Illustrative Math Alignment: Grade 8 Unit 3
Linear Equations and Linear Systems
Lesson 9: When Are They the Same?
Use the following Media4Math resources with this Illustrative Math lesson.
| Thumbnail Image | Title | Body | Curriculum Topic |
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Definition--Equation Concepts--The Unknown | The UnknownTopicEquations DefinitionThe unknown is the variable in an equation that needs to be solved for. DescriptionThe unknown in an equation represents the value that needs to be determined. For example, in the equation x + 3 = 7 x is the unknown. Identifying and solving for the unknown is a core aspect of algebra. In real-world applications, finding the unknown is crucial for solving problems in various fields such as science, engineering, and finance. Understanding how to identify and solve for the unknown helps students develop problem-solving skills and apply mathematical concepts to real-life situations. |
Variables and Unknowns |
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Definition--Equation Concepts--Transitive Property of Equality | Transitive Property of EqualityTopicEquations DefinitionThe Transitive Property of Equality states that if a = b and b = c, then a = c. DescriptionThe Transitive Property of Equality is a fundamental principle in mathematics. It states that if one quantity equals a second quantity, and the second quantity equals a third, then the first and third quantities are equal. For example, if x = y and y = z then x = z This property is used to justify steps in solving equations and proving mathematical statements. |
Applications of Equations and Inequalities |
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Definition--Equation Concepts--True Equation | True EquationTopicEquations DefinitionA true equation is an equation that holds true for the given values of the variable(s). DescriptionA true equation is an equation that is valid for specific values of the variable(s). For example, the equation 2 + 3 = 5 is true because both sides are equal. Identifying true equations is important in verifying the correctness of mathematical statements. In real-world applications, recognizing true equations helps in ensuring the accuracy of mathematical models and solutions. Understanding true equations helps students develop critical thinking and analytical skills. |
Applications of Equations and Inequalities |
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Definition--Equation Concepts--Two-Step Equation | Two-Step EquationTopicEquations DefinitionA two-step equation requires two operations to solve. DescriptionTwo-step equations involve performing two operations to isolate the variable. For example, solving 2x + 3 = 7 requires subtracting 3 from both sides and then dividing by 2 to find x = 2. These equations are common in algebra and require a systematic approach to solve. In real-world applications, two-step equations are used in problem-solving scenarios such as calculating costs or determining measurements. Understanding how to solve two-step equations helps students develop critical thinking and problem-solving skills. |
Solving Two-Step Equations |
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Definition--Equation Concepts--Variable Expression | Variable ExpressionTopicEquations DefinitionA variable expression is a mathematical phrase involving variables, numbers, and operation symbols. DescriptionVariable expressions consist of variables, numbers, and operations such as addition, subtraction, multiplication, and division. For example, 3x + 4 is a variable expression. These expressions are used to represent quantities and relationships in algebra. |
Variable Expressions |
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Definition--Equation Concepts--Visual Models for Equations | Visual Models for EquationsTopicEquations DefinitionVisual models for equations use graphical representations to illustrate the relationships between variables. DescriptionVisual models for equations include graphs, charts, and diagrams that represent the relationships between variables. For example, a graph of the equation y = 2x + 3 shows a straight line with a slope of 2 and a y-intercept of 3. These models help in understanding and interpreting equations. |
Applications of Equations and Inequalities |
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Definition--Finite | Definition | Finite
This is part of a collection of math definitions from Media4Math's Visual Glossary. |
Numerical Expressions and Variable Expressions |
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Definition--Infinite | Definition--Infinite
This is part of a collection of images that cover key vocabulary on a variety of math topics. |
Numerical Expressions and Variable Expressions |
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Definition--Systems Concepts--Graphical Solutions to Linear Systems | Definition--Systems Concepts--Graphical Solutions to Linear Systems
This is part of a collection of definitions related to the topic of systems of equations. The focus of most of the terms is linear systems. |
Solving Systems of Equations |
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Definition--Systems Concepts--Linear System | Definition--Systems Concepts--Linear System
This is part of a collection of definitions related to the topic of systems of equations. The focus of most of the terms is linear systems. |
Solving Systems of Equations |
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Definition--Systems Concepts--Non-Linear Systems | Definition--Systems Concepts--Non-Linear Systems
This is part of a collection of definitions related to the topic of systems of equations. The focus of most of the terms is linear systems. |
Solving Systems of Equations |
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Definition--Systems Concepts--Solving a Linear System Using Elimination | Definition--Systems Concepts--Solving a Linear System Using Elimination
