Illustrative Math Alignment: Grade 8 Unit 3

Topic

Linear Functions

Description

This image presents a variation of the previous image, showing other Linear Function Machine examples. It helps students understand that there are many different types of linear functions, each with its own unique rule for transforming inputs into outputs.

By incorporating this visual aid, teachers can expand students' understanding of the variety of linear functions. This image is particularly useful for demonstrating how different rules lead to different relationships between inputs and outputs.

Topic

Linear Functions

Description

This image presents a variation of the previous image, showing other Linear Function Machine examples. It helps students understand that there are many different types of linear functions, each with its own unique rule for transforming inputs into outputs.

By incorporating this visual aid, teachers can expand students' understanding of the variety of linear functions. This image is particularly useful for demonstrating how different rules lead to different relationships between inputs and outputs.

Topic

Linear Functions

Description

This image shows a function rule and its corresponding function equation for f(x) = 2x. It illustrates how a verbal description of a function rule can be translated into a mathematical equation, bridging the gap between conceptual understanding and algebraic representation.

By using this visual aid, teachers can help students make the connection between the intuitive understanding of a function's behavior and its formal mathematical expression. This image is particularly useful for introducing the concept of variable notation and function notation.

Topic

Linear Functions

Description

This image shows a function rule and its corresponding function equation for f(x) = 2x. It illustrates how a verbal description of a function rule can be translated into a mathematical equation, bridging the gap between conceptual understanding and algebraic representation.

By using this visual aid, teachers can help students make the connection between the intuitive understanding of a function's behavior and its formal mathematical expression. This image is particularly useful for introducing the concept of variable notation and function notation.

Topic

Linear Functions

Description

This image shows a function rule and its corresponding function equation for f(x) = 2x. It illustrates how a verbal description of a function rule can be translated into a mathematical equation, bridging the gap between conceptual understanding and algebraic representation.

By using this visual aid, teachers can help students make the connection between the intuitive understanding of a function's behavior and its formal mathematical expression. This image is particularly useful for introducing the concept of variable notation and function notation.

Topic

Linear Functions

Description

This image serves as a title card for a series of 9 clip art images that explore using the point-slope form to find a linear equation and graph. It sets the stage for understanding this important representation of linear functions, providing a visual introduction to the concept.

Using visual aids like this title card can help engage students and prepare them for the upcoming content. It provides a clear introduction to the topic and helps organize the learning material in a visually appealing way.

Topic

Linear Functions

Description

This image serves as a title card for a series of 9 clip art images that explore using the point-slope form to find a linear equation and graph. It sets the stage for understanding this important representation of linear functions, providing a visual introduction to the concept.

Using visual aids like this title card can help engage students and prepare them for the upcoming content. It provides a clear introduction to the topic and helps organize the learning material in a visually appealing way.

Topic

Linear Functions

Description

This image serves as a title card for a series of 9 clip art images that explore using the point-slope form to find a linear equation and graph. It sets the stage for understanding this important representation of linear functions, providing a visual introduction to the concept.

Using visual aids like this title card can help engage students and prepare them for the upcoming content. It provides a clear introduction to the topic and helps organize the learning material in a visually appealing way.

Topic

Linear Functions

Description

This image presents a linear graph with a stair step showing the rise over the run, illustrating the concept of slope. It introduces the idea that knowing the slope of a line and the coordinates of a point on the line allows us to find the equation in slope-intercept form.

By incorporating this visual aid, teachers can help students understand the connection between the graphical representation of slope and its use in forming equations. This image is particularly useful for bridging the gap between visual and algebraic representations of linear functions.

Topic

Linear Functions

Description

This image presents a linear graph with a stair step showing the rise over the run, illustrating the concept of slope. It introduces the idea that knowing the slope of a line and the coordinates of a point on the line allows us to find the equation in slope-intercept form.

By incorporating this visual aid, teachers can help students understand the connection between the graphical representation of slope and its use in forming equations. This image is particularly useful for bridging the gap between visual and algebraic representations of linear functions.

Topic

Linear Functions

Description

This image presents a linear graph with a stair step showing the rise over the run, illustrating the concept of slope. It introduces the idea that knowing the slope of a line and the coordinates of a point on the line allows us to find the equation in slope-intercept form.

