1. Introduction to Integers
August 21, 2014
LT- I can develop a definition for the word “integer” and create a list of key words.

2. Integers Defined…
Integers are the set of whole numbers and their opposites
Integers are positive and negative numbers
The number line goes on forever in both directions and is indicated by arrows
Whole numbers greater than zero are called positive integers and these numbers are to the right of zero on the number line
opposite integers
negative integers
positive integers

3. Integers Defined…
Whole numbers less than zero are called negative integers and these numbers are to the left of zero on the number line.
The integer zero is neither positive nor negative
The sign of an integer is either positive (+) or negative (-), except zero, which has no sign.
Opposite Integers: when two numbers are the same distance away from zero, on opposite sides of the number line, one will have a positive sign, the other a negative sign.

4. Write an integer to represent each situation:
15degrees above zero
+15
a loss of 11 dollars
-11
a gain of 8 points +8
3 steps backward -3

5. Name the opposite of each integer.
-11
+11
+27
-27
-14
+14 +4 -4

6. 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 or losing yards in a football game
Note: A positive integer does not have to have a + sign.
For example, +3 and 3 are the same.

7. Key Words for Positive Integers
Above
Deposit Up
Gain
Ascend
More
Earning $

8. Key Words for Negative Integers
Below
Withdrawal
Down
Loss
Descend
Less
Under
Spending $

9. The Problem:
The highest elevation in Northern Lookout is Snow Peak, which is feet above sea level. The lowest elevation is Tree Valley, which is 368 feet below sea level. What is the distance from the top of Snow Peak to the bottom of Tree Valley?

10. Solution We can represent each elevation as an integer: Elevation
Elevation
Integer
feet above sea level
Sea level
368 feet below sea level
-368
The distance from the top of Snow Peak to the bottom of Tree Valley is the same as the distance from to -368 on the number line. We add the distance from to 0, and the distance from 0 to -368, for a total of feet.

11. Points to Remember:
Integers are the set of whole numbers and their opposites
Whole numbers larger than zero are called positive integers; whole numbers less than zero are called negative integers
The integer zero is neither positive nor negative.
Two integers are opposites if they are the same distance away from zero, but on opposite sides of the number line.
Positive integers may be written with or without a sign.