Learn on PengiBig Ideas Math, Course 1Chapter 7: Equations and Inequalities

Lesson 1: Writing Equations in One Variable

In this Grade 6 lesson from Big Ideas Math, Course 1, students learn how to write one-variable equations by translating word sentences into mathematical statements using key phrases like "decreased by," "the product of," and "the same as." The lesson covers identifying the equal sign placement and defining variables to represent unknown quantities in real-life scenarios. Students also practice simplifying word problems to isolate the essential information needed to set up an equation.

Section 1

Distinguishing Between Expressions and Equations

Property

An expression is a mathematical phrase that contains numbers, variables, and operations but has no equal sign: $3x + 5$ or $2y - 7$ .

An equation is a mathematical sentence that shows two expressions are equal using an equal sign: $3x + 5 = 14$ or $2y - 7 = 11$ .

Section 2

Identifying Key Words for Operations and Equations

Property

Operation keywords: sum ( $+$ ), difference ( $-$ ), product ( $\times$ ), quotient ( $\div$ )

Equal sign keywords: is, equals, the same as, results in ( $=$ )

Section 3

Writing Equations from Real-World Situations

Property

To translate a word problem into an equation, follow these steps:

Read & Understand: Identify what the problem is asking.
Define a Variable: Choose a variable to represent the unknown quantity.
Identify Key Information: Find the numbers and mathematical relationships (operations, equals) described in the problem.
Write the Equation: Assemble the variable and key information into an equation that represents the situation.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Distinguishing Between Expressions and Equations

Property

An expression is a mathematical phrase that contains numbers, variables, and operations but has no equal sign: $3x + 5$ or $2y - 7$ .

An equation is a mathematical sentence that shows two expressions are equal using an equal sign: $3x + 5 = 14$ or $2y - 7 = 11$ .

Section 2

Identifying Key Words for Operations and Equations

Property

Operation keywords: sum ( $+$ ), difference ( $-$ ), product ( $\times$ ), quotient ( $\div$ )

Equal sign keywords: is, equals, the same as, results in ( $=$ )

Section 3

Writing Equations from Real-World Situations

Property

To translate a word problem into an equation, follow these steps:

Read & Understand: Identify what the problem is asking.
Define a Variable: Choose a variable to represent the unknown quantity.
Identify Key Information: Find the numbers and mathematical relationships (operations, equals) described in the problem.
Write the Equation: Assemble the variable and key information into an equation that represents the situation.

Examples

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Distinguishing Between Expressions and Equations

Property

An expression is a mathematical phrase that contains numbers, variables, and operations but has no equal sign: $3x + 5$ or $2y - 7$ .

An equation is a mathematical sentence that shows two expressions are equal using an equal sign: $3x + 5 = 14$ or $2y - 7 = 11$ .

Section 2

Identifying Key Words for Operations and Equations

Property

Operation keywords: sum ( $+$ ), difference ( $-$ ), product ( $\times$ ), quotient ( $\div$ )

Equal sign keywords: is, equals, the same as, results in ( $=$ )

Section 3

Writing Equations from Real-World Situations

Property

To translate a word problem into an equation, follow these steps:

Read & Understand: Identify what the problem is asking.
Define a Variable: Choose a variable to represent the unknown quantity.
Identify Key Information: Find the numbers and mathematical relationships (operations, equals) described in the problem.
Write the Equation: Assemble the variable and key information into an equation that represents the situation.