By incorporating this visual aid, teachers can help students understand the connection between the graphical representation of slope and its use in forming equations. This image is particularly useful for bridging the gap between visual and algebraic representations of linear functions.

Topic

Linear Functions

Description

This image continues from the previous one, now labeling two coordinates on the graph and showing the general form of the slope formula. It emphasizes that typically, the slope formula is used when two points on the line are known.

By using this visual aid, teachers can help students understand how the slope formula relates to points on a line. This image is particularly useful for reinforcing the concept of slope calculation before introducing the point-slope form.

Topic

Linear Functions

Description

This image continues from the previous one, now labeling two coordinates on the graph and showing the general form of the slope formula. It emphasizes that typically, the slope formula is used when two points on the line are known.

By using this visual aid, teachers can help students understand how the slope formula relates to points on a line. This image is particularly useful for reinforcing the concept of slope calculation before introducing the point-slope form.

Topic

Linear Functions

Description

This image continues from the previous one, now labeling two coordinates on the graph and showing the general form of the slope formula. It emphasizes that typically, the slope formula is used when two points on the line are known.

By using this visual aid, teachers can help students understand how the slope formula relates to points on a line. This image is particularly useful for reinforcing the concept of slope calculation before introducing the point-slope form.

Topic

Linear Functions

Description

This image presents a variation of the previous graph, now with one coordinate highlighted. It introduces the case where the coordinates of one point are known, along with the slope of the line. This scenario sets the stage for introducing the point-slope form of a linear equation.

By incorporating this visual aid, teachers can help students transition from the two-point slope formula to the point-slope form. This image is particularly useful for demonstrating how different pieces of information about a line can be used to determine its equation.

Topic

Linear Functions

Description

This image presents a variation of the previous graph, now with one coordinate highlighted. It introduces the case where the coordinates of one point are known, along with the slope of the line. This scenario sets the stage for introducing the point-slope form of a linear equation.

By incorporating this visual aid, teachers can help students transition from the two-point slope formula to the point-slope form. This image is particularly useful for demonstrating how different pieces of information about a line can be used to determine its equation.

Topic

Linear Functions

Description

This image presents a variation of the previous graph, now with one coordinate highlighted. It introduces the case where the coordinates of one point are known, along with the slope of the line. This scenario sets the stage for introducing the point-slope form of a linear equation.

By incorporating this visual aid, teachers can help students transition from the two-point slope formula to the point-slope form. This image is particularly useful for demonstrating how different pieces of information about a line can be used to determine its equation.

Topic

Linear Functions

Description

This image continues from the previous one, showing a rearrangement of the slope formula to derive the point-slope form. It demonstrates how algebraic manipulation can lead to a new, useful form of a linear equation.

By using this visual aid, teachers can guide students through the process of deriving the point-slope form. This image is particularly useful for students who benefit from seeing the step-by-step transformation of mathematical expressions.

Topic

Linear Functions

Description

This image continues from the previous one, showing a rearrangement of the slope formula to derive the point-slope form. It demonstrates how algebraic manipulation can lead to a new, useful form of a linear equation.

By using this visual aid, teachers can guide students through the process of deriving the point-slope form. This image is particularly useful for students who benefit from seeing the step-by-step transformation of mathematical expressions.

Topic

Linear Functions

Description

This image continues from the previous one, showing a rearrangement of the slope formula to derive the point-slope form. It demonstrates how algebraic manipulation can lead to a new, useful form of a linear equation.

By using this visual aid, teachers can guide students through the process of deriving the point-slope form. This image is particularly useful for students who benefit from seeing the step-by-step transformation of mathematical expressions.

Topic

Linear Functions

Description

This image continues from the previous one, now showing the single coordinate values plugged into the point-slope equation. It demonstrates how to use the point-slope form when you know the coordinates of one point and the slope of the line.

By incorporating this visual aid, teachers can help students understand how to apply the point-slope form in practice. This image is particularly useful for bridging the gap between the abstract form of the equation and its practical application.

Topic

Linear Functions

Description

This image continues from the previous one, now showing the single coordinate values plugged into the point-slope equation. It demonstrates how to use the point-slope form when you know the coordinates of one point and the slope of the line.

By incorporating this visual aid, teachers can help students understand how to apply the point-slope form in practice. This image is particularly useful for bridging the gap between the abstract form of the equation and its practical application.

