Learn on PengiBig Ideas Math, Course 1Chapter 6: Integers and the Coordinate Plane

Lesson 2: Comparing and Ordering Integers

In this Grade 6 lesson from Big Ideas Math, Course 1, students learn how to compare and order integers using both horizontal and vertical number lines, applying the concepts of greater than and less than with positive and negative values. Students practice using inequality symbols to compare integers such as -5 and -3, and order sets of integers from least to greatest by plotting them on a number line. The lesson also connects integer comparison to real-life contexts like temperature readings and rocket launch countdowns.

Section 1

Comparing Integers on a Horizontal Number Line

Property

For any two integers $a$ and $b$ :

$a < b$ means " $a$ is less than $b$ ."
$a \leq b$ means " $a$ is less than or equal to $b$ ."
$a > b$ means " $a$ is greater than $b$ ."
$a \geq b$ means " $a$ is greater than or equal to $b$ ."

On a number line, $a < b$ means that $a$ lies to the left of $b$ , and $a > b$ means that $a$ lies to the right of $b$ .

Section 2

Comparing Integers on a Vertical Number Line

Property

On a vertical number line, integers positioned higher are greater than integers positioned lower.
If integer $a$ is above integer $b$ on a vertical number line, then $a > b$ .
If integer $a$ is below integer $b$ on a vertical number line, then $a < b$ .

Examples

Section 3

Graphing Method for Ordering Multiple Integers

Property

To order multiple integers from least to greatest using a number line:
(1) Draw a horizontal number line with appropriate scale;
(2) Plot each integer as a point on the number line;
(3) Read the integers from left to right to get the order from least to greatest.

Examples

Section 4

Integer Problem Solving and Reasoning

Property

Real-world problems can be solved by translating scenarios into integer inequalities.
To find the greatest or least integer value satisfying an inequality, use a number line to identify the integer closest to the boundary value that is within the solution set.

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Comparing Integers on a Horizontal Number Line

Property

For any two integers $a$ and $b$ :

$a < b$ means " $a$ is less than $b$ ."
$a \leq b$ means " $a$ is less than or equal to $b$ ."
$a > b$ means " $a$ is greater than $b$ ."
$a \geq b$ means " $a$ is greater than or equal to $b$ ."

On a number line, $a < b$ means that $a$ lies to the left of $b$ , and $a > b$ means that $a$ lies to the right of $b$ .

Section 2

Comparing Integers on a Vertical Number Line

Property

Examples

Section 3

Graphing Method for Ordering Multiple Integers

Property

Examples

Section 4

Integer Problem Solving and Reasoning

Property

Examples

Overview

Lesson overview

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

Overview

Section 1

Comparing Integers on a Horizontal Number Line

Property

For any two integers $a$ and $b$ :

$a < b$ means " $a$ is less than $b$ ."
$a \leq b$ means " $a$ is less than or equal to $b$ ."
$a > b$ means " $a$ is greater than $b$ ."
$a \geq b$ means " $a$ is greater than or equal to $b$ ."

On a number line, $a < b$ means that $a$ lies to the left of $b$ , and $a > b$ means that $a$ lies to the right of $b$ .

Section 2

Comparing Integers on a Vertical Number Line

Property

Examples

Section 3

Graphing Method for Ordering Multiple Integers

Property

Examples

Section 4

Integer Problem Solving and Reasoning