Learn on PengiBig Ideas Math, Course 1Chapter 3: Algebraic Expressions and Properties

Lesson 1: Algebraic Expressions

In this Grade 6 lesson from Big Ideas Math, Course 1, students learn to identify the parts of an algebraic expression, including terms, coefficients, constants, and variables. They practice writing expressions using exponents and evaluating algebraic expressions with one or two variables by substituting values and applying the order of operations. Real-life scenarios, such as calculating hourly wages and total costs, help students connect expression writing and evaluation to everyday problems.

Section 1

Introduction to Algebraic Expressions

Property

An algebraic expression is the same as an arithmetic expression, except that some of the entries are letters representing numbers.

These symbols are called variables and represent an unknown quantity.

To evaluate an algebraic expression, substitute specific values for the variables and perform the arithmetic operations according to the order of operations.

Section 2

Repeated Multiplication and Exponential Form

Property

Any repeated multiplication can be written in exponential form: $a \cdot a \cdot a \cdot \ldots \cdot a$ ( $n$ factors) = $a^n$ .

Conversely, any exponential expression can be expanded back into repeated multiplication. The base ( $a$ ) indicates what number is being multiplied, and the exponent ( $n$ ) indicates how many times the base appears as a factor.

Examples

$5 \cdot 5 \cdot 5 \cdot 5 = 5^4$ (four factors of 5)
$x^6 = x \cdot x \cdot x \cdot x \cdot x \cdot x$ (six factors of $x$ )
$(-3) \cdot (-3) \cdot (-3) = (-3)^3$ (three factors of -3)

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Introduction to Algebraic Expressions

Property

An algebraic expression is the same as an arithmetic expression, except that some of the entries are letters representing numbers.

These symbols are called variables and represent an unknown quantity.

To evaluate an algebraic expression, substitute specific values for the variables and perform the arithmetic operations according to the order of operations.

Section 2

Repeated Multiplication and Exponential Form

Property

Any repeated multiplication can be written in exponential form: $a \cdot a \cdot a \cdot \ldots \cdot a$ ( $n$ factors) = $a^n$ .

Examples

$5 \cdot 5 \cdot 5 \cdot 5 = 5^4$ (four factors of 5)
$x^6 = x \cdot x \cdot x \cdot x \cdot x \cdot x$ (six factors of $x$ )
$(-3) \cdot (-3) \cdot (-3) = (-3)^3$ (three factors of -3)

Overview

Lesson overview

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

Overview

Section 1

Introduction to Algebraic Expressions

Property

An algebraic expression is the same as an arithmetic expression, except that some of the entries are letters representing numbers.

These symbols are called variables and represent an unknown quantity.

To evaluate an algebraic expression, substitute specific values for the variables and perform the arithmetic operations according to the order of operations.

Section 2

Repeated Multiplication and Exponential Form

Property

Any repeated multiplication can be written in exponential form: $a \cdot a \cdot a \cdot \ldots \cdot a$ ( $n$ factors) = $a^n$ .

Examples

$5 \cdot 5 \cdot 5 \cdot 5 = 5^4$ (four factors of 5)
$x^6 = x \cdot x \cdot x \cdot x \cdot x \cdot x$ (six factors of $x$ )
$(-3) \cdot (-3) \cdot (-3) = (-3)^3$ (three factors of -3)