geometry section 0-4 1112

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