Illustrative Math Alignment: Grade 7 Unit 2

Topic

Linear Functions

Description

This image is part of a series demonstrating applications of linear functions, specifically focusing on Hooke's Law. It builds upon the previous images by introducing the general form of the linear function equation that describes the relationship observed in the weight scale experiment.

Topic

Linear Functions

Description

This image is part of a series demonstrating applications of linear functions, specifically focusing on Hooke's Law. It builds upon the previous images by introducing the general form of the linear function equation that describes the relationship observed in the weight scale experiment.

Topic

Linear Functions

Description

This image is part of a series illustrating applications of linear functions, focusing on Hooke's Law. It builds upon previous images by demonstrating how to calculate the spring constant 'k' using the data collected from the weight scale experiment.

Note: Here is the link to the video referenced: https://www.media4math.com/library/42143/asset-preview

Topic

Linear Functions

Description

This image is part of a series illustrating applications of linear functions, focusing on Hooke's Law. It builds upon previous images by demonstrating how to calculate the spring constant 'k' using the data collected from the weight scale experiment.

Note: Here is the link to the video referenced: https://www.media4math.com/library/42143/asset-preview

Topic

Linear Functions

Description

This image represents the culmination of our exploration into applications of linear functions, specifically focusing on Hooke's Law. It serves as the final piece in a series of eight images, tying together all the concepts we've examined throughout this study of spring behavior and weight measurement.

Topic

Linear Functions

Description

This image represents the culmination of our exploration into applications of linear functions, specifically focusing on Hooke's Law. It serves as the final piece in a series of eight images, tying together all the concepts we've examined throughout this study of spring behavior and weight measurement.

Topic

Linear Functions

Description

This image serves as an introduction to a series of math clip art illustrations demonstrating applications of linear functions, specifically focusing on temperature conversion. The title card presents "Applications of Linear Functions: Temperature Conversion," setting the stage for a comprehensive exploration of how linear models can be used to convert between Celsius and Fahrenheit temperatures.

Topic

Linear Functions

Description

This image is the second in a series illustrating applications of linear functions, focusing on temperature conversion. It presents a visual representation of thermometers alongside a data table that displays Celsius temperatures (x) and their corresponding Fahrenheit temperatures f(x). This pairing of visual and tabular data helps students connect the abstract concept of linear functions to the concrete idea of temperature scales.

Topic

Linear Functions

Description

This image is the third in a series demonstrating applications of linear functions through temperature conversion. It builds upon the previous image by highlighting a key observation: for every degree Celsius increase, there is a corresponding 1.8° increase in the Fahrenheit temperature. This insight is crucial in understanding the linear relationship between Celsius and Fahrenheit scales.

Topic

Linear Functions

Description

This image is part of a series illustrating applications of linear functions, focusing on temperature conversion. It builds upon previous images by introducing a data graph that visually represents the relationship between Celsius and Fahrenheit temperatures. The graph reinforces the key observation that for every degree Celsius increase, there is a corresponding 1.8° increase in the Fahrenheit temperature.

Topic

Linear Functions

Description

This image continues the series on applications of linear functions in temperature conversion. It builds upon the previous graph by connecting the data points with a straight line. This visual representation emphasizes the continuous nature of temperature values and clearly illustrates the linear relationship between Celsius and Fahrenheit scales.

Topic

Linear Functions

Description

This image is a crucial part of the series on applications of linear functions in temperature conversion. It introduces the mathematical equation f(x) = 1.8x + 32, which represents the temperature conversion function from Celsius to Fahrenheit. This equation is the culmination of the observations and data analysis from the previous images in the series.

Topic

Linear Functions

Description

This image continues the exploration of linear functions in temperature conversion by introducing the concepts of domain and range. It specifies that the domain of the temperature conversion function is x ≥ -273.15, and the range is y ≥ -459.67. These limits are crucial in understanding the real-world constraints on the mathematical model.

Topic

Linear Functions

Description

This image delves deeper into the concept of domain and range in the context of temperature conversion. It explains that the limits of the temperature function are based on the concept of absolute zero, the lowest theoretically possible temperature. This fundamental principle of physics determines the lower bounds of both the domain and range of the temperature conversion function.

