Use the following Media4Math resources with this Illustrative Math lesson.
Thumbnail Image | Title | Body | Curriculum Topic |
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Definition--Equation Concepts--Isolating the Variable | Isolating the VariableTopicEquations DefinitionIsolating the variable involves manipulating an equation to get the variable alone on one side. DescriptionIsolating the variable is a fundamental technique in algebra used to solve equations. It involves performing operations to both sides of an equation to get the variable by itself. For example, solving 2x + 3 = 7 involves subtracting 3 and then dividing by 2 to isolate x, resulting in x = 2. |
Variables and Unknowns | |
Definition--Equation Concepts--Left Side of the Equation | Left Side of the EquationTopicEquations DefinitionThe left side of the equation refers to the expression on the left side of the equals sign. DescriptionThe left side of an equation is the part of the equation that appears before the equals sign. For example, in the equation 2x + 3 = 7 the left side is 2x + 3. Understanding the left side of the equation is crucial for solving and balancing equations. In real-world applications, recognizing the left side of an equation helps in setting up and solving problems accurately. It is essential for students to understand this concept to manipulate and solve equations effectively. |
Applications of Equations and Inequalities | |
Definition--Equation Concepts--Linear Equation | Linear EquationTopicEquations DefinitionA linear equation is an equation that does not have an variables raised to a power higher than one. A linear equation can have one or more variables. DescriptionLinear equations are fundamental in algebra and describe relationships are summarized below. |
Applications of Linear Functions | |
Definition--Equation Concepts--Literal Equation | Literal EquationTopicEquations DefinitionA literal equation is an equation that involves two or more variables. DescriptionLiteral equations involve multiple variables and are used to express relationships between them. For example, the formula for the area of a rectangle, A = l•w is a literal equation involving the variables l and w. Solving literal equations often involves isolating one variable in terms of the others. |
Applications of Equations and Inequalities | |
Definition--Equation Concepts--Multi-Step Equation | Multi-Step EquationTopicEquations DefinitionA multi-step equation requires more than one step to solve. DescriptionMulti-step equations involve multiple operations to isolate the variable. For example, solving 3x + 2 = 11 requires subtracting 2 and then dividing by 3 to find x=3. These equations are common in algebra and require a systematic approach to solve. In real-world applications, multi-step equations are used in complex problem-solving scenarios such as engineering and finance. Understanding how to solve multi-step equations helps students develop critical thinking and problem-solving skills. |
Solving Multistep Equations | |
Definition--Equation Concepts--Multiplication Property of Equality | Multiplication Property of EqualityTopicEquations DefinitionThe Multiplication Property of Equality states that if you multiply both sides of an equation by the same nonzero value, the equality remains true. DescriptionThe Multiplication Property of Equality is a fundamental principle in algebra. It states that for any real numbers a, b, and c (where 𝑐 ≠ 0), if a = b, then ac = bc This property is used to solve equations by isolating variables. For example, to solve x/3 = 4 you multiply both sides by 3 to get x = 12. |
Applications of Equations and Inequalities | |
Definition--Equation Concepts--Nonlinear Equation | Nonlinear EquationTopicEquations DefinitionA nonlinear equation is an equation that graphs as a curve and does not form a straight line. DescriptionNonlinear equations are equations that involve variables raised to powers other than one or involve products of variables. For example, the equation y = x2 is nonlinear because it graphs as a parabola. These equations are used to model more complex relationships than linear equations. |
Applications of Equations and Inequalities | |
Definition--Equation Concepts--Numerical Expression | Numerical ExpressionTopicEquations DefinitionA numerical expression is a mathematical phrase involving numbers and operation symbols, but no variables. DescriptionNumerical expressions consist of numbers and operations such as addition, subtraction, multiplication, and division. For example, 3 + 4 × 2 is a numerical expression. These expressions are evaluated to find their value. In real-world applications, numerical expressions are used in everyday calculations such as budgeting, measuring, and data analysis. Understanding numerical expressions helps students perform arithmetic operations and develop computational skills. |
Numerical Expressions | |
Definition--Equation Concepts--One-Step Equation | One-Step EquationTopicEquations DefinitionA one-step equation requires only one operation to solve. DescriptionOne-step equations are the simplest type of equations in algebra. They involve a single operation to isolate the variable. For example, solving x + 3 = 7 requires subtracting 3 from both sides to find x = 4. These equations are used in basic problem-solving scenarios and form the foundation for understanding more complex equations. Understanding one-step equations helps students develop confidence in solving algebraic problems and prepares them for advanced algebraic concepts. |
Solving One-Step Equations | |
