Download Chapter 5 Algebraic Expressions

Chapter 5
Expressions
Day…..
1. Order of Operations
2. No School
3. Algebraic Properties
4. Algebraic Properties Cont….
5. Quiz and Review
Day 1
Bell Work
Complete the provided page.
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+10÷2=
Group Work
Please take out your maker boards
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 2
No School
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
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 ÷ 7 + 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.
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.
1x4x3=4x3x1
(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 4
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)
Your Turn….
• Clear your desk of everything but a calculator
and a pencil.
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 5
Bell Work
Use distributive property to expand the following expressions.
I.
5(4+6)
II. 4(x+b)
III. 3(4-x)
IV. (2+3)7
V. (8-k)5
VI. y(6+w)
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
pOp Quiz
• Take out a pencil and a calculator
• Clear everything else from your desk
Group Work
Before we begin…….
1. Complete an exit ticket.
2. Pack up everything except for your
pencil and calculator.
3. Sit quietly unit everyone is ready.
Wrap it Up
• Review
• Questions
• Exit Tickets