Illustrative Math Alignment: Grade 8 Unit 9

Putting It All Together

Lesson 4: What Influences Temperature?

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Topic
Closed Captioned Video: Algebra Applications: Linear Functions, 1	Closed Captioned Video: Algebra Applications: Linear Functions, Segment 1: Introduction Linear Expressions, Equations, and Functions Linear Expres	Special Functions and Applications of Linear Functions
Closed Captioned Video: Algebra Applications: Linear Functions, 3	Closed Captioned Video: Algebra Applications: Linear Functions, Segment 3: Oil Exploration Linear Expressions, Equations, and Functions Linear Exp	Special Functions and Applications of Linear Functions
Closed Captioned Video: Algebra Applications: Linear Functions, 4	Closed Captioned Video: Algebra Applications: Linear Functions, Segment 4: Exercise Linear Expressions, Equations, and Functions Linear Expression	Special Functions and Applications of Linear Functions
Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability	Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability What are the two meanings of statistics? What does it really mean that an event has a 50% probability of occurring? Why are data analysis and probability always taught together? Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, this video answers these questions and addresses fundamental concepts such as the law of large numbers and the notion of regression analysis. Both engaging investigations are based on true stories and real data, utilize different Nspire applications, and model the seamless connection among various problem representations. Concepts explored: statistics, data analysis, regression analysis.	Data Analysis and Data Gathering
Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability, 1	Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability, Segment 1 In this Investigation we explore uncertainty and randomness. This video is Segment 1 of a 4 segment series related to Data Analysis and Probability. Segments 1 and 2 are grouped together.	Data Analysis and Data Gathering
Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability, 3	Closed Captioned Video: Algebra Nspirations: Data Analysis and Probability, Segment 3 In this Investigation we look at real-world data involving endangered wolf populations. This video is Segment 3 of a 4 segment series related to Data Analysis and Probability. Segments 3 and 4 are grouped together.	Data Analysis and Data Gathering
Closed Captioned Video: Algebra Nspirations: Functions and Relations	Closed Captioned Video: Algebra Nspirations: Functions and Relations 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.	Applications of Functions and Relations, Conic Sections and Relations and Functions
Closed Captioned Video: Algebra Nspirations: Linear Functions	Closed Captioned Video: Algebra Nspirations: Linear Functions 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.	Applications of Linear Functions
Closed Captioned Video: Algebra Nspirations: Linear Functions, 1	Closed Captioned Video: Algebra Nspirations: Linear Functions, Segment 1 In this Investigation we look at linear models for objects moving at a constant speed. This video is Segment 1 of a 4 segment series related to Algebra Nspirations: Linear Functions. Segments 1 and 2 are grouped together.	Applications of Linear Functions
Closed Captioned Video: Algebra Nspirations: Linear Functions, 3	Closed Captioned Video: Algebra Nspirations: Linear Functions, Segment 3 In this Investigation we look at a linear regression for carbon dioxide emission data. This video is Segment 3 of a 4 segment series related to Algebra Nspirations: Linear Functions. Segments 3 and 4 are grouped together.	Applications of Linear Functions
Closed Captioned Video: Probability Simulation 1	Closed Captioned Video: Probability Simulation 1 In this TI Nspire tutorialthe Spreadsheet and Statistics windows are used to create a probability simulation of tossing two dice. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. .	Probability
Closed Captioned Video: Random Number Table	Closed Captioned Video: Random Number Table In this TI Nspire tutorial, the Spreadsheet window is used to create a random number table. This video supports the TI-Nspire Clickpad and Touchpad. This Mini-Tutorial Video includes a worksheet. . This is part of a collection of closed captioned videos on various math topics. To see the complete collection of the videos, click on this link. Note: The download is Media4Math's guide to closed captioned videos. Related Resources To see additional resources on this topic, click on the Related Resources tab. Video Transcripts This video has a transcript available. To see the complete collection of video transcripts, click on this link.	Probability
Definition--Functions and Relations Concepts--Absolute Value Function	Absolute Value Function Topic Functions and Relations Definition An absolute value function is a function that contains an algebraic expression within absolute value symbols. It is defined as $$ f(x) = \|x\| $$ where \|x\| denotes the absolute value ofx. Description The absolute value function is significant in mathematics because it measures the distance of a number from zero on the number line, regardless of direction. This function is linear in nature, as it can be broken into two linear pieces: one for $$ x \geq 0 $$ and one for $$ x < 0 $$	Special Functions
