Illustrative Math Alignment: Grade 6 Unit 7

Rational Numbers

Lesson 1: Positive and Negative Numbers

Use the following Media4Math resources with this Illustrative Math lesson.

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Definition--Rationals and Radicals--Rational Functions	Rational Functions Topic Rationals and Radicals Definition Rational functions are functions that are the ratio of two polynomials. Description Rational Functions are a key concept in the study of Rational Numbers, Expressions, Equations, and Functions. These functions are the ratio of two polynomials, such as $$f(x) = \frac{P(x)}{Q(x)}$$ where P(x) and Q(x) are polynomials. Understanding rational functions involves analyzing their behavior, including identifying asymptotes, intercepts, and discontinuities. For example, the function $$f(x) = \frac{1}{x}$$	Rational Functions and Equations
Definition--Rationals and Radicals--Rational Numbers	Rational Numbers Topic Rationals and Radicals Definition Rational numbers are numbers that can be expressed as a ratio of two integers, where the denominator is not zero.	Rational Functions and Equations
Definition--Rationals and Radicals--Rationalizing a Radical	Rationalizing a Radical Topic Rationals and Radicals Definition Rationalizing a radical is the process of eliminating radicals from the denominator of a fraction by multiplying both the numerator and denominator by an appropriate factor. Description Rationalizing a Radical is an important technique in the study of Radical Numbers, Expressions, Equations, and Functions. This process involves eliminating radicals from the denominator of a fraction, which simplifies the expression and often makes it easier to work with or compare to other expressions. For example, to rationalize the denominator of $$\frac{1}{\sqrt{3}}$$	Radical Expressions
Definition--Rationals and Radicals--Rationalizing the Denominator	Rationalizing the Denominator Topic Rationals and Radicals Definition Rationalizing the denominator is the process of eliminating radicals or complex numbers from the denominator of a fraction by multiplying both the numerator and denominator by an appropriate factor. Description Rationalizing the Denominator is a crucial technique in the study of Radical Numbers, Expressions, Equations, and Functions. This process involves removing radicals or complex numbers from the denominator of a fraction, which simplifies the expression and often makes it easier to evaluate or compare with other expressions. For example, to rationalize the denominator of	Radical Expressions
Definition--Rationals and Radicals--Simplifying a Radical Expression	Simplifying a Radical Expression Topic Rationals and Radicals Definition Simplifying a radical expression involves reducing the expression to its simplest form by factoring the radicand and removing any perfect square factors (for square roots) or perfect cube factors (for cube roots). Description Simplifying a Radical Expression is a fundamental skill in the study of Radical Numbers, Expressions, Equations, and Functions. This process involves reducing a radical expression to its simplest form, which often makes it easier to work with and understand. For example, simplifying $$\sqrt{18}$$ results in	Radical Expressions
Definition--Rationals and Radicals--Simplifying a Rational Expression	Simplifying a Rational Expression Topic Rationals and Radicals Definition Simplifying a rational expression involves reducing the fraction to its lowest terms by factoring both the numerator and denominator and canceling common factors. Description Simplifying a Rational Expression is a crucial skill in the study of Rational Numbers, Expressions, Equations, and Functions. This process involves reducing a rational expression to its simplest form by factoring both the numerator and denominator and canceling common factors. For example, simplifying $$\frac{x^2 - 1}{x - 1}$$ results in x + 1 for	Rational Expressions
Definition--Rationals and Radicals--Square Root	Square Root Topic Rationals and Radicals Definition The square root of a number is a value that, when multiplied by itself, gives the number. It is denoted by the radical symbol √.	Radical Expressions
Definition--Rationals and Radicals--Vertical Asymptote	Vertical Asymptote Topic Rationals and Radicals Definition A vertical asymptote is a vertical line that the graph of a function approaches but never reaches as the input values get closer to a certain point. Description Vertical Asymptotes are a crucial concept in the study of Rational Numbers, Expressions, Equations, and Functions. They occur in rational functions when the denominator equals zero for certain input values, causing the function to approach infinity or negative infinity. For example, the function $$f(x) = \frac{1}{x-2}$$	Rational Functions and Equations
INSTRUCTIONAL RESOURCE: Tutorial: Adding and Subtracting Integers	INSTRUCTIONAL RESOURCE: Tutorial: Adding and Subtracting Integers In this Slide Show, learn how to add and subtract integers. Includes links to several Media4Math videos. This is part of a collection of tutorials on a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file. Library of Instructional Resources To see the complete library of Instructional Resources , click on this link.	Numerical Expressions
INSTRUCTIONAL RESOURCE: Tutorial: Adding Integers	INSTRUCTIONAL RESOURCE: Tutorial: Adding Integers In this Slide Show, learn how to add integers. Includes links to Quizlet flash cards and YouTube video. This is part of a collection of tutorials on a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file. Library of Instructional Resources To see the complete library of Instructional Resources , click on this link.	Numerical Expressions
INSTRUCTIONAL RESOURCE: Tutorial: Dividing Integers	INSTRUCTIONAL RESOURCE: Tutorial: Dividing Integers In this Slide Show, review the rules for dividing integers and see some worked-out examples. This is part of a collection of tutorials on a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file. Library of Instructional Resources To see the complete library of Instructional Resources , click on this link.	Numerical Expressions
