Positive & Negative Integers

1. Positive & Negative Integers Course 1 Warm Up Cornell Notes on 11-1 & 11-2

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 > > < =

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

4. Vocabulary positive number negative number opposites integer

5. Where do we see examples of negative numbers?

6. 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

7. 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

8. 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

9. 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

10. –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.

11. –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.

12. 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.”

13. –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

14. 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

15. –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.

16. –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.

17. 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