Illustrative Math Alignment: Grade 8 Unit 8

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This is part of a collection of math examples that focus on rational number concepts. This includes rational numbers, expressions, and functions.

This Teacher's Guide provides an overview of the 28 worked-out examples that show how to simplify a variety of rational expressions.

Related Resources

To see resources related to this topic click on the Related Resources tab above.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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

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

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

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

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

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

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

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

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

Topic

Rationals and Radicals

Description

Addition of rational expressions involves combining rational expressions to create a new rational expression, often requiring a common denominator. Examples include 1 / x + 1 / 2x = 3 / 2x and 1 / (x + 1) + 1 / (x - 1) = 2x / (x2 - 1). This term introduces the concept of combining rational expressions, which is fundamental to operations involving fractions with polynomial expressions.

Topic

Rationals and Radicals

Topic

Rationals and Radicals

Description

The geometric mean is the nth root of the product of n terms. Examples include the geometric mean of 3 and 12, √(3 × 12) = 6, and the geometric mean of 3, 4, and 12, ∛(3 × 4 × 12) ≈ 5.24. Geometric mean connects multiplication and roots, commonly used in statistics, geometry, and proportional reasoning.

Topic

Rationals and Radicals

Description

The geometric mean is the nth root of the product of n terms. Examples include the geometric mean of 3 and 12, √(3 × 12) = 6, and the geometric mean of 3, 4, and 12, ∛(3 × 4 × 12) ≈ 5.24. Geometric mean connects multiplication and roots, commonly used in statistics, geometry, and proportional reasoning.

This video includes Spanish audio and can be used with multilingual learners.

Topic

Rationals and Radicals

Description

Graphs of radical functions have a characteristic shape where the domain is limited to values resulting in a positive radicand. For y = √x, the domain is x >= 0, and the range is y >= 0. This highlights the inherent properties of square root functions. Introduces the concept of radical graphs and their domain/range constraints, setting a foundation for graph behavior analysis.

Topic

Rationals and Radicals

Topic

Rationals and Radicals

Description

Graphs of rational functions often feature asymptotes, which are lines the graph approaches but never touches. For example, f(x) = 1 / x has vertical and horizontal asymptotes at x = 0 and y = 0, respectively. The domain and range exclude zero. Explains the unique characteristics of rational function graphs and the significance of asymptotes in defining their behavior.

Topic

Rationals and Radicals

Description

Graphs of rational functions often feature asymptotes, which are lines the graph approaches but never touches. For example, f(x) = 1 / x has vertical and horizontal asymptotes at x = 0 and y = 0, respectively. The domain and range exclude zero. Explains the unique characteristics of rational function graphs and the significance of asymptotes in defining their behavior.

Topic

Rationals and Radicals

Description

Horizontal asymptotes describe the behavior of a graph as x approaches infinity or negative infinity. For example, the equation y = (x + 1) / (x - 2) has a horizontal asymptote at y = 1, demonstrating long-term behavior of the function. Focuses on the role of horizontal asymptotes in describing the long-term trends of rational functions.

Topic

Rationals and Radicals

Description

Horizontal asymptotes describe the behavior of a graph as x approaches infinity or negative infinity. For example, the equation y = (x + 1) / (x - 2) has a horizontal asymptote at y = 1, demonstrating long-term behavior of the function. Focuses on the role of horizontal asymptotes in describing the long-term trends of rational functions.

Topic

Rationals and Radicals

Description

The index of a radical specifies the root being taken, such as the square root (index 2) or cube root (index 3). Examples include √25 for index 2 and the cube root of 27 for index 3. Defines and applies the concept of indices in radicals, foundational for understanding roots and powers.

Topic

Rationals and Radicals

Description

The index of a radical specifies the root being taken, such as the square root (index 2) or cube root (index 3). Examples include √25 for index 2 and the 3√27 for index 3. Defines and applies the concept of indices in radicals, foundational for understanding roots and powers.

This video includes Spanish audio and can be used with multilingual learners.

Topic

Rationals and Radicals

Description

Integers are a subset of rational numbers including positive, negative, and zero values, represented by {..., -3, -2, -1, 0, 1, 2, 3, ...}. This emphasizes their role in forming the basis of discrete mathematics. Introduces integers as a key component of number systems, aiding comprehension of rational numbers.

Topic

Rationals and Radicals

Description

Integers are a subset of rational numbers including positive, negative, and zero values, represented by {..., -3, -2, -1, 0, 1, 2, 3, ...}. This emphasizes their role in forming the basis of discrete mathematics. Introduces integers as a key component of number systems, aiding comprehension of rational numbers.

This video includes Spanish audio and can be used with multilingual learners.

Topic

Rationals and Radicals

Description

Inverse variation describes a non-linear relationship where the product of two variables is a constant k. For instance, xy = k is graphically represented by a hyperbola, illustrating how one variable inversely depends on the other. Describes inverse variation as a key relationship in algebra, foundational for understanding non-linear equations.

Topic

Rationals and Radicals

Description

Inverse variation describes a non-linear relationship where the product of two variables is a constant k. For instance, xy = k is graphically represented by a hyperbola, illustrating how one variable inversely depends on the other. Describes inverse variation as a key relationship in algebra, foundational for understanding non-linear equations.

Topic

Rationals and Radicals

Description

Irrational numbers cannot be expressed as ratios of integers. Examples include pi and √2, demonstrating their importance in representing real-world measurements and non-terminating decimals. Highlights the significance of irrational numbers in advanced mathematics and real-world applications.

Topic

Rationals and Radicals

Description

Irrational numbers cannot be expressed as ratios of integers. Examples include pi and √2, demonstrating their importance in representing real-world measurements and non-terminating decimals. Highlights the significance of irrational numbers in advanced mathematics and real-world applications.

This video includes Spanish audio and can be used with multilingual learners.

Topic

Rationals and Radicals

Description

Another definition of irrational numbers emphasizes their non-representability as fractions. Examples include e and √3, reinforcing their role in mathematical constants and transcendental equations. Reinforces the understanding of irrational numbers by presenting additional examples and contexts.

Topic

Rationals and Radicals

Description

Another definition of irrational numbers emphasizes their non-representability as fractions. Examples include e and √3, reinforcing their role in mathematical constants and transcendental equations. Reinforces the understanding of irrational numbers by presenting additional examples and contexts.

This video includes Spanish audio and can be used with multilingual learners.