Illustrative Math Alignment: Grade 7 Unit 5
Rational Number Arithmetic
Lesson 4: Money and Debts
Use the following Media4Math resources with this Illustrative Math lesson.
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 15 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 15TopicRational Functions DescriptionThis math example illustrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (x + 1) + 1. The image presents both the table of x-y coordinates and the resulting graph. The table contains specific x-y coordinates: (-2, 2), (-1.5, 3), (0, 0), (1.5, 0.6), (2, 0.667), which are plotted on the graph. This example demonstrates how negating the numerator of a rational function and adding a constant affects its graph. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 16 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 16TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = -1 / (x + 1) - 1. The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The table contains specific x-y coordinates: (-2, 0), (-1.5, 1), (0, -2), (1.5, -1.4), (2, -1.333), which are plotted on the graph. This example illustrates how negating the numerator of a rational function and subtracting a constant affects its graph. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 17 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 17TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (-x + 1) + 1. The image showcases both the table of x-y coordinates and the resulting graph. Points plotted include (-2, 1.333), (-1.5, 1.4), (0, 2), (1.5, -1), and (2, 0). The graph features a hyperbola with asymptotes, illustrating how negating the x-term in the denominator and adding a constant affects the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 18 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 18TopicRational Functions DescriptionThis math example illustrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (-x + 1) - 1. The image presents both the table of x-y coordinates and the resulting graph. Points plotted include (-2, -0.667), (-1.5, -0.6), (0, 0), (1.5, -3), and (2, -2). The graph shows a hyperbola with vertical and horizontal shifts, demonstrating how negating the x-term in the denominator and subtracting a constant affects the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 19 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 19TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = 1 / (x - 1) + 1. The image provided shows both a table of x-y coordinates and the corresponding graph of the function. Points include (-2, 0.667), (-1.5, 0.6), (0, 0), (1.5, 3), and (2, 2). The graph is a hyperbola with asymptotes at x = 1 and y = 1, illustrating how subtracting a constant in the denominator and adding a constant to the entire fraction affects the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 2 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 2TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / x. The image showcases both the table of x-y coordinates and the resulting graph. The graph is a hyperbola with branches in the second and fourth quadrants, illustrating how the negative sign affects the function's shape compared to the previous example. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 20 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 20TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (x - 1) - 1. The image showcases both the table of x-y coordinates and the resulting graph. The table contains specific x-y coordinates: (-2, -1.333), (-1.5, -1.4), (0, -2), (1.5, 1), and (2, 0). The graph is a hyperbola with shifted asymptotes at x = 1 and y = -1, illustrating how subtracting a constant in the denominator and from the entire fraction affects the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 21 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 21TopicRational Functions DescriptionThis math example illustrates the creation of a table of x-y coordinates and the graphing of the function y = (-1) / (-x + 1) + 1. The image presents both the table of x-y coordinates and the resulting graph. It includes a table of x-y coordinates: (-2, 0.667), (-1.5, 0.6), (0, 0), (1.5, 3), and (2, 2). The graph is plotted on a grid, demonstrating how negating both the numerator and x-term in the denominator, while adding a constant to the entire fraction, affects the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 22 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 22TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = (-1) / (-x + 1) - 1. The image provided shows both a table of x-y coordinates and the corresponding graph of the function. It includes a table of x-y coordinates: (-2, -1.333), (-1.5, -1.4), (0, -2), (1.5, 1), and (2, 0). The graph is plotted on a grid, illustrating how negating both the numerator and x-term in the denominator, while subtracting a constant from the entire fraction, affects the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 23 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 23TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = (-1) / (x - 1) + 1. The image shows both a table of x-y coordinates and the corresponding graph. The table includes points such as (-2, 1.333), (-1.5, 1.4), (0, 2), (1.5, -1), and (2, 0). The graph is plotted on a grid, illustrating how subtracting a constant in the denominator and adding a constant to the entire fraction affects the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 24 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 24TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = (-1) / (x - 1) - 1. The image shows both a table of x-y coordinates and the corresponding graph. The table includes points such as (-2, -0.667), (-1.5, -0.6), (0, 0), (1.5, -3), and (2, -2). The graph is plotted on a grid, illustrating how subtracting constants both in the denominator and from the entire fraction affects the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 25 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 25TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (-x - 1) + 1. The image showcases both the table of x-y coordinates and the resulting graph. The graph shows points plotted at (-2, 2), (-1.5, 3), (0, 0), (1.5, 0.6), and (2, 0.667), illustrating how negating both terms inside the parentheses and adding a constant to the entire fraction affects