INSTRUCTIONAL RESOURCE: Math Examples 11	INSTRUCTIONAL RESOURCE: Math Examples--Dividing Integers This set of tutorials provides 24 examples of dividing integers. This is part of a collection of math examples for a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file. Library of Instructional Resources To see the complete library of Instructional Resources , click on this link.	Numerical and Algebraic Expressions
INSTRUCTIONAL RESOURCE: Math Examples 31	INSTRUCTIONAL RESOURCE: Math Examples--Modeling Integers Using Algebra Tiles What Are Algebra Tiles? Numerical Models	Numerical and Algebraic Expressions
INSTRUCTIONAL RESOURCE: Math Examples 33	INSTRUCTIONAL RESOURCE: Math Examples--Multiplying Integers This set of tutorials provides 12 examples of multiplying integers. This is part of a collection of math examples for a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file. Library of Instructional Resources To see the complete library of Instructional Resources , click on this link.	Numerical and Algebraic Expressions
INSTRUCTIONAL RESOURCE: Math Examples 59	MATH EXAMPLES--Adding and Subtracting Integers This set of tutorials provides13 examples of adding and subtracting integers. NOTE: The download is a PPT file.	Numerical and Algebraic Expressions
INSTRUCTIONAL RESOURCE: Tutorial: Multiplying Integers	INSTRUCTIONAL RESOURCE: Tutorial: Multiplying Integers In this Slide Show, learn about multiplying integers. This is part of a collection of tutorials on a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file. Library of Instructional Resources To see the complete library of Instructional Resources , click on this link.	Numerical Expressions
INSTRUCTIONAL RESOURCE: Tutorial: Subtracting Integers	INSTRUCTIONAL RESOURCE: Tutorial: Subtracting Integers In this Slide Show, learn how to subtract integers. Includes links to Quizlet flash cards and YouTube video. This is part of a collection of tutorials on a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file. < Library of Instructional Resources To see the complete library of Instructional Resources , click on this link.	Numerical Expressions
INSTRUCTIONAL RESOURCE: Tutorial: What Are Integers?	INSTRUCTIONAL RESOURCE: Tutorial: What Are Integers? In this Slide Show, learn about integers. This is part of a collection of tutorials on a variety of math topics. To see the complete collection of these resources, click on this link. Note: The download is a PPT file. Library of Instructional Resources To see the complete library of Instructional Resources , click on this link.	Numerical Expressions
Interactive Math Game--Algebra Jeopardy: Integers	Interactive Math Game--Algebra Jeopardy: Integers Use this Jeopardy-style math game to review integer operations. This Jeopardy game has a bank of hundreds of questions for thousands of unique game experiences. Best viewed in Chrome. To see the complete set of Math Games and Puzzles, click on this link. This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide. Related Resources To see additional resources on this topic, click on the Related Resources tab.	Numerical and Algebraic Expressions
Interactive Math Game--Sub-Zero Zapper	Interactive Math Game--Sub-Zero Zapper Use this game to review positive and negative integers. Drop positive number bombs on negative number submarines. Your score is the sum of the integers. Get 20 points when two opposite numbers collide. This is part of a collection of math games and interactives. To see the complete collection of the games, click on this link. Note: The download is the teacher's guide. Related Resources To see additional resources on this topic, click on the Related Resources tab.	Numerical Expressions
Interactive Quiz: Adding Integers, Quiz 01, Level 1	Interactive Quiz: Adding Integers, Quiz 01, Level 1 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 01, Level 2	Interactive Quiz: Adding Integers, Quiz 01, Level 2 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 01, Level 3	Interactive Quiz: Adding Integers, Quiz 01, Level 3 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 02, Level 1	Interactive Quiz: Adding Integers, Quiz 02, Level 1 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 02, Level 2	Interactive Quiz: Adding Integers, Quiz 02, Level 2 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 02, Level 3	Interactive Quiz: Adding Integers, Quiz 02, Level 3 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 03, Level 1	Interactive Quiz: Adding Integers, Quiz 03, Level 1 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 03, Level 2	Interactive Quiz: Adding Integers, Quiz 03, Level 2 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 03, Level 3	Interactive Quiz: Adding Integers, Quiz 03, Level 3 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 04, Level 1	Interactive Quiz: Adding Integers, Quiz 04, Level 1 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 04, Level 2	Interactive Quiz: Adding Integers, Quiz 04, Level 2 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 04, Level 3	Interactive Quiz: Adding Integers, Quiz 04, Level 3 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 05, Level 1	Interactive Quiz: Adding Integers, Quiz 05, Level 1 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 05, Level 2	Interactive Quiz: Adding Integers, Quiz 05, Level 2 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 05, Level 3	Interactive Quiz: Adding Integers, Quiz 05, Level 3 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 06, Level 1	Interactive Quiz: Adding Integers, Quiz 06, Level 1 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 06, Level 2	Interactive Quiz: Adding Integers, Quiz 06, Level 2 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 06, Level 3	Interactive Quiz: Adding Integers, Quiz 06, Level 3 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 07, Level 1	Interactive Quiz: Adding Integers, Quiz 07, Level 1 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions
Interactive Quiz: Adding Integers, Quiz 07, Level 2	Interactive Quiz: Adding Integers, Quiz 07, Level 2 This is part of a collection of math quizzes on the topic of adding integers. Some quizzes are interactive and some are in PDF format. 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.	Numerical and Algebraic Expressions

Illustrative Math Alignment: Grade 6 Unit 7

Rational Numbers

Lesson 1: Positive and Negative Numbers

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