Ms. Reilly’s Math Class
Course 1 – Chapter 10
Integers
Notes
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10-1 Using a Number Line
Objective 1 – Graphing Integers on a Number Line
Suppose you play tug-of-war against the team on the left shown below. Your team begins by gaining 2
feet. The position of the flag is positive 2 feet, or +2. The expression +2 is usually written simply 2.
If, instead, your team begins by losing 2 feet, the position of the flag would be negative 2 feet, or -2.
The positions can be graphed on a number line.
The numbers 2 and -2 are opposites. To numbers are opposites if they are the same distance from 0 on
a number line but in opposite directions. ________________ are the set of positive whole numbers,
their opposites, and 0. They opposite of 0 is 0.
EXAMPLE 1 – REPRESENTING SITUATIONS WITH INTEGERS
Dry ice is composed of pressurized carbon dioxide that has a freezing point to 190 degrees below zero.
Use an integer to represent the freezing point of dry ice.
The altitude of New Orleans, LA is 8 feet below sea level. Use an integer to represent this altitude.
________________
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EXAMPLE 2 – IDENTIFYING OPPOSITES
Name the opposite of -5 _______________
The _______________________________ of a number is its distance from 0 on a number line. You
write “the absolute value of negative 3” as |−3|. Opposites have the same absolute value.
EXAMPLE 3 – FINDING ABSOLUTE VALUES
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Objective 2 – Comparing and Ordering Integers
EXAMPLE 4 – COMPARING INTEGERS
Compare using > or >: a) 5 _____ -3
b) -12 _____ 9 c) -9 _____ -17 d) 2 _____ -12
You can also use a number line to help you order integers from least to greatest.
EXAMPLE 5 – ORDERING INTEGERS
Order these scores from least to greatest: -25, 100, -50, 75
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10-2 Adding Integers
Adding integers with the SAME signs:
Positive + Positive = Positive
2+3=5
Negative + Negative = Negative
-2 + (-3) = -5
Adding integers with DIFFERENT signs:
1st : find the absolute value of each integer.
2nd: subtract the lesser absolute value from the
greater.
3rd: make the sum have the original sign of the
integer with the greater absolute value.
2 + (-3) = -1
-2 + 3 = 1
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10-2 Adding Integers
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10-3 Subtracting Integers
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Adding and Subtracting Integers … as Dogs and Cats!
Dogs = Positive #
Cats = Negative #
*************************************************************************
+3 + (-2) =
1st – get rid of all + signs in the problem
+3 + (-2) =
2nd – circle remaining numbers/signs
+3 + (-2) =
3rd – Assign numbers “D’s” for DOGS (positive #) and “C’s” for CATS (negative #)
+3 + (-2) =
Dogs chase cats away  you have 1 D left  D’s are positive so = +1
DDD CC
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+ 2 – (-5) =
1st – If you see two negatives together, put the two lines together to give you 1 plus sign
+ 2 – (-5) = + 2 + 5
2nd – get rid of all + signs in the problem
+2+5
3rd – circle remaining numbers/signs
+ 2 + 5 = +7
DD DDDDD
Adding/Subtracting Integers (dogs and cats)
http://www.youtube.com/watch?v=btk5Q_hLljM&feature=related
5 + (-3)
4 + (-6)
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Multiplying Integers
The product of 2 integers with the SAME sign is POSITIVE
4 x 5 = 20
- 4 x (- 5) = 20
The product of 2 integers with DIFFERENT signs is NEGATIVE
4 x ( - 5) = - 20
- 4 x 5 = - 20
Let’s Practice:
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Dividing Integers
The quotient of 2 integers with the SAME sign is POSITIVE
20 ÷ 4 = 5
- 20 ÷ (- 4) = 5
The quotient of 2 integers with DIFFERENT signs is NEGATIVE
20 ÷ (- 4) = - 5
- 20 ÷ 4 = - 5
Let’s Practice:
Solving Equations with Integers
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Finding the Average Rate of Change for Real World Situations
Let’s Practice: Find the rate of change.
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Chapter 10 Lesson 6: Graphing in the Coordinate Plane
The _____________________________ is a grid that is formed by the intersection of 2 number lines.
The plane is divided into 4 regions, called ____________________. The _______________ is the place
where the 2 number lines intersect.
An ______________________ is a pair of numbers that describes the location of a point in a coordinate
plane. The ordered pair (0, 0) describes the origin.
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Naming Coordinates:
Find the coordinates of Point B.
Point B is 3 units to the left of the y-axis. So the x-coordinate is -3.
Point B is 2 units above the x-axis, so the y-coordinate is 2.
B ( -3, 2 )
Point C ____________ Point D ______________ Point E _____________
Graphing Ordered Pairs
You can graph points given their coordinates. You move horizontally (along the x-axis) 1st. Then move
vertically (along the y-axis).
Graph the following:
A(-4,-4) B(-3,2) C(1, -2)
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Using Map Coordinates
Suppose you leave the library and walk 2 blocks south and then 5 blocks east.
At which building are you located? _______________________________
What are the coordinates of the building? _________________________
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Course 1 Chapter 10 Lesson 8: Graphing Functions
A function is a rule that assigns exactly one output value to each input value.
This function table shows “multiply by 4”
Rule: Output = Input ÷ 4
Rule: Output = Input - 8
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Graphing Functions
You can write the function rule using variables:
 INPUT = x-value (graphed on the horizontal axis)
 OUTPUT = y-value (graphed on the vertical axis)
Output = Input • (-2)
CAN BE WRITEN AS
y = x • (-2) or y = -2x
Because all of the points lie in a line, the example above is a linear function.
Make a table of values for the function y = x – 3 using the input values x = –2, 0, 2, and 6.
x-value
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equation
y-value
(x, y)
Workers at a grocery store start off making $7 an hour. The function m = 7h shows how the money
they earn relates to the number of hours they work. Make a table and graph the function.
Henry receives $8.00 per hour for babysitting. The function e= 8h
shows how the earning e relate to the number of hours h that Henry
babysits. Make a table and graph the function.
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