the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 26 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 26TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = 1 / (-x - 1) - 1. The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The graph shows points plotted at (-2, 0), (-1.5, 1), (0, -2), (1.5, -1.4), and (2, -1.333), illustrating how negating both terms inside the parentheses and subtracting a constant from the entire fraction affects the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 27 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 27TopicRational Functions DescriptionThis math example illustrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (-x - 1) + 1. The image presents both the table of x-y coordinates and the resulting graph. The graph shows points plotted at (-2, 0), (-1.5, -1), (0, 2), (1.5, 1.4), and (2, 1.333), demonstrating how negating both the numerator and the terms inside the parentheses, while adding a constant to the entire fraction, affects the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 28 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 28TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (-x - 1) - 1. The image showcases both the table of x-y coordinates and the resulting graph. The graph shows points plotted at (-2, -2), (-1.5, -3), (0, 0), (1.5, -0.6), and (2, -0.667), illustrating how negating both the numerator and the terms inside the parentheses, while subtracting a constant from the entire fraction, affects the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 3 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 3TopicRational Functions DescriptionThis math example illustrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (-x). The image presents both the table of x-y coordinates and the resulting graph. Interestingly, the graph is identical to that of y = -1 / x, showing a hyperbola with branches in the second and fourth quadrants. This example demonstrates how different forms of rational functions can produce the same graph. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 4 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 4TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (-x). The image showcases both the table of x-y coordinates and the resulting graph. Notably, the graph is identical to that of y = 1 / x, displaying a hyperbola with branches in the first and third quadrants. This example further illustrates how different forms of rational functions can produce the same graph. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 5 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 5TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = 1 / (x + 1). The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The graph is a hyperbola with points marked at specific coordinates, illustrating how the addition of a constant in the denominator affects the graph's position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 6 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 6TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (x + 1). The image showcases both the table of x-y coordinates and the resulting graph. The graph displays a hyperbola with labeled points on the curve, illustrating how the negative sign in the numerator and the constant in the denominator affect the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 7 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 7TopicRational Functions DescriptionThis math example focuses on creating a table of x-y coordinates and graphing the function y = 1 / (-x + 1). The image provided shows both a table of x-y coordinates and the corresponding graph of the function. The graph is a hyperbola with specific points highlighted, illustrating how the negative sign and constant in the denominator affect the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 8 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 8TopicRational Functions DescriptionThis math example demonstrates the creation of a table of x-y coordinates and the graphing of the function y = 1 / (x - 1). The image showcases both the table of x-y coordinates and the resulting graph. The graph features a hyperbola with marked points on its curve, illustrating how the constant in the denominator affects the graph's position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 9 | Math Example--Rational Concepts--Rational Functions in Tabular and Graph Form: Example 9TopicRational Functions DescriptionThis math example illustrates the creation of a table of x-y coordinates and the graphing of the function y = -1 / (-x + 1). The image presents both the table of x-y coordinates and the resulting graph. The graph is plotted with points labeled at specific coordinates, demonstrating how the negative signs in both the numerator and denominator affect the graph's shape and position. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Rational vs Irrational--Example 1 | Math Example--Rational Concepts--Rational vs Irrational--Example 1
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Rational Expressions |
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Math Example--Rational Concepts--Rational vs Irrational--Example 10 | Math Example--Rational Concepts--Rational vs Irrational--Example 10
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Rational Expressions |
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Math Example--Rational Concepts--Rational vs Irrational--Example 2 | Math Example--Rational Concepts--Rational vs Irrational--Example 2
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Rational Expressions |
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Math Example--Rational Concepts--Rational vs Irrational--Example 3 | Math Example--Rational Concepts--Rational vs Irrational--Example 3
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Rational Expressions |
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Math Example--Rational Concepts--Rational vs Irrational--Example 4 | Math Example--Rational Concepts--Rational vs Irrational--Example 4
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Rational Expressions |
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Math Example--Rational Concepts--Rational vs Irrational--Example 5 | Math Example--Rational Concepts--Rational vs Irrational--Example 5
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Rational Expressions |
