Illustrative Math Alignment: Grade 7 Unit 7
Expressions, Equations, and Inequalities
Lesson 19: Expanding and Factoring
Use the following Media4Math resources with this Illustrative Math lesson.
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Definition--Rationals and Radicals--Factoring a Radical | Factoring a RadicalTopicRationals and Radicals DefinitionFactoring a radical involves expressing it as a product of simpler expressions. DescriptionFactoring radicals is a key technique in the study of Radical Numbers, Expressions, Equations, and Functions. It simplifies complex radical expressions, making them easier to work with. This process is essential for solving equations and for performing algebraic manipulations involving radicals. Understanding how to factor radicals is also important for simplifying expressions in calculus and higher-level mathematics. It helps in breaking down complex problems into more manageable parts. |
Radical Functions and Equations |
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Definition--Ratios, Proportions, and Percents Concepts--Scale Factor | Scale FactorTopicRatios, Proportions, and Percents DefinitionA scale factor is a number that scales, or multiplies, some quantity. DescriptionScale factors are used in various applications, such as resizing images, models, and maps. For instance, if a model car is built at a scale factor of 1:24, it means the model is 1/24th the size of the actual car. This concept is crucial in fields requiring accurate scaling, such as architecture and engineering. |
Proportions |
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Elementary Definition--Multiplication and Division Concepts--Factor | FactorTopicMultiplication and Division DefinitionA factor is a number that divides another number exactly without leaving a remainder. |
Multiplication Expressions and Equations |
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Factor Bingo Game | A bingo-style game where students identify the factors of numbers I the range 1-20. Note: The download is a PDF file. Related ResourcesTo see the complete Worksheet Library, click on this link: https://media4math.com/worksheet-library |
Numerical and Algebraic Expressions |
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Factor Table, 1-10 | A table that lists all the factors for the numbers 1-10. Note: The download is a PDF file. Related ResourcesTo see the complete Worksheet Library, click on this link: https://media4math.com/worksheet-library |
Numerical and Algebraic Expressions |
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Factor Table, 1-20 | A table that lists all the factors for the numbers 1-20. Note: The download is a PDF file. Related ResourcesTo see the complete Worksheet Library, click on this link: https://media4math.com/worksheet-library |
Numerical and Algebraic Expressions |
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Factor Table, 1-5 | A table that lists all the factors for the numbers 1-5. Note: The download is a PDF file. Related ResourcesTo see the complete Worksheet Library, click on this link: https://media4math.com/worksheet-library |
Numerical and Algebraic Expressions |
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Formulas--Factorial | Formulas--Factorial
The formula for Factorial. This is part of a collection of math formulas. To see the complete collection of formulas, click on this link. Note: The download is a JPG file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Numerical Expressions |
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INSTRUCTIONAL RESOURCE: Tutorial: Adding and Subtracting Rational Numbers | INSTRUCTIONAL RESOURCE: Tutorial: Adding and Subtracting Rational Numbers
In this Slide Show, learn how to add and subtract rational numbers. Includes links to several Media4Math videos and a math game. 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 ResourcesTo see the complete library of Instructional Resources , click on this link. |
Rational Expressions and Rational Functions and Equations |
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INSTRUCTIONAL RESOURCE: Tutorial: Analyzing Graphs of Quadratic Functions in Factored Form | INSTRUCTIONAL RESOURCE: Tutorial: Analyzing Graphs of Quadratic Functions in Factored Form
This slide show provides 8 examples of quadratic functions in factored form and analyzes their graphs. 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 ResourcesTo see the complete library of Instructional Resources , click on this link. |
Quadratic Equations and Functions |
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INSTRUCTIONAL RESOURCE: Math Examples 64 | MATH EXAMPLES--The Language of Math--Numerical Expressions--Addition
This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve addition. Note: The download is a PPT file. NOTE: The download is a PPT file. |
Numerical and Algebraic Expressions |
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INSTRUCTIONAL RESOURCE: Math Examples 65 | MATH EXAMPLES--The Language of Math--Numerical Expressions--Division
This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve division. Note: The download is a PPT file. NOTE: The download is a PPT file. |
Numerical and Algebraic Expressions |
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INSTRUCTIONAL RESOURCE: Math Examples 66 | MATH EXAMPLES--The Language of Math--Numerical Expressions--Grouping Symbols
This set of tutorials provides 32 examples of converting verbal expressions into numerical expressions that involve grouping symbols. Note: The download is a PPT file. NOTE: The download is a PPT file. |
Numerical and Algebraic Expressions |
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INSTRUCTIONAL RESOURCE: Math Examples 67 | MATH EXAMPLES--The Language of Math--Numerical Expressions--Multiplication
This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve multiplication. Note: The download is a PPT file. NOTE: The download is a PPT file. |
Numerical and Algebraic Expressions |
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INSTRUCTIONAL RESOURCE: Math Examples 68 | MATH EXAMPLES--The Language of Math--Numerical Expressions--Subtraction