Topic

Linear Functions

Description

This final image in the series on applications of linear functions in temperature conversion focuses on the significance of the coefficient of x in the linear equation. It emphasizes that this coefficient, 1.8 in the equation f(x) = 1.8x + 32, represents both the slope of the line and the temperature conversion rate.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, specifically focusing on linear function tables. It serves as a title card for a set of 10 clip art images that explore linear functions in tabular and graph form. This visual introduction sets the stage for understanding how linear functions can be represented and analyzed using tables.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, specifically focusing on linear function tables. It serves as a title card for a set of 10 clip art images that explore linear functions in tabular and graph form. This visual introduction sets the stage for understanding how linear functions can be represented and analyzed using tables.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, focusing on linear function tables. It presents a data table demonstrating that a linear function table shows a common difference for values of f(x). This visual representation helps students understand the fundamental characteristic of linear functions - the constant rate of change.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, focusing on linear function tables. It presents a data table demonstrating that a linear function table shows a common difference for values of f(x). This visual representation helps students understand the fundamental characteristic of linear functions - the constant rate of change.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, specifically linear function tables. It builds on the previous image by showing that the common difference in a linear function can also be negative. This concept is crucial for understanding decreasing linear functions and their representation in tabular form.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, specifically linear function tables. It builds on the previous image by showing that the common difference in a linear function can also be negative. This concept is crucial for understanding decreasing linear functions and their representation in tabular form.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, focusing on linear function tables. It presents a new version of the previous table, this time demonstrating that the common difference can also be zero. This concept introduces students to constant functions, a special case of linear functions where the output remains the same regardless of the input.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, focusing on linear function tables. It presents a new version of the previous table, this time demonstrating that the common difference can also be zero. This concept introduces students to constant functions, a special case of linear functions where the output remains the same regardless of the input.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, focusing on the relationship between linear function tables and graphs. It shows both a data table and a linear graph of data points, demonstrating that the graph of a Linear Function Table is a series of collinear points. This visual representation helps students connect tabular and graphical representations of linear functions.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, focusing on the relationship between linear function tables and graphs. It shows both a data table and a linear graph of data points, demonstrating that the graph of a Linear Function Table is a series of collinear points. This visual representation helps students connect tabular and graphical representations of linear functions.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, focusing on linear function tables and their corresponding graphs. It presents a variation of the previous image with a new set of data, demonstrating that when the common difference is positive, the orientation of the graph is upward from left to right. This helps students understand the concept of positive slope in linear functions.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, focusing on linear function tables and their corresponding graphs. It presents a variation of the previous image with a new set of data, demonstrating that when the common difference is positive, the orientation of the graph is upward from left to right. This helps students understand the concept of positive slope in linear functions.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, focusing on linear function tables and their corresponding graphs. It shows a variation of the previous image with a new set of data, demonstrating that when the common difference is negative, the orientation of the graph is downward from left to right. This helps students understand the concept of negative slope in linear functions.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, focusing on linear function tables and their corresponding graphs. It shows a variation of the previous image with a new set of data, demonstrating that when the common difference is negative, the orientation of the graph is downward from left to right. This helps students understand the concept of negative slope in linear functions.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, focusing on linear function tables and their corresponding graphs. It presents a variation of the previous image with a new set of data, showing that when the common difference is zero, the orientation of the graph is horizontal. This helps students understand the concept of zero slope in linear functions, also known as constant functions.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, focusing on linear function tables and their corresponding graphs. It presents a variation of the previous image with a new set of data, showing that when the common difference is zero, the orientation of the graph is horizontal. This helps students understand the concept of zero slope in linear functions, also known as constant functions.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, focusing on linear function tables. It shows a variation of the previous image with a new set of data, demonstrating that data gathered in a table can show a linear pattern. This concept helps students understand how to identify linear relationships from tabular data.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, focusing on linear function tables. It shows a variation of the previous image with a new set of data, demonstrating that data gathered in a table can show a linear pattern. This concept helps students understand how to identify linear relationships from tabular data.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, focusing on linear function tables and equations. It continues from the previous image, now including the equation f(x) = 0.5x - 3. This demonstrates that when a data set shows a linear pattern, it can be modeled by a linear function equation. This concept helps students understand the connection between tabular data and algebraic representations of linear functions.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, focusing on linear function tables and equations. It continues from the previous image, now including the equation f(x) = 0.5x - 3. This demonstrates that when a data set shows a linear pattern, it can be modeled by a linear function equation. This concept helps students understand the connection between tabular data and algebraic representations of linear functions.

Topic

Linear Functions

Description

This image serves as a title card for a series of 10 clip art images that explore graphs of linear functions. It sets the stage for understanding how linear functions can be represented and analyzed graphically, introducing students to the visual aspect of these mathematical concepts.

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 10 clip art images that explore graphs of linear functions. It sets the stage for understanding how linear functions can be represented and analyzed graphically, introducing students to the visual aspect of these mathematical concepts.

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 is the final in a series illustrating key concepts in linear functions, focusing on the special case of vertical lines. It presents a variation of the previous image, now including a vertical line in the graph to demonstrate an important exception in linear functions.

The image highlights that vertical lines are the only orientation not allowed in standard linear functions. This concept is crucial for students to understand the limitations of the slope-intercept form and to recognize when they need to use alternative representations.

Topic

Linear Functions

Description

This image is the final in a series illustrating key concepts in linear functions, focusing on the special case of vertical lines. It presents a variation of the previous image, now including a vertical line in the graph to demonstrate an important exception in linear functions.

