Illustrative Math-Media4Math Alignment

 

 

Illustrative Math Alignment: Grade 7 Unit 7

Expressions, Equations, and Inequalities

Lesson 23: Applications of Expressions

Use the following Media4Math resources with this Illustrative Math lesson.

Thumbnail Image Title Body Curriculum Topic
Video Definition 1--Rationals and Radicals--Addition of Rational Expressions (Spanish Audio) Video Definition 1--Rationals and Radicals--Addition of Rational Expressions (Spanish Audio) Video Definition 1--Rationals and Radicals--Addition of Rational Expressions (Spanish Audio)

Topic

Rationals and Radicals

Rational Functions and Equations
Video Definition 20--Rationals and Radicals--Multiplication of Rational Expressions Video Definition 20--Rationals and Radicals--Multiplication of Rational Expressions Video Definition 20--Rationals and Radicals--Multiplication of Rational Expressions

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.

Rational Functions and Equations
Video Definition 20--Rationals and Radicals--Multiplication of Rational Expressions (Spanish Audio) Video Definition 20--Rationals and Radicals--Multiplication of Rational Expressions (Spanish Audio) Video Definition 20--Rationals and Radicals--Multiplication of Rational Expressions (Spanish Audio)

Topic

Rationals and Radicals

Rational Functions and Equations
Video Definition 23--Rationals and Radicals--Partial Fraction Decomposition of a Rational Expression Video Definition 23--Rationals and Radicals--Partial Fraction Decomposition of a Rational Expression Video Definition 23--Rationals and Radicals--Partial Fraction Decomposition of a Rational Expression

Topic

Rationals and Radicals

Rational Expressions
Video Definition 23--Rationals and Radicals--Partial Fraction Decomposition of a Rational Expression (Spanish Audio) Video Definition 23--Rationals and Radicals--Partial Fraction Decomposition of a Rational Expression (Spanish Audio) Video Definition 23--Rationals and Radicals--Partial Fraction Decomposition of a Rational Expression (Spanish Audio)

Topic

Rationals and Radicals

Rational Expressions
Video Definition 24--Equation Concepts--Numerical Expression Video Definition 24--Equation Concepts--Numerical Expression Video Definition 24--Equation Concepts--Numerical Expression

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.

Numerical Expressions
Video Definition 27--Linear Function Concepts--Linear Expression Video Definition 27--Linear Function Concepts--Linear Expression Video Definition 27--Linear Function Concepts--Linear Expression

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.

Variable Expressions
Video Definition 28--Rationals and Radicals--Radical Expression Video Definition 28--Rationals and Radicals--Radical Expression Video Definition 28--Rationals and Radicals--Radical Expression

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.

Radical Expressions
Video Definition 28--Rationals and Radicals--Radical Expression (Spanish Audio) Video Definition 28--Rationals and Radicals--Radical Expression (Spanish Audio) Video Definition 28--Rationals and Radicals--Radical Expression (Spanish Audio)

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.

Radical Expressions
Video Definition 35--Rationals and Radicals--Rational Expressions Video Definition 35--Rationals and Radicals--Rational Expressions Video Definition 35--Rationals and Radicals--Rational 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.

Rational Expressions
Video Definition 35--Rationals and Radicals--Rational Expressions (Spanish Audio) Video Definition 35--Rationals and Radicals--Rational Expressions (Spanish Audio) Video Definition 35--Rationals and Radicals--Rational Expressions (Spanish Audio)

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.

Rational Expressions
Video Definition 39--Equation Concepts--Variable Expression Video Definition 39--Equation Concepts--Variable Expression Video Definition 39--Equation Concepts--Variable Expression

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.

Variable Expressions
Video Definition 39--Rationals and Radicals--Rationalizing an Expression Video Definition 39--Rationals and Radicals--Rationalizing an Expression Video Definition 39--Rationals and Radicals--Rationalizing an Expression

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.

Rational Functions and Equations
Video Definition 39--Rationals and Radicals--Rationalizing an Expression (Spanish Audio) Video Definition 39--Rationals and Radicals--Rationalizing an Expression (Spanish Audio) Video Definition 39--Rationals and Radicals--Rationalizing an Expression (Spanish Audio)

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.

Rational Functions and Equations
Video Definition 4--Equation Concepts--Algebraic Expression Video Definition 4--Equation Concepts--Algebraic Expression Video Definition 4--Equation Concepts--Algebraic Expression

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.