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Math Example--Rational Concepts--Rational vs Irrational--Example 6 | Math Example--Rational Concepts--Rational vs Irrational--Example 6
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Rational Expressions |
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Math Example--Rational Concepts--Rational vs Irrational--Example 7 | Math Example--Rational Concepts--Rational vs Irrational--Example 7
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Rational Expressions |
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Math Example--Rational Concepts--Rational vs Irrational--Example 8 | Math Example--Rational Concepts--Rational vs Irrational--Example 8
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Rational Expressions |
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Math Example--Rational Concepts--Rational vs Irrational--Example 9 | Math Example--Rational Concepts--Rational vs Irrational--Example 9
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Rational Expressions |
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Math Example--Solving Equations--Extraneous Or No Solutions--Example 1 | Extraneous Or No Solutions--Example 1TopicEquations |
Radical Functions and Equations and Rational Functions and Equations |
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Math Example--Solving Equations--Extraneous Or No Solutions--Example 2 | Extraneous Or No Solutions--Example 2TopicEquations |
Radical Functions and Equations and Rational Functions and Equations |
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Math Example--Solving Equations--Extraneous Or No Solutions--Example 3 | Extraneous Or No Solutions--Example 3TopicEquations |
Radical Functions and Equations and Rational Functions and Equations |
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Math Example--Solving Equations--Extraneous Or No Solutions--Example 4 | Extraneous Or No Solutions--Example 4TopicEquations |
Radical Functions and Equations and Rational Functions and Equations |
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Math Example--Solving Equations--Extraneous Or No Solutions--Example 5 | Extraneous Or No Solutions--Example 5TopicEquations |
Radical Functions and Equations and Rational Functions and Equations |
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Math Example--Solving Equations--Extraneous Or No Solutions--Example 6 | Extraneous Or No Solutions--Example 6TopicEquations |
Radical Functions and Equations and Rational Functions and Equations |
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MATH EXAMPLES--Teacher's Guide: Graphs of Rational Functions | MATH EXAMPLES--Teacher's Guide: Graphs of Rational Functions
This Teacher's Guide provides an overview of the 28 worked-out examples that show how to graph Rational Functions. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Rational Functions and Equations |
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MATH EXAMPLES--Teacher's Guide: Rational Expressions | MATH EXAMPLES--Teacher's Guide: Rational Expressions
This Teacher's Guide provides an overview of the 28 worked-out examples that show how to simplify a variety of rational expressions. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Rational Expressions and Rational Functions and Equations |
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Math in the News: Issue 97--The Washington Monument: Repaired | Math in the News: Issue 97--The Washington Monument: Repaired
July 2015. This Math in the News explores the construction of the iconic landmark the Washington Monument and its recent renovations due to the 2011 earthquake. Students will be able to convert dollar values based on inflation and determine the combined expense of the Washington Monument between construction and recent renovations. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Numerical Expressions and Variable Expressions |
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Math in the News: Issue 99--What Is Bitcoin? | Math in the News: Issue 99--What Is Bitcoin?
May 2014. In this issue of Math in the News we explore Bitcoin. We look at how it's used for making purchases and how it differs from other currencies. This provides an opportunity to apply the concept of currency exchange. This is part of the Math in the News collection. To see the complete collection, click on this link. Note: The download is a PPT file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of Ratios, Proportions, and Percents and Proportions |
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MathClipArt--EU Currency--10 Euros | MathClipArt--EU Currency--10 Euros
This is part of a collection of math clip art images that show different currencies. |
Money |
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MathClipArt--EU Currency--100 Euros | MathClipArt--EU Currency--100 Euros
This is part of a collection of math clip art images that show different currencies. |
Money |
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MathClipArt--EU Currency--20 Euros | MathClipArt--EU Currency--20 Euros
This is part of a collection of math clip art images that show different currencies. |
Money |
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MathClipArt--EU Currency--5 Euros | MathClipArt--EU Currency--5 Euros
This is part of a collection of math clip art images that show different currencies. |
Money |
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MathClipArt--EU Currency--50 Euros | MathClipArt--EU Currency--50 Euros
This is part of a collection of math clip art images that show different currencies. |
Money |
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MathClipArt--US Currency-- Dollar Back | MathClipArt--US Currency-- Dollar Back
This is part of a collection of math clip art images that show different currencies. |
Money |
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MathClipArt--US Currency-- Dollar Front | MathClipArt--US Currency-- Dollar Front
This is part of a collection of math clip art images that show different currencies. |
Money |
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MathClipArt--US Currency--Fifty Dollar Back | MathClipArt--US Currency--Fifty Dollar Back
This is part of a collection of math clip art images that show different currencies. |
Money |
