Learn on PengiReveal Math, Course 1Module 4: Integers, Rational Numbers, and the Coordinate Plane

4-1 Represent Integers

In this Grade 6 lesson from Reveal Math, Course 1, students learn to identify and represent integers, including positive integers, negative integers, and zero, using real-world contexts such as temperature, football yardage, and elevation. Students also practice graphing sets of integers on both horizontal and vertical number lines.

Section 1

Defining the Set of Integers

Property

Integers are the set of whole numbers and their opposites: {...,−3,−2,−1,0,1,2,3,...}\{..., -3, -2, -1, 0, 1, 2, 3, ...\}

Zero is neither positive nor negative.

Section 2

Writing Integers with Positive and Negative Signs

Property

Positive integers can be written with or without a positive sign: +5=5+5 = 5.
Negative integers must always be written with a negative sign: −3-3.
Zero is written without any sign: 00.

Examples

Section 3

Representing Change with Signed Numbers

Property

We can use negative numbers to indicate a decrease or a loss, and positive numbers to indicate an increase or a gain.
An increase or decrease is called a net change.

Examples

  • If the temperature was 8∘8^{\circ} and changed by −12∘-12^{\circ}, the new temperature is −4∘-4^{\circ}.
  • A stock was worth 25 dollars per share and is now worth 18 dollars. The net change in value is −7-7 dollars.
  • Corinne's bank account had 150 dollars, and she wrote a check for 200 dollars. Her account's value changed by −200-200 dollars, resulting in a balance of −50-50 dollars.

Explanation

Signed numbers are perfect for showing change. A positive number shows a gain or increase, like the temperature rising. A negative number shows a loss or decrease, like a stock price dropping. This is the 'net change.'

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Defining the Set of Integers

Property

Integers are the set of whole numbers and their opposites: {...,−3,−2,−1,0,1,2,3,...}\{..., -3, -2, -1, 0, 1, 2, 3, ...\}

Zero is neither positive nor negative.

Section 2

Writing Integers with Positive and Negative Signs

Property

Positive integers can be written with or without a positive sign: +5=5+5 = 5.
Negative integers must always be written with a negative sign: −3-3.
Zero is written without any sign: 00.

Examples

Section 3

Representing Change with Signed Numbers

Property

We can use negative numbers to indicate a decrease or a loss, and positive numbers to indicate an increase or a gain.
An increase or decrease is called a net change.

Examples

  • If the temperature was 8∘8^{\circ} and changed by −12∘-12^{\circ}, the new temperature is −4∘-4^{\circ}.
  • A stock was worth 25 dollars per share and is now worth 18 dollars. The net change in value is −7-7 dollars.
  • Corinne's bank account had 150 dollars, and she wrote a check for 200 dollars. Her account's value changed by −200-200 dollars, resulting in a balance of −50-50 dollars.

Explanation

Signed numbers are perfect for showing change. A positive number shows a gain or increase, like the temperature rising. A negative number shows a loss or decrease, like a stock price dropping. This is the 'net change.'