Numerical and Algebraic Expressions
Video Definition 41--Rationals and Radicals--Simplifying a Radical Expression Video Definition 41--Rationals and Radicals--Simplifying a Radical Expression Video Definition 41--Rationals and Radicals--Simplifying a Radical Expression

Topic

Rationals and Radicals

Radical Expressions
Video Definition 41--Rationals and Radicals--Simplifying a Radical Expression (Spanish Audio) Video Definition 41--Rationals and Radicals--Simplifying a Radical Expression (Spanish Audio) Video Definition 41--Rationals and Radicals--Simplifying a Radical Expression (Spanish Audio)

Topic

Rationals and Radicals

Radical Expressions
Video Definition 42--Rationals and Radicals--Simplifying a Rational Expression Video Definition 42--Rationals and Radicals--Simplifying a Rational Expression Video Definition 42--Rationals and Radicals--Simplifying a Rational Expression

Topic

Rationals and Radicals

Rational Expressions
Video Definition 42--Rationals and Radicals--Simplifying a Rational Expression (Spanish Audio) Video Definition 42--Rationals and Radicals--Simplifying a Rational Expression (Spanish Audio) Video Definition 42--Rationals and Radicals--Simplifying a Rational Expression (Spanish Audio)

Topic

Rationals and Radicals

Rational Expressions
Video Definition 45--Rationals and Radicals--Subtraction of Rational Expressions Video Definition 45--Rationals and Radicals--Subtraction of Rational Expressions Video Definition 45--Rationals and Radicals--Subtraction of Rational Expressions

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.

Rational Functions and Equations
Video Definition 45--Rationals and Radicals--Subtraction of Rational Expressions (Spanish Audio) Video Definition 45--Rationals and Radicals--Subtraction of Rational Expressions (Spanish Audio) Video Definition 45--Rationals and Radicals--Subtraction of Rational Expressions (Spanish Audio)

Topic

Rationals and Radicals

Rational Functions and Equations
Video Definition 6--Rationals and Radicals--Division of Rational Expressions Video Definition 6--Rationals and Radicals--Division of Rational Expressions Video Definition 6--Rationals and Radicals--Division of Rational Expressions

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.

Rational Functions and Equations
Video Definition 6--Rationals and Radicals--Division of Rational Expressions (Spanish Audio) Video Definition 6--Rationals and Radicals--Division of Rational Expressions (Spanish Audio) Video Definition 6--Rationals and Radicals--Division of Rational Expressions (Spanish Audio)

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.

Rational Functions and Equations
Video Transcript: Algebra Nspirations: Rational Functions and Expressions Video Transcript: Algebra Nspirations: Rational Functions and Expressions Video Transcript: Algebra Nspirations: Rational Functions and Expressions

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

Rational Expressions and Rational Functions and Equations
Video Transcript: Algebra Nspirations: Rational Functions and Expressions, Part 1 Video Transcript: Algebra Nspirations: Rational Functions and Expressions, 1 Video Transcript: Algebra Nspirations: Rational Functions and Expressions, Part 1

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.

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

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

Rational Expressions and Rational Functions and Equations
Video Transcript: Algebra Nspirations: Rational Functions and Expressions, Part 2 Video Transcript: Algebra Nspirations: Rational Functions and Expressions, 2 Video Transcript: Algebra Nspirations: Rational Functions and Expressions, Part 2

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

This is part of a collection of video transcript from the Algebra Nspirations video series. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

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

Rational Expressions and Rational Functions and Equations
Video Transcript: Algebra Tiles: Modeling Variable Expressions Using Algebra Tiles Video Transcript: Algebra Tiles: Modeling Variable Expressions Using Algebra Tiles Video Transcript: Algebra Tiles: Modeling Variable Expressions Using Algebra Tiles

What Are Algebra Tiles?

Numerical Models
Algebra Tiles--Expressions and Equations
Video Transcript: Algebra Tiles: Simplifying Variable Expressions Using Algebra Tiles Video Transcript: Algebra Tiles: Simplifying Variable Expressions Using Algebra Tiles Video Transcript: Algebra Tiles: Simplifying Variable Expressions Using Algebra Tiles

What Are Algebra Tiles?

Numerical Models
Algebra Tiles--Expressions and Equations
Video Transcript: Integers: Numerical Expressions with Integers Video Transcript: Integers: Numerical Expressions with Integers Video Transcript: Integers: Numerical Expressions with Integers

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

This is part of a collection of video transcripts for the video tutorial series on Integers. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

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Numerical Expressions
Video Transcript: Integers: Variable Expressions with Integers Video Transcript: Integers: Variable Expressions with Integers Video Transcript: Integers: Variable Expressions with Integers

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

This is part of a collection of video transcripts for the video tutorial series on Integers. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

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Numerical Expressions
Video Transcript: Rational Numbers: Numerical Expressions with Rational Numbers Video Transcript: Rational Numbers: Numerical Expressions with Rational Numbers Video Transcript: Rational Numbers: Numerical Expressions with Rational Numbers

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

This is part of a collection of video transcripts for the video tutorial series on Rational Numbers. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

