see the complete collection of Desmos resources.

Use a custom Desmos graphing calculator activity to explore the slope formula. The Desmos activity includes the slope formula equation. Students input the values for the two coordinates. They can also use the provided sliders to input the values. The Desmos interactive will calculate the slope of the line connecting the two points, as well as the graph of the line itself. There is a companion worksheet for this activity, which subscribers can download. The worksheet is a PDF file.

Slope
Desmos Activity: Exploring the Slope Formula Desmos Activity: Exploring the Slope Formula Desmos Activity: Exploring the Slope Formula Click on this link to see the complete collection of Desmos resources.

Use a custom Desmos graphing calculator activity to explore the slope formula. The Desmos activity includes the slope formula equation. Students input the values for the two coordinates. They can also use the provided sliders to input the values. The Desmos interactive will calculate the slope of the line connecting the two points, as well as the graph of the line itself. There is a companion worksheet for this activity, which subscribers can download. The worksheet is a PDF file.

Slope
Desmos Activity: Exploring the Slope Formula Desmos Activity: Exploring the Slope Formula Desmos Activity: Exploring the Slope Formula Click on this link to see the complete collection of Desmos resources.

Use a custom Desmos graphing calculator activity to explore the slope formula. The Desmos activity includes the slope formula equation. Students input the values for the two coordinates. They can also use the provided sliders to input the values. The Desmos interactive will calculate the slope of the line connecting the two points, as well as the graph of the line itself. There is a companion worksheet for this activity, which subscribers can download. The worksheet is a PDF file.

Slope
Desmos Activity: Exploring the Slope Formula Desmos Activity: Exploring the Slope Formula Desmos Activity: Exploring the Slope Formula Click on this link to see the complete collection of Desmos resources.

Use a custom Desmos graphing calculator activity to explore the slope formula. The Desmos activity includes the slope formula equation. Students input the values for the two coordinates. They can also use the provided sliders to input the values. The Desmos interactive will calculate the slope of the line connecting the two points, as well as the graph of the line itself. There is a companion worksheet for this activity, which subscribers can download. The worksheet is a PDF file.

Slope
Desmos activity Desmos Activity: Slope As Rate of Change Desmos Activity: Slope As Rate of Change

Use this activity to explore slope as a rate of change. In this Desmos activity, the slope of the line is the rate (cost per pound) for purchasing fruit. Students manipulate the slider for m to see the impact on the cost.

Slope and Ratios and Rates
Desmos activity Desmos Activity: Slope As Rate of Change Desmos Activity: Slope As Rate of Change

Use this activity to explore slope as a rate of change. In this Desmos activity, the slope of the line is the rate (cost per pound) for purchasing fruit. Students manipulate the slider for m to see the impact on the cost.

Slope and Ratios and Rates
Desmos activity Desmos Activity: Slope As Rise Over Run Desmos Activity: Slope As Rise Over Run

This Desmos activity allows students to explore slope as the ratio of the rise over the run. Click Preview to launch the activity. In the activity students click on the points to create a line segment connecting two points. Use the background grid to determine the rise and the run and calculate the slope.

Slope
Desmos activity Desmos Activity: Slope As Rise Over Run Desmos Activity: Slope As Rise Over Run

This Desmos activity allows students to explore slope as the ratio of the rise over the run. Click Preview to launch the activity. In the activity students click on the points to create a line segment connecting two points. Use the background grid to determine the rise and the run and calculate the slope.

Slope
Desmos activity Desmos Activity: Slope As Rise Over Run Desmos Activity: Slope As Rise Over Run

This Desmos activity allows students to explore slope as the ratio of the rise over the run. Click Preview to launch the activity. In the activity students click on the points to create a line segment connecting two points. Use the background grid to determine the rise and the run and calculate the slope.

Slope
Desmos activity Desmos Activity: Slope As Rise Over Run 2

Desmos Activity: Slope As Rise Over Run 2

In this activity, students input different values for the coordinates to create a new line. They can then measure the rise and run to calculate the slope.

Slope
Desmos activity Desmos Activity: Slope As Rise Over Run 2

Desmos Activity: Slope As Rise Over Run 2

In this activity, students input different values for the coordinates to create a new line. They can then measure the rise and run to calculate the slope.

Slope
Formulas--Slope Formula Formulas--Slope Formula Formulas | Slope Formula

The formula for the Slope Formula. This is part of a collection of math formulas. 

—PRESS PREVIEW TO SEE THE IMAGE— To see the complete collection of formulas, click on this link.

The following section includes background information on slope. This background also includes video resources and accompanying transcripts.

What Is Slope?

Watch this video to learn about the slope formula. (The transcript is also included.)

Slope
Formulas--Slope Formula Formulas--Slope Formula Formulas | Slope Formula

The formula for the Slope Formula. This is part of a collection of math formulas. 

—PRESS PREVIEW TO SEE THE IMAGE— To see the complete collection of formulas, click on this link.

The following section includes background information on slope. This background also includes video resources and accompanying transcripts.

