Lesson 1 Opposites Module 3 Rational Numbers

Use integers and absolute value to describe real-world mathematical situations. I can…

Integers are the set of whole numbers and their opposites. O Whole numbers: do not contain decimals or fractions O Positive (+) integers are greater than zero. O Negative (-) Integers are less than zero.

Opposite numbers are the same distance from zero on a number line O 0 is its own opposite O The opposite of the opposite of a number is the number itself, e.g., −(−3) = 3.

The |absolute value| of a rational number is its distance from 0 on the number line. O We use the mathematical symbol | | to indicate absolute value. O For example: O |-3| = 3 is read, “the absolute value of negative 3 is 3.”

What’s the connection? Opposites Absolute Value Opposites have the same absolute value since they are the same distance from zero on either side.

Integers and absolute value are used together to describe quantities in real-world situations Temperature: above (+)/below (-) zero Bank Account: Credit (+)/Debit (-) Electrical Charges: Elevation: above (+)/below (-) Sea level

The magnitude of a positive or negative quantity in a real-world situation is the “size” of the quantity. O The magnitude of a quantity is indicated by its absolute value since when we speak; we typically do not say “negative.” O For example: O We would say, “I owe thirty dollars.” O We would NOT say, “I owe negative thirty dollars.” O We would write |-30| = 30 to show the magnitude of the debt.

“The bigger the negative, the smaller the number.” O Negative quantities are confusing because they are the opposite of that we are used to working with. O For example, -30 has more negative than -25 which means -30 is smaller than -25. O If a person has an account balance that is less than -30 dollars it means that they owe more than 30 dollars.