geometry section 0-4 1112
DESCRIPTION
Algebraic ExpressionsTRANSCRIPT
SECTION 0-4Algebraic Expressions
Monday, September 12, 2011
ESSENTIAL QUESTION
How do you use the order of operations to evaluate algebraic expressions?
Monday, September 12, 2011
ORDER OF OPERATIONS
Monday, September 12, 2011
ORDER OF OPERATIONS
P
E
M
D
A
SMonday, September 12, 2011
ORDER OF OPERATIONS
P
E
M
D
A
S
arentheses
Monday, September 12, 2011
ORDER OF OPERATIONS
P
E
M
D
A
S
arentheses
xponents
Monday, September 12, 2011
ORDER OF OPERATIONS
P
E
M
D
A
S
arentheses
xponents
ultiplication
Monday, September 12, 2011
ORDER OF OPERATIONS
P
E
M
D
A
S
arentheses
xponents
ultiplication
ivision
Monday, September 12, 2011
ORDER OF OPERATIONS
P
E
M
D
A
S
arentheses
xponents
ultiplication
ivision} from left to right
Monday, September 12, 2011
ORDER OF OPERATIONS
P
E
M
D
A
S
arentheses
xponents
ultiplication
ivision} from left to right
ddition
Monday, September 12, 2011
ORDER OF OPERATIONS
P
E
M
D
A
S
arentheses
xponents
ultiplication
ivision} from left to right
ddition
ubtractionMonday, September 12, 2011
ORDER OF OPERATIONS
P
E
M
D
A
S
arentheses
xponents
ultiplication
ivision} from left to right
ddition
ubtraction} from left to right
Monday, September 12, 2011
ORDER OF OPERATIONS
P
E
M
D
A
S
arentheses
xponents
ultiplication
ivision} from left to right
ddition
ubtraction} from left to right
Old way!
Monday, September 12, 2011
ORDER OF OPERATIONS
Monday, September 12, 2011
ORDER OF OPERATIONS
G
E
M
D
A
SMonday, September 12, 2011
ORDER OF OPERATIONS
G
E
M
D
A
S
rouping Symbols
Monday, September 12, 2011
ORDER OF OPERATIONS
G
E
M
D
A
S
rouping SymbolsParentheses, brackets, division bars, etc.
Monday, September 12, 2011
ORDER OF OPERATIONS
G
E
M
D
A
S
rouping Symbols
xponents
ultiplication
ivision} from left to right
ddition
ubtraction} from left to right
Parentheses, brackets, division bars, etc.
Monday, September 12, 2011
ORDER OF OPERATIONS
G
E
M
D
A
S
rouping Symbols
xponents
ultiplication
ivision} from left to right
ddition
ubtraction} from left to right
New & Improved!
Parentheses, brackets, division bars, etc.
Monday, September 12, 2011
QUESTION
What does it mean to evaluate an expression?
Monday, September 12, 2011
EXAMPLE 1
a. 3x − 7 + 2y
Evaluate when x = 4 and y = −
12
b. − x − 8y
Monday, September 12, 2011
EXAMPLE 1
a. 3x − 7 + 2y
Evaluate when x = 4 and y = −
12
3(4)− 7 + 2(−
12
)
b. − x − 8y
Monday, September 12, 2011
EXAMPLE 1
a. 3x − 7 + 2y
Evaluate when x = 4 and y = −
12
3(4)− 7 + 2(−
12
)
12 − 7 −1
b. − x − 8y
Monday, September 12, 2011
EXAMPLE 1
a. 3x − 7 + 2y
Evaluate when x = 4 and y = −
12
3(4)− 7 + 2(−
12
)
12 − 7 −1
5 −1
b. − x − 8y
Monday, September 12, 2011
EXAMPLE 1
a. 3x − 7 + 2y
Evaluate when x = 4 and y = −
12
3(4)− 7 + 2(−
12
)
12 − 7 −1
5 −1
4
b. − x − 8y
Monday, September 12, 2011
EXAMPLE 1
a. 3x − 7 + 2y
Evaluate when x = 4 and y = −
12
3(4)− 7 + 2(−
12
)
12 − 7 −1
5 −1
4
b. − x − 8y
−4 − 8(−
12
)
Monday, September 12, 2011
EXAMPLE 1
a. 3x − 7 + 2y
Evaluate when x = 4 and y = −
12
3(4)− 7 + 2(−
12
)
12 − 7 −1
5 −1
4
b. − x − 8y
−4 − 8(−
12
)
−4 + 4
Monday, September 12, 2011
EXAMPLE 1
a. 3x − 7 + 2y
Evaluate when x = 4 and y = −
12
3(4)− 7 + 2(−
12
)
12 − 7 −1
5 −1
4
b. − x − 8y
−4 − 8(−
12
)
−4 + 4
0
Monday, September 12, 2011
EXAMPLE 2
Evaluate when x = 2 and y = 3.
