Illustrative Math Alignment: Grade 6 Unit 7

Rational Numbers

Lesson 16: Common Factors

Use the following Media4Math resources with this Illustrative Math lesson.

Title	Body	Curriculum Nodes
Math Example--Quadratics--Graphs of Quadratic Functions in Factored Form--Example 2	Graphs of Quadratic Functions in Factored Form--Example 2 Topic Quadratics Description In this example, the quadratic function is presented in factored form, highlighting its roots and facilitating the graphing process. Unlike the standard form, the factored form provides immediate insight into the x-intercepts of the graph, allowing for a quick and accurate sketch of the parabola. This form is particularly useful for visualizing the solutions of the equation and understanding the function's behavior.	Graphs of Quadratic Functions
Math Example--Quadratics--Graphs of Quadratic Functions in Factored Form--Example 3	Graphs of Quadratic Functions in Factored Form--Example 3 Topic Quadratics Description This example demonstrates the graphing of a quadratic function in factored form. The factored form is advantageous because it clearly indicates where the graph will intersect the x-axis, making it easier to plot the parabola accurately. This form simplifies the process of identifying the roots and understanding the quadratic's graphical representation.	Graphs of Quadratic Functions
Math Example--Quadratics--Graphs of Quadratic Functions in Factored Form--Example 4	Graphs of Quadratic Functions in Factored Form--Example 4 Topic Quadratics Description The factored form of this quadratic function allows for easy identification of the roots, which are the x-intercepts of the graph. This form is different from the standard form in that it directly provides the points where the parabola crosses the x-axis, simplifying the graphing process. This example illustrates how the factored form can be used to quickly and effectively graph a quadratic function.	Graphs of Quadratic Functions
Math Example--Quadratics--Graphs of Quadratic Functions in Factored Form--Example 5	Graphs of Quadratic Functions in Factored Form--Example 5 Topic Quadratics Description This example highlights the advantages of using the factored form for graphing quadratic functions. The factored form makes it straightforward to determine the roots, which are the x-intercepts of the graph. This simplifies the process of plotting the parabola and understanding the function's behavior, as the roots are immediately visible and can be used to sketch the graph accurately.	Graphs of Quadratic Functions
Math Example--Quadratics--Graphs of Quadratic Functions in Factored Form--Example 6	Graphs of Quadratic Functions in Factored Form--Example 6 Topic Quadratics Description The factored form of a quadratic function provides a clear and efficient way to graph the function by identifying the roots directly. This example shows how the factored form differs from the standard form by offering immediate insight into the x-intercepts, simplifying the graphing process and enhancing understanding of the function's graphical representation.	Graphs of Quadratic Functions
Math Example--Quadratics--Graphs of Quadratic Functions in Factored Form--Example 7	Graphs of Quadratic Functions in Factored Form--Example 7 Topic Quadratics Description In this example, the quadratic function is expressed in factored form, which simplifies the process of graphing by providing the roots directly. This form contrasts with the standard form, where additional calculations are needed to find the roots. The factored form allows for a more straightforward and intuitive graphing process, as it clearly indicates the x-intercepts of the parabola.	Graphs of Quadratic Functions
Math Example--Quadratics--Graphs of Quadratic Functions in Factored Form--Example 8	Graphs of Quadratic Functions in Factored Form--Example 8 Topic Quadratics Description This example illustrates the benefits of using the factored form for graphing quadratic functions. The factored form provides immediate information about the roots, making it easier to sketch the parabola by pinpointing the x-intercepts. This form is a simpler alternative to the standard form when graphing, as it eliminates the need for additional calculations to determine the roots.	Graphs of Quadratic Functions
Math Example--Quadratics--Solving Quadratics by Factoring--Example 1	Solving Quadratics by Factoring--Example 1 Topic Quadratics Description Factoring is a technique used to solve quadratic equations by expressing them as a product of binomials. Once in factored form, finding the roots of the quadratic becomes straightforward as it involves setting each binomial equal to zero. In this example, the quadratic equation is factored into two binomials, allowing for easy identification of the roots. The graphic illustrates the step-by-step process of factoring and solving, highlighting the efficiency of this method for certain types of quadratic equations.	Quadratic Equations and Functions
