Illustrative Math Alignment: Grade 7 Unit 5
Rational Number Arithmetic
Lesson 3: Changing Elevation
Use the following Media4Math resources with this Illustrative Math lesson.
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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 |
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Math Example--Rational Concepts--Graphs of Rational Functions: Example 18 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 18TopicRational Functions DescriptionThis example illustrates the graph of the rational function y = (x - 8) / ((x + 3)(x - 3)). The graph features vertical asymptotes at x = -3 and x = 3, highlighted by dashed red 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 19 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 19TopicRational Functions DescriptionThis example presents the graph of the rational function y = -(x + 1) / (x + 2). The graph features a single vertical asymptote at x = -2, indicated by a dashed red line. 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 2 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 2TopicRational Functions DescriptionThis example illustrates the graph of the rational function y = -1 / x. The graph is a hyperbola with vertical and horizontal asymptotes, with the vertical asymptote at x = 0. 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 20 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 20TopicRational Functions DescriptionThis example showcases the graph of the rational function y = -(x - 3) / (x + 4). The graph features a vertical asymptote at x = -4, but it is incorrectly labeled as x = -2. 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 21 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 21TopicRational Functions DescriptionThis example illustrates the graph of the rational function y = -(x - 5) / (x - 4). The graph features a vertical asymptote at x = 4, which is correctly labeled. 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 22 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 22TopicRational Functions DescriptionThis example presents the graph of the rational function y = -(x + 2) / ((x + 4)(x + 1)). The graph features vertical asymptotes at x = -4 and x = -1. 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 23 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 23TopicRational Functions DescriptionThis example illustrates the graph of the rational function y = -(x - 4) / ((x + 5)(x + 2)). The graph features vertical asymptotes at x = -5 and x = -2. 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 24 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 24TopicRational Functions DescriptionThis example showcases the graph of the rational function y = -(x + 2) / ((x - 3)(x + 7)). The graph features vertical asymptotes at x = -7 and x = 3. 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 25 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 25TopicRational Functions DescriptionThis example illustrates the graph of the rational function y = -(x + 1) / ((x + 2)(x - 8)). The graph features vertical asymptotes at x = -2 and x = 8. 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 26 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 26TopicRational Functions DescriptionThis example showcases the graph of the rational function y = -(x - 4) / ((x - 3)(x + 2)). The graph features vertical asymptotes at x = -2 and x = 3. 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 27 | Math Example--Rational Concepts--Graphs of Rational Functions: Example 27TopicRational Functions DescriptionThis example presents the graph of the rational function y = -(x - 3) / ((x + 3)(x - 1)). The graph features vertical asymptotes at x = -3 and x = 1. Students are tasked with graphing the function and determining its vertical asymptotes. |
Rational Functions and Equations |