This set of tutorials provides 40 examples of converting verbal expressions into numerical expressions that involve subtraction. Note: The download is a PPT file. NOTE: The download is a PPT file. |
Numerical and Algebraic Expressions |
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INSTRUCTIONAL RESOURCE: Math Examples 69 | MATH EXAMPLES--The Language of Math--Variable Expressions--Multiplication and Addition
This set of tutorials provides 32 examples of converting verbal expressions into variable expressions that involve multiplication and addition. Note: The download is a PPT file. NOTE: The download is a PPT file. |
Numerical and Algebraic Expressions |
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INSTRUCTIONAL RESOURCE: Math Examples 70 | MATH EXAMPLES--The Language of Math--Variable Expressions--Multiplication and Subtraction
This set of tutorials provides 32 examples of converting verbal expressions into variable expressions that involve multiplication and subtraction. Note: The download is a PPT file. NOTE: The download is a PPT file. |
Numerical and Algebraic Expressions |
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INSTRUCTIONAL RESOURCE: Tutorial: Multiples and Factors | INSTRUCTIONAL RESOURCE: Tutorial: Multiples and Factors
This tutorial provides an overview of multiples and factors. This includes an exploration of generating multiples by skip-counting. This is part of a collection of math tutorials on a variety of math topics. To see the complete collection of these resources, click on this link.Library of Instructional ResourcesTo see the complete library of Instructional Resources , click on this link. |
Complete Number Patterns |
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Instructional Resource: Tutorial: What Are Rational Expressions? | Instructional Resource: Tutorial: What Are Rational Expressions?
In this tutorial students learn about rational expressions and use the properties of fractions to combine them. —Press PREVIEW to see the tutorial— |
Rational Expressions |
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Interactive Math Game--Factor Tree | Interactive Math Game--Factor Tree
Find the factors of the numbers in the Christmas wreath. The possible factors are on the ornaments in the tree. Click on the right factor and earn 5 points. Click on the wrong number and lose two points. Practice your factoring skills and have fun! 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 ResourcesTo see additional resources on this topic, click on the Related Resources tab. |
Numerical Expressions |
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Interactive Math Game--DragNDrop--The Language of Math--Numerical Expressions--Addition | Interactive Math Game--DragNDrop Math--The Language of Math--Numerical Expressions--Addition
In this drag-and-drop game, a verbal expression to a numerical expression with addition. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format. 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 ResourcesTo see additional resources on this topic, click on the Related Resources tab. |
Numerical Expressions and Variable Expressions |
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Interactive Math Game--DragNDrop--The Language of Math--Numerical Expressions--Division | Interactive Math Game--DragNDrop Math--The Language of Math--Numerical Expressions--Division
In this drag-and-drop game, match a verbal description of an addition expression with its numerical counterpart. 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 ResourcesTo see additional resources on this topic, click on the Related Resources tab. |
Numerical Expressions and Variable Expressions |
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Interactive Math Game--DragNDrop--The Language of Math--Numerical Expressions--Grouping Symbols | Interactive Math Game--DragNDrop Math--The Language of Math--Numerical Expressions--Grouping Symbols
In this drag-and-drop game, a verbal expression to a numerical expression with grouping symbols. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format. 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 ResourcesTo see additional resources on this topic, click on the Related Resources tab. |
Numerical Expressions and Variable Expressions |
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Interactive Math Game--DragNDrop--The Language of Math--Numerical Expressions--Multiplication | Interactive Math Game--DragNDrop Math--The Language of Math--Numerical Expressions--Multiplication
In this drag-and-drop game, match a verbal expression to a numerical expression with multiplication. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format. 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 ResourcesTo see additional resources on this topic, click on the Related Resources tab. |
Numerical Expressions and Variable Expressions |
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Interactive Math Game--DragNDrop--The Language of Math--Numerical Expressions--Subtraction | Interactive Math Game--DragNDrop Math--The Language of Math--Numerical Expressions--Subtraction
In this drag-and-drop game, match a verbal description of a subtraction expression with its numerical counterpart. 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 ResourcesTo see additional resources on this topic, click on the Related Resources tab. |
Numerical Expressions and Variable Expressions |
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Interactive Math Game--DragNDrop--The Language of Math--Variable Expressions--Multiplication and Addition | Interactive Math Game--DragNDrop Math--The Language of Math--Variable Expressions--Multiplication and Addition
In this drag-and-drop game, a verbal expression to a variable expression with multiplication and addition. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format. 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 ResourcesTo see additional resources on this topic, click on the Related Resources tab. |
Numerical Expressions and Variable Expressions |
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Interactive Math Game--DragNDrop--The Language of Math--Variable Expressions--Multiplication and Subtraction | Interactive Math Game--DragNDrop Math--The Language of Math--Variable Expressions--Multiplication and Subtraction
