Download Chapter 5 Algebraic Expressions part 1 2015

Chapter 5
Expressions
Day…..
1. Exponents
2. Order of Operations
3. Numerical Expressions
4. Algebraic Properties
5. Distributive Property
Day 1
Vocabulary
• Algebraic Expressions - A combination of variables, numbers, and at least
one operation. Ex. 4x + 3
• Equivalent Expressions- Expressions that have the same value.
Ex. 5+9 = 20-6
To find the value of an algebraic expression by replacing variables
Evaluate•
with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57
• Numerical Expression - A combination of numbers and operations. Ex.
10 + 5 - 8
• Order of Operations- The rules that tell which operation to preform first
when more than one operation is used. (PEMDAS)
• Properties - Mathematical statements that are true of any number belonging
to the set of numbers for which the properties are defined.
• Variable -
A letter or symbol used to represent an unknown number.
I Can….
Write and evaluate
expressions involving
exponents
Exponent
Essential Understanding:
• Exponents are a shorthand way to show how many
times a number, called the base, is multiplied times
itself.
• A number with an exponent is said to be "raised to
the power" of that exponent.
• The "Laws of Exponents” come from three ideas:
1. The exponent says how many times to use the number in
a multiplication.
2. A negative exponent means divide, because the opposite
of multiplying is dividing
3. A fractional exponent like 1/n means take the nth root
Laws of Exponents
①
②
③
④
⑤
⑥
⑦
⑧
⑨
Law:
x1 = x
x0 = 1
x-1 = 1/x
xmxn = xm+n
xm/xn = xm-n
(xm)n = xmn
(xy)n = xnyn
(x/y)n = xn/yn
x-n = 1/xn
Examples:
61 = 6
70 = 1
4-1 = ¼
x2x3 = x2+3 = x5
x6/x2 = x6-2 = x4
(x2)3 = x2×3 = x6
(xy)3 = x3y3
(x/y)2 = x2 / y2
x-3 = 1/x3
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 2
Bell Work
Complete the provide page in your book.
Homework Check
Vocabulary
• Algebraic Expressions - A combination of variables, numbers, and at least
one operation. Ex. 4x + 3
• Equivalent Expressions- Expressions that have the same value.
Ex. 5+9 = 20-6
To find the value of an algebraic expression by replacing variables
Evaluate•
with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57
• Numerical Expression - A combination of numbers and operations. Ex.
10 + 5 - 8
• Order of Operations- The rules that tell which operation to preform first
when more than one operation is used. (PEMDAS)
• Properties - Mathematical statements that are true of any number belonging
to the set of numbers for which the properties are defined.
• Variable -
A letter or symbol used to represent an unknown number.
I Can….
Solve expressions involving
multiple operations.
Order of Operations
Essential Understanding:
Order of operation is the rule that states the order in which an expression or
equation is solved. You can remember this order with simple mnemonic devices
such as “Please Excuse My Dear Aunt Sally”.
Where as:
P stands for parenthesis
E stands for Exponents
M stands for multiply
D stands for divide
A stands for addition
S stands for subtraction
Examples:
1) 4+6*8-6(12-9) =
2) 14-8+5*5+102=
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 3
Bell Work
Directions: Use your knowledge of the order of operations to
simplify each expression.
I.
II.
III.
IV.
V.
17 + 3 * 6 – 1 + 10
42 + 10 – 5
12 * 4 * 2 3 + 50 – 11
6 + 21 * 5 – 3 * 7 + 9
1+2+3*4*5 6+7–8*9
Justify your response.
Homework Check
Vocabulary
• Algebraic Expressions - A combination of variables, numbers, and at least
one operation. Ex. 4x + 3
• Equivalent Expressions- Expressions that have the same value.
Ex. 5+9 = 20-6
To find the value of an algebraic expression by replacing variables
Evaluate•
with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57
• Numerical Expression - A combination of numbers and operations. Ex.
10 + 5 - 8
• Order of Operations- The rules that tell which operation to preform first
when more than one operation is used. (PEMDAS)
• Properties - Mathematical statements that are true of any number belonging
to the set of numbers for which the properties are defined.
• Variable -
A letter or symbol used to represent an unknown number.
I Can….
Solve expressions involving
multiple operations.
Order of Operations
Your Turn….
• Clear your desk of everything but a pencil.
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 4
Homework Check
Vocabulary
• Algebraic Expressions - A combination of variables, numbers, and at least
one operation. Ex. 4x + 3
• Equivalent Expressions- Expressions that have the same value.
