6th Grade Math HOMEWORK9-1

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9-1 Understanding Integers

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Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Warm UpAdd or subtract.

1. 16 + 252. 84 – 123. Graph the even numbers from 1 to 10 on

a number line.

4172

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0 1 2 3 4 5 6 7 8 9 10

Problem of the Day

Carlo uses a double-pan balance and three different weights to weigh bird seed. If his weights are 1 lb, 2 lb, and 5 lb, what whole pound amounts is he able to weigh?

1, 2, 3, 5, 6, 7, and 8 lb

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9-1 Understanding Integers

Today’s Learning Goal Assignment

Learn to identify and graph integers, find opposites, and find the absolute value of an integer.

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Vocabulary

positive numbernegative numberoppositesintegerabsolute value

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Positive numbers are greater than 0. They may be written with a positive sign (+), but they are usually written without it.

Negative numbers are less than 0. They are always written with a negative sign (–).

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Additional Example 1A & 1B: Identifying Positive and Negative Numbers in the Real World

Name a positive or negative number to represent each situation.

A. a jet climbing to an altitude of 20,000 feet

B. taking $15 out of the bank

Positive numbers can represent climbing or rising.

+20,000

Negative numbers can represent taking out or withdrawing.

–15

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Additional Example 1 Continued

Name a positive or negative number to represent each situation.

C. 7 degrees below zero

Negative numbers can represent values below or less than a certain value.

–7

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Try This: Additional Example 1A & 1B

Name a positive or negative number to represent each situation.

A. 300 feet below sea level

B. a hiker hiking to an altitude of 4,000 feet

Negative numbers can represent values below or less than a certain value.

–300

Positive numbers can represent climbing or rising.

+4,000

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Try This: Example 1C

Name a positive or negative number to represent each situation?

C. spending $34

Negative numbers can represent losses or decreases.

–34

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You can graph positive and negative numbers on a number line.On a number line, opposites are the same distance from 0 but on different sides of 0.

Integers are the set of all whole numbers and their opposites.

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

Opposites

Positive IntegersNegative Integers

0 is neither negative nor positive.

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The set of whole numbers includes zero and the counting numbers.

{0, 1, 2, 3, 4, …}

Remember!

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Additional Example 2A & 2B: Graphing Integers

Graph each integer and its opposite on a number line.

A. +2

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

B. –3

–2 is the same distance from 0 as +2.

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

+3 is the same distance from 0 as –3.

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Additional Example 2C: Graphing Integers

Graph each integer and its opposite on a number line.

C. +1

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

–1 is the same distance from 0 as +1.

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Try This: Example 2A & 2B

Graph each integer and its opposite on a number line.

A. +5

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

B. –4

–5 is the same distance from 0 as +5.

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

+4 is the same distance from 0 as –4.

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Try This: Example 2C

Graph each integer and its opposite on a number line.

C. +4

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

–4 is the same distance from 0 as +4.

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|–3| = 3 |3| = 3

The absolute value of an integer is its distance from 0 on a number line. The symbol for absolute value is | |.

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

3 units 3 units

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• Absolute values are never negative.

• Opposite integers have the same absolute value.

• |0| = 0

Read |3| as “the absolute value of 3.”

Read |–3| as “the absolute value of negative 3.”

Reading Math

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Additional Example 3A & 3B: Finding Absolute Value

Use the number line to find the absolute value of each integer.

A. |–4|

B. |2|

–4 is 4 units from 0, so |–4| = 4.4

2 is 2 units from 0, so |2| = 2.2

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

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Try This: Example 3A & 3B

Use the number line to find the absolute value of each integer.

A. |–3|

B. |1|

–3 is 3 units from 0, so |–3| = 3.3

1 is 1 unit from 0, so |1| = 1.1

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

Lesson QuizName a positive or negative number to represent each situation.

1. saving $15

2. 12 feet below sea level

3. What is the opposite of –6?

4. What is the absolute value of –12?

5. When the Swanton Bulldogs football team

passed the football, they gained 25 yards. Write

an integer to represent this situation.

–12

+15

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6

12

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+25