11-1 Integers and Absolute Value Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

11-1 Integers and Absolute Value

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


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


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


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

Sunshine State Standards


Vocabulary

positive numbernegative numberoppositesintegerabsolute 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 (–).


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


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


C. 7 degrees below zero

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

–7


Check It Out: Example 1


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




C. spending $34

Negative numbers can represent losses or decreases.

–34


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.


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

{0, 1, 2, 3, 4, …}

Remember!


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.


Additional Example 2: Graphing Integers


C. +1

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5





A. +3

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

B. –4


–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

+4 is the same distance from 0 as –4.




C. 0

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

Zero is its own opposite.


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


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


Additional Example 3B: Finding Absolute Value


B. |8|

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

8

–1 0 1 2 3 4 5 6 7 8 9


Check It Out: Example 3A


A. |6|

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

6

–1 0 1 2 3 4 5 6 7 8 9


Check It Out: Example 3B


B. |–4|

–4 is 4 units from 0, so |–4| = 4

4

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz


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


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

A. +10

B. –10

C.

D.



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.



3. What is the opposite of –15?

A. +15

B. –15

C. 0

D.



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

A. +3

B. –3

C. 0

D.


11-1 Integers and Absolute Value Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

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