Transcript 11-1

11-1
11-1Integers
IntegersininReal-World
Real-WorldSituations
Situations
Warm Up
Problem of the Day
Lesson Presentation
Course
Course
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11-1 Integers in Real-World Situations
Warm Up
Add or subtract.
1. 16 + 25
41
2. 84 – 12
72
3. Graph the even numbers from 1 to 10 on
a number line.
0
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11-1 Integers in Real-World Situations
Problem of the Day
Carlo uses a double-pan balance and
three different weights to weigh bird
seed. If his weights are 1 lb, 2 lb, and 5
lb, what whole pound amounts is he
able to weigh?
1, 2, 3, 5, 6, 7, and 8 lb
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11-1 Integers in Real-World Situations
Learn to identify and graph integers, and
find opposites.
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11-1 Integers in Real-World Situations
Vocabulary
positive number
negative number
opposites
integer
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11-1 Integers in Real-World Situations
Positive numbers are greater than
0. They may be written with a
positive sign (+), but they are
usually written without it.
Negative numbers are less than 0.
They are always written with a
negative sign (–).
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11-1 Integers in Real-World Situations
Additional Example 1: Identifying Positive and
Negative Numbers in the Real World
Name a positive or negative number to represent
each situation.
A. a jet climbing to an altitude of 20,000 feet
Positive numbers can represent climbing or rising.
+20,000
B. taking $15 out of the bank
Negative numbers can represent taking out or
withdrawing.
–15
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11-1 Integers in Real-World Situations
Additional Example 1: Identifying Positive and
Negative Numbers in the Real World
Name a positive or negative number to
represent each situation.
C. 7 degrees below zero
Negative numbers can represent values below or
less than a certain value.
–7
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11-1 Integers in Real-World Situations
Check It Out: Example 1
Name a positive or negative number to
represent each situation.
A. 300 feet below sea level
Negative numbers can represent values below or
less than a certain value.
–300
B. a hiker hiking to an altitude of 4,000 feet
Positive numbers can represent climbing or rising.
+4,000
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11-1 Integers in Real-World Situations
Check It Out: Example 1
Name a positive or negative number to
represent each situation.
C. spending $34
Negative numbers can represent losses or
decreases.
–34
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11-1 Integers in Real-World Situations
You can graph positive and negative numbers on a
number line.
On a number line, opposites are the same
distance from 0 but on different sides of 0.
Integers are the set of all whole numbers and
their opposites.
Opposites
–5
–4 –3 –2
–1
Negative Integers
0 +1 +2 +3 +4 +5
Positive Integers
0 is neither negative nor positive.
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11-1 Integers in Real-World Situations
Remember!
The set of whole numbers includes zero and the
counting numbers.
{0, 1, 2, 3, 4, …}
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11-1 Integers in Real-World Situations
Additional Example 2: Graphing Integers
Graph each integer and its opposite on a
number line.
A. +2
–2 is the same distance from 0 as +2.
–5
–4
–3 –2
–1
0
+1 +2
+3 +4
+5
B. –5
+5 is the same distance from 0 as –5.
–5
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–4
–3 –2
–1
0
+1 +2
+3 +4
+5
11-1 Integers in Real-World Situations
Additional Example 2: Graphing Integers
Graph each integer and its opposite on a
number line.
C. +1
–1 is the same distance from 0 as +1.
–5
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–4
–3 –2
–1
0
+1 +2
+3 +4
+5
11-1 Integers in Real-World Situations
Check It Out: Example 2
Graph each integer and its opposite on a
number line.
A. +3
–3 is the same distance from 0 as +3.
–5
–4
–3 –2
–1
0
+1 +2
+3 +4
+5
B. –4
+4 is the same distance from 0 as –4.
–5
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–4
–3 –2
–1
0
+1 +2
+3 +4
+5
11-1 Integers in Real-World Situations
Check It Out: Example 2
Graph each integer and its opposite on a
number line.
C. 0
Zero is its own opposite.
–5
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–4
–3 –2
–1
0
+1 +2
+3 +4
+5
11-1 Integers in Real-World Situations
Additional Example 3: Writing Integer
Expressions to Represent Situations
Mark enters his office building on the ground
floor. Using the elevator, he goes up 6 floors to
place a call, then down 4 floors for lunch, and
then up 8 floors for a meeting. Write an
expression to represent this situation. 10
+8
You can use a number line to model Mark’s
8
movements on the elevator.
0
Mark starts on the ground floor, 0.
6
6
Mark goes up 6 floors.
4
-4
8
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Mark goes down 4 floors.
Mark goes up 8 floors.
+6–4+8
2
0
+6
-4
11-1 Integers in Real-World Situations
Check It Out: Example 3
Maryl enters her office building on the ground
floor. Using the elevator, she goes up 5 floors to
her desk, then down 4 floors for lunch, and then
up 6 floors for the restroom. Write an
expression to represent this situation.
You can use a number line to model
10
Maryl’s movements on the elevator.
0
Maryl starts on the ground floor, 0.
6
Maryl goes up 5 floors.
-4
8
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Maryl goes down 4 floors.
8
6
4
Maryl goes up 6 floors.
2
+5–4+6
0
+6
+5
-4
11-1 Integers in Real-World Situations
Lesson Quiz
Name a positive or negative number to
represent each situation.
1. saving $15 +15
2. 12 feet below sea level –12
3. What is the opposite of –6? 6
5. When the Swanton Bulldogs football team
passed the football, they gained 25 yards.
Write an integer to represent this situation.
+25
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