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.

Title	Body	Curriculum Nodes
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 3 Topic Rational Functions Description This 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
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 4 Topic Rational Functions Description This 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
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 5 Topic Rational Functions Description This 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
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 6 Topic Rational Functions Description This 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
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 7 Topic Rational Functions Description This 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
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 8 Topic Rational Functions Description This 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
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 9 Topic Rational Functions Description This 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
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
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
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
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
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
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
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
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
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
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
Math Example--Solving Equations--Extraneous Or No Solutions--Example 1	Extraneous Or No Solutions--Example 1 Topic Equations	Radical Functions and Equations and Rational Functions and Equations
Math Example--Solving Equations--Extraneous Or No Solutions--Example 2	Extraneous Or No Solutions--Example 2 Topic Equations	Radical Functions and Equations and Rational Functions and Equations
Math Example--Solving Equations--Extraneous Or No Solutions--Example 3	Extraneous Or No Solutions--Example 3 Topic Equations	Radical Functions and Equations and Rational Functions and Equations
Math Example--Solving Equations--Extraneous Or No Solutions--Example 4	Extraneous Or No Solutions--Example 4 Topic Equations	Radical Functions and Equations and Rational Functions and Equations
Math Example--Solving Equations--Extraneous Or No Solutions--Example 5	Extraneous Or No Solutions--Example 5 Topic Equations	Radical Functions and Equations and Rational Functions and Equations
Math Example--Solving Equations--Extraneous Or No Solutions--Example 6	Extraneous Or No Solutions--Example 6 Topic Equations	Radical Functions and Equations and Rational Functions and Equations
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 Resources To see resources related to this topic click on the Related Resources tab above.	Rational Functions and Equations
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 Resources To see resources related to this topic click on the Related Resources tab above.	Rational Expressions and Rational Functions and Equations
Promethean Flipchart: Algebra Applications: Biology	All living things take up a certain amount of space, and therefore have volume. They also have a certain amount of surface area. The ratio of surface area to volume, which is a rational function, reveals important information about the organism. Students look at different graphs of these functions for different organisms. Note: The download for this resources is the Promethean Flipchart. To view the full video [Algebra Applications: Rational Functions, Segment 2: Biology]: https://www.media4math.com/library/algebra-applications-rational-functions-segment-2-biology	Rational Functions and Equations
Promethean Flipchart: Algebra Applications: Hubble	The Hubble Telescope, like all telescopes, relies on the lens formula to focus an image. The lens formula results in a rational equation that can be solved for determining the settings on the lens. Note: The download for this resources is the Promethean Flipchart. To access the full video [Algebra Applications: Rational Functions, Segment 3: Hubble Telescope]: https://www.media4math.com/library/algebra-applications-rational-functions-segment-3-hubble-telescope	Rational Functions and Equations
Promethean Flipchart: Algebra Applications: Submarines	In spite of their massive size, submarines are precision instruments. A submarine must withstand large amounts of water pressure; otherwise, a serious breach can occur. Rational functions are used to study the relationship between water pressure and volume. Students graph rational functions to study the forces at work with a submarine. Note: The download for this resources is the Promethean Flipchart. To access the full video [Algebra Applications: Rational Functions, Segment 1: Submarines]: https://www.media4math.com/library/algebra-applications-rational-functions-segment-1-submarines	Rational Functions and Equations
Promethean Flipchart: Algebra Nspirations: Rational Functions	After briefly reviewing the concept of inverse variation, this video explores Boyle’s law, a real world example of an inversely proportional relationship between pressure and volume of a gas. Written and hosted by internationally acclaimed math educator Dr. Monica Neagoy, it goes on to examine similarities and differences among rational functions and numbers. Finally, it takes a look at rational functions graphs and ends with a delightful example merging Euclidean and analytic geometry, thanks to the TI-Nspire technology. Concepts explored: functions, rational expressions, rational functions, asymptotes Note: The download for this resources is the Promethean Flipchart. To access the full video [Algebra Nspirations: Rational Functions and Expressions]: https://media4math.com/library/algebra-nspirations-rational-functions-and-expressions	Rational Functions and Equations
Quizlet Flash Cards: Adding Rational Numbers, Set 01	Description Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Numerical Expressions
Quizlet Flash Cards: Adding Rational Numbers, Set 02	Description Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Numerical Expressions
Quizlet Flash Cards: Adding Rational Numbers, Set 03	Description Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Numerical Expressions
Quizlet Flash Cards: Adding Rational Numbers, Set 04	Description Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Numerical Expressions
Quizlet Flash Cards: Adding Rational Numbers, Set 05	Description Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Numerical Expressions
Quizlet Flash Cards: Adding Rational Numbers, Set 06	Description Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Numerical Expressions
Quizlet Flash Cards: Adding Rational Numbers, Set 07	Description Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Numerical Expressions
Quizlet Flash Cards: Adding Rational Numbers, Set 08	Description Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Numerical Expressions
Quizlet Flash Cards: Adding Rational Numbers, Set 09	Description Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Numerical Expressions
Quizlet Flash Cards: Adding Rational Numbers, Set 10	Description Add rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see other resources related to this topic, click on the Resources tab above. Quizlet Library To see the complete Quizlet Flash Card Library, click on this Link to see the collection.	Numerical Expressions
Quizlet Flash Cards: Subtracting Rational Numbers, Set 01	Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq	Subtract Multiple-Digit Numbers
Quizlet Flash Cards: Subtracting Rational Numbers, Set 02	Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq	Subtract Multiple-Digit Numbers
Quizlet Flash Cards: Subtracting Rational Numbers, Set 03	Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq	Subtract Multiple-Digit Numbers
Quizlet Flash Cards: Subtracting Rational Numbers, Set 04	Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq	Subtract Multiple-Digit Numbers
Quizlet Flash Cards: Subtracting Rational Numbers, Set 05	Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq	Subtract Multiple-Digit Numbers
Quizlet Flash Cards: Subtracting Rational Numbers, Set 06	Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq	Subtract Multiple-Digit Numbers
Quizlet Flash Cards: Subtracting Rational Numbers, Set 07	Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq	Subtract Multiple-Digit Numbers
Quizlet Flash Cards: Subtracting Rational Numbers, Set 08	Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq	Subtract Multiple-Digit Numbers
Quizlet Flash Cards: Subtracting Rational Numbers, Set 09	Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq	Subtract Multiple-Digit Numbers
Quizlet Flash Cards: Subtracting Rational Numbers, Set 10	Subtract rational numbers in this 20-flash card set. The values of the numerators and denominators are in the range -10 to 10. Note: The download is the teacher's guide for using Media4Math's Quizlet Flash Cards. Related Resources To see the complete collection of Quizlet Flash Cards on this topic, click on this link: https://bit.ly/3gT8TIq	Subtract Multiple-Digit Numbers
Video Definition 1--Rationals and Radicals--Addition of Rational Expressions	Video Definition 1--Rationals and Radicals--Addition of Rational Expressions This is part of a collection of math video definitions related to the topics of rationals and radicals. Note: The download is an MP4 video.	Rational Functions and Equations