Download CHAPTER 3:

LORD MAY THY WILL BE DONE IN ALL THINGS. 
CHAPTER 1:
Variables,
Expressions, and
Integers
NAME:
SECTION: 1.1 Expressions and Variables
Objective: TLW evaluate and write variable expressions.
Standards: M7.D.2.1, M7.D.2.1.2, M7.D.2.2, M7.D.2.2.1
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Vocabulary:
Numerical Expression:
Variable:
Variable Expression:
Evaluate:
Verbal Model:
Common Words and Phrases that Indicate Operations
Plus
The sum of
Increased by
Total
More than
Added to
+ = + = + = + =
Example 1:
Days
1
2
10
d
Minus the
difference of
Decreased by
Lower than
Less than
Subtracted from
+ = + = + = + = +
Times
The product of
Multiplied by
Of
Divided by
Divided into
The quotient of
= + = + = + = + = + = + = + = +
During its summer feeding season, a blue whale eats about 4 tons of food
every day. Find about how many tons of food a blue whale eats according to
the number of days listed within the table.
Tons of food eaten
Evaluate your variable expression when:
d = 120
d = 240
d = 365
***How many pounds (lbs.) are in a ton? _____lbs. = 1 ton
Can you use this information to determine the total pounds of food eaten
in the three examples above?
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Example 2: Evaluate the expression when x = 10 and y = 4.
a. x + y =
b. xy =
Example 2 You try:
Evaluate the following expressions when x = 6 and y = 12.
a.
24
y
b. 9 – x
c. y – x
d. xy
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Example 3: You plan to divide the 120 players in a baseball league into teams with the
same number of players. Use a verbal model to write a variable expression
for the number of teams if you know the number of players on each team.
Know
Want to Know
Operation
Example 3 You try: Your birthday is coming up and you plan to give each
of your friends, f, 3 cookies. Write a variable expression for the number
of cookies you will need if you know the number of friends attending your
party.
Know
Want to Know
Operation
Example 4: Write a variable expression to represent the phrase.
The product of 72 and a number:
15 more than a number:
The quotient of a number and 3:
The difference of a number and 1:
HOMEWORK:
SECTION: 1.2 Powers and Exponents
Objective: TLW use powers to describe repeated
multiplication.
Standards: M7.A.1.1, M7.B.2.1
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Vocabulary:
Power:
Base:
Exponent:
Power
In words
Value
1
12
(0.5)2
43
84
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 1: Write the product using an exponent.
a. 13 13 13 13 =
b. (0.2)(0.2)(0.2) =
c. n  n  n  n  n  n  n =
d. t  t  t  t  t =
Example 1 You try: Write the product using an exponent.
a.
10 10 10
b.
(4.3)( 4.3)
c. x  x  x  x
Evaluate each power: 02, 03, 04.
Can you state a rule about what you just found?
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 2: Evaluate the expression x4 when x = 0.5.
Example 2 You try: Evaluate the expression when m = 3.
a.
m2
b.
m3
4
c. m
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Formulas:
Area A of a square
Volume V of a cube
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 3: An artist uses a cube-shaped block of ice to make an ice
sculpture. Find the volume of the block of ice.
20 in.
20 in.
20 in.
HOMEWORK:
SECTION: 1.3 Order of Operations
Objective: TLW use order of operations to evaluate expressions.
Standards: M7.A.2.1, M7.A.2.1.1, M7.A.3.2, M7.A.3.2.1,
M7.D.2.1, M7.D.2.1.2, M7.D.2.2, M7.D.2.2.1
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
ORDER OF OPERATIONS
1.
2.
3.
4.
Evaluate expressions inside grouping symbols.
Evaluate powers.
Multiply and divide from left to right.
Add and subtract from left to right.
Example 1: Use the order of operations to evaluate the expression.
a. 28  63  7
b. 52  12.5  4
c. 9  6  27  3
70  9.2
d.
35
Examples 1 and 2 You Try:
a. 15  3  4
GROUPING SYMBOLS:
b. 48  6  2
c.
18  12
72
Example 2: Evaluate the expressions containing grouping symbols.
a. 8(17  2.3)
2
b. 17  (3  2)
c. 7[2.5  3(12  7)]
d. 84  [(18  16)  3]
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 3: Evaluate the expression when x = 4 and y = 2.
a. 1.2( x  3)
b. 1.2 x  3
c. 3x  2 y
d.
e.
0.5[ y  ( x  2)]
2( x  y ) 2
Example 4:
You buy a pattern and enough material to make two pillows. The pattern
costs $5. Each pillow requires $3.95 worth of fabric and a button that
costs $.75. Find the total cost.
