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.

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Video Definition 37--Equation Concepts--True Equation	Video Definition 37--Equation Concepts--True Equation Topic Equations Description True Equation. A mathematically accurate equation. If variables are involved, the true equation is for the values of the variable that make the equation true. Examples: 2 + 1 = 3; (2 + 3)2 = 25; x + 3 = 9 for x = 6 The topic of this video is closely tied to Equations, providing an essential understanding of its fundamental concepts. This video explores the mathematics behind this topic by delving into how key principles are applied in practical contexts.	Applications of Equations and Inequalities
Video Definition 38--Equation Concepts--Two-Step Equation	Video Definition 38--Equation Concepts--Two-Step Equation Topic Equations Description Two-Step Equation. A two-step equation is an equation that involves two mathematical operations to solve. The example given is 2x + 2 = 8, where the first operation is subtraction, leading to 2x = 6, followed by division to solve for x = 3. This concept extends the understanding of solving equations by introducing a sequence of operations, crucial for solving more complex equations.	Solving Two-Step Equations
Video Definition 39--Equation Concepts--Variable Expression	Video Definition 39--Equation Concepts--Variable Expression Topic Equations Description Variable Expression. A variable expression is made up of numbers, operations, and variables. Examples include 2x + 3 = 5 (expression on the left), 4 = 3x + 7 (expression on the right), and 4x + 3 = x - 5 (expressions on both sides). This connects variables to equations and highlights their role in forming relationships within mathematical contexts.	Variable Expressions
Video Definition 4--Equation Concepts--Algebraic Expression	Video Definition 4--Equation Concepts--Algebraic Expression Topic Equations Description An Algebraic Expression consists of numbers, operations, and variables. Unlike equations, expressions may not have an equality. Examples include 2x + 3, 4 = 3x + 7, and 4x + 3 = x - 5, demonstrating their versatility in representing mathematical relationships. This term distinguishes between expressions and equations, forming the basis for manipulating algebraic forms before solving equations.	Numerical and Algebraic Expressions
Video Definition 40--Equation Concepts--Visual Models for Equations	Video Definition 40--Equation Concepts--Visual Models for Equations Topic Equations Description Visual Model of an Equation. A visual model of an equation represents the numbers, operations, and equality using visuals. The example shows 1 + 2 = 3 with blocks illustrating the balance of the equation. This visual approach reinforces the foundational concept of equality and provides an intuitive way to understand equations, especially for visual learners.	Applications of Equations and Inequalities
Video Definition 41--Equation Concepts--Approximately Equal To	Video Definition 41--Equation Concepts--Approximately Equal To Topic Equations Description The Approximately Equal To Sign (≈) indicates that two expressions are close in value but not equal. Examples include estimating sums (58 + 49 ≈ 100), square roots (√50 ≈ 7), and function values (f(x) ≈ 25). This term relates to the topic by introducing estimation techniques, valuable for checking solutions or simplifying problems.	Applications of Equations and Inequalities
Video Definition 42--Equation Concepts--Proportional To	Video Definition 42--Equation Concepts--Proportional To Topic Equations Description Proportional To indicates a linear relationship between two variables. For example, distance (d) is proportional to time (t), written as d ∝ t. This term links linear equations to real-world relationships, reinforcing practical applications of mathematical concepts.	Applications of Equations and Inequalities
Video Definition 43--Equation Concepts--Similar To	Video Definition 43--Equation Concepts--Similar To Topic Equations Description Similar To. When two geometric shapes are similar, corresponding sides are proportional. ΔABC ~ ΔDEF; AB ∝ DE The topic of this video is closely tied to Equations, providing an essential understanding of its fundamental concepts. This video explores the mathematics behind this topic by delving into how key principles are applied in practical contexts.	Applications of Equations and Inequalities
Video Definition 44--Equation Concepts--Congruent To	Video Definition 44--Equation Concepts--Congruent To Topic Equations Description Congruent To signifies that two geometric shapes are congruent, meaning their corresponding sides and angles are equal. For example, triangles ABC and DEF are congruent, so side AB equals side DE. This term introduces geometric equality, tying equations to geometric properties and congruence criteria.	Applications of Equations and Inequalities
Video Definition 5--Equation Concepts--Assigning Values to Variables	Video Definition 5--Equation Concepts--Assigning Values to Variables Topic Equations Description Assigning Values to Variables involves assigning a numerical value to a variable for evaluating functions. For instance, let x = 3 in f(x) = 2x + 8 yields f(3) = 14. This term supports understanding how to evaluate equations and functions by substituting values, a key step in problem-solving.	Variable Expressions
Video Definition 6--Equation Concepts--Conditional Equation	Video Definition 6--Equation Concepts--Conditional Equation Topic Equations Description A Conditional Equation is true only for specific variable values. Examples include x + 1 = 4 (x = 3), x2 - 25 = 0 (x = ±5), and 2x - 5 = x + 9 (x = 14). This term supports solving equations by emphasizing that solutions depend on satisfying the given conditions.	Applications of Equations and Inequalities
