Illustrative Math Alignment: Grade 8 Unit 3

Topic

Linear Functions

Description

The term is "The Equation of a Line from Two Coordinates," defined as deriving the equation of a line in slope-intercept form from two given points. The slope is calculated as m = (y2 - y1) / (x2 - x1), and the equation is written as y - y1 = m(x - x1). This term builds the connection between points on a graph and their corresponding linear equation, demonstrating practical derivations.

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

Linear Expressions, Equations, and Functions

This is the transcript for the video of same title. Video contents: Functions are relationships between quantities that change. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video explores the definition of a function, its vocabulary and notations, and distinguishes the concept of function from a general relation. Multiple representations of functions are provided using the TI-Nspire, while dynamic visuals and scenarios put them into real-world contexts. Concepts explored: functions, relations, equations, quadratic functions, linear functions, multiple representations

This is the transcript for the video of same title. Video contents: In this Investigation we explore the definition of a Relation.

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This is the transcript for the video of same title. Video contents: In this Investigation we look at functions.

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This is the transcript for the video of same title. Video contents: In this program, internationally acclaimed mathematics educator Dr. Monica Neagoy, explores the nature of linear functions through the use TI graphing calculators. Examples ranging from air travel, construction, engineering, and space travel provide real-world examples for discovering algebraic concepts. All examples are solved algebraically and then reinforced through the use of the TI-Nspire. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series. Concepts explored: Standard form, slope-intercept form, point-slope form, solving linear equations

This is the transcript for the video of same title. Video contents: In this Investigation we look at linear models for objects moving at a constant speed.

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This is the transcript for the video of same title. Video contents: In this Investigation we look at a linear regression for carbon dioxide emission data.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript for the video of same title. Video contents: Ever since the mathematics of the Babylonians, equations have played a central role in the development of algebra. Written and hosted by internationally acclaimed mathematics educator Dr. Monica Neagoy, this video traces the history and evolution of equations. It explores the two principal equations encountered in an introductory algebra course -- linear and quadratic -- in an engaging way. The foundations of algebra are explored and fundamental questions about the nature of algebra are answered. In addition, problems involving linear and quadratic equations are solved using the TI-Nspire graphing calculator. Algebra teachers looking to integrate hand-held technology and visual media into their instruction will benefit greatly from this series.

This is the transcript that goes with the video segment entitled Video: Linear Functions: Negative Slope, Negative y-Intercept.

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This is the transcript that goes with the video segment entitled Video: Linear Functions: Negative Slope, Positive y-Intercept.

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This is the transcript that goes with the video segment entitled Video: Linear Functions: Negative Slope, Zero y-Intercept.

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This is the transcript that goes with the video segment entitled Video: Linear Functions: Positive Slope, Negative y-Intercept.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript that goes with the video segment entitled Video: Linear Functions: Positive Slope, Positive y-Intercept.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript that goes with the video segment entitled Video: Linear Functions: Positive Slope, Zero y-Intercept.

To see the complete collection of video transcriptsy, click on this link.

This YouTube video describes the relationship between the number of cricket chirps and outside temperature. This is an application of linear functions of the form y = mx + b.

Learn the basics of direct variations. Graphical and algebraic representations of direct variations are shown, as well as examples of such functions.

This YouTube video describes Hooke's Law, which is an application of linear functions of the form y = kx.

This video looks at the identity function. Students review the identity properties of addition and multiplication as a means of better understanding the identity function.

Topic

Linear Functions

Description

The video covers linear functions with positive slope and positive y-intercept. It explains the slope-intercept form y = mx + b, where m is the slope indicating steepness, calculated as rise over run, and b is the y-intercept, the y-value at the point where the line intersects the y-axis. For this function, the slope is 2, and the y-intercept is 2. The graph is demonstrated by moving up two units and one to the right, confirming the slope. The y-intercept at point (0, 2) is also identified.

Topic

Linear Functions

Description

This video discusses linear functions with positive slope and negative y-intercept. It reviews the slope-intercept form y = mx + b. The slope measures steepness as the ratio of rise to run, and the y-intercept is the point where the line meets the y-axis. Here, the slope is 2, and the y-intercept is -3, evidenced by the graph where the line starts at (0, -3) and rises two units for every unit right.

Topic

Linear Functions

Description

The video explains linear functions with a positive slope and zero y-intercept. In slope-intercept form y = mx + b, the slope, m, represents the steepness, while the y-intercept, b, is zero. The slope of 2 is confirmed by graphing: moving up two units and one to the right. The line passes through the origin, demonstrating a y-intercept of 0.

Topic

Linear Functions

Description

This video focuses on linear functions with a negative slope and positive y-intercept. Using the slope-intercept form y = mx + b, the slope of -3 indicates a downward slope, and the y-intercept of 2 is the point (0, 2). Graphically, moving down three units and one unit to the left confirms the slope of -3.

Topic

Linear Functions

Description

The video covers linear functions with a negative slope and negative y-intercept. It explains the slope-intercept form y = mx + b, with a slope of -3 and a y-intercept of -2 at (0, -2). The graph shows a downward slope with three units down and one unit left, confirming the slope.

Topic

Linear Functions

Description

This video addresses linear functions with a negative slope and zero y-intercept. In slope-intercept form y = mx + b, the slope is -3, indicating a downward trend. The line passes through the origin, confirming the zero y-intercept, and graphing demonstrates the negative slope.

