1. 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

2. Course 1 11-1 Integers in Real-World Situations 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. Course 1 11-1 Integers in Real-World Situations Warm Up Add or subtract. 1. 16 + 25 2. 84 – 12 3. Graph the even numbers from 1 to 10 on a number line. 41 72 0 1 2 3 4 5 6 7 8 9 10

4. Course 1 11-1 Integers in Real-World Situations 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, 5, 6, 7, and 8 lb

5. Course 1 11-1 Integers in Real-World Situations Learn to identify and graph integers, and find opposites.

6. Course 1 11-1 Integers in Real-World Situations Vocabulary positive number negative number opposites integer

7. Course 1 11-1 Integers in Real-World Situations Where do we see examples of negative numbers?

8. Course 1 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 (–).

9. Course 1 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

10. Course 1 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

11. Course 1 11-1 Integers in Real-World Situations 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

12. Course 1 11-1 Integers in Real-World Situations 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

13. Course 1 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.

14. Course 1 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 Integers Negative Integers 0 is neither negative nor positive.

15. Course 1 11-1 Integers in Real-World Situations The set of whole numbers includes zero and the counting numbers. {0, 1, 2, 3, 4, …} Remember!

16. Course 1 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.

17. Course 1 11-1 Integers in Real-World Situations 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.

18. Course 1 11-1 Integers in Real-World Situations 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.

19. Course 1 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 | |.

20. Course 1 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

21. Course 1 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

22. Course 1 11-1 Integers in Real-World Situations Check It Out: Example 3 Maryl enters her office building on the ground floor. Using the elevator, she goes up 5 floors to her desk, then down 4 floors for lunch, and then up 6 floors for the restroom. Write an expression to represent this situation. Maryl starts on the ground floor, 0.0 Maryl goes up 5 floors.6 Maryl goes down 4 floors.-4 Maryl goes up 6 floors. 8 You can use a number line to model Maryl’s movements on the elevator. +6 +5 -4 + 5 – 4 + 6 0 2 4 6 8 10

23. Course 1 11-1 Integers in Real-World Situations Additional Example 1: Comparing Integers Use the number line to compare each pair of integers. Write. 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 > –53 is to the right of –5 on the number line. –1 is to the right of –4 on the number line.–1 > –4

24. Course 1 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.

25. Course 1 11-1 Integers in Real-World Situations 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. –12 +15 6 +25