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

Lesson 1: Integers

In this Grade 6 lesson from Big Ideas Math Course 1, Chapter 6, students learn what integers are — the set of whole numbers and their opposites — and how to represent positive and negative integers in real-world contexts such as temperature, elevation, and financial gains or losses. Students practice writing and graphing integers on a number line, identifying opposites, and recognizing that zero is neither positive nor negative.

Section 1

Defining Negative Numbers

Property

A negative number is a number less than zero.
The symbol −- in front of a number means negative or opposite of.

Examples

  • A debt of 100 dollars is represented by −100-100 dollars.
  • A location 50 feet below sea level has an elevation of −50-50 feet.
  • A loss of 5 points in a game is recorded as −5-5 points.

Explanation

Negative numbers represent values less than zero, like debt, temperatures below freezing, or depths below sea level. They are the opposites of positive numbers, existing on the other side of zero.

Section 2

Understanding Opposites

Property

Two numbers are opposites when they are the same distance away from zero, but in opposite directions.
For example, “3” represents the point that is 3 units to the right of 0, and “−3-3” is its opposite, three units to the left of 0.
Zero is its own opposite.

Examples

  • The opposite of 9 is −9-9, as both numbers are 9 units away from 0.
  • The opposite of the opposite of −4-4 is −(−(−4))=−4-(-(-4)) = -4. The first opposite is 4, and the opposite of 4 is −4-4.
  • If earning 5 points in a game is represented by +5+5, its opposite is losing 5 points, represented by −5-5.

Explanation

Opposites are mirror images of each other across zero. They have the same distance from zero, just in different directions. Taking the opposite of an opposite brings you right back to where you started!

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Defining Negative Numbers

Property

A negative number is a number less than zero.
The symbol −- in front of a number means negative or opposite of.

Examples

  • A debt of 100 dollars is represented by −100-100 dollars.
  • A location 50 feet below sea level has an elevation of −50-50 feet.
  • A loss of 5 points in a game is recorded as −5-5 points.

Explanation

Negative numbers represent values less than zero, like debt, temperatures below freezing, or depths below sea level. They are the opposites of positive numbers, existing on the other side of zero.

Section 2

Understanding Opposites

Property

Two numbers are opposites when they are the same distance away from zero, but in opposite directions.
For example, “3” represents the point that is 3 units to the right of 0, and “−3-3” is its opposite, three units to the left of 0.
Zero is its own opposite.

Examples

  • The opposite of 9 is −9-9, as both numbers are 9 units away from 0.
  • The opposite of the opposite of −4-4 is −(−(−4))=−4-(-(-4)) = -4. The first opposite is 4, and the opposite of 4 is −4-4.
  • If earning 5 points in a game is represented by +5+5, its opposite is losing 5 points, represented by −5-5.

Explanation

Opposites are mirror images of each other across zero. They have the same distance from zero, just in different directions. Taking the opposite of an opposite brings you right back to where you started!