I can identify positive and negative integers SPI 6.2.8

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 (–). 2

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 3

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 4

Representing Integers 11-2 SPI 6.1.3 I CAN use pictorial, concrete, and symbolic representation for 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. Opposites –5 –4 –3 –2 –1 0 +1 +2 +3 +4 +5 Negative Integers Positive Integers 0 is neither negative nor positive. 6

|<--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 7

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 8

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 9

Mt. McKinley The total distance is 20,602 feet.

–2 is to the left of 2 on the number line. Additional Example 1: Comparing Integers Use the number line to compare each pair of integers. Write < or >. A. –2 2 B. 3 –5 C. –1 –4 –5 –4 –3 –2 –1 0 1 2 3 4 5 –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. 11

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. –3 –2 –1 0 1 2 3 Then read the numbers from left to right: –2, –1, 3. Graph the integers on the same number line. –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 Then read the numbers from left to right: –5, –3, 2, 4. 12

Understand the Problem Additional Example 3: Problem Solving Application In a golf match, Craig scored +2, Cameron scored +3, and Rob scored –1. Who won the golf match? 1 Understand the Problem The answer will be the player with the lowest score. List the important information: Craig scored +2. Cameron scored +3. Rob scored –1. 13

Check It Out: Example 3 Continued 2 Make a Plan You can draw a diagram to order the scores from least to greatest. Solve 3 Draw a number line and graph each player’s score on it. • • • –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 Trista’s score, –3, is farthest to the left, so it is the lowest score. Trista won the golf match. 14

Check It Out: Example 3 Continued 4 Look Back Negative integers are always less than positive integers, so Melissa cannot be the winner. Since Trista’s score of –3 is less than Alyssa’s score of –1, Trista won. 15

Name 4 real life situations in which integers can be used. Spending and earning money. Rising and falling temperatures. Stock market gains and losses. Gaining and losing yards in a football game.