Illustrative Math Alignment: Grade 7 Unit 7
Expressions, Equations, and Inequalities
Lesson 5: Reasoning about Equations and Tape Diagrams (Part 2)
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--Variables, Unknowns, and Constants--Algebraic Expression | Definition--Variables, Unknowns, and Constants--Algebraic Expression
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Assigning Values to Variables | Definition--Variables, Unknowns, and Constants--Assigning Values to Variables
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Coefficient | What Is a Coefficient?
This is part of a series of definitions that focus on constants, variables, and coefficients. These definition cards can easily be incorporated into a lesson plan. —PRESS PREVIEW TO SEE THE DEFINITION— To see the complete collection of definitions on this topic, click on this link.The following section provides a brief review of number properties that are helpful in working with numerical and variable expressions. |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Constant | Definition--Variables, Unknowns, and Constants--Constant
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Constant of Proportionality | Definition--Variables, Unknowns, and Constants--Constant of Proportionality
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Constant of Variation | Definition--Variables, Unknowns, and Constants--Constant of Variation
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Constant Term | Definition--Variables, Unknowns, and Constants--Constant Term
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Evaluating an Algebraic Expression | Definition--Variables, Unknowns, and Constants--Evaluating an Algebraic Expression
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Models for Numbers | Definition--Variables, Unknowns, and Constants--Models for Numbers
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Models for Variables | Definition--Variables, Unknowns, and Constants--Models for Variables
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Numerical Expression | Definition--Variables, Unknowns, and Constants--Numerical Expression
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Parameter | Definition--Variables, Unknowns, and Constants--Parameter
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Random Variable | Definition--Variables, Unknowns, and Constants--Random Variable
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Range of a Variable | Definition--Variables, Unknowns, and Constants--Range of a Variable
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Solving for the Unknown | Definition--Variables, Unknowns, and Constants--Solving for the Unknown
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Special Constants | Definition--Variables, Unknowns, and Constants--Special Constants
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Unknown | Definition--Variables, Unknowns, and Constants--Unknown
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Variable | Definition | Variables, Unknowns, and Constants | Variable
This is part of a collection of definitions on the topic of variables and constants. These definitions can easily be incorporated into your lesson plans. —PRESS PREVIEW TO SEE THE DEFINITION— To see the complete collection of definitions on this topic, click on this link.The following section provides additional information on the topic. Watch this video about variables and equations. (The transcript is included.) |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Variable Expression | Definition--Variables, Unknowns, and Constants--Variable Expression
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns |
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Definition--Variables, Unknowns, and Constants--Verbal Representations for Unknowns | Definition--Variables, Unknowns, and Constants--Verbal Representations for Unknowns
This is part of a collection of definitions related to variables, unknowns, and constants. This includes general definitions for variables, unknowns, and constants, as well as related terms that describe their properties. |
Variables and Unknowns |
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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 |
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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 |
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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 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 |
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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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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 |
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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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Math Clip Art--Rates and Tape Diagrams: Cooking 1 | Math Clip Art--Rates and Tape Diagrams: Cooking 1 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems. |
Ratios and Rates |
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Math Clip Art--Rates and Tape Diagrams: Cooking 1 | Math Clip Art--Rates and Tape Diagrams: Cooking 1 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems. |
Ratios and Rates |
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Math Clip Art--Rates and Tape Diagrams: Cooking 10 | Math Clip Art--Rates and Tape Diagrams: Cooking 10 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems. |
Ratios and Rates |
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Math Clip Art--Rates and Tape Diagrams: Cooking 10 | Math Clip Art--Rates and Tape Diagrams: Cooking 10 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems. |
Ratios and Rates |
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Math Clip Art--Rates and Tape Diagrams: Cooking 11 | Math Clip Art--Rates and Tape Diagrams: Cooking 11 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems. |
Ratios and Rates |
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Math Clip Art--Rates and Tape Diagrams: Cooking 11 | Math Clip Art--Rates and Tape Diagrams: Cooking 11 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems. |
Ratios and Rates |
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Math Clip Art--Rates and Tape Diagrams: Cooking 2 | Math Clip Art--Rates and Tape Diagrams: Cooking 2 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems. |
Ratios and Rates |
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Math Clip Art--Rates and Tape Diagrams: Cooking 2 | Math Clip Art--Rates and Tape Diagrams: Cooking 2 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems. |
Ratios and Rates |
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Math Clip Art--Rates and Tape Diagrams: Cooking 3 | Math Clip Art--Rates and Tape Diagrams: Cooking 3 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems. |
Ratios and Rates |
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Math Clip Art--Rates and Tape Diagrams: Cooking 3 | Math Clip Art--Rates and Tape Diagrams: Cooking 3 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems. |
Ratios and Rates |
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Math Clip Art--Rates and Tape Diagrams: Cooking 4 | Math Clip Art--Rates and Tape Diagrams: Cooking 4 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems. |
Ratios and Rates |
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Math Clip Art--Rates and Tape Diagrams: Cooking 4 | Math Clip Art--Rates and Tape Diagrams: Cooking 4 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems. |
Ratios and Rates |
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Math Clip Art--Rates and Tape Diagrams: Cooking 5 | Math Clip Art--Rates and Tape Diagrams: Cooking 5 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems. |
Ratios and Rates |
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Math Clip Art--Rates and Tape Diagrams: Cooking 5 | Math Clip Art--Rates and Tape Diagrams: Cooking 5 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems. |
Ratios and Rates |
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Math Clip Art--Rates and Tape Diagrams: Cooking 6 | Math Clip Art--Rates and Tape Diagrams: Cooking 6 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems. |
Ratios and Rates |
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Math Clip Art--Rates and Tape Diagrams: Cooking 6 | Math Clip Art--Rates and Tape Diagrams: Cooking 6 This is a collection of clip art images that show how to use tape diagrams to solve ratio and rate problems. |
Ratios and Rates |
