11-1 Integers and Absolute Value

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes

11-1 Integers and Absolute Value

Warm UpAdd or subtract.

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

4172

0 1 2 3 4 5 6 7 8 9 10

11-1 Integers and Absolute Value

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, 4, 5, 6, 7, and 8 lb

11-1 Integers and Absolute Value

Preview of MA.7.A.3.1 Use and justify the rules for…finding absolute value of integers.

Sunshine State Standards

11-1 Integers and Absolute Value

Vocabulary

positive numbernegative numberoppositesintegerabsolute value

11-1 Integers and Absolute Value

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 (–).

11-1 Integers and Absolute Value

Additional Example 1: 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

11-1 Integers and Absolute Value

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

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

11-1 Integers and Absolute Value

Check It Out: Example 1

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

11-1 Integers and Absolute Value

Check It Out: Example 1

Name a positive or negative number to represent each situation.

C. spending $34

Negative numbers can represent losses or decreases.

–34

11-1 Integers and Absolute Value

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.

11-1 Integers and Absolute Value

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

{0, 1, 2, 3, 4, …}

Remember!

11-1 Integers and Absolute Value

Additional Example 2: 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. –5

–2 is the same distance from 0 as +2.

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

+5 is the same distance from 0 as –5.

11-1 Integers and Absolute Value

Additional Example 2: 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.

11-1 Integers and Absolute Value

Check It Out: Example 2

Graph each integer and its opposite on a number line.

A. +3

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

B. –4

–3 is the same distance from 0 as +3.

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

+4 is the same distance from 0 as –4.

11-1 Integers and Absolute Value

Check It Out: Example 2

Graph each integer and its opposite on a number line.

C. 0

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

Zero is its own opposite.

11-1 Integers and Absolute Value

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| = 3 |3| = 3

|<--3 units--> | <--3 units-->|

• Absolute values are never negative.

• Opposite integers have the same absolute value.

• |0| = 0

11-1 Integers and Absolute Value

Additional Example 3A: Finding Absolute Value

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

A. |–2|

–2 is 2 units from 0, so |–2| = 2

2

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

11-1 Integers and Absolute Value

Additional Example 3B: Finding Absolute Value

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

B. |8|

8 is 8 units from 0, so |8| = 8

8

–1 0 1 2 3 4 5 6 7 8 9

11-1 Integers and Absolute Value

Check It Out: Example 3A

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

A. |6|

6 is 6 units from 0, so |6| = 6

6

–1 0 1 2 3 4 5 6 7 8 9

11-1 Integers and Absolute Value

Check It Out: Example 3B

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

B. |–4|

–4 is 4 units from 0, so |–4| = 4

4

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

11-1 Integers and Absolute Value

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

11-1 Integers and Absolute Value

Lesson Quiz

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

4. |–7| 5. |4|

–12

+15

6

7 4

11-1 Integers and Absolute Value

1. Identify a positive or negative number to represent the given situation. 10 more students joining music class.

A. +10

B. –10

C.

D.

Lesson Quiz for Student Response Systems

11-1 Integers and Absolute Value

2. Identify a positive or negative number to represent the given situation. A basement for car parking at 12 feet below the ground level.

A. +12

B. –12

C.

D.

Lesson Quiz for Student Response Systems

11-1 Integers and Absolute Value

3. What is the opposite of –15?

A. +15

B. –15

C. 0

D.

Lesson Quiz for Student Response Systems

11-1 Integers and Absolute Value

4. Gold rate has increased by $3. Identify an integer to represent this situation.

A. +3

B. –3

C. 0

D.

Lesson Quiz for Student Response Systems