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Incredible Integers
Lesson 10.1
CCS: 6.NS.5. Understand that positive and negative
numbers are used together to describe quantities having
opposite directions or values (e.g., temperature above/below
zero, elevation above/below sea level, credits/debits,
positive/negative electric charge); use positive and negative
numbers to represent quantities in real-world contexts,
explaining the meaning of 0 in each situation.
6.NS.6. Understand a rational number as a point on the
number line. Extend number line diagrams and coordinate
axes familiar from previous grades to represent points on the
line and in the plane with negative number coordinates.
6.NS.6. a 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, and that 0 is its own opposite.
Objectives
Students will be able to:
• Locate positive and negative integers on a
number line
• Identify opposite integers on a number line
• Describe real-world situations involving
positive and negative integers
What is an
integer?
Integers are the
whole numbers and
their opposites.
Okay…but what
does that mean?
Two integers are opposites if
they are the same distance
from 0 in either the positive
or negative direction on a
number line.
This means…
• Positive integers
are all the whole
numbers greater
than zero: 1, 2, 3,
4, 5, ...
• Negative integers
are all the
opposites of these
whole numbers: -1,
-2, -3, -4, -5, …
• Negative numbers
are less than zero.
Let’s look at some
examples of opposites!
• -4 and +4
• -2 and +2
• -5 and +5
Integers can also
represent situations
Here are some examples:
• Sarah went up four
steps
• +4
• The temperature is
twelve below zero.
• -12
• The elevation of
the mountain is
52,000 feet
• +52,000
And a few more…
• The football team
lost 8 yards
• -8
• Anne gained 10
pounds
• +10
• Tara spent $20 of
her checking
account.
• -$20
You try some!!
• The stock market
showed a gain of 212
points today
• Death Valley,
California is 282
feet below sea level
• The elevator went
down two floors.
• +212
• -282
• -2
Now let’s talk
about
Absolute Value
Absolute Value
is…
The distance a number is from
zero on the number line.
So…
• Absolute value is shown by two bars
on either side of an integer.
• The absolute value of the number is
really just the number without a sign
(or neither negative nor positive)
4
Unless…
• The negative sign is OUTSIDE
of the absolute value bars.
= -4
Here are some examples!
• Example 1:
• Example 2:
=9
INTRODUCTION TO INTEGERS
• REMEMBER…Integers are positive and negative
numbers.
…, -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, …
• Each negative number is paired with a positive
number the same distance from 0 on a number line.
-3 -2 -1 0 1 2 3
INTRODUCTION TO INTEGERS
• We can represent integers using red and
yellow counters.
• Red tiles will represent negative integers,
and yellow tiles will represent positive
integers.
Negative integer
Positive integer
INTRODUCTION TO INTEGERS
• The diagrams below show 2 ways to
represent -3.
-3
• Represent -3 in 2 more ways.
-3
INTRODUCTION TO INTEGERS
• Tell which integer each group of tiles represents.
+1
-2
+2
INTRODUCTION TO INTEGERS
• If there are the same number of red tiles as yellow
tiles, what number is represented?
• It represents 0.
Number Lines
-10
-5
0
5
• A number line is a line with marks on it that are
placed at equal distances apart.
• One mark on the number line is usually labeled
zero and then each successive mark to the left or
to the right of the zero represents a particular unit
such as 1 or ½.
• On the number line above, each small mark
represents ½ unit and the larger marks represent 1
unit.
10
Number Lines
-10
-5
0
5
Number lines can be used to represent:
A. Whole numbers – the set {0, 1, 2, 3, …}
B. Positive numbers – any number that is greater than zero
C. Negative numbers – any number that is less than zero
D. Integers – the set of numbers represented as
{…, -3, -2, -1, 0, 1, 2, 3, …}
The arrows at the ends of the number line show that the
number line continues in both directions without ending.
10
Graphing on Number Lines
-5
-10
0
5
A number can be graphed on a number line by placing a
point at the appropriate position on the number line.
Example
a)
{4}
(blue point)
b)
{integers between –10 and –5}
(purple)
10
Graphing on Number Lines
-10
-5
0
5
• Name the set of numbers that is graphed.
{-8, -4, 1, 5, 8}
{-8, -4, 1, 5, 8}
10
Moving on Number Lines
-10
-5
0
5
• Movement to the right on the number line is in the positive
direction (increasing). Do this to add a positive #.
• Movement to the left on the number line is in the negative
direction (decreasing). Do this to add a negative #.
• Make the following moves on the number line. Start at 5
and move left 7 integers.
• Where did you stop?
-2
How can we represent this mathematically?
5 + (-7) = -2
10
Video Time!
• Watch this video to help you graph and order
numbers on a number line
10.1 Video
You Try It!
1) Graph these pairs of
numbers on a number line.
Write two inequalities
comparing the two
numbers.
a) -2, 7
b) -9, -4
2) Find each sum using a
number line. Place the 1st
# on a # line, then move to
the right or left.
a) 3 + 7
b) -1 + (-7)
c) -9 + 5
d) -6 + 6
Problems 1 a & b
-10
a)
-10
b)
-5
2  7
-5
9  4
0
5
10
5
10
7  2
0
4  9
Problems 2 a & b
-5
-10
0
5
10
5
10
Show 3 + 7 using the number line.
Start at 3 and move 7 places to the right.
3 + 7 = 10
-10
-5
0
Show -1 +(-7) using a number line.
Start at -1 and move 7 places to the left.
-1 + (-7) = -8
Problems 2c & d
-5
-10
0
5
10
5
10
Show –9 + 5 using the number line.
Start at –9 and move 5 places to the right.
–9 + 5 = –4
-5
-10
0
Show -6 + 6 using a number line.
Start at -6 and move 6 places to the left.
-6 + 6 = 0
Classwork:
Homework