Illustrative Math Alignment: Grade 7 Unit 7

Topic

Rationals and Radicals

Topic

Rationals and Radicals

Description

Multiplication of rational expressions involves multiplying the numerators and denominators of each expression. For example, (x / (x + 1)) * ((x - 1) / 3) simplifies to (x * (x - 1)) / (3 * (x + 1)), illustrating its application in simplifying complex expressions. Covers the multiplication of rational expressions, essential for algebraic simplifications and solving equations.

Topic

Rationals and Radicals

Topic

Rationals and Radicals

Topic

Rationals and Radicals

Topic

Equations

Description

A Numerical Expression consists of numbers and operations without variables. Examples include 2 + 3 = 5 and 2(4 + 3) = 14. This term highlights fundamental operations, foundational for understanding and solving equations.

The topic of this video is closely tied to Equations, providing an essential understanding of its fundamental concepts. This video explores the mathematics behind this topic by delving into how key principles are applied in practical contexts.

Topic

Linear Functions

Description

The term is "Linear Expression," defined as an algebraic expression consisting of at least one term where the variable has an exponent of 1. Examples include x, 2x - 3, and -4x + 8. This term establishes the foundation of linear algebra by focusing on the simplest forms of linear relationships.

Topic

Rationals and Radicals

Description

A radical expression includes terms under a radical sign, such as √2 or x + √(b2 - a). Examples illustrate simple and complex radical forms. Defines and illustrates the structure of radical expressions, serving as a basis for simplification and operations.

Topic

Rationals and Radicals

Description

A radical expression includes terms under a radical sign, such as √2 or x + √(b2 - a). Examples illustrate simple and complex radical forms. Defines and illustrates the structure of radical expressions, serving as a basis for simplification and operations.

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

Topic

Rationals and Radicals

Description

Rational Expressions are ratios of two polynomials, such as (x + 1) / (x - 1). They demonstrate how polynomials can form fractions with numerical denominators. Demonstrates how polynomials form the basis for more complex fractional expressions.

Topic

Rationals and Radicals

Description

Rational Expressions are ratios of two polynomials, such as (x + 1) / (x - 1). They demonstrate how polynomials can form fractions with numerical denominators. Demonstrates how polynomials form the basis for more complex fractional expressions.

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

Topic

Equations

Description

Variable Expression. A variable expression is made up of numbers, operations, and variables. Examples include 2x + 3 = 5 (expression on the left), 4 = 3x + 7 (expression on the right), and 4x + 3 = x - 5 (expressions on both sides). This connects variables to equations and highlights their role in forming relationships within mathematical contexts.

Topic

Rationals and Radicals

Description

Rationalizing an Expression involves removing radicals in the denominator by multiplying by a conjugate term. For example, 1 / (√2 + 1) is rationalized by multiplying by (√2 - 1). Focuses on simplifying expressions to remove radicals, aiding in creating standard forms for fractions.

Topic

Rationals and Radicals

Description

Rationalizing an Expression involves removing radicals in the denominator by multiplying by a conjugate term. For example, 1 / (√2 + 1) is rationalized by multiplying by (√2 - 1). Focuses on simplifying expressions to remove radicals, aiding in creating standard forms for fractions.

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

Topic

Equations

Description

An Algebraic Expression consists of numbers, operations, and variables. Unlike equations, expressions may not have an equality. Examples include 2x + 3, 4 = 3x + 7, and 4x + 3 = x - 5, demonstrating their versatility in representing mathematical relationships. This term distinguishes between expressions and equations, forming the basis for manipulating algebraic forms before solving equations.

Topic

Rationals and Radicals

Topic

Rationals and Radicals

Topic

Rationals and Radicals

Topic

Rationals and Radicals

Topic

Rationals and Radicals

Description

Subtraction of Rational Expressions involves subtracting one rational expression from another, resulting in another rational expression. The example simplifies 1/(x + 1) - 1/(x - 1) into -2/(x2 - 1) by finding a common denominator and combining the terms. This term supports the topic by illustrating how operations on rational expressions, like subtraction, can be performed systematically.

Topic

Rationals and Radicals

Topic

Rationals and Radicals

Description

Division of rational expressions involves dividing one rational expression by another, resulting in a new rational expression. Examples include 1 / (2x2) ÷ 1 / (3x) = 3 / 2x and 2 / (x + 1) ÷ (3 / (x - 1)) = 2(x - 1) / 3(x + 1). This operation is crucial for manipulating and simplifying rational expressions in algebra.

Topic

Rationals and Radicals

Description

Division of rational expressions involves dividing one rational expression by another, resulting in a new rational expression. Examples include 1 / (2x2) ÷ 1 / (3x) = 3 / 2x and 2 / (x + 1) ÷ (3 / (x - 1)) = 2(x - 1) / 3(x + 1). This operation is crucial for manipulating and simplifying rational expressions in algebra.

This is the transcript for the video of same title. Video contents: 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

This is the transcript for the video of same title. Video contents: In this Investigation we look at an application of rational functions: Boyle's Law.

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This is the transcript for the video of same title. Video contents: In this Investigation we look at graphs of rational functions.

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What Are Algebra Tiles?

What Are Algebra Tiles?

This is the transcript that goes with the video segment entitled Video: Integers: Numerical Expressions with Integers.

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This is the transcript that goes with the video segment entitled Video Tutorial: Integers: Variable Expressions with Integers.

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This is the transcript that goes with the video segment entitled Video: Rational Numbers: Numerical Expressions with Rational Numbers.

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This is the transcript that goes with the video segment entitled Video Tutorial: Rational Numbers: Variable Expressions with Rational Numbers.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Adding and Subtracting Rational Expressions.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Multiplying Rational Expressions.

To see the complete collection of video transcriptsy, click on this link.

This is the transcript for the TI-Nspire Mini-Tutorial entitled, Simplifying Rational Expressions.

To see the complete collection of video transcriptsy, click on this link.

Topic

Polynomials

Description

This video discusses factorials and their applications in counting, permutations, and combinations. It explains the growth of factorials, illustrating how they are used for calculating arrangements and combinations. Examples cover permutations of objects, arranging items, and deriving combinations for groups. Key terms include factorials, permutations, combinations, and the fundamental counting principle. Applications extend to password generation and probability calculations. The segment bridges counting techniques with practical problem-solving.

This is part of a collection of math worksheets on the topic of analyzing linear and quadratic expressions to identify specific terms based on a description.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of analyzing linear and quadratic expressions to identify specific terms based on a description.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of analyzing linear and quadratic expressions to identify specific terms based on a description.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of analyzing linear and quadratic expressions to identify specific terms based on a description.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of analyzing linear and quadratic expressions to identify specific terms based on a description.

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Worksheet Library

This is part of a collection of math worksheets on the topic of evaluating exponential expressions.

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This is part of a collection of math worksheets on the topic of evaluating exponential expressions.

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Worksheet Library

This is part of a collection of math worksheets on the topic of evaluating exponential expressions.

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Worksheet Library

This is part of a collection of math worksheets on the topic of evaluating exponential expressions.

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This is part of a collection of math worksheets on the topic of evaluating exponential expressions.

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This is part of a collection of math worksheets on the topic of evaluating exponential expressions.

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Worksheet Library

This is part of a collection of math worksheets on the topic of evaluating exponential expressions.

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Worksheet Library

This is part of a collection of math worksheets on the topic of evaluating exponential expressions.

Related Resources

Worksheet Library

This is part of a collection of math worksheets on the topic of evaluating exponential expressions.

Related Resources

Worksheet Library