HOMEWORK:
SECTION: 1.4 Comparing and Ordering Integers
Objective: TLW compare and order integers.
Standards: M7.A.1.2, M7.A.1.2.2, M7.A.1.2.3
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Vocabulary:
Integer:
Negative Integer:
Positive integer:
Absolute value:
Opposite:
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 1: Use a number line to order these integers from least to
greatest: -8, 5, -4, 2, 0, 3
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 2: State the absolute value of the number.
a. 5
b. -7
c. -1
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 3: State the opposite of the number.
a. 10
b. -15
c. 7
Example 4: Evaluate the expression when y = -5.
a. -y
b. 12  y
c.  y
a.
b. 8  y
c. y  1
y 9
HOMEWORK:
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Sections 1.1-1.4 Review
SECTION: 1.5 Adding Integers
Objective: TLW add integers
Standards: M7.A.1.2.3, M7.A.3.2.1, M7.A.3.2.2
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 1: Use a number line to find the sum.
a. -11 + 6
b. -1 + (-8)
c. 10 + (-5)
ADDING INTEGERS
Words:
Numbers:
1. Same sign: Add the absolute values and use
the common sign.
2. Different signs: Subtract the lesser absolute
value from the greater
absolute value and use the
sign of the number with
greater absolute value.
3. Opposites: The sum of a number and its opposite
is 0.
Example 2: Find the sum without the aid of a number line.
a.  54  (28)
b.  4  (72)  61
c.  19  (11)
d. 52  (30)  (46)
Example 2 You try:
a. 1 + (-17)
b. -4 + 13
c. -54 + 40
d. -20 + (-32)
e. 19 + (-45)
f. -72 + (-30)
g. 7 + (-9) + 15
h. 55 + (-28) + (-8)
HOMEWORK:
SECTION: 1.6 Subtracting Integers
Objective: TLW subtract integers.
Standards: M7.A.3.2, M7.A.3.2.1, M7.A.3.2.2
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
SUBTRACTING INTEGERS
Words: To subtract an integer, add its opposite.
Algebra:
Numbers:
Example 1: Find the difference.
a.
4  10
b.
7  (5)
c.
 2  (9)
d.
37
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 1 You try:
a.
89
b.
94
c.
 5  (17)
c.
x 8
Example 2: Evaluate the expression when x = -9.
a.
x  (40)
HOMEWORK:
b.
7x
SECTION: 1.7 Multiplying and Dividing Integers
Objective: TLW multiply and divide integers.
Standards: M7.A.3.2, M7.A.3.2.1, M7.E.2.1, M7.E.2.1.1
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
MULTIPLYING INTEGERS
Words:
Numbers:
1. The product of two integers with the
same sign is positive.
2. The product of two integers with
different signs is negative.
3. The product of any integer and 0 is 0.
Example 1: Multiply the following integers.
a.
 3( 12)
b.
 7(9)
c.
0(100)
d.
4(8)
DIVIDING INTEGERS
Words:
Numbers:
1. The quotient of two integers with the
same sign is positive.
2. The quotient of two integers with
different signs is negative.
3. The quotient of 0 and any integer is 0.
Example 2: Divide the following integers.
a.
 24  3
b.
 35
7
c.
0  ( 25)
d.
 840
7
HOMEWORK:
SECTION: 1.8 The Coordinate Plane
Objective: TLW identify and plot points in a coordinate plane.
Standards: M7.C.2.1, M7.C.2.1.1, M7.C.2.1.2
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Vocabulary:
Coordinate plane:
x-axis
y-axis
origin
quadrants
Ordered pair:
x-coordinate
y-coordinate
+ = + = + = + = + = + = + = + = + = + = + = + = + = + = + = + = +
Example 1: Give the coordinates of the point.
a. A
b. B
c. C
d. D
e. E
f. F
g. G
h. H
***Notice the labeling that is given to points.***
Example 2: Plot the following points in the coordinate plane. Describe
the location of the point.
a. A (4,1)
Quadrant ___
Axis ___
b. B(0, -3)
Quadrant ___
Axis ___
c. C (-2, -5)
Quadrant ___
Axis ___
d. D(-1, -1)
Quadrant ___
Axis ___
e. E (4, -5)
Quadrant ___
Axis ___
f. F(0, 0)
Quadrant ___
Axis ___
g. G (-2, 0)
Quadrant ___
Axis ___
h. H(3, 4)
Quadrant ___
Axis ___
HOMEWORK: