Integers & Using the

Number LineComparing Rational Numbers

IntegersMCC6.NS.5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values.MCC6.NS.6a: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself , e.g., -(-3) = 3.MCC6.NS.6c: Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

- 3 -1526

16

-70

Integers are defined as the set of whole numbers and their opposites.

Integers include• Positive numbers, also called the counting

numbers, (1,2,3,4, . . .) • Their opposites, negative numbers,

(-1,-2,-3,. . .)• And zero, which is neither positive nor

negative.

Integers are represented by small slashes on the number lines, and do not include the fractions or

decimals (those are in between the slashes).

Creating a Number Line

Numbers left of 0 are negative.

Numbers right of 0 are positive.

Reading the Number Line

Numbers get larger toward the right.

Numbers get smaller toward the left.

A number line visually shows how numbers are organized from least to greatest.

Reading the Number Line

Numbers get smaller going down.

Numbers get larger going up.

A number line visually shows how numbers are organized from least to greatest.

Positive Integers• Depositing money in a

checking account

• Elevation above sea level

• Any temperature above zero

• Yardage gained in football

Negative Integers• Withdrawing money

from a checking account

• An elevation below sea level

• Below zero temperatures

• Yardage lost in football

Now you give examples into your mathberries.

Example 1A sea gull is flying 25 feet above sea level and a shark is

swimming 10 feet below sea level.

1) What elevation does the surface of the water represent?

2) What is the elevation of the bird?

3) What is the elevation of the fish?

What is the temperature on this thermometer?

What is the temperature on this thermometer?

Opposites

Numbers describe their distance from zero.

3 is three spaces from 0 and -3 is three spaces from 0.

3 and -3 are opposites.

Opposites

Every number has an opposite.For every positive number, there is

a negative number.

*Zero is its own opposite!

Using the Number Line

When comparing numbers use the number line.

The number on the right is the bigger number. The number on the left is the smaller number.

Ex: -3 is less than -1-3 < -1

(-3 is on the left of -1 on the number line.)

-3 -1

Common Misconception with Comparing Numbers

Some students think the greatest number is the number closest to zero.

NOPE! Because that rule is not always true.

-5 -2 0 10

-2 is closer to 0 than -5 and is greater than -5… but -2 is closer to 0 than 10 but is less than 10.

Practice

What is the opposite of the following integers?1) 2,345 -2,3452) -16 163) 0 04) 8 -8

Using the number line, determine which integer is greater:5) 2 -2 >6) -5 -7 >7) 0 3 <8) 0 -8 >

Signs of Numbers - GPS

means turn Left or turn Down on the number line.

means turn Right or Up on the number line.

The signs of a number tell which way to go on the number line, like a GPS gives directions!