Definition--Functions and Relations Concepts--Composite Function	Composite Function Topic Functions and Relations Definition A composite function is a function that is formed when one function is applied to the result of another function. Description Composite functions are significant in mathematics because they allow the combination of two functions to form a new function. This is denoted as (f∘g)(x) = f(g(x)). Composite functions are widely used in various fields, including computer science for function composition in programming and in calculus for chain rule applications. For example, if f(x) = 2x and g(x) = x + 3, then the composite function (f∘g)(x) = f(g(x)) = 2(x + 3) = 2x+6	Composite Functions
Definition--Functions and Relations Concepts--Conic Sections	Conic Sections Topic Functions and Relations Definition Conic sections are the curves obtained by intersecting a plane with a double-napped cone. Description Conic sections include circles, ellipses, parabolas, and hyperbolas, which are fundamental in the study of geometry and algebra. These shapes are described by quadratic equations and have numerous applications in physics, engineering, and astronomy. For example, the orbits of planets are ellipses, and parabolic mirrors are used in telescopes and satellite dishes. The general quadratic equation for conic sections is Ax2 + Bxy + Cy2 + Dx + Ey + F = 0	Conic Sections
Definition--Functions and Relations Concepts--Constant Function	Constant Function Topic Functions and Relations Definition A constant function is a function that always returns the same value, no matter the input. Description The constant function is one of the simplest types of functions in mathematics, expressed as f(x) = c	Relations and Functions
Definition--Functions and Relations Concepts--Continuous Function	Continuous Function Topic Functions and Relations Definition A continuous function is a function that does not have any breaks, holes, or gaps in its domain. Description Continuous functions are fundamental in calculus and mathematical analysis because they allow for the application of limits, derivatives, and integrals. A function f(x) is continuous if, for every point 𝑐 c in its domain, lim x→c f(x) = f(c)	Relations and Functions
Definition--Functions and Relations Concepts--Decreasing Function	Decreasing Function Topic Functions and Relations Definition A decreasing function is a function where the value of the function decreases as the input increases. Description Decreasing functions are important in mathematics because they describe scenarios where an increase in one variable leads to a decrease in another. This is mathematically represented as f(x1) > f(x2) for any 𝑥1 < 𝑥2	Relations and Functions
Definition--Functions and Relations Concepts--Dependent Variable	Dependent Variable Topic Functions and Relations Definition A dependent variable is a variable whose value depends on one or more other variables.	Relations and Functions
Definition--Functions and Relations Concepts--Discontinuous Function	Discontinuous Function Topic Functions and Relations Definition A discontinuous function is a function that has one or more points where it is not continuous.	Relations and Functions
Definition--Functions and Relations Concepts--Discrete Functions	Discrete Functions Topic Functions and Relations Definition Discrete functions are functions that are defined only for a set of discrete points.	Special Functions
Definition--Functions and Relations Concepts--Distorting a Function Horizontally	Distorting a Function Horizontally Topic Functions and Relations Definition Distorting a function horizontally involves stretching or compressing the graph of the function along the x-axis. Description Horizontal distortions of functions are significant because they alter the input values while maintaining the overall shape of the graph. This is mathematically represented as f(kx) where k is a constant. If k > 1, the function compresses horizontally, and if 0 < 𝑘 < 1, it stretches.	Relations and Functions
Definition--Functions and Relations Concepts--Distorting a Function Vertically	Distorting a Function Vertically Topic Functions and Relations Definition Distorting a function vertically involves stretching or compressing the graph of the function along the y-axis. Description Vertical distortions of functions are significant because they alter the output values while maintaining the overall shape of the graph. This is mathematically represented as kf(x)	Relations and Functions
Definition--Functions and Relations Concepts--Domain of a Function	Domain of a Function Topic Functions and Relations Definition The domain of a function is the set of all possible input values (x-values) for which the function is defined.	Relations and Functions
Definition--Functions and Relations Concepts--Even Function	Even Function Topic Functions and Relations Definition An even function is a function that satisfies the condition f(x) = f(−x) for all x in its domain. Description Even functions are important in mathematics because they exhibit symmetry about the y-axis. This property is useful in various fields, including physics and engineering, where symmetry simplifies analysis and problem-solving. For example, the function f(x)=x2	Relations and Functions