Math Example--Quadratics--Solving Quadratics by Factoring--Example 2	Solving Quadratics by Factoring--Example 2 Topic Quadratics Description This example demonstrates solving a quadratic equation by factoring. The equation is rewritten as a product of binomials, simplifying the process of finding the roots. The graphic shows how each binomial is set to zero to find the solutions, illustrating the straightforward nature of this method when applicable. For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection.	Quadratic Equations and Functions
Math Example--Quadratics--Solving Quadratics by Factoring--Example 3	Solving Quadratics by Factoring--Example 3 Topic Quadratics Description In this example, the quadratic equation is solved by factoring, which involves expressing the equation as a product of binomials. The process makes it easy to find the roots by setting each factor equal to zero. The graphic provides a detailed walkthrough of the factoring steps, showcasing the simplicity and effectiveness of this approach for solving quadratics. For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection.	Quadratic Equations and Functions
Math Example--Quadratics--Solving Quadratics by Factoring--Example 4	Solving Quadratics by Factoring--Example 4 Topic Quadratics Description This example illustrates the process of solving a quadratic equation by factoring. The equation is factored into binomials, and the roots are found by setting each binomial to zero. The graphic highlights the steps involved in factoring and solving, emphasizing the method's efficiency for certain quadratic equations. For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection.	Quadratic Equations and Functions
Math Example--Quadratics--Solving Quadratics by Factoring--Example 5	Solving Quadratics by Factoring--Example 5 Topic Quadratics Description In this example, the quadratic equation is solved by factoring, a method that involves rewriting the equation as a product of binomials. This approach simplifies finding the roots, as each binomial is set to zero to solve for the variable. The graphic provides a step-by-step guide to the factoring process, demonstrating its practicality and ease of use. For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection.	Quadratic Equations and Functions
Math Example--Quadratics--Solving Quadratics by Factoring--Example 6	Solving Quadratics by Factoring--Example 6 Topic Quadratics Description This example demonstrates solving a quadratic equation by factoring. The equation is expressed as a product of binomials, allowing for straightforward determination of the roots by setting each factor to zero. The graphic illustrates the factoring process, highlighting its effectiveness for solving quadratic equations. For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection.	Quadratic Equations and Functions
Math Example--Quadratics--Solving Quadratics by Factoring--Example 7	Solving Quadratics by Factoring--Example 7 Topic Quadratics Description In this example, the quadratic equation is solved by factoring, which involves expressing it as a product of binomials. This method simplifies finding the roots, as each binomial is set to zero. The graphic provides a clear demonstration of the factoring process, showcasing its simplicity and utility in solving quadratic equations. For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection.	Quadratic Equations and Functions
Math Example--Quadratics--Solving Quadratics by Factoring--Example 8	Solving Quadratics by Factoring--Example 8 Topic Quadratics Description This example illustrates solving a quadratic equation by factoring. The equation is rewritten as a product of binomials, and the roots are found by setting each factor to zero. The graphic highlights the steps involved in factoring and solving, emphasizing the method's efficiency and applicability to certain quadratic equations. For a complete collection of math examples related to Quadratics click on this link: Math Examples: Quadratics Collection.	Quadratic Equations and Functions
MATH EXAMPLES--Teacher's Guide: Factoring Quadratics	MATH EXAMPLES--Teacher's Guide: Factoring Quadratics This Teacher's Guide provides an overview of the 11 worked-out examples that show how to factor quadratic 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.	Polynomial Expressions
Math Video Definition 20--Multiplication and Division Concepts--Factor	Math Video Definition 20--Multiplication and Division Concepts--Factor This is part of a collection of math video definitions related to the topics of Multiplication and Division, ideal for use in an early elementary classroom. Note: The download is an MP4 video.	Multiplication Expressions and Equations
Math Video Definition 22--Multiplication and Division Concepts--Greatest Common Factor (GCF)	Math Video Definition 22--Multiplication and Division Concepts--Greatest Common Factor (GCF) This is part of a collection of math video definitions related to the topics of Multiplication and Division, ideal for use in an early elementary classroom. Note: The download is an MP4 video.	Multiplication Expressions and Equations