In this drag-and-drop game, a verbal expression to a variable expression with multiplication and subtraction. This game generates thousands of different equation combinations, offering an ideal opportunity for skill review in a game format. 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 ResourcesTo see additional resources on this topic, click on the Related Resources tab. |
Numerical Expressions and Variable Expressions |
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Interactive Math Game--Easter Egg (Factor) Hunt | Interactive Math Game | Easter Egg (Factor) Hunt
In this Easter Egg hunt, students find the factors of a given number from a group of eggs with numbers on them. —PRESS PREVIEW TO PLAY THE GAME— 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 ResourcesTo see additional resources on this topic, click on the Related Resources tab. |
Division Expressions and Equations and Numerical Expressions |
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Math Example--Arithmetic--Division and Unknown Factors: Example 1 | Math Example--Arithmetic--Division and Unknown Factors: Example 1TopicArithmetic DescriptionSimplify 36 ÷ 9 by using the inverse operation of multiplication. The example illustrates the method of column multiplication. The caption explains the process step-by-step, emphasizing the sequential multiplication and any necessary regrouping. In general, column multiplication is a foundational arithmetic skill that develops a student's ability to handle larger numbers systematically. Examples in this collection present varied scenarios, building confidence through exposure to different configurations of numbers. |
Division Facts and Multiplication Facts |
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Math Example--Arithmetic--Division and Unknown Factors: Example 10 | Math Example--Arithmetic--Division and Unknown Factors: Example 10TopicArithmetic DescriptionSimplify 81 ÷ 9 by using the inverse operation of multiplication. The example illustrates the method of column multiplication. The caption explains the process step-by-step, emphasizing the sequential multiplication and any necessary regrouping. In general, column multiplication is a foundational arithmetic skill that develops a student's ability to handle larger numbers systematically. Examples in this collection present varied scenarios, building confidence through exposure to different configurations of numbers. |
Division Facts and Multiplication Facts |
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Math Example--Arithmetic--Division and Unknown Factors: Example 2 | Math Example--Arithmetic--Division and Unknown Factors: Example 2TopicArithmetic DescriptionSimplify 24 ÷ 8 by using the inverse operation of multiplication. The example illustrates the method of column multiplication. The caption explains the process step-by-step, emphasizing the sequential multiplication and any necessary regrouping. In general, column multiplication is a foundational arithmetic skill that develops a student's ability to handle larger numbers systematically. Examples in this collection present varied scenarios, building confidence through exposure to different configurations of numbers. |
Division Facts and Multiplication Facts |
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Math Example--Arithmetic--Division and Unknown Factors: Example 3 | Math Example--Arithmetic--Division and Unknown Factors: Example 3TopicArithmetic DescriptionSimplify 32 ÷ 4 by using the inverse operation of multiplication. The example illustrates the method of column multiplication. The caption explains the process step-by-step, emphasizing the sequential multiplication and any necessary regrouping. In general, column multiplication is a foundational arithmetic skill that develops a student's ability to handle larger numbers systematically. Examples in this collection present varied scenarios, building confidence through exposure to different configurations of numbers. |
Division Facts and Multiplication Facts |
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Math Example--Arithmetic--Division and Unknown Factors: Example 4 | Math Example--Arithmetic--Division and Unknown Factors: Example 4TopicArithmetic DescriptionSimplify 42 ÷ 7 by using the inverse operation of multiplication. The example illustrates the method of column multiplication. The caption explains the process step-by-step, emphasizing the sequential multiplication and any necessary regrouping. In general, column multiplication is a foundational arithmetic skill that develops a student's ability to handle larger numbers systematically. Examples in this collection present varied scenarios, building confidence through exposure to different configurations of numbers. |
Division Facts and Multiplication Facts |
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Math Example--Arithmetic--Division and Unknown Factors: Example 5 | Math Example--Arithmetic--Division and Unknown Factors: Example 5TopicArithmetic DescriptionSimplify 55 ÷ 5 by using the inverse operation of multiplication. The example illustrates the method of column multiplication. The caption explains the process step-by-step, emphasizing the sequential multiplication and any necessary regrouping. In general, column multiplication is a foundational arithmetic skill that develops a student's ability to handle larger numbers systematically. Examples in this collection present varied scenarios, building confidence through exposure to different configurations of numbers. |
Division Facts and Multiplication Facts |
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Math Example--Arithmetic--Division and Unknown Factors: Example 6 | Math Example--Arithmetic--Division and Unknown Factors: Example 6TopicArithmetic DescriptionSimplify 49 ÷ 7 by using the inverse operation of multiplication. The example illustrates the method of column multiplication. The caption explains the process step-by-step, emphasizing the sequential multiplication and any necessary regrouping. In general, column multiplication is a foundational arithmetic skill that develops a student's ability to handle larger numbers systematically. Examples in this collection present varied scenarios, building confidence through exposure to different configurations of numbers. |