−2x + y
3− 5x
Monday, September 12, 2011
EXAMPLE 2
Evaluate when x = 2 and y = 3.
−2x + y
3− 5x
−2(2)+ 33− 5(2)
Monday, September 12, 2011
EXAMPLE 2
Evaluate when x = 2 and y = 3.
−2x + y
3− 5x
−2(2)+ 33− 5(2)
−4 + 33−10
Monday, September 12, 2011
EXAMPLE 2
Evaluate when x = 2 and y = 3.
−2x + y
3− 5x
−2(2)+ 33− 5(2)
−4 + 33−10
−1−7
Monday, September 12, 2011
EXAMPLE 2
Evaluate when x = 2 and y = 3.
−2x + y
3− 5x
−2(2)+ 33− 5(2)
−4 + 33−10
−1−7
17
Monday, September 12, 2011
EXAMPLE 3
Evaluate when x = 8 and y = −3.
a. 2 x − y
b.
13
y − x
Monday, September 12, 2011
EXAMPLE 3
Evaluate when x = 8 and y = −3.
a. 2 x − y
2 8 − (−3)
b.
13
y − x
Monday, September 12, 2011
EXAMPLE 3
Evaluate when x = 8 and y = −3.
a. 2 x − y
2 8 − (−3)
2 8 + 3
b.
13
y − x
Monday, September 12, 2011
EXAMPLE 3
Evaluate when x = 8 and y = −3.
a. 2 x − y
2 8 − (−3)
2 8 + 3
2 11
b.
13
y − x
Monday, September 12, 2011
EXAMPLE 3
Evaluate when x = 8 and y = −3.
a. 2 x − y
2 8 − (−3)
2 8 + 3
2 11
2(11)
b.
13
y − x
Monday, September 12, 2011
EXAMPLE 3
Evaluate when x = 8 and y = −3.
a. 2 x − y
2 8 − (−3)
2 8 + 3
2 11
2(11)
22
b.
13
y − x
Monday, September 12, 2011
EXAMPLE 3
Evaluate when x = 8 and y = −3.
a. 2 x − y
2 8 − (−3)
2 8 + 3
2 11
2(11)
22
b.
13
y − x
13−3− 8
Monday, September 12, 2011
EXAMPLE 3
Evaluate when x = 8 and y = −3.
a. 2 x − y
2 8 − (−3)
2 8 + 3
2 11
2(11)
22
b.
13
y − x
13−3− 8
13−11
Monday, September 12, 2011
EXAMPLE 3
Evaluate when x = 8 and y = −3.
a. 2 x − y
2 8 − (−3)
2 8 + 3
2 11
2(11)
22
b.
13
y − x
13−3− 8
13−11
13
(11)Monday, September 12, 2011
EXAMPLE 3
Evaluate when x = 8 and y = −3.
a. 2 x − y
2 8 − (−3)
2 8 + 3
2 11
2(11)
22
b.
13
y − x
13−3− 8
13−11
13
(11)
113
Monday, September 12, 2011
PROBLEM SET
Monday, September 12, 2011
PROBLEM SET
p. P10 #1-12 all
“The true sign of intelligence is not knowledge but imagination.” - Albert Einstein
Monday, September 12, 2011