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

Lesson 1: Integers

In this Grade 6 lesson from Big Ideas Math Advanced 1, students learn to identify and work with integers, including positive numbers, negative numbers, and opposites, and understand how they extend the whole number system below zero. Students practice writing positive and negative integers to represent real-world situations such as temperature changes, point gains or losses, and building floors, then graph integers and their opposites on a number line. The lesson builds foundational vocabulary and number sense needed for Chapter 6's exploration of integers and the coordinate plane.

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

The Integer Number Line

Property

The number line consists of a straight line extending indefinitely in two directions from a central point, denoted as 00 (zero), and a line segment starting at 00, denoted as the unit distance.
For each counting number nn, a tick mark is made on the straight line that is nn units distance from 00 (the origin).
The marks on the right side of 00 are denoted by the positive integers 1,2,3,4,1, 2, 3, 4, \ldots, and the marks on the left side are denoted by the negative integers 1,2,3,4,-1, -2, -3, -4, \ldots, called the opposites of the positive integers.

Examples

Section 3

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

Book overview

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Chapter 6: Integers and the Coordinate Plane

  1. Lesson 1Current

    Lesson 1: Integers

  2. Lesson 2

    Lesson 2: Comparing and Ordering Integers

  3. Lesson 3

    Lesson 3: Fractions and Decimals on the Number Line

  4. Lesson 4

    Lesson 4: Absolute Value

  5. Lesson 5

    Lesson 5: The Coordinate Plane

Lesson overview

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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

The Integer Number Line

Property

The number line consists of a straight line extending indefinitely in two directions from a central point, denoted as 00 (zero), and a line segment starting at 00, denoted as the unit distance.
For each counting number nn, a tick mark is made on the straight line that is nn units distance from 00 (the origin).
The marks on the right side of 00 are denoted by the positive integers 1,2,3,4,1, 2, 3, 4, \ldots, and the marks on the left side are denoted by the negative integers 1,2,3,4,-1, -2, -3, -4, \ldots, called the opposites of the positive integers.

Examples

Section 3

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

Book overview

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

Continue this chapter

Chapter 6: Integers and the Coordinate Plane

  1. Lesson 1Current

    Lesson 1: Integers

  2. Lesson 2

    Lesson 2: Comparing and Ordering Integers

  3. Lesson 3

    Lesson 3: Fractions and Decimals on the Number Line

  4. Lesson 4

    Lesson 4: Absolute Value

  5. Lesson 5

    Lesson 5: The Coordinate Plane