This is part of a collection of definitions related to the topic of systems of equations. The focus of most of the terms is linear systems. |
Solving Systems of Equations |
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Definition--Systems Concepts--Solving a Linear System Using Matrices | Definition--Systems Concepts--Solving a Linear System Using Matrices
This is part of a collection of definitions related to the topic of systems of equations. The focus of most of the terms is linear systems. |
Solving Systems of Equations |
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Definition--Systems Concepts--Solving a Linear System Using Substitution | Definition--Systems Concepts--Solving a Linear System Using Substitution
This is part of a collection of definitions related to the topic of systems of equations. The focus of most of the terms is linear systems. |
Solving Systems of Equations |
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INSTRUCTIONAL RESOURCE: Tutorial: Solving Non-linear Systems | INSTRUCTIONAL RESOURCE: Tutorial: Solving Non-linear Systems
This slide show defines non-linear systems, showing examples of linear and quadratic systems. 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. |
Solving Systems of Equations |
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INSTRUCTIONAL RESOURCE: Tutorial: Solving Systems: The Elimination Method | INSTRUCTIONAL RESOURCE: Tutorial: Solving Systems: The Elimination Method
This slide show shows how to solve a system using the elimination method. 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. |
Solving Systems of Equations |
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INSTRUCTIONAL RESOURCE: Tutorial: Solving Systems: The Substitution Method | INSTRUCTIONAL RESOURCE: Tutorial: Solving Systems: The Substitution Method
This slide show shows how to solve a system using the substitution method. 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. |
Solving Systems of Equations |
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INSTRUCTIONAL RESOURCE: Tutorial: The Equals Sign Is Not an Operator! | INSTRUCTIONAL RESOURCE: Tutorial: The Equals Sign Is Not an Operator!
In this presentation, learn the basics of equations and dispel the misconception that the equals sign is an operator. The tutorial will ground the student in the properties of equality, the structure of an equation, and the important role of the equals sign. 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. |
Applications of Equations and Inequalities |
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INSTRUCTIONAL RESOURCE: Tutorial: Addition and Subtraction Equations | INSTRUCTIONAL RESOURCE: Tutorial: Addition and Subtraction Equations
Review the basics of addition and subtraction equations with this interactive. 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. |
Addition Expressions and Equations and Subtraction Expressions and Equations |
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INSTRUCTIONAL RESOURCE: Tutorial: Interactive: Basic Addition and Subtraction Vocabulary, Part 2 | INSTRUCTIONAL RESOURCE: Tutorial: Interactive: Basic Addition and Subtraction Vocabulary, Part 2
This interactive reviews key first and second grade vocabulary on addition and subtraction. 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. |
Addition Expressions and Equations and Subtraction Expressions and Equations |
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INSTRUCTIONAL RESOURCE: Tutorial: Introduction to Addition and Subtraction Equations | INSTRUCTIONAL RESOURCE: Tutorial: Introduction to Addition and Subtraction Equations
Explore the basics of addition and subtraction equations with this interactive. 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. |
Addition Expressions and Equations and Subtraction Expressions and Equations |
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INSTRUCTIONAL RESOURCE: Tutorial: Solving a Linear System | INSTRUCTIONAL RESOURCE: Tutorial: Solving a Linear System
In this Slide Show, learn how to solve a linear system by the elimination method. 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. |
Applications of Linear Systems and Solving Systems of Equations |
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INSTRUCTIONAL RESOURCE: Tutorial: Visual Models for Equations | INSTRUCTIONAL RESOURCE: Tutorial: Visual Models for Equations
An equation shows a relationship between two quantities. The download is a PDF. 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. |
Algebra Tiles--Expressions and Equations and Applications of Equations and Inequalities |
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INSTRUCTIONAL RESOURCE: Tutorial: What Is an Equation? | INSTRUCTIONAL RESOURCE: Tutorial: What Is an Equation?
An equation shows a relationship between two quantities. Note: The download is a PDF. 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. |
Applications of Equations and Inequalities and Variables and Unknowns |
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INSTRUCTIONAL RESOURCE: Tutorial: What Is an Identity? | INSTRUCTIONAL RESOURCE: Tutorial: What Is an Identity?
An identity is a special type of equation. It includes at least one variable and an identity is true for all values of the variable. Note: The download is a PDF. 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. |
Applications of Equations and Inequalities |
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INSTRUCTIONAL RESOURCE: Tutorial: Variables and Variable Expressions | INSTRUCTIONAL RESOURCE: Tutorial: Variables and Variable Expressions
In this Slide Show, learn about variables and variable expressions. 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. |
Variable Expressions, Applications of Equations and Inequalities and Variables and Unknowns |
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INSTRUCTIONAL RESOURCE: Tutorial: What Is a System of Equations? | INSTRUCTIONAL RESOURCE: Tutorial: What Is a System of Equations?
