Transcript The Value of the Number Line

Integers & Using
the Number Line
Comparing Rational Numbers
Integers
MCC6.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.
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).
Numbers right of 0 are
positive.
Numbers left of 0 are
negative.
Creating a Number Line
A number line visually shows how numbers are
organized from least to greatest.
Numbers get larger toward the right.
Numbers get smaller toward the left.
Reading the Number Line
A number line visually shows how numbers are
organized from least to greatest.
Numbers get larger
going up.
Numbers get smaller
going down.
Reading the Number Line
Positive Integers
Negative Integers
• Depositing money in a
checking account
• Withdrawing money
from a checking account
• Elevation above sea level
• An elevation below sea
level
• Any temperature above
zero
• Yardage gained in
football
• Below zero temperatures
• Yardage lost in football
Now you give examples
into your mathberries.
Example 1
A 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?
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!
Opposites
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
Using the Number Line
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.
Common Misconception
with Comparing Numbers
What is the opposite of the following integers?
1) 2,345
-2,345
2) -16
16
3) 0
0
4) 8
-8
Using the number line, determine which integer is greater:
1) 2
-2
>
2) -5 -7
>
3) 0
3
<
4) 0
-8
>
Practice
The signs of a number tell which way to go on
the number line, like a GPS gives directions!
means turn Left or turn Down on the number line.
means turn Right or Up on the number line.
Signs of Numbers - GPS