Definition--Functions and Relations Concepts--Function	Function Topic Functions and Relations Definition A function is a relation that uniquely associates each element of a set with exactly one element of another set.	Relations and Functions
Definition--Functions and Relations Concepts--Function Machine	Function Machine Topic Functions and Relations Definition A function machine is a conceptual tool used to understand how functions work by visualizing inputs and outputs. Description The function machine is a useful educational tool that helps students grasp the concept of functions by visualizing the process of converting inputs into outputs. It emphasizes the idea that a function takes an input, processes it according to a specific rule, and produces an output. For example, if the function is f(x) = x + 2	Relations and Functions
Definition--Functions and Relations Concepts--Function Notation	Function Notation Topic Functions and Relations Definition Function notation is a way to represent functions in the form f(x), where f denotes the function and x denotes the input variable. Description Function notation is a standardized way to write functions, making it easier to understand and communicate mathematical relationships. It is widely used in algebra, calculus, and other branches of mathematics. For example, the notation f(x) = x2	Relations and Functions
Definition--Functions and Relations Concepts--Function Table	Function Table Topic Functions and Relations Definition A function table is a table that lists input values and their corresponding output values for a given function. Description Function tables are useful tools in mathematics for organizing and analyzing the relationship between inputs and outputs of a function. They help in visualizing how a function behaves and in identifying patterns. For example, a function table for f(x) = 2x + 1	Relations and Functions
Definition--Functions and Relations Concepts--Graphs of Functions	Graphs of Functions Topic Functions and Relations Definition Graphs of functions are visual representations of the relationship between input values and output values of a function. Description Graphs of functions are essential tools in mathematics for visualizing how a function behaves. They provide a clear picture of the relationship between the input and output values, making it easier to analyze and interpret the function. For example, the graph of f(x) = x2	Relations and Functions
Definition--Functions and Relations Concepts--Graphs of Relations	Graphs of Relations Topic Functions and Relations Definition Graphs of relations are visual representations of the relationship between two sets of values, not necessarily functions.	Relations and Functions
Definition--Functions and Relations Concepts--Increasing Function	Increasing Function Topic Functions and Relations Definition An increasing function is a function where the value of the function increases as the input increases.	Relations and Functions
Definition--Functions and Relations Concepts--Independent Variable	Independent Variable Topic Functions and Relations Definition An independent variable is a variable that represents the input or cause and is manipulated to observe its effect on the dependent variable.	Relations and Functions
Definition--Functions and Relations Concepts--Inverse Function	Inverse Function Topic Functions and Relations Definition An inverse function is a function that reverses the effect of the original function, such that f(f−1(x)) = x.	Functions and Their Inverses
Definition--Functions and Relations Concepts--Odd Function	Odd Function Topic Functions and Relations Definition An odd function is a function that satisfies the condition f(−x) = −f(x) for all x in its domain.	Relations and Functions
Definition--Functions and Relations Concepts--Parametric Equations	Parametric Equations Topic Functions and Relations Definition Parametric equations are a set of equations that express the coordinates of the points of a curve as functions of a variable called a parameter.	Relations and Functions
Definition--Functions and Relations Concepts--Piecewise Functions	Piecewise Functions Topic Functions and Relations Definition Piecewise functions are functions defined by multiple sub-functions, each applying to a certain interval of the domain.	Special Functions
Definition--Functions and Relations Concepts--Range of a Function	Range of a Function Topic Functions and Relations Definition The range of a function is the set of all possible output values (y-values) that the function can produce. Description Understanding the range of a function is crucial in mathematics because it defines the scope of possible outputs. The range is determined by the function's rule and the domain. For example, the range of the function f(x) = x2	Relations and Functions
Definition--Functions and Relations Concepts--Recursive Function	Recursive Function Topic Functions and Relations Definition A recursive function is a function that calls itself in its definition. Description Recursive functions are important in mathematics and computer science because they provide a way to solve problems by breaking them down into simpler sub-problems. They are defined by a base case and a recursive case. For example, the factorial function f(n) = n⋅f(n−1) with f(0)=1	Relations and Functions
