**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 > > < =

**Learn to identify and graph integers, and find opposites.**

**Vocabulary** positive number negative number opposites integer

**Where do we see examples of negative numbers?**

**Positive 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 (–). Negative numbers

**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 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

**On a number line, opposites are the same distance from 0 but** on different sides of 0. Defineopposites the set of all whole numbers and their opposites. Defineintegers

**–5 –4 –3 –2 –1 0 +1 +2 +3 +4** +5 You can graph positive and negative numbers on a number line. Opposites Negative Integers Positive Integers 0 is neither negative nor positive.

**–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5** –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 Additional Example 2: Graphing Integers Graph each integer and its opposite on a number line. A. +2 –2 is the same distance from 0 as +2. B. –5 +5 is the same distance from 0 as –5.

**Define absolute value** The distance of a number from zero on a number line. The symbol for absolute value is | |. • We read |3| as “the absolute value of 3.” • We read |-3| as “the absolute value of negative 3.”

**–5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5** Example 3 Use a number line to find the absolute value of each integer A. |-2| -2 is 2 units from 0, so |-2| is 2

**10** 8 +6 +8 6 4 -4 2 0 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. You can use a number line to model Mark’s movements on the elevator. 0 Mark starts on the ground floor, 0. 6 Mark goes up 6 floors. -4 Mark goes down 4 floors. 8 Mark goes up 8 floors. + 6 – 4 + 8

** –5 –4 –3 –2 –1 0 1 2 3 4 5** Additional Example 1: Comparing IntegersUse the number line to compare each pair of integers. Write < or >. A. –2 2 B. 3 –5 C. –1 –4 –2 < 2 –2 is to the left of 2 on the number line. 3 > –5 3 is to the right of –5 on the number line. –1 > –4 –1 is to the right of –4 on the number line.

**–6 –5 –4 –3 –2 –1 0 1 2 3 4 ** 5 6 –3 –2 –1 0 1 2 3 Additional Example 2: Ordering Integers Order the integers in each set from least to greatest. A. –2, 3, –1 B. 4, –3, –5, 2 Graph the integers on the same number line. Then read the numbers from left to right: –2, –1, 3. Graph the integers on the same number line. Then read the numbers from left to right: –5, –3, 2, 4.

**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? 4. |4| 5. When the Swanton Bulldogs football team passed the football, they gained 25 yards. Write an integer to represent this situation. +15 –12 6 +25