M3: Sections 1.5 to 1.8 Notes
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Academic
Pre-Algebra
Sections 1.5 to 1.8
Notes
Variables, Expressions, &
Integers
Name___________Pd___
M3: Sections 1.5 to 1.8 Notes
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Sections 1.5-1.6 Vocabulary Words
Mean, Median, Mode, and Range Notes:
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Mean
Median
Mode
Range
Section 1.5 Notes:
 Additive inverse
 Whole numbers
Sections 1.7-1.8 Vocabulary Words
Section 1.8 Notes:
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Origin
Scatter plot
Quadrant
Coordinate plane
Ordered pair
X-coordinate
Y-coordinate
X-axis
Y-axis
M3: Sections 1.5 to 1.8 Notes
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Mean, Median, Mode, and Range
Learning Goal: We will find the mean, median, mode, and range of a set of data.
 Mean – the sum of the data values divided by the number of data
values
 Median – the middle value when the values are written in
numerical order
 Mode – the data value that occurs most often (may have no mode
or more than one)
M3: Sections 1.5 to 1.8 Notes
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 Range – the difference of the greatest data value and the least
data value
Practice:
M3: Sections 1.5 to 1.8 Notes
Section 1.5: Adding Integers
Learning Goal: We will add positive and negative integers.
USING A NUMBER LINE:
Example 1: Adding Integers Using a Number Line
ON YOUR OWN:
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M3: Sections 1.5 to 1.8 Notes
ADDING INTEGERS:
1. Same Signs
2. Different Signs
3. Opposites
Additive Inverse Property:
 Additive Inverse –
Example 2: Adding Two Integers
Example 3: Adding More Than Two Integers
Find the sum
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M3: Sections 1.5 to 1.8 Notes
ON YOUR OWN:
Example 4: Evaluating Variable Expressions
ON YOUR OWN:
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M3: Sections 1.5 to 1.8 Notes
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Section 1.6: Subtracting Integers
Learning Goal: We will subtract positive and negative integers.
Relating Subtraction to Addition:
Example 1: Subtracting Integers
a.
3  11
ON YOUR OWN:
b.
4  (7)
c.
 6  (14)
M3: Sections 1.5 to 1.8 Notes
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Example 2: Evaluating Variable Expressions
ON YOUR OWN:
Finding Change Using Subtraction
**You can use subtraction to find the change of a variable quantity.
***Subtract the _____________________ of the quantity from the
___________________________.
Example 3: Evaluating Change
Eruptions have caused the volcano to grow. In 1962, the summit
elevation of Kick-‘em-Jenny was -235 meters. In 2002, the summit
elevation was -182 meters. By how many meters did the elevation of
the volcano change?
M3: Sections 1.5 to 1.8 Notes
ON YOUR OWN:
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M3: Sections 1.5 to 1.8 Notes
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Section 1.7: Multiplying Integers and Dividing
Learning Goal: We will multiply and divide integers.
Multiplying Two Integers:
1. Product of Same Signs
2. Product of Different Signs
3. Product of An Integer and Zero
Example 1: Multiplying Integers
a.
 3(7)
ON YOUR OWN:
Find the product.
b.
11(4)
c.
 52(0)
M3: Sections 1.5 to 1.8 Notes
Example 2: Multiplying Integers
Dividing Integers
1. Quotient of Same Signs
2. Quotient of Different Signs
3. Quotient of An Integer and Zero
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M3: Sections 1.5 to 1.8 Notes
Example 3: Dividing Integers
b.  30  5
a.  56  (7)
ON YOUR OWN:
Find the quotient.
Example 4: Finding a Mean
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c.
03
M3: Sections 1.5 to 1.8 Notes
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Section 1.8: The Coordinate Plane
Learning Goal: We identify and plot points in a coordinate plane.
Vocabulary:
 Coordinate plane – a system formed
by the intersection of a horizontal
number line called the x-axis and a
vertical number line called the yaxis
 Ordered pair – a pair of numbers
(x, y) that can be used to represent
a point in a coordinate plane. The
first number is the x-coordinate, and the second number is the
y-coordinate.
 Quadrant – one of four regions that a coordinate plane is divided
into by the x-axis and y-axis.
 Origin – the point (0, 0) where the x-axis intersects the y-axis
 x-axis – the horizontal number line in a coordinate plane
 y-axis – the vertical number line in a coordinate plane
Example 1: Naming Points in a Coordinate Plane
M3: Sections 1.5 to 1.8 Notes
ON YOUR OWN:
Give the coordinates o the point.
1. C
2. D
3. E
Example 2: Plotting Points in a Coordinate Plane
ON YOUR OWN:
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M3: Sections 1.5 to 1.8 Notes
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 scatter plot - a graph in a coordinate plane that displays paired
data. Each data pair is plotted as a point.
Example 3: Making a Scatter Plot