This slide show shows what a system of equations is. 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. |
Solving Systems of Equations |
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Interactive Crossword Puzzle--Equations 2 | Interactive Crossword Puzzle--Equations 2
Review key vocabulary on the topic of equations with this interactive and printable crossword puzzle. 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. |
Applications of Equations and Inequalities, Solving One-Step Equations and Solving Two-Step Equations |
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Interactive Crossword Puzzle: Equations | Interactive Crossword Puzzle: Equations
Review key vocabulary on the topic of equations with this interactive and printable crossword puzzle. 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. |
Applications of Equations and Inequalities |
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Interactive Math Game--DragNDrop--One-Step Equations | Interactive Math Game--DragNDrop Math--One-Step Equations
In this drag-and-drop game, match a one-step equation to its solution. Includes Addition, subtraction, multiplication, and division one-step equations. 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. |
Solving One-Step Equations |
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Interactive Math Game--DragNDrop--Two-Step Equations | Interactive Math Game--DragNDrop Math--Two-Step Equations
In this drag-and-drop game, match a two-step equation to its solution. Includes all four operations. 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. |
Solving Two-Step Equations |
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Interactive Math Game: Equation Sort 2 | Interactive Math Game: Equation Sort 2
Use this math game to review one-step equations. Students are shown four equations and are asked to correctly label the equation with drag-and-drop. The game provides feedback. 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. |
Applications of Equations and Inequalities and Solving One-Step Equations |
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Interactive Math Game: Equation Sort 3 | Interactive Math Game: Equation Sort 3
Use this math game to review two-step equations. Students are shown four equations and are asked to correctly label the equation with drag-and-drop. The game provides feedback. 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. |
Solving Two-Step Equations |
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Interactive Math Game: Math Riddles--Expressions and Equations | Interactive Math Game: Math Riddles--Expressions and Equations
In this Math Riddles Game, have your students review vocabulary around the topic of expressions and equations. The Math Riddles games are useful for practicing: Math Vocabulary, Key Concepts, Critical Thinking. 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 and Algebraic Expressions |
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Interactive Word Search Puzzle: Equations | Interactive Word Search Puzzle: Equations
Review key vocabulary on the topic of equations with this interactive and printable word search puzzle. 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. |
Applications of Equations and Inequalities |
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Math Clip Art--Equations and Inequalities--Equation Models--Balance Scale 1 | Math Clip Art--Equations and Inequalities--Equation Models--Balance Scale 1
This is part of a collection of math clip art images about equations and inequalities. |
Applications of Equations and Inequalities |
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Math Clip Art--Equations and Inequalities--Equation Models--Balance Scale 2 | Math Clip Art--Equations and Inequalities--Equation Models--Balance Scale 2
This is part of a collection of math clip art images about equations and inequalities. |
Applications of Equations and Inequalities |
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Math Clip Art--Equations and Inequalities--Equation Models--Balance Scale 3 | Math Clip Art--Equations and Inequalities--Equation Models--Balance Scale 3
This is part of a collection of math clip art images about equations and inequalities. |
Applications of Equations and Inequalities |
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Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation | Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation
This is part of a collection of math clip art images about equations and inequalities. |
Applications of Equations and Inequalities |
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Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation 1 | Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation 1
This is part of a collection of math clip art images about equations and inequalities. |
Applications of Equations and Inequalities |
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Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation 2 | Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation 2
This is part of a collection of math clip art images about equations and inequalities. |
Applications of Equations and Inequalities |
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Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation 3 | Math Clip Art--Equations and Inequalities--Equation Models--Balanced Equation 3
This is part of a collection of math clip art images about equations and inequalities. |
Applications of Equations and Inequalities |
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Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 1 Left | Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 1 Left
This is part of a collection of math clip art images about equations and inequalities. |
Applications of Equations and Inequalities |
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Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 1 Right | Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 1 Right
This is part of a collection of math clip art images about equations and inequalities. |
Applications of Equations and Inequalities |
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Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 2 Left | Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 2 Left
This is part of a collection of math clip art images about equations and inequalities. |
Applications of Equations and Inequalities |
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Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 2 Right | Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 2 Right
This is part of a collection of math clip art images about equations and inequalities. |
Applications of Equations and Inequalities |
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Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 3 Left | Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 3 Left
This is part of a collection of math clip art images about equations and inequalities. |
Applications of Equations and Inequalities |
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Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 3 Right | Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation 3 Right
This is part of a collection of math clip art images about equations and inequalities. |
Applications of Equations and Inequalities |
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Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation Left | Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation Left
This is part of a collection of math clip art images about equations and inequalities. |
Applications of Equations and Inequalities |
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Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation Right | Math Clip Art--Equations and Inequalities--Equation Models--Unbalanced Equation Right
This is part of a collection of math clip art images about equations and inequalities. |
Applications of Equations and Inequalities |