Definition--Functions and Relations Concepts--Reflecting a Function	Reflecting a Function Topic Functions and Relations Definition Reflecting a function involves flipping the graph of the function over a specified axis. Description Reflecting functions is significant in mathematics because it helps in understanding the symmetry and transformations of functions. A function can be reflected over the x-axis or y-axis, changing its orientation. For example, reflecting the function f(x) = x2	Relations and Functions
Definition--Functions and Relations Concepts--Relation	Relation Topic Functions and Relations Definition A relation is a set of ordered pairs, where each element from one set is paired with an element from another set.	Relations and Functions
Definition--Functions and Relations Concepts--Step Function	Step Function Topic Functions and Relations Definition A step function is a function that increases or decreases abruptly at certain points, creating a series of steps.	Special Functions
Definition--Functions and Relations Concepts--Translating a Function	Translating a Function Topic Functions and Relations Definition Translating a function involves shifting the graph of the function horizontally, vertically, or both, without changing its shape. Description Translating functions is significant in mathematics because it helps in understanding how functions behave under shifts. A function can be translated horizontally by adding or subtracting a constant to the input, and vertically by adding or subtracting a constant to the output. For example, translating the function f(x) = x2 horizontally by 2 units results in	Relations and Functions
Definition--Functions and Relations Concepts--Vertical Line Test	Vertical Line Test Topic Functions and Relations Definition The vertical line test is a method used to determine if a graph represents a function by checking if any vertical line intersects the graph more than once. Description The vertical line test is important in mathematics because it helps in identifying whether a given graph represents a function. If a vertical line intersects the graph at more than one point, then the graph does not represent a function. This test is used in various fields, including computer science for validating functions in programming and in mathematics for analyzing graphs. For example, the graph of	Relations and Functions
Definition--Functions and Relations Concepts--Visual Models of Functions	Visual Models of Functions Topic Functions and Relations Definition Visual models of functions are graphical representations that illustrate the relationship between input and output values of functions. Description Visual models of functions are important in mathematics because they provide a clear and intuitive way to understand how functions behave. These models include graphs, tables, and diagrams that show the relationship between input and output values. For example, the graph of f(x) = x2	Relations and Functions
Definition--Functions and Relations Concepts--Visual Models of Relations	Visual Models of Relations Topic Functions and Relations Definition Visual models of relations are graphical representations that illustrate the relationship between two sets of values, not necessarily functions.	Relations and Functions
Definition--Functions and Relations Concepts--Visualization of the Dependent Variable	Visualization of the Dependent Variable Topic Functions and Relations Definition Visualization of the dependent variable involves graphically representing the outcomes or responses that depend on the independent variable.	Relations and Functions
Definition--Functions and Relations Concepts--Visualization of the Independent Variable	Visualization of the Independent Variable Topic Functions and Relations Definition Visualization of the independent variable involves graphically representing the variable that is manipulated to observe its effect on the dependent variable.	Relations and Functions
Definition--Linear Function Concepts--Constant Function	Constant Function Topic Linear Functions Definition A constant function is a linear function of the form f(x) = b, where b is a constant. The graph of a constant function is a horizontal line. Description Constant functions are a fundamental concept in linear functions. They represent scenarios where the output value remains unchanged, regardless of the input value. This is depicted graphically as a horizontal line, indicating that the function's rate of change is zero. In real-world applications, constant functions can model situations where a quantity remains steady over time. For example, a flat fee service charge that does not vary with usage can be represented as a constant function.	Slope-Intercept Form
Definition--Linear Function Concepts--Converting from Standard Form to Slope-Intercept Form	Converting from Standard Form to Slope-Intercept Form Topic Linear Functions Definition Converting from standard form to slope-intercept form involves rewriting a linear equation from the form Ax + By = C to the form y = mx + b, where m is the slope and b is the y-intercept. Description Converting linear equations from standard form to slope-intercept form is a key skill in algebra. This conversion allows for easier graphing and interpretation of the equation's slope and y-intercept.	Slope-Intercept Form