The image highlights that vertical lines are the only orientation not allowed in standard linear functions. This concept is crucial for students to understand the limitations of the slope-intercept form and to recognize when they need to use alternative representations.

Topic

Linear Functions

Description

This image presents a data table alongside a linear graph with the slope and y-intercept labeled. It demonstrates the connection between tabular data and graphical representation of linear functions, helping students understand how numerical values translate into visual patterns.

By incorporating this visual aid, teachers can enhance students' comprehension of the relationship between data points and their graphical representation. This image serves as a bridge between algebraic and geometric interpretations of linear functions.

Topic

Linear Functions

Description

This image presents a data table alongside a linear graph with the slope and y-intercept labeled. It demonstrates the connection between tabular data and graphical representation of linear functions, helping students understand how numerical values translate into visual patterns.

By incorporating this visual aid, teachers can enhance students' comprehension of the relationship between data points and their graphical representation. This image serves as a bridge between algebraic and geometric interpretations of linear functions.

Topic

Linear Functions

Description

This image displays the general form of the slope-intercept equation (y = mx + b) with definitions of m and b. It provides a crucial link between the algebraic representation of linear functions and their graphical interpretation, helping students understand how each component of the equation affects the graph.

Using this visual aid can significantly enhance students' understanding of the slope-intercept form and its relationship to linear graphs. It serves as a reference point for discussing how changes in m and b impact the line's appearance on a coordinate plane.

Topic

Linear Functions

Description

This image displays the general form of the slope-intercept equation (y = mx + b) with definitions of m and b. It provides a crucial link between the algebraic representation of linear functions and their graphical interpretation, helping students understand how each component of the equation affects the graph.

Using this visual aid can significantly enhance students' understanding of the slope-intercept form and its relationship to linear graphs. It serves as a reference point for discussing how changes in m and b impact the line's appearance on a coordinate plane.

Topic

Linear Functions

Description

This image continues from the previous one, now with labeled slope and y-intercept. It provides a visual breakdown of the general equation for a linear function, helping students understand this fundamental concept in a step-by-step manner.

By using this visual aid, teachers can guide students through the process of understanding the slope-intercept form, reinforcing the connection between the algebraic definition and its graphical representation. This image is particularly useful for students who benefit from seeing mathematical concepts broken down into clear, visual steps.

Topic

Linear Functions

Description

This image continues from the previous one, now with labeled slope and y-intercept. It provides a visual breakdown of the general equation for a linear function, helping students understand this fundamental concept in a step-by-step manner.

By using this visual aid, teachers can guide students through the process of understanding the slope-intercept form, reinforcing the connection between the algebraic definition and its graphical representation. This image is particularly useful for students who benefit from seeing mathematical concepts broken down into clear, visual steps.

Topic

Linear Functions

Description

This image continues from the previous one, showing the slope calculation ratio. It demonstrates the importance of expressing slope as a ratio, which can help students more easily interpret and compare different linear functions.

Incorporating this visual aid into lessons can help reinforce the concept of slope simplification and its importance in analyzing linear functions. It provides a clear example of how mathematical operations can be applied to make expressions more manageable and meaningful.

Topic

Linear Functions

Description

This image continues from the previous one, showing the slope calculation ratio. It demonstrates the importance of expressing slope as a ratio, which can help students more easily interpret and compare different linear functions.

Incorporating this visual aid into lessons can help reinforce the concept of slope simplification and its importance in analyzing linear functions. It provides a clear example of how mathematical operations can be applied to make expressions more manageable and meaningful.

Topic

Linear Functions

Description

This image presents a variation of the previous image with the y-intercept highlighted. It emphasizes the significance of the y-intercept in linear functions, helping students understand its role in determining where the line crosses the y-axis.

By using this visual aid, teachers can draw attention to the y-intercept and its importance in interpreting linear functions. This image can help students connect the 'b' value in the slope-intercept form to its graphical representation, enhancing their understanding of how equations relate to graphs.

Topic

Linear Functions

Description

This image presents a variation of the previous image with the y-intercept highlighted. It emphasizes the significance of the y-intercept in linear functions, helping students understand its role in determining where the line crosses the y-axis.

By using this visual aid, teachers can draw attention to the y-intercept and its importance in interpreting linear functions. This image can help students connect the 'b' value in the slope-intercept form to its graphical representation, enhancing their understanding of how equations relate to graphs.

Topic

Linear Functions

Description

This image is part of a series illustrating key concepts in linear functions, focusing on the domain of linear functions. It continues from the previous images in the series, now highlighting the concept of domain in linear functions.

The image presents a continuation of the previous graph with the domain identified. This visual representation helps students understand that the domain of a linear function extends infinitely in both directions on the x-axis.