1. 6 th Grade Math HOMEWORK 9-1 Page 452 #1-22

2. 9-1 Understanding Integers Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

3. 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 Course 1 9-1 Understanding Integers 0 1 2 3 4 5 6 7 8 9 10

4. 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 Course 1 9-1 Understanding Integers

5. Today’s Learning Goal Assignment Learn to identify and graph integers, find opposites, and find the absolute value of an integer. Course 1 9-1 Understanding Integers

6. Vocabulary positive number negative number opposites integer absolute value Insert Lesson Title Here Course 1 9-1 Understanding Integers

7. Course 1 9-1 Understanding Integers 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 (–).

8. Course 1 9-1 Understanding Integers Additional Example 1A & 1B: 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

9. Course 1 9-1 Understanding Integers Additional Example 1 Continued 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

10. Course 1 9-1 Understanding Integers Try This: Additional Example 1A & 1B 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

11. Course 1 9-1 Understanding Integers Try This: Example 1C Name a positive or negative number to represent each situation? C. spending $34 Negative numbers can represent losses or decreases. –34

12. Course 1 9-1 Understanding Integers 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.

13. Course 1 9-1 Understanding Integers The set of whole numbers includes zero and the counting numbers. {0, 1, 2, 3, 4, …} Remember!

14. Course 1 9-1 Understanding Integers Additional Example 2A & 2B: 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. –3 –2 is the same distance from 0 as +2. –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 +3 is the same distance from 0 as –3.

15. Course 1 9-1 Understanding Integers Additional Example 2C: 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.

16. Course 1 9-1 Understanding Integers Try This: Example 2A & 2B Graph each integer and its opposite on a number line. A. +5 –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 B. –4 –5 is the same distance from 0 as +5. –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 +4 is the same distance from 0 as –4.

17. Course 1 9-1 Understanding Integers Try This: Example 2C Graph each integer and its opposite on a number line. C. +4 –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 –4 is the same distance from 0 as +4.

18. Course 1 9-1 Understanding Integers |–3| = 3 |3| = 3 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 units

19. Course 1 9-1 Understanding Integers Absolute values are never negative. Opposite integers have the same absolute value. |0| = 0 Read |3| as “the absolute value of 3.” Read |–3| as “the absolute value of negative 3.” Reading Math

20. Course 1 9-1 Understanding Integers Additional Example 3A & 3B: Finding Absolute Value Use the number line to find the absolute value of each integer. A. |–4| B. |2| –4 is 4 units from 0, so |–4| = 4.4 2 is 2 units from 0, so |2| = 2.2 –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

21. Course 1 9-1 Understanding Integers Try This: Example 3A & 3B Use the number line to find the absolute value of each integer. A. |–3| B. |1| –3 is 3 units from 0, so |–3| = 3.3 1 is 1 unit from 0, so |1| = 1.1 –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5

22. 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. What is the absolute value of –12? 5. When the Swanton Bulldogs football team passed the football, they gained 25 yards. Write an integer to represent this situation. –12 +15 Insert Lesson Title Here 6 12 Course 1 9-1 Understanding Integers +25