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Rational Expressions
Video Transcript: Rational Numbers: Variable Expressions with Rational Numbers Video Transcript: Rational Numbers: Variable Expressions with Rational Numbers Video Transcript: Rational Numbers: Variable Expressions with Rational Numbers

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

This is part of a collection of video transcripts for the video tutorial series on Rational Numbers. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

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

Rational Expressions
Video Transcript: TI-Nspire Mini-Tutorial: (CAS) Adding and Subtracting Rational Expressions Video Transcript: TI-Nspire Mini-Tutorial: (CAS) Adding and Subtracting Rational Expressions Video Transcript: TI-Nspire Mini-Tutorial: (CAS) Adding and Subtracting Rational Expressions

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

This is part of a collection of video transcripts for the video tutorial series on using the TI-Nspire Graphing Calculator. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

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Rational Expressions
Video Transcript: TI-Nspire Mini-Tutorial: (CAS) Multiplying Rational Expressions Video Transcript: TI-Nspire Mini-Tutorial: (CAS) Multiplying Rational Expressions Video Transcript: TI-Nspire Mini-Tutorial: (CAS) Multiplying Rational Expressions

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

This is part of a collection of video transcripts for the video tutorial series on using the TI-Nspire Graphing Calculator. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

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

Rational Expressions
Video Transcript: TI-Nspire Mini-Tutorial: (CAS) Simplifying Rational Expressions Video Transcript: TI-Nspire Mini-Tutorial: (CAS) Simplifying Rational Expressions Video Transcript: TI-Nspire Mini-Tutorial: (CAS) Simplifying Rational Expressions

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

This is part of a collection of video transcripts for the video tutorial series on using the TI-Nspire Graphing Calculator. To see the complete collection of transcripts, click on this link. Note: The download is a PDF file. Video Transcript Library

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

Rational Expressions
Video Tutorial: Factorial Expressions Video Tutorial: Factorial Expressions Video Tutorial: Factorial Expressions

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.

Combinatorics and Factoring Polynomials
WorksheetThumbnail.jpg Worksheet: Analyzing Expressions, Worksheet 1 Worksheet: Analyzing Expressions, Worksheet 1

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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Numerical and Algebraic Expressions
WorksheetThumbnail.jpg Worksheet: Analyzing Expressions, Worksheet 2 Worksheet: Analyzing Expressions, Worksheet 2

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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Numerical and Algebraic Expressions
WorksheetThumbnail.jpg Worksheet: Analyzing Expressions, Worksheet 3 Worksheet: Analyzing Expressions, Worksheet 3

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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Numerical and Algebraic Expressions
WorksheetThumbnail.jpg Worksheet: Analyzing Expressions, Worksheet 4 Worksheet: Analyzing Expressions, Worksheet 4

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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Numerical and Algebraic Expressions
WorksheetThumbnail.jpg Worksheet: Analyzing Expressions, Worksheet 5 Worksheet: Analyzing Expressions, Worksheet 5

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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Related Resources

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Numerical and Algebraic Expressions
WorksheetThumbnail.jpg Worksheet: Evaluating Exponential Expressions, Set 1 Worksheet: Evaluating Exponential Expressions, Set 1

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

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Exponential and Logarithmic Functions and Equations
WorksheetThumbnail.jpg Worksheet: Evaluating Exponential Expressions, Set 10 Worksheet: Evaluating Exponential Expressions, Set 10

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Exponential and Logarithmic Functions and Equations
WorksheetThumbnail.jpg Worksheet: Evaluating Exponential Expressions, Set 11 Worksheet: Evaluating Exponential Expressions, Set 11

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Exponential and Logarithmic Functions and Equations
WorksheetThumbnail.jpg Worksheet: Evaluating Exponential Expressions, Set 12 Worksheet: Evaluating Exponential Expressions, Set 12

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Exponential and Logarithmic Functions and Equations
WorksheetThumbnail.jpg Worksheet: Evaluating Exponential Expressions, Set 13 Worksheet: Evaluating Exponential Expressions, Set 13

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Exponential and Logarithmic Functions and Equations
WorksheetThumbnail.jpg Worksheet: Evaluating Exponential Expressions, Set 14 Worksheet: Evaluating Exponential Expressions, Set 14

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Exponential and Logarithmic Functions and Equations
WorksheetThumbnail.jpg Worksheet: Evaluating Exponential Expressions, Set 15 Worksheet: Evaluating Exponential Expressions, Set 15

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Exponential and Logarithmic Functions and Equations
WorksheetThumbnail.jpg Worksheet: Evaluating Exponential Expressions, Set 16 Worksheet: Evaluating Exponential Expressions, Set 16

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Exponential and Logarithmic Functions and Equations
WorksheetThumbnail.jpg Worksheet: Evaluating Exponential Expressions, Set 17 Worksheet: Evaluating Exponential Expressions, Set 17

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Exponential and Logarithmic Functions and Equations