Topic

Linear Functions

Description

This image continues from the previous one, now showing the single coordinate values plugged into the point-slope equation. It demonstrates how to use the point-slope form when you know the coordinates of one point and the slope of the line.

By incorporating this visual aid, teachers can help students understand how to apply the point-slope form in practice. This image is particularly useful for bridging the gap between the abstract form of the equation and its practical application.

Topic

Linear Functions

Description

This image presents a graph crossing the origin and the corresponding point-slope form. It provides the simplest example of using the point-slope form, where a line passes through the origin (0,0) with a slope of 1.

By using this visual aid, teachers can help students understand the point-slope form in its most basic application. This image is particularly useful for building confidence before moving on to more complex examples.

Topic

Linear Functions

Description

This image presents a graph crossing the origin and the corresponding point-slope form. It provides the simplest example of using the point-slope form, where a line passes through the origin (0,0) with a slope of 1.

By using this visual aid, teachers can help students understand the point-slope form in its most basic application. This image is particularly useful for building confidence before moving on to more complex examples.

Topic

Linear Functions

Description

This image presents a graph crossing the origin and the corresponding point-slope form. It provides the simplest example of using the point-slope form, where a line passes through the origin (0,0) with a slope of 1.

By using this visual aid, teachers can help students understand the point-slope form in its most basic application. This image is particularly useful for building confidence before moving on to more complex examples.

Topic

Linear Functions

Description

This image presents a variation of the previous example, now with the coordinate (0, 1) and a slope of 1. It demonstrates how to use the point-slope form when the y-intercept is not at the origin.

By incorporating this visual aid, teachers can help students understand how the point-slope form can be used with different y-intercepts. This image is particularly useful for showing how the form adapts to different scenarios while maintaining its basic structure.

Topic

Linear Functions

Description

This image presents a variation of the previous example, now with the coordinate (0, 1) and a slope of 1. It demonstrates how to use the point-slope form when the y-intercept is not at the origin.

By incorporating this visual aid, teachers can help students understand how the point-slope form can be used with different y-intercepts. This image is particularly useful for showing how the form adapts to different scenarios while maintaining its basic structure.

Topic

Linear Functions

Description

This image presents a variation of the previous example, now with the coordinate (0, 1) and a slope of 1. It demonstrates how to use the point-slope form when the y-intercept is not at the origin.

By incorporating this visual aid, teachers can help students understand how the point-slope form can be used with different y-intercepts. This image is particularly useful for showing how the form adapts to different scenarios while maintaining its basic structure.

Topic

Linear Functions

Description

This image shows a variation of the previous example, now with a line having a negative slope of -2 and crossing the y-axis at (0, -2). It demonstrates how to use the point-slope form with negative slopes and y-intercepts.

By using this visual aid, teachers can help students understand how the point-slope form accommodates negative values. This image is particularly useful for expanding students' understanding of the form's versatility.

Topic

Linear Functions

Description

This image shows a variation of the previous example, now with a line having a negative slope of -2 and crossing the y-axis at (0, -2). It demonstrates how to use the point-slope form with negative slopes and y-intercepts.

By using this visual aid, teachers can help students understand how the point-slope form accommodates negative values. This image is particularly useful for expanding students' understanding of the form's versatility.

Topic

Linear Functions

Description

This image shows a variation of the previous example, now with a line having a negative slope of -2 and crossing the y-axis at (0, -2). It demonstrates how to use the point-slope form with negative slopes and y-intercepts.

By using this visual aid, teachers can help students understand how the point-slope form accommodates negative values. This image is particularly useful for expanding students' understanding of the form's versatility.

Topic

Linear Functions

Description

This image is the first in a series of 6 clip art images that show step by step how to use the slope formula. It serves as an introduction, with the title "Introduction" and includes the text "In this presentation, we walk you through the steps of using the Slope Formula." The image features a linear graph with two generic points highlighted and the slope formula displayed.

Topic

Linear Functions

Description

This image is the first in a series of 6 clip art images that show step by step how to use the slope formula. It serves as an introduction, with the title "Introduction" and includes the text "In this presentation, we walk you through the steps of using the Slope Formula." The image features a linear graph with two generic points highlighted and the slope formula displayed.