Division Facts and Multiplication Facts |
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Math Example--Arithmetic--Division and Unknown Factors: Example 7 | Math Example--Arithmetic--Division and Unknown Factors: Example 7TopicArithmetic DescriptionSimplify 54 ÷ 6 by using the inverse operation of multiplication. The example illustrates the method of column multiplication. The caption explains the process step-by-step, emphasizing the sequential multiplication and any necessary regrouping. In general, column multiplication is a foundational arithmetic skill that develops a student's ability to handle larger numbers systematically. Examples in this collection present varied scenarios, building confidence through exposure to different configurations of numbers. |
Division Facts and Multiplication Facts |
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Math Example--Arithmetic--Division and Unknown Factors: Example 8 | Math Example--Arithmetic--Division and Unknown Factors: Example 8TopicArithmetic DescriptionSimplify 63 ÷ 9 by using the inverse operation of multiplication. The example illustrates the method of column multiplication. The caption explains the process step-by-step, emphasizing the sequential multiplication and any necessary regrouping. In general, column multiplication is a foundational arithmetic skill that develops a student's ability to handle larger numbers systematically. Examples in this collection present varied scenarios, building confidence through exposure to different configurations of numbers. |
Division Facts and Multiplication Facts |
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Math Example--Arithmetic--Division and Unknown Factors: Example 9 | Math Example--Arithmetic--Division and Unknown Factors: Example 9TopicArithmetic DescriptionSimplify 72 ÷ 8 by using the inverse operation of multiplication. The example illustrates the method of column multiplication. The caption explains the process step-by-step, emphasizing the sequential multiplication and any necessary regrouping. In general, column multiplication is a foundational arithmetic skill that develops a student's ability to handle larger numbers systematically. Examples in this collection present varied scenarios, building confidence through exposure to different configurations of numbers. |
Division Facts and Multiplication Facts |
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Math Example--Combinatorics--Factorial Expressions: Example 1 | Math Example--Combinatorics--Factorial Expressions: Example 1
This is part of a collection of math examples that focus on combinatorics and factorial expressions. |
Data Analysis and Combinatorics |
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Math Example--Combinatorics--Factorial Expressions: Example 10 | Math Example--Combinatorics--Factorial Expressions: Example 10
This is part of a collection of math examples that focus on combinatorics and factorial expressions. |
Combinatorics |
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Math Example--Combinatorics--Factorial Expressions: Example 11 | Math Example--Combinatorics--Factorial Expressions: Example 11
This is part of a collection of math examples that focus on combinatorics and factorial expressions. |
Combinatorics |
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Math Example--Combinatorics--Factorial Expressions: Example 12 | Math Example--Combinatorics--Factorial Expressions: Example 12
This is part of a collection of math examples that focus on combinatorics and factorial expressions. |
Combinatorics |
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Math Example--Combinatorics--Factorial Expressions: Example 13 | Math Example--Combinatorics--Factorial Expressions: Example 13
This is part of a collection of math examples that focus on combinatorics and factorial expressions. |
Combinatorics |
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Math Example--Combinatorics--Factorial Expressions: Example 14 | Math Example--Combinatorics--Factorial Expressions: Example 14
This is part of a collection of math examples that focus on combinatorics and factorial expressions. |
Combinatorics |
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Math Example--Combinatorics--Factorial Expressions: Example 2 | Math Example--Combinatorics--Factorial Expressions: Example 2
This is part of a collection of math examples that focus on combinatorics and factorial expressions. |
Combinatorics |
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Math Example--Combinatorics--Factorial Expressions: Example 3 | Math Example--Combinatorics--Factorial Expressions: Example 3
This is part of a collection of math examples that focus on combinatorics and factorial expressions. |
Combinatorics |
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Math Example--Combinatorics--Factorial Expressions: Example 4 | Math Example--Combinatorics--Factorial Expressions: Example 4
This is part of a collection of math examples that focus on combinatorics and factorial expressions. |
Combinatorics |
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Math Example--Combinatorics--Factorial Expressions: Example 5 | Math Example--Combinatorics--Factorial Expressions: Example 5
This is part of a collection of math examples that focus on combinatorics and factorial expressions. |
Combinatorics |
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Math Example--Combinatorics--Factorial Expressions: Example 6 | Math Example--Combinatorics--Factorial Expressions: Example 6
This is part of a collection of math examples that focus on combinatorics and factorial expressions. |
Combinatorics |
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Math Example--Combinatorics--Factorial Expressions: Example 7 | Math Example--Combinatorics--Factorial Expressions: Example 7
This is part of a collection of math examples that focus on combinatorics and factorial expressions. |
Combinatorics |
