Download Algebraic expressions (part 2) 2016

Algebraic
Expressions
(Part 2)
Day…..
1. Distributive Property
2. Parts of an Expression
3. Combining Like Terms
4. Simplifying Expressions
5. Mid-Unit Assessment
Day 1
Bell Work
Directions: Identify the property used to rewrite each expression.
1.4x + 5x + 7y = 7y +5x +4x
2.(5 + 3) + 9 = 3 + (5 +9)
3.4(x + y) = (4*x) + (4*y)
4.1 * (2 * 3) = ( 1* 2) * 3
5.5w – 2w = w (5 – 2)
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.
Vocabulary
• Term-
Each part of an algebraic expression or equation separated by a plus
or minus sign. ( ex. 2x, -3, y, +10 )
• Variable- A letter or symbol used to represent an unknown number.
• Coefficient- The numerical part of a term followed by a variable.
• Constant- Part of an algebraic expression that is unchanged by a variable.
A numerical term without a variable ( ex. +5 or -10 )
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
Today’s Standard
Apply the properties of
operations to generate
equivalent 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)
9 Square
Please clear your desk of everything
except for a pencil and a blank piece of
paper.
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 2
Homework Critique
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.
Vocabulary
• Term-
Each part of an algebraic expression or equation separated by a plus
or minus sign. ( ex. 2x, -3, y, +10 )
• Variable- A letter or symbol used to represent an unknown number.
• Coefficient- The numerical part of a term followed by a variable.
• Constant- Part of an algebraic expression that is unchanged by a variable.
A numerical term without a variable ( ex. +5 or -10 )
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
Today’s Standard
Identify parts of an
expression using
mathematical terms (sum,
term, product, factor,
quotient, coefficient); view
one or more parts of an
expression as a single entity.
Parts of an Expression
Essential Understanding:
•Expressions can be simplified by combining like terms. Terms are parts
of an expression separated by a positive or negative sign.
Example:
•There are three parts of an expression that make up terms; variables,
coefficients, and constants
I.
Variables are lower case letters or shapes used to represent an unknown
quantity. They are called variables because, until they are defined, their
value could vary from one end of the spectrum to the other. (in other words
it could be any number imaginable)
II. Coefficients are numbers that are being multiplied by a variables. They are
called coefficients because the prefix co- means together.
III. Constants are numbers that stand alone. They are called constants because
their value is consistent regardless of the variables.
Your Turn….
Please take out a pencil and any
highlighters you may have.
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 3
Bell Work
Directions: Use your highlighters and the key below to identify the parts of the
following expressions.
Key:
Green – Variables
Orange- Coefficients
Pink – Constants
Terms – Boxed with a pencil
1.18x + 4y + 6y – 14x + 21ab
2.3r – 7s + 21r – 14p
3.15st + 42s + 51t – 9st
Homework Critique
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.
Vocabulary
• Term-
Each part of an algebraic expression or equation separated by a plus
or minus sign. ( ex. 2x, -3, y, +10 )
• Variable- A letter or symbol used to represent an unknown number.
• Coefficient- The numerical part of a term followed by a variable.
• Constant- Part of an algebraic expression that is unchanged by a variable.
A numerical term without a variable ( ex. +5 or -10 )
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
Today’s Standard
Write, read, and evaluate
expressions in which
letters stand for numbers.
Combining Like Terms
Essential Understandings:
•Expressions that can not be solved , can often be simplified by combining like terms. To
simplify like terms, you must begin by identifying the types of terms you have. Terms are
defined by their variables or lack of one. They must have the exact same variable with
exact same exponent to be considered like terms.
Example:
•To give your self a visual, you can use shapes to code expression before combining the like
terms. Be sure to keep the sign with the term.
Example:
•After you have coded the terms, you can rearrange them using your knowledge of
commutative property. This will make combing the like terms easier.
Example:
•Once you have rearranged the terms, you can simply combine like terms. You should have
the same number of terms in your final answer as the number of shapes you used to code
the expression
Example:
Monster Math
Please Pack up all of your belongings.
Yes, even your pencil!!! 
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 4
Bell Work
Directions: simplify the following expressions.
1.3x + 5x + 7y – 2x + 11y
2.17t – 12v + 8tv + 5v + 3tv – 12t
3.5(a + b) – 3a + 9b – 6a + 2a - 31b
4.10fx + 5f(2x + 3x) – 13fx
5.8(2d + 5c) - 6d + 19c + 4(5d – 3c)
Homework Critique
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.
Vocabulary
• Term-
Each part of an algebraic expression or equation separated by a plus
or minus sign. ( ex. 2x, -3, y, +10 )
• Variable- A letter or symbol used to represent an unknown number.
• Coefficient- The numerical part of a term followed by a variable.
• Constant- Part of an algebraic expression that is unchanged by a variable.
A numerical term without a variable ( ex. +5 or -10 )
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
Today’s Standard
Write, read, and evaluate
expressions in which
letters stand for numbers.
Simplifying Algebraic Expressions
Essential Understandings:
•
An algebraic term represents a multiplicative relationship between a number(the coefficient)
and a variable (a letter of symbol).
Example: 3a = 3 *a
• Algebraic expression can be simplified by combining like terms.
Proof:
•
But, unlike terms can not be combined (added/subtracted), because the variables do not
represent the same unknown quantity. Thus, they can not be put together until the value is
known.
Proof:
•
Unlike terms can, however, be distributed (multiplied), because algebraic terms are
multiplication.
Proof:
• This is how you must clear a set of parenthesis, containing unlike terms.
Example:
•
Because the order of operations states you must multiply/ divide before adding/subtracting,
sometimes you have to use distributive property to multiply/get rid of the parenthesis before
you can combine any like terms
Example:
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 5
Bell Work
Silent Study
Mid-Unit
Assessment
Please Clear Your
Desk.
Homework Critique
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.
Vocabulary
• Term-
Each part of an algebraic expression or equation separated by a plus
or minus sign. ( ex. 2x, -3, y, +10 )
• Variable- A letter or symbol used to represent an unknown number.
• Coefficient- The numerical part of a term followed by a variable.
• Constant- Part of an algebraic expression that is unchanged by a variable.
A numerical term without a variable ( ex. +5 or -10 )
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