Warm Up Problem of the Day Lesson Presentation Lesson Quizzes 1

3. Graph the even numbers from 1 to 10 on a number line. 41 72 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 2

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, 4, 5, 6, 7, and 8 lb 3

Sunshine State Standards Preview of MA.7.A.3.1 Use and justify the rules for…finding absolute value of integers.

Vocabulary positive number negative number opposites integer absolute value 5

Positive numbers are greater than 0 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 (–). 6

Name a positive or negative number to represent each situation. 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 7

Name a positive or negative number to represent each situation. 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 8

Name a positive or negative number to represent each situation. 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 9

Name a positive or negative number to represent each situation. 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 10

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. Opposites –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 Negative Integers Positive Integers 0 is neither negative nor positive. 11

The set of whole numbers includes zero and the counting numbers. {0, 1, 2, 3, 4, …} Remember! 12

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. –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 B. –5 +5 is the same distance from 0 as –5. –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 13

Additional Example 2: Graphing Integers Graph each integer and its opposite on a number line. C. +1 –1 is the same distance from 0 as +1. –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 14

Graph each integer and its opposite on a number line. Check It Out: Example 2 Graph each integer and its opposite on a number line. A. +3 –3 is the same distance from 0 as +3. –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 B. –4 +4 is the same distance from 0 as –4. –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 15

Graph each integer and its opposite on a number line. Check It Out: Example 2 Graph each integer and its opposite on a number line. C. 0 Zero is its own opposite. –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 16

|<--3 units--> | <--3 units-->| The absolute value of an integer is its distance from 0 on a number line. The symbol for absolute value is ||. |–3| = 3 |3| = 3 |<--3 units--> | <--3 units-->| –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 Absolute values are never negative. Opposite integers have the same absolute value. |0| = 0 17

Additional Example 3A: Finding Absolute Value 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| = 2 2 18

Additional Example 3B: Finding Absolute Value Use a number line to find the absolute value of each integer. B. |8| –1 0 1 2 3 4 5 6 7 8 9 8 is 8 units from 0, so |8| = 8 8 19

Check It Out: Example 3A Use a number line to find the absolute value of each integer. A. |6| –1 0 1 2 3 4 5 6 7 8 9 6 is 6 units from 0, so |6| = 6 6 20

Check It Out: Example 3B Use a number line to find the absolute value of each integer. B. |–4| –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 –4 is 4 units from 0, so |–4| = 4 4 21