Learn on PengienVision, Mathematics, Grade 6Chapter 2: Integers and Rational Numbers

Lesson 1: Understand Integers

In this Grade 6 lesson from enVision Mathematics Chapter 2, students learn to define integers, including positive integers, negative integers, and zero, and identify opposites as numbers equidistant from zero on a number line. Students practice comparing and ordering integers and use positive and negative integers to represent real-world quantities such as temperature, altitude, elevation, and depth. The lesson aligns with Common Core Standards 6.NS.C.5, 6.NS.C.6a, and 6.NS.C.6c.

Section 1

What is an Integer?

Property

Integers are counting numbers, their opposites, and zero.

3,2,1,0,1,2,3 \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

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!

Book overview

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Chapter 2: Integers and Rational Numbers

  1. Lesson 1Current

    Lesson 1: Understand Integers

  2. Lesson 2

    Lesson 2: Represent Rational Numbers on the Number Line

  3. Lesson 3

    Lesson 3: Absolute Values of Rational Numbers

  4. Lesson 4

    Lesson 4: Represent Rational Numbers on the Coordinate Plane

  5. Lesson 5

    Lesson 5: Find Distances on the Coordinate Plane

  6. Lesson 6

    Lesson 6: Represent Polygons on the Coordinate Plane

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.

3,2,1,0,1,2,3 \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

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!

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 2: Integers and Rational Numbers

  1. Lesson 1Current

    Lesson 1: Understand Integers

  2. Lesson 2

    Lesson 2: Represent Rational Numbers on the Number Line

  3. Lesson 3

    Lesson 3: Absolute Values of Rational Numbers

  4. Lesson 4

    Lesson 4: Represent Rational Numbers on the Coordinate Plane

  5. Lesson 5

    Lesson 5: Find Distances on the Coordinate Plane

  6. Lesson 6

    Lesson 6: Represent Polygons on the Coordinate Plane