Illustrative Math Alignment: Grade 6 Unit 7
Rational Numbers
Lesson 5: Using Negative Numbers to Make Sense of Contexts
Use the following Media4Math resources with this Illustrative Math lesson.
| Thumbnail Image | Title | Body | Curriculum Nodes |
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Math Example--Exponential Concepts--Integer and Rational Exponents--Example 9 | Math Example--Exponential Concepts--Integer and Rational Exponents--Example 9TopicExponents DescriptionShows Example 9 with the expression (-1)2•43. The solution explains simplifying each term individually before multiplying. Example 9: Simplify (-1)2•43. Evaluate each exponential term separately, then multiply: 1•64 = 64. |
Numerical Expressions |
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Math Example--Graphical Solutions to Rational Equations--Example 1 | This is part of a collection of math examples that show how to use graphical techniques to solve rational equations.
Note: The download is an image file.
Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Create a Slide ShowSubscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link:AccessibilityThis resource can also be used with a screen reader. |
Rational Functions and Equations |
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Math Example--Graphical Solutions to Rational Equations--Example 10 | This is part of a collection of math examples that show how to use graphical techniques to solve rational equations.
Note: The download is an image file.
Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Create a Slide ShowSubscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link:AccessibilityThis resource can also be used with a screen reader. |
Rational Functions and Equations |
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Math Example--Graphical Solutions to Rational Equations--Example 2 | This is part of a collection of math examples that show how to use graphical techniques to solve rational equations.
Note: The download is an image file.
Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Create a Slide ShowSubscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link:AccessibilityThis resource can also be used with a screen reader. |
Rational Functions and Equations |
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Math Example--Graphical Solutions to Rational Equations--Example 3 | This is part of a collection of math examples that show how to use graphical techniques to solve rational equations.
Note: The download is an image file.
Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Create a Slide ShowSubscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link:AccessibilityThis resource can also be used with a screen reader. |
Rational Functions and Equations |
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Math Example--Graphical Solutions to Rational Equations--Example 4 | This is part of a collection of math examples that show how to use graphical techniques to solve rational equations.
Note: The download is an image file.
Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Create a Slide ShowSubscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link:AccessibilityThis resource can also be used with a screen reader. |
Rational Functions and Equations |
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Math Example--Graphical Solutions to Rational Equations--Example 5 | This is part of a collection of math examples that show how to use graphical techniques to solve rational equations.
Note: The download is an image file.
Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Create a Slide ShowSubscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link:AccessibilityThis resource can also be used with a screen reader. |
Rational Functions and Equations |
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Math Example--Graphical Solutions to Rational Equations--Example 6 | This is part of a collection of math examples that show how to use graphical techniques to solve rational equations.
Note: The download is an image file.
Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Create a Slide ShowSubscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link:AccessibilityThis resource can also be used with a screen reader. |
Rational Functions and Equations |
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Math Example--Graphical Solutions to Rational Equations--Example 7 | This is part of a collection of math examples that show how to use graphical techniques to solve rational equations.
Note: The download is an image file.
Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Create a Slide ShowSubscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link:AccessibilityThis resource can also be used with a screen reader. |
Rational Functions and Equations |
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Math Example--Graphical Solutions to Rational Equations--Example 8 | This is part of a collection of math examples that show how to use graphical techniques to solve rational equations.
Note: The download is an image file.
Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Create a Slide ShowSubscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link:AccessibilityThis resource can also be used with a screen reader. |
Rational Functions and Equations |
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Math Example--Graphical Solutions to Rational Equations--Example 9 | This is part of a collection of math examples that show how to use graphical techniques to solve rational equations.
Note: The download is an image file.
