Positive & Negative Integers

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Course 1 11-1 Integers in Real-World Situations Positive & Negative Integers Course 1 Warm Up Warm Up Cornell Notes on 11-1 & 11-2 Cornell Notes on 11-1 & 11-2

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Positive & Negative Integers. Course 1. Warm Up. Cornell Notes on 11-1 & 11-2. Warm Up Compare. Write , or =. 1. 8,426 8,246 2. 9,625 6,852 3. 2,071 2,171 4. 2,250 2,250. >. >.

Transcript of Positive & Negative Integers

Page 1: Positive & Negative Integers

Course 1

11-1 Integers in Real-World SituationsPositive & Negative Integers

Course 1

Warm UpWarm Up

Cornell Notes on 11-1 & 11-2Cornell Notes on 11-1 & 11-2

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11-1 Integers in Real-World Situations

Warm UpCompare. Write <, >, or =.

1. 8,426 8,246

2. 9,625 6,852

3. 2,071 2,171

4. 2,250 2,250

>

>

<

=

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11-1 Integers in Real-World Situations

Learn to identify and graph integers, and find opposites.

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11-1 Integers in Real-World Situations

Vocabulary

positive numbernegative numberoppositesinteger

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11-1 Integers in Real-World Situations

Where do we see examples of negative numbers?

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11-1 Integers in Real-World Situations

Positive numbers

Negative numbers

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

Numbers that are are less than 0. They are always written with a negative sign (–).

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11-1 Integers in Real-World Situations

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

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11-1 Integers in Real-World Situations

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

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11-1 Integers in Real-World Situations

Define opposites

Define integers

On a number line, opposites are the same distance from 0 but on different sides of 0.

the set of all whole numbers and their opposites.

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11-1 Integers in Real-World Situations

You can graph positive and negative numbers on a number line.

–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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11-1 Integers in Real-World Situations

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.

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11-1 Integers in Real-World Situations

• We read |3| as “the absolute value of 3.”

• We read |-3| as “the absolute value of negative 3.”

Define absolute value The distance of a number from zero on a number line. The symbol for absolute value is | |.

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11-1 Integers in Real-World Situations

Example 3

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

A. |-2|

–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

-2 is 2 units from 0, so |-2| is 2

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11-1 Integers in Real-World Situations

Additional Example 3: Writing Integer Expressions to Represent Situations

Mark enters his office building on the ground floor. Using the elevator, he goes up 6 floors to place a call, then down 4 floors for lunch, and then up 8 floors for a meeting. Write an expression to represent this situation.

Mark starts on the ground floor, 0.0

Mark goes up 6 floors.6

Mark goes down 4 floors.-4

Mark goes up 8 floors. 8

You can use a number line to model Mark’s movements on the elevator.

+8

0

2

4

6

8

10

+6

-4

+ 6 – 4 + 8

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11-1 Integers in Real-World Situations

Additional Example 1: Comparing Integers Use the number line to compare each pair of integers. Write < or >.

A. –2 2

B. 3 –5

C. –1 –4

–5 –4 –3 –2 –1 0 1 2 3 4 5

–2 is to the left of 2 on the number line.–2 < 2

3 > –5 3 is to the right of –5 on the number line.

–1 is to the right of –4 on the number line.–1 > –4

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11-1 Integers in Real-World Situations

Additional Example 2: Ordering Integers

Order the integers in each set from least to greatest.

A. –2, 3, –1

B. 4, –3, –5, 2

–3 –2 –1 0 1 2 3

Graph the integers on the same number line.

Then read the numbers from left to right: –2, –1, 3.

–6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6

Graph the integers on the same number line.

Then read the numbers from left to right: –5, –3, 2, 4.

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11-1 Integers in Real-World SituationsLesson 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?

4. |4|

5. When the Swanton Bulldogs football team

passed the football, they gained 25 yards.

Write an integer to represent this situation.

–12

+15

6

+25