Topic

Linear Functions

Description

This image is a continuation of the previous one, focusing on Step 1 of using the slope formula: "Identify the Coordinates." The example in this series of images deals with coordinates (3, 4) and (-5, -4), demonstrating how to select two points on a line to calculate its slope.

Teachers can guide students through this step by saying: "The first step in using the slope formula is to identify two points on our line. In this example, we're using the points (3, 4) and (-5, -4). Can you locate these points on the graph? Why do you think it's important to choose two different points?"

Topic

Linear Functions

Description

This image is a continuation of the previous one, focusing on Step 1 of using the slope formula: "Identify the Coordinates." The example in this series of images deals with coordinates (3, 4) and (-5, -4), demonstrating how to select two points on a line to calculate its slope.

Teachers can guide students through this step by saying: "The first step in using the slope formula is to identify two points on our line. In this example, we're using the points (3, 4) and (-5, -4). Can you locate these points on the graph? Why do you think it's important to choose two different points?"

Topic

Linear Functions

Description

This image continues the series, focusing on Step 2 of using the slope formula: "Match Coordinates to Formula." It demonstrates how to correctly assign the chosen coordinates to the variables in the slope formula.

Topic

Linear Functions

Description

This image continues the series, focusing on Step 2 of using the slope formula: "Match Coordinates to Formula." It demonstrates how to correctly assign the chosen coordinates to the variables in the slope formula.

Topic

Linear Functions

Description

This image focuses on Step 3 of using the slope formula: "Assign Values to Formula." It shows how to substitute the actual coordinate values into the slope formula, preparing for the calculation of the slope.

Topic

Linear Functions

Description

This image focuses on Step 3 of using the slope formula: "Assign Values to Formula." It shows how to substitute the actual coordinate values into the slope formula, preparing for the calculation of the slope.

Topic

Linear Functions

Description

This image continues the series, focusing on Step 4 of using the slope formula: "Assign Values to Formula." It completes the assignment of coordinate values in the slope formula. In this case we deal with x2 and y2.

Teachers can walk students through this step by saying: "Now we complete the assignment of coordinate values into the slope formula. In this case we deal with x2 and y2. Do you see how those coordinates are highlighted in the formula?"

Topic

Linear Functions

Description

This image continues the series, focusing on Step 4 of using the slope formula: "Assign Values to Formula." It completes the assignment of coordinate values in the slope formula. In this case we deal with x2 and y2.

Teachers can walk students through this step by saying: "Now we complete the assignment of coordinate values into the slope formula. In this case we deal with x2 and y2. Do you see how those coordinates are highlighted in the formula?"

Topic

Linear Functions

Description

This final image in the series focuses on Step 5 of using the slope formula: "Simplify." It shows how to express the calculated slope in its simplest form, if necessary.

Teachers can conclude the lesson with this step by saying: "Our last step is to simplify our result if possible. Sometimes, our slope might be a fraction that can be reduced. Other times, it might already be in its simplest form. Why is it important to express our slope in the simplest possible way? How does this final step help us interpret what the slope means in the context of our line?"

Topic

Linear Functions

Description

This final image in the series focuses on Step 5 of using the slope formula: "Simplify." It shows how to express the calculated slope in its simplest form, if necessary.

Teachers can conclude the lesson with this step by saying: "Our last step is to simplify our result if possible. Sometimes, our slope might be a fraction that can be reduced. Other times, it might already be in its simplest form. Why is it important to express our slope in the simplest possible way? How does this final step help us interpret what the slope means in the context of our line?"

Use this selection of images to show steepness of stairs as a way of introducing the concept of slope.

Use this selection of images to show steepness of stairs as a way of introducing the concept of slope.

In these clip art images, show students the difference between ratios and rates. These images are useful when talking about slope as both a ratio and a rate. In particular, this is useful when talking about slope as a rate of change.

In these clip art images, show students the difference between ratios and rates. These images are useful when talking about slope as both a ratio and a rate. In particular, this is useful when talking about slope as a rate of change.

In these clip art images, show students the difference between ratios and rates. These images are useful when talking about slope as both a ratio and a rate. In particular, this is useful when talking about slope as a rate of change.

Have students compare the slopes of the pairs of lines from these clip art images. Have them use the background grid for measuring the rise and the run.