Definition--Equation Concepts--Polynomial Equation | Polynomial EquationTopicEquations DefinitionA polynomial equation is an equation that involves a polynomial expression. DescriptionPolynomial equations involve expressions that include terms with variables raised to whole-number exponents. For example, the equation x2 − 4x + 4 = 0 is a polynomial equation. These equations can be linear, quadratic, cubic, etc., depending on the highest power of the variable. |
Polynomial Functions and Equations | |
Definition--Equation Concepts--Quadratic Equation | Quadratic EquationTopicEquations DefinitionA quadratic equation is a polynomial equation of degree 2, typically in the form ax2 + bx + c = 0. DescriptionQuadratic equations are fundamental in algebra and involve variables raised to the second power. For example, the equation x2 − 4x + 4 = 0 is quadratic. These equations can be solved using methods such as factoring, completing the square, and the quadratic formula. |
Quadratic Equations and Functions | |
Definition--Equation Concepts--Reflexive Property of Equality | Reflexive Property of EqualityTopicEquations DefinitionThe Reflexive Property of Equality states that any value is equal to itself. DescriptionThe Reflexive Property of Equality is a basic principle in mathematics. It states that for any value a, a = a This property is used to justify steps in solving equations and proving mathematical statements. In real-world applications, the reflexive property underlies the concept of identity and is fundamental in logical reasoning and proofs. Understanding this property helps students build a strong foundation in algebra and develop rigorous mathematical arguments. |
Applications of Equations and Inequalities | |
Definition--Equation Concepts--Right Side of the Equation | Right Side of the EquationTopicEquations DefinitionThe right side of the equation refers to the expression on the right side of the equals sign. DescriptionThe right side of an equation is the part of the equation that appears after the equals sign. For example, in the equation 2x + 3 = 7 the right side is 7. Understanding the right side of the equation is crucial for solving and balancing equations. |
Applications of Equations and Inequalities | |
Definition--Equation Concepts--Roots of an Equation | Roots of an EquationTopicEquations DefinitionThe roots of an equation are the values of the variable that satisfy the equation. DescriptionThe roots of an equation are the solutions that make the equation true. For example, the roots of the quadratic equation x2 − 4x + 4 = 0 are x = 2 because substituting 2 into the equation satisfies it. Finding roots is a fundamental task in algebra. |
Applications of Equations and Inequalities | |
Definition--Equation Concepts--Solution | SolutionTopicEquations DefinitionA solution is the value(s) of the variable(s) that satisfy an equation. DescriptionThe concept of solution is fundamental in equations, referring to the values that make the equation true. For example, in the equation x + 2 = 5 the solution is x = 3 because substituting 3 in place of x results in a true statement. Solutions can exist for various types of equations, whether single-variable, multi-variable, linear, or nonlinear. |
Applications of Equations and Inequalities | |
Definition--Equation Concepts--Solving an Equation | Solving an EquationTopicEquations DefinitionSolving an equation involves finding the value(s) of the variable(s) that make the equation true. DescriptionSolving an equation is a key skill in algebra, where one determines the values of variables that satisfy the equation. For example, in the equation 2x + 3 = 7 one can find that x = 2 by isolating the variable through algebraic manipulations. Different techniques such as substitution, factoring, or using the quadratic formula may apply depending on the complexity of the equation. |
Applications of Equations and Inequalities | |
Definition--Equation Concepts--Subtraction Property of Equality | Subtraction Property of EqualityTopicEquations DefinitionThe Subtraction Property of Equality states that if you subtract the same value from both sides of an equation, the equality remains true. DescriptionThe Subtraction Property of Equality is a fundamental principle in algebra. It states that for any real numbers a, b, and c, if a = b, then a − c = b − c This property is used to solve equations by isolating variables. For example, to solve x + 3 = 7 you subtract 3 from both sides to get x = 4. |
Applications of Equations and Inequalities | |
Definition--Equation Concepts--Symmetric Property of Equality | Symmetric Property of EqualityTopicEquations DefinitionThe Symmetric Property of Equality states that if a = b, then b = a. DescriptionThe Symmetric Property of Equality is a basic principle in mathematics. It asserts that the equality relation is symmetric, meaning that if one quantity equals another, then the second quantity equals the first. For example, if x = y then y = x This property is used to justify steps in solving equations and proving mathematical statements. |
Applications of Equations and Inequalities | |
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 | |
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 | |
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 | |
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 | |
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 | |
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 | |
Equations Word Search Puzzle 2 | Equations Word Search Puzzle 2
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, Solving One-Step Equations and Solving Two-Step Equations | |
Geometry Applications Teachers Guide: 3D Geometry | Geometry Applications Teachers Guide: 3D Geometry
This is the Teacher's Guide that accompanies Geometry Applications: 3D Geometry. This is part of a collection of teacher's guides. To see the complete collection of teacher's guides, click on this link. Note: The download is a PDF file.Related ResourcesTo see resources related to this topic click on the Related Resources tab above. |