What Is Slope?

Watch this video to learn about the slope formula. (The transcript is also included.)

Slope
Formulas--Slope Formula Formulas--Slope Formula Formulas | Slope Formula

The formula for the Slope Formula. This is part of a collection of math formulas. 

—PRESS PREVIEW TO SEE THE IMAGE— To see the complete collection of formulas, click on this link.

The following section includes background information on slope. This background also includes video resources and accompanying transcripts.

What Is Slope?

Watch this video to learn about the slope formula. (The transcript is also included.)

Slope
Formulas--Slope Formula Formulas--Slope Formula Formulas | Slope Formula

The formula for the Slope Formula. This is part of a collection of math formulas. 

—PRESS PREVIEW TO SEE THE IMAGE— To see the complete collection of formulas, click on this link.

The following section includes background information on slope. This background also includes video resources and accompanying transcripts.

What Is Slope?

Watch this video to learn about the slope formula. (The transcript is also included.)

Slope
Formulas--Slope Formula Formulas--Slope Formula Formulas | Slope Formula

The formula for the Slope Formula. This is part of a collection of math formulas. 

—PRESS PREVIEW TO SEE THE IMAGE— To see the complete collection of formulas, click on this link.

The following section includes background information on slope. This background also includes video resources and accompanying transcripts.

What Is Slope?

Watch this video to learn about the slope formula. (The transcript is also included.)

Slope
Strategy Pack Instructional Resource--Strategy Pack--The Slope of a Line Instructional Resource | Strategy Pack | The Slope of a Line

Learn different strategies for finding the slope of a line. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems.

—PRESS PREVIEW TO LAUNCH THE PRESENTATION— To see the complete collection of Instructional Resources, click on this link.

Note: The download is a PPT file.

Slope
Strategy Pack Instructional Resource--Strategy Pack--The Slope of a Line Instructional Resource | Strategy Pack | The Slope of a Line

Learn different strategies for finding the slope of a line. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems.

—PRESS PREVIEW TO LAUNCH THE PRESENTATION— To see the complete collection of Instructional Resources, click on this link.

Note: The download is a PPT file.

Slope
Strategy Pack Instructional Resource--Strategy Pack--The Slope of a Line Instructional Resource | Strategy Pack | The Slope of a Line

Learn different strategies for finding the slope of a line. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems.

—PRESS PREVIEW TO LAUNCH THE PRESENTATION— To see the complete collection of Instructional Resources, click on this link.

Note: The download is a PPT file.

Slope
INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter

In this Algebra Application, students study the direction between diameter and circumference of a circle. Through measurement and data gathering students analyze the line of best fit and explore ways of calculating pi. The math topics covered include: Mathematical modeling, Linear functions, Data gathering and analysis, Ratios, Direct variation. This is a great back-to-school activity for middle school or high school students. This is also a great crossover activity that ties algebra and geometry.

Applications of Linear Functions, Applications of Ratios, Proportions, and Percents and Applications of Circles
INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter

In this Algebra Application, students study the direction between diameter and circumference of a circle. Through measurement and data gathering students analyze the line of best fit and explore ways of calculating pi. The math topics covered include: Mathematical modeling, Linear functions, Data gathering and analysis, Ratios, Direct variation. This is a great back-to-school activity for middle school or high school students. This is also a great crossover activity that ties algebra and geometry.

Applications of Linear Functions, Applications of Ratios, Proportions, and Percents and Applications of Circles
INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter

In this Algebra Application, students study the direction between diameter and circumference of a circle. Through measurement and data gathering students analyze the line of best fit and explore ways of calculating pi. The math topics covered include: Mathematical modeling, Linear functions, Data gathering and analysis, Ratios, Direct variation. This is a great back-to-school activity for middle school or high school students. This is also a great crossover activity that ties algebra and geometry.

Applications of Linear Functions, Applications of Ratios, Proportions, and Percents and Applications of Circles
INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter INSTRUCTIONAL RESOURCE: Algebra Application: Linear Functions: Circumference vs. Diameter

In this Algebra Application, students study the direction between diameter and circumference of a circle. Through measurement and data gathering students analyze the line of best fit and explore ways of calculating pi. The math topics covered include: Mathematical modeling, Linear functions, Data gathering and analysis, Ratios, Direct variation. This is a great back-to-school activity for middle school or high school students. This is also a great crossover activity that ties algebra and geometry.

Applications of Linear Functions, Applications of Ratios, Proportions, and Percents and Applications of Circles
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Circumference vs. Diameter

In this Slide Show, apply concepts of linear functions to the context of circumference vs. diameter.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions
PowerPointPresentations.jpg Instructional Resource: Applications of Linear Functions: Circumference vs. Diameter

In this Slide Show, apply concepts of linear functions to the context of circumference vs. diameter.

Note: The download is a PPT file.

Related Resources

To see the complete collection of Tutorials on this topic, click on this link: https://bit.ly/3g0P3cN
Applications of Linear Functions