Learn on PengiBig Ideas Math, Course 2Chapter 1: Integers

Lesson 1: Integers and Absolute Value

In this Grade 7 lesson from Big Ideas Math Course 2, students learn to define and find the absolute value of integers and explore how positive and negative integers represent velocity and speed in real-world contexts. Through activities involving falling parachutes and rising balloons, students discover that the absolute value of velocity equals speed and practice comparing integers on a number line.

Section 1

What is an Integer?

Property

Integers are counting numbers, their opposites, and zero.

\ldots -3, -2, -1, 0, 1, 2, 3 \ldots

Examples

To plot the number 4 on a number line, we move 4 units to the right of 0.

To plot the number -5, we start at 0 and move 5 units to the left into the negative side.

Section 2

Integers on the Number Line

Property

The positive whole numbers, the negative whole numbers, and zero make up a set of numbers called the integers. On a number line, integers are positioned with negative numbers to the left of zero and positive numbers to the right of zero. Numbers increase in value as we move from left to right on the number line.

Examples

Section 3

Absolute Value

Property

The absolute value of a number is its distance from $0$ on the number line. The absolute value of a number $n$ is written as $|n|$ .

Property of Absolute Value
$|n| \geq 0$ for all numbers. Absolute values are always greater than or equal to zero!

Examples

The absolute value of $-18$ is its distance from 0, so $|-18| = 18$ .
To simplify $30 - |12 - 4(5)|$ , we calculate inside the bars first: $30 - |12 - 20| = 30 - |-8| = 30 - 8 = 22$ .
Compare $|-11|$ and $-|-11|$ . We get $11$ and $-11$ . So, $|-11| > -|-11|$ .

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

What is an Integer?

Property

Integers are counting numbers, their opposites, and zero.

\ldots -3, -2, -1, 0, 1, 2, 3 \ldots

Examples

To plot the number 4 on a number line, we move 4 units to the right of 0.

To plot the number -5, we start at 0 and move 5 units to the left into the negative side.

Section 2

Integers on the Number Line

Property

Examples

Section 3

Absolute Value

Property

The absolute value of a number is its distance from $0$ on the number line. The absolute value of a number $n$ is written as $|n|$ .

Property of Absolute Value
$|n| \geq 0$ for all numbers. Absolute values are always greater than or equal to zero!

Examples

The absolute value of $-18$ is its distance from 0, so $|-18| = 18$ .
To simplify $30 - |12 - 4(5)|$ , we calculate inside the bars first: $30 - |12 - 20| = 30 - |-8| = 30 - 8 = 22$ .
Compare $|-11|$ and $-|-11|$ . We get $11$ and $-11$ . So, $|-11| > -|-11|$ .

Overview

Lesson overview

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

Overview

Section 1

What is an Integer?

Property

Integers are counting numbers, their opposites, and zero.

\ldots -3, -2, -1, 0, 1, 2, 3 \ldots

Examples

To plot the number 4 on a number line, we move 4 units to the right of 0.

To plot the number -5, we start at 0 and move 5 units to the left into the negative side.

Section 2

Integers on the Number Line

Property

Examples

Section 3

Absolute Value

Property

The absolute value of a number is its distance from $0$ on the number line. The absolute value of a number $n$ is written as $|n|$ .

Property of Absolute Value
$|n| \geq 0$ for all numbers. Absolute values are always greater than or equal to zero!

Examples

The absolute value of $-18$ is its distance from 0, so $|-18| = 18$ .
To simplify $30 - |12 - 4(5)|$ , we calculate inside the bars first: $30 - |12 - 20| = 30 - |-8| = 30 - 8 = 22$ .
Compare $|-11|$ and $-|-11|$ . We get $11$ and $-11$ . So, $|-11| > -|-11|$ .