Related ResourcesTo see additional resources on this topic, click on the Related Resources tab.Create a Slide ShowSubscribers can use Slide Show Creator to create a slide show from the complete collection of math examples on this topic. To see the complete clip art collection, click on this Link. To learn more about Slide Show Creator, click on this Link:AccessibilityThis resource can also be used with a screen reader. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 1 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 1
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 10 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 10
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 2 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 2
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 3 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 3
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 4 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 4
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 5 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 5
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 6 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 6
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 7 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 7
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 8 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 8
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 9 | Math Example--Rational Concepts--Comparing and Ordering Integers and Rational Numbers--Example 9
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 1 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 1
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 10 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 10
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 2 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 2
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 3 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 3
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 4 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 4
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 5 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 5
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 6 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 6
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 7 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 7
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 8 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 8
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 9 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers on a Coordinate Grid--Example 9
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 1 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 1
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 10 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 10
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 2 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 2
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 3 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 3
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 4 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 4
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 5 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 5
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 6 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 6
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 7 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 7
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 8 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 8
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 9 | Math Example--Rational Concepts--Graphing Integers and Rational Numbers--Example 9
This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions. |
Numerical Expressions |
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Math Example--Rational Concepts--Graphs of Rational Functions: Example 1 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 1TopicRational Functions DescriptionThis example demonstrates the graph of the rational function y = 1 / x. The graph is a hyperbola with vertical and horizontal asymptotes, with the vertical asymptote occurring at x = 0. Students are tasked with graphing the function and determining its vertical asymptote. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Graphs of Rational Functions: Example 10 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 10TopicRational Functions DescriptionThis example showcases the graph of the rational function y = (x - 5) / (x + 4). The graph features a vertical asymptote at x = -4 and displays two branches, one in the first quadrant and one in the third quadrant. Students are asked to graph the function and identify its vertical asymptote. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Graphs of Rational Functions: Example 11 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 11TopicRational Functions DescriptionThis example showcases the graph of the rational function y = (x - 1) / (x - 3). The graph features a vertical asymptote at x = 3 and displays two distinct branches, one in the first quadrant and another in the third quadrant. Students are tasked with graphing the function and identifying its vertical asymptote. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Graphs of Rational Functions: Example 12 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 12TopicRational Functions DescriptionThis example illustrates the graph of the rational function y = (x + 1) / ((x + 2)(x + 4)). The graph features two vertical asymptotes at x = -2 and x = -4, and displays three distinct branches, with one in each of the first, second, and third quadrants. Students are asked to graph the function and identify its vertical asymptotes. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Graphs of Rational Functions: Example 13 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 13TopicRational Functions DescriptionThis example presents the graph of the rational function y = (x - 3) / ((x + 3)(x + 5)). The graph features vertical asymptotes at x = -3 and x = -5, illustrating how the function behaves near these lines. Students are tasked with graphing the function and determining its vertical asymptotes. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Graphs of Rational Functions: Example 14 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 14TopicRational Functions DescriptionThis example illustrates the graph of the rational function y = (x + 3) / ((x - 1)(x + 4)). The graph features vertical asymptotes at x = -4 and x = 1, displaying how the function behaves near these lines. Students are asked to graph the function and identify its vertical asymptotes. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Graphs of Rational Functions: Example 15 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 15TopicRational Functions DescriptionThis example showcases the graph of the rational function y = (x + 4) / ((x + 2)(x - 5)). The graph features vertical asymptotes at x = -2 and x = 5, demonstrating the behavior of the function near these asymptotes. Students are tasked with graphing the function and determining its vertical asymptotes. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Graphs of Rational Functions: Example 16 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 16TopicRational Functions DescriptionThis example illustrates the graph of the rational function y = (x - 9) / ((x - 1)(x + 3)). The graph features vertical asymptotes at x = -3 and x = 1, showing the function's behavior around these asymptotes. Students are asked to graph the function and identify its vertical asymptotes. |
Rational Functions and Equations |
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Math Example--Rational Concepts--Graphs of Rational Functions: Example 17 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 17TopicRational Functions DescriptionThis example presents the graph of the rational function y = (x - 1) / ((x - 2)(x - 3)). The graph features vertical asymptotes at x = 2 and x = 3, marked with dashed red lines. Students are tasked with graphing the function and determining its vertical asymptotes. |
Rational Functions and Equations |