Applications of 3D Geometry | |
Instructional Resource--Strategy Pack--One-Step Addition Equations | Instructional Resource | Strategy Pack | One-Step Addition Equations
Learn different strategies for solving one-step addition equations. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems. —PRESS PREVIEW TO LAUNCH THE PRESENTATION— To see the complete collection of Instructional Resources, click on this link.Note: The download is a PPT file. |
Solving One-Step Equations | |
Instructional Resource--Strategy Pack--One-Step Multiplication Equations | Instructional Resource | Strategy Pack | One-Step Multiplication Equations
Learn different strategies for solving one-step multiplication equations. The Strategy Packs provide alternate ways of solving the same problem, giving your students different approaches to the same problem. The goal of the Strategy Packs is to encourage your students to think strategically when solving math problems. —PRESS PREVIEW TO LAUNCH THE PRESENTATION— To see the complete collection of Instructional Resources, click on this link.Note: The download is a PPT file. |
Solving One-Step Equations | |
INSTRUCTIONAL RESOURCE: Math Examples 13 | INSTRUCTIONAL RESOURCE: Math Examples--Equations with Fractions
The complete set of 13 examples that make up this set of tutorials. This is part of a collection of math examples for 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 Fraction Equations | |
INSTRUCTIONAL RESOURCE: Math Examples 14 | INSTRUCTIONAL RESOURCE: Math Examples--Equations with Percents
The complete set of 42 examples that make up this set of tutorials. This is part of a collection of math examples for 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 Percent Equations | |
INSTRUCTIONAL RESOURCE: Math Examples 28 | INSTRUCTIONAL RESOURCE: Math Examples--Linear Inequalities
The complete set of 12 examples that make up this set of tutorials. This is part of a collection of math examples for 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. |
Inequalities | |
INSTRUCTIONAL RESOURCE: Math Examples 34 | INSTRUCTIONAL RESOURCE: Math Examples--One-Variable Equations
The complete set of 21 examples that make up this set of tutorials. This is part of a collection of math examples for 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 | |
INSTRUCTIONAL RESOURCE: Math Examples 55 | INSTRUCTIONAL RESOURCE: Math Examples--Surface Area
This set of tutorials provides an overview of the 24 worked-out examples that show how to calculate the surface area of different three-dimensional figures. This is part of a collection of math examples for 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. |
Surface Area | |
INSTRUCTIONAL RESOURCE: Math Examples 62 | MATH EXAMPLES--Algebra Tiles
The complete set of 39 examples that make up this set of tutorials. NOTE: The download is a PPT file. |
Algebra Tiles--Expressions and Equations | |
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 | |
INSTRUCTIONAL RESOURCE: Tutorial: Solving Two-Step Equations Using the Properties of Equality | INSTRUCTIONAL RESOURCE: Tutorial: Solving Two-Step Equations Using the Properties of Equality
This tutorial goes over the steps of solving a two-step equation by using the properties of equality. Note: The download is a PDF version of this tutorial. 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. |
Solving Two-Step Equations | |
INSTRUCTIONAL RESOURCE: Tutorial: Summary of One-Step Equations | INSTRUCTIONAL RESOURCE: Tutorial: Summary of One-Step Equations
This tutorials provides a summary of the properties of one-step equations. Note: The download is a PDF version of this tutorial. 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. |
Solving One-Step Equations | |
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 | |
INSTRUCTIONAL RESOURCE: Tutorial: What Are Two-Step Equations? | INSTRUCTIONAL RESOURCE: Tutorial: What Are Two-Step Equations?
This tutorial provides an overview of two-step equations. Note: The download is a PDF version of this tutorial. 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. |
Solving Two-Step Equations | |
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 | |
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 | |
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 | |
Interactive Math Game: Equation Sort | Description
Use this math game to review true equations, false equations, and conditional equations. The game provides feedback. |
Applications of Equations and Inequalities | |
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 | |
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 | |
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 | |
Math Clip Art--Algebra Tiles--Algebra Tiles Set | Math Clip Art--Algebra Tiles--Algebra Tiles Set
This is part of a collection of math clip art images that model numbers and expressions using algebra tiles. |
Algebra Tiles--Expressions and Equations | |
Math Clip Art--Algebra Tiles--Negative 1 Algebra Tiles | Math Clip Art--Algebra Tiles--Negative 1 Algebra Tiles
This is part of a collection of math clip art images that model numbers and expressions using algebra tiles. |
Algebra Tiles--Expressions and Equations | |
Math Clip Art--Algebra Tiles--Positive 1 Algebra Tiles | Math Clip Art--Algebra Tiles--Positive 1 Algebra Tiles
This is part of a collection of math clip art images that model numbers and expressions using algebra tiles. |
Algebra Tiles--Expressions and Equations | |
Math Clip Art--Algebra Tiles--X Algebra Tiles | Math Clip Art--Algebra Tiles--X Algebra Tiles
This is part of a collection of math clip art images that model numbers and expressions using algebra tiles. |
Algebra Tiles--Expressions and Equations |