Video Definition 7--Equation Concepts--Constant Term	Video Definition 7--Equation Concepts--Constant Term Topic Equations Description A Constant Term in an algebraic equation is a number without a variable. Examples include 2 in x2 + 3x + 2 = 0, -10 in x3 - 2x2 + 4x - 10 = 0, and 5 in x4 - 2x3 + 4x2 - x + 5 = 0. This term explains the role of constants in equations, crucial for identifying and isolating terms when solving equations.	Variables and Unknowns
Video Definition 8--Equation Concepts--Division Property of Equality	Video Definition 8--Equation Concepts--Division Property of Equality Topic Equations Description The Division Property of Equality allows division by the same non-zero quantity on both sides of an equation, maintaining equality. For example, if a = b, then a / c = b / c, where c ≠ 0. Solving 5x = 15 yields x = 3 by dividing both sides by 5. This term builds on equality principles, showing another method to isolate variables and solve equations.	Applications of Equations and Inequalities
Video Definition 9--Equation Concepts--Equality	Video Definition 9--Equation Concepts--Equality Topic Equations Description Equality refers to a mathematical statement where two expressions are equal. Examples include 1 + 2 = 3 and x + 3 = 7, where both sides represent the same value. This term defines the core concept of equations, ensuring all manipulations preserve equality to find solutions.	Applications of Equations and Inequalities
Worksheet: Solving Two-Step Division/Addition, Division/Subtraction Equations	Worksheet: Solving Two-Step Division/Addition, Division/Subtraction Equations This is part of a collection of math worksheets on the topic of solving two-step equations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Solving Two-Step Equations
Worksheet: Solving Two-Step Multiplication/Addition, Multiplication/Subtraction Equations	Worksheet: Solving Two-Step Multiplication/Addition, Multiplication/Subtraction Equations This is part of a collection of math worksheets on the topic of solving two-step equations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Solving Two-Step Equations
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 1	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 1 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 10	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 10 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 2	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 2 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 3	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 3 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 4	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 4 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 5	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 5 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 6	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 6 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 7	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 7 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 8	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 8 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 9	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Addition--Set 9 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 1	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 1 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 10	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 10 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 2	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 2 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 3	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 3 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 4	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 4 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 5	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 5 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 6	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 6 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 7	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 7 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 8	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 8 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 9	Worksheet: The Language of Math--Variable Expressions Word Problems--Multiplication and Subtraction--Set 9 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions--Multiplication and Addition--Set 1	Worksheet: The Language of Math--Variable Expressions--Multiplication and Addition--Set 1 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions--Multiplication and Addition--Set 10	Worksheet: The Language of Math--Variable Expressions--Multiplication and Addition--Set 10 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions--Multiplication and Addition--Set 2	Worksheet: The Language of Math--Variable Expressions--Multiplication and Addition--Set 2 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions
Worksheet: The Language of Math--Variable Expressions--Multiplication and Addition--Set 3	Worksheet: The Language of Math--Variable Expressions--Multiplication and Addition--Set 3 This is part of a collection of math worksheets on the topic of the language of math in which students translate verbal expressions into numerical expressions and then perform the calculations. To see the complete worksheet collection on this topic, click on this link. Note: The download is a PDF file. Related Resources To see additional resources on this topic, click on the Related Resources tab. Worksheet Library To see the complete collection of Worksheets, click on this link.	Numerical Expressions and Variable Expressions

Illustrative Math Alignment: Grade 7 Unit 7

Expressions, Equations, and Inequalities

Lesson 5: Reasoning about Equations and Tape Diagrams (Part 2)

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