Ex. 5+9 = 20-6
To find the value of an algebraic expression by replacing variables
Evaluate•
with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57
• Numerical Expression - A combination of numbers and operations. Ex.
10 + 5 - 8
• Order of Operations- The rules that tell which operation to preform first
when more than one operation is used. (PEMDAS)
• Properties - Mathematical statements that are true of any number belonging
to the set of numbers for which the properties are defined.
• Variable -
A letter or symbol used to represent an unknown number.
Properties
• Commutative- states that the order in which numbers are added
or multiplied does not change the sum or product.
Ex: 4+3=7 or 3+4=7
• Associative- states that the way in which numbers are grouped
does not change the sum or product.
Ex: 1 + (2+3) = 6 or (1+2) +3= 6
• Identity- states that any number added to 0 or multiplied by 1 will
be itself.
Ex: 6 + 0 = 6 or 4 x 1 = 4
• Distributive- is used to simplify or rewrite expressions by
multiplying a number outside the parenthesis by each number or
term inside the parenthesis.
Ex: 4(2 + 3) = 8 +12
I Can….
Apply the properties of
operations to generate
equivalent expressions.
Algebraic Properties
Essential Understanding:
Algebraic properties can be used to rewrite
expressions or generate equivalent expressions. For
instance, the expression 3+4+2 can be rewritten like
this 4+3+2 using commutative property of addition to
rearrange the numbers.
Examples of other algebraic properties:
I.
II.
III.
IV.
1 x 4 x 3 = 4 x 3 x 1 -_____________________
(6 + 3) +8 = (8 +3) + 6-____________________
9 x (3 x 2) = (9 x 3) x 2-____________________
4(3 – 2)-______________________
Watch This
• Associative property:
http://learnzillion.com/lessons/137-combineparts-of-an-expression-using-the-associativeproperty ( 5 mins)
• Commutative property:
http://learnzillion.com/lessons/2357-thecommutative-property (3 mins)
Group Work
Please take out your maker boards
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 5
pOp Quiz
• Take out a pencil and a calculator
• Clear everything else from your desk
Bell Work
Directions: Use your knowledge of associative and commutative
properties to rewrite the following expressions.
I.
3*3*8
II.
5+7+9+6
III. 2 * (7 * 6)
IV. 5 + (4 + 3)
V. 4 + 5 + 6 – 2
VI. 15 ÷ 3
Justify Your Methods
Homework Check
Vocabulary
• Algebraic Expressions - A combination of variables, numbers, and at least
one operation. Ex. 4x + 3
• Equivalent Expressions- Expressions that have the same value.
Ex. 5+9 = 20-6
To find the value of an algebraic expression by replacing variables
Evaluate•
with numbers. 10a + 3 when a = 6. 10(6) + 3 = 57
• Numerical Expression - A combination of numbers and operations. Ex.
10 + 5 - 8
• Order of Operations- The rules that tell which operation to preform first
when more than one operation is used. (PEMDAS)
• Properties - Mathematical statements that are true of any number belonging
to the set of numbers for which the properties are defined.
• Variable -
A letter or symbol used to represent an unknown number.
Properties
• Commutative- states that the order in which numbers are added
or multiplied does not change the sum or product.
Ex: 4+3=7 or 3+4=7
• Associative- states that the way in which numbers are grouped
does not change the sum or product.
Ex: 1 + (2+3) = 6 or (1+2) +3= 6
• Identity- states that any number added to 0 or multiplied by 1 will
be itself.
Ex: 6 + 0 = 6 or 4 x 1 = 4
• Distributive- is used to simplify or rewrite expressions by
multiplying a number outside the parenthesis by each number or
term inside the parenthesis.
Ex: 4(2 + 3) = 8 +12
I Can….
Apply the properties of
operations to simplify
expressions.
Distributive Property
Essential Understanding:
Distributive property can be used to rewrite algebraic
expressions by multiplying the number outside the
parenthesis by each number, term, or variable inside. For
instance the expression 3(p+2) can be rewritten as 3p + 6
Examples:
I.
II.
III.
IV.
V.
VI.
2(3+7)
(6-3)3
5(3+6d)
(4-a)8
(5b+6c)8
9(ab + 4c)
Watch This
• Distributive property:
http://learnzillion.com/lessons/2338-create-anequivalent-expression-using-the-standardalgorithm ( 5 mins)
Puzzle Time
Before we begin…….
1. Complete an exit ticket.
2. Pack up everything except for your
pencil.
3. Sit quietly unit everyone is ready.
Wrap it Up
• Review
• Questions
• Exit Tickets