This video looks at multiple representations of functions, including symbolic, tabular, and graphic. Examples of linear, quadratic, polynomial, and exponential functions are shown.

This is part of a collection of video tutorials on using the point-slope form to find the equation of a line that passes through a given point. Each video is a step-by-step tutorial.

Note: The download is a PDF template for use in modeling the examples shown in the videos.

This is part of a collection of video tutorials on using the point-slope form to find the equation of a line that passes through a given point. Each video is a step-by-step tutorial.

Note: The download is a PDF template for use in modeling the examples shown in the videos.

This is part of a collection of video tutorials on using the point-slope form to find the equation of a line that passes through a given point. Each video is a step-by-step tutorial.

Note: The download is a PDF template for use in modeling the examples shown in the videos.

This is part of a collection of video tutorials on using the point-slope form to find the equation of a line that passes through a given point. Each video is a step-by-step tutorial.

Note: The download is a PDF template for use in modeling the examples shown in the videos.

Topic

Linear Functions

Description

Applies linear functions to cycling, calculating hill grades and distances using slope formulas and graphing.

Linear functions are fundamental in understanding mathematical relationships between two variables. The video demonstrates their application in real-life scenarios, enhancing comprehension of key concepts like slope, intercepts, and graphical representation. This foundational knowledge prepares students for more advanced mathematical topics.

Topic

Linear Functions

Topic

Linear Functions

Description

Introduces linear functions with examples like staircases, explaining slope, intercepts, and applications in real-world scenarios.

Linear functions are fundamental in understanding mathematical relationships between two variables. The video demonstrates their application in real-life scenarios, enhancing comprehension of key concepts like slope, intercepts, and graphical representation. This foundational knowledge prepares students for more advanced mathematical topics.

Topic

Linear Functions

Description

Uses linear regression to analyze US oil consumption trends, projecting future usage and potential impact of Alaskan oil production.

Linear functions are fundamental in understanding mathematical relationships between two variables. The video demonstrates their application in real-life scenarios, enhancing comprehension of key concepts like slope, intercepts, and graphical representation. This foundational knowledge prepares students for more advanced mathematical topics.

Topic

Linear Functions

Description

Models maximum heart rate during aerobic exercise with linear equations, creating exercise charts for various age groups.

Linear functions are fundamental in understanding relationships where one quantity depends linearly on another. This video provides clear examples and context that make the topic relevant and engaging. Linear equations often represent real-world scenarios, from economic trends to scientific measurements, helping students relate the math to everyday life.

Topic

Functions and Relations

Description

This section defines relations and functions, emphasizing domain, range, and dependent versus independent variables. Using examples like USB flash drive pricing, it illustrates tabular, graphical, and mapping representations. Key concepts include ordered pairs, Cartesian plane, and scatter plots. The TI-Nspire is utilized to model relationships and introduce functional analysis.

Topic

Functions and Relations

Description

In this Math Lab explore domain-to-range mappings for functions and relations.

Relevance to the Topic: This video is an essential resource for understanding Functions and Relations. By exploring the concepts and examples in this video, students will gain insights into the practical applications and theoretical underpinnings of Functions and Relations. It builds a strong foundation for future learning.

Topic

Functions and Relations

Description

Building on the prior section, this video elaborates on function rules and notation, graphing diverse functions such as linear, quadratic, and step functions. Key terms include domain, range, and vertical line test. Applications highlight real-world uses like analyzing study hours and grades. Technology aids in demonstrating increasing and decreasing functions visually.

Topic

Functions and Relations

Description

In this Math Lab use toothpicks to create unit squares and square arrays. Explore the functional relationship between length of the side of the square and the total number of toothpicks.

Topic

Linear Functions

Description

This video explores linear functions, emphasizing their applications in motion contexts like airplane altitude. Key topics include slope, y-intercept, and function representation using tools like the TI-Nspire. Vocabulary includes linear function, slope-intercept form, and dependent variable. Applications include predicting motion scenarios.

Topic

Linear Functions

Description

In this Math Lab explore the slopes of staircases. Compare the slope of a staircase when walking it in a straight path and compare it to the slope of a staircase walked in a staggered path.

In this video, students explore the mathematical concept of linear functions, gaining a deeper understanding of its applications. The video emphasizes how this concept helps in problem-solving and real-world scenarios, bridging the gap between abstract mathematics and practical application.

Topic

Linear Functions

Description

This video applies linear functions to environmental data analysis, predicting carbon dioxide levels using regression models. Key terms include regression, scatter plot, and slope. Applications highlight global warming trends and their impact using predictive analytics.

Topic

Linear Functions

Description

In this Math Lab explore water pressure by comparing the height of a column of water and the length of the corresponding jet of water.

In this video, students explore the mathematical concept of linear functions, gaining a deeper understanding of its applications. The video emphasizes how this concept helps in problem-solving and real-world scenarios, bridging the gap between abstract mathematics and practical application.

In this Nspire CX tutorial absolute functions are graphed, including graphs centered at the origin, graphs displaced along the x-axis, and graphs displaced along the y-axis. Note: This video does not include audio.

In this TI-Nspire CX tutorial learn how to graph quadratic functions in standard form using sliders for the values of a, b, and c.

In this TI-Nspire CX tutorial learn how to graph quadratic functions in vertex form using sliders for the values of h and k.