Math Video Definition 44--Multiplication and Division Concepts--Prime Factorization	Math Video Definition 44--Multiplication and Division Concepts--Prime Factorization This is part of a collection of math video definitions related to the topics of Multiplication and Division, ideal for use in an early elementary classroom. Note: The download is an MP4 video.	Multiplication Expressions and Equations
Paper-and-Pencil Quiz: Factoring Quadratics (Easy)	Paper-and-Pencil Quiz: Factoring Quadratics (Easy) This is part of a collection of math quizzes on the topic of Factoring Quadratics. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Factoring Quadratics
Paper-and-Pencil Quiz: Factoring Quadratics (Hard)	Paper-and-Pencil Quiz: Factoring Quadratics (Hard) This is part of a collection of math quizzes on the topic of Factoring Quadratics. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Factoring Quadratics
Paper-and-Pencil Quiz: Factoring Quadratics (Medium)	Paper-and-Pencil Quiz: Factoring Quadratics (Medium) This is part of a collection of math quizzes on the topic of Factoring Quadratics. To see the complete quiz collection on this topic, click on this link. Note: The download is the PDF version of the quiz (with answer key). Related Resources To see additional resources on this topic, click on the Related Resources tab. Quiz Library To see the complete collection of Quizzes, click on this link. ary">click on this link.	Factoring Quadratics
Quizlet Flash Card Set: Factoring Polynomials	Description In this set of interactive flash cards students practice factoring quadratic polynomials. 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.	Factoring Polynomials
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 01	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 01	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 02	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 02	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 03	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 03	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 04	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 04	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 05	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 05	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 06	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 06	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 07	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 07	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 08	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 08	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 09	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 09	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 10	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Quizlet Flash Cards: Solving Quadratic Equations by Factoring, Set 10	Solve quadratic equations by factoring in this 20-flash card set. The values of the quadratic equation terms 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/3cwZzXj	Factoring Quadratics and Quadratic Equations and Functions
Video Definition 11--Polynomial Concepts--Factored Polynomial	Video Definition 11--Polynomial Concepts--Factored Polynomial This is part of a collection of math video definitions related to to the topic of polynomials. Note: The download is an MP4 video.	Factoring Polynomials
Video Definition 11--Polynomial Concepts--Factored Polynomial (Spanish Audio)	Video Definition 11--Polynomial Concepts--Factored Polynomial (Spanish Audio) This is part of a collection of math video definitions related to to the topic of polynomials. Note: The download is an MP4 video.	Factoring Polynomials
Video Definition 12--Polynomial Concepts--Factored Quadratic	Video Definition 12--Polynomial Concepts--Factored Quadratic This is part of a collection of math video definitions related to to the topic of polynomials. Note: The download is an MP4 video.	Factoring Polynomials
Video Definition 12--Polynomial Concepts--Factored Quadratic (Spanish Audio)	Video Definition 12--Polynomial Concepts--Factored Quadratic (Spanish Audio) This is part of a collection of math video definitions related to to the topic of polynomials. Note: The download is an MP4 video.	Factoring Polynomials
Video Definition 13--Polynomial Concepts--Factored Cubic	Video Definition 13--Polynomial Concepts--Factored Cubic This is part of a collection of math video definitions related to to the topic of polynomials. Note: The download is an MP4 video.	Factoring Polynomials
Video Definition 13--Polynomial Concepts--Factored Cubic (Spanish Audio)	Video Definition 13--Polynomial Concepts--Factored Cubic (Spanish Audio) This is part of a collection of math video definitions related to to the topic of polynomials. Note: The download is an MP4 video.	Factoring Polynomials
Video Definition 17--Primes and Composites--Factor	Video Definition 17--Primes and Composites--Factor This is part of a collection of math video definitions related to the topics of primes and composites. Note: The download is an MP4 video.	Prime and Composite Numbers