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Transcript
```Chapter 5
Expressions
Day…..
1.
Parts of an Expression
2. Simplifying Expressions
3.
Simplifying Expressions Continued…
4. Evaluating 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 )
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
I Can….
identify parts of an
expression using
mathematical terms.
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.
except for a pencil and several
highlighters.
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 2
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 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.
Vocabulary
• Term•
Each part of an algebraic expression or equation separated by a plus
or minus sign. ( ex. 2x, -3, y, +10 )
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
I Can….
combine like terms to
simplify expressions.
I Can….
combine like terms to
simplify expressions.
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:
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 3
Bell Work
Directions: Simplify the following expression.
1.
3x + 6x + 8y +10x – 4y
2.
12a – 17c – 11b + 25c - 6c + 13b
3.
6x + y + 7y + 5x
4.
13x- 5xy + 20xy – 6x
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.
Vocabulary
• Term•
Each part of an algebraic expression or equation separated by a plus
or minus sign. ( ex. 2x, -3, y, +10 )
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
Combining Like Terms
Essential Understandings:
• Algebraic expression can be simplified by combining (adding or subtracting)
like terms.
Example:
• Unlike terms can not be combined (added or subtracted), but they can be
distributed (multiplied) to clear a set of parenthesis.
Example:
• Remember the order of operations states you must multiply before adding or
subtracting. Thus you must distribute before combining like terms
Example:
Partner Work
Clear your desk of everything except
for a pencil and a calculator.
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 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.
Vocabulary
• Term•
Each part of an algebraic expression or equation separated by a plus
or minus sign. ( ex. 2x, -3, y, +10 )
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
I Can….
evaluate expressions using
substitution.
Evaluating Expressions
Essential Understanding:
To evaluate an expression using substitution, you simply replace
the variable(s) with the defined quantity.
Examples:
1. 3x + 5 when x=2
2. 4w +5w when w=8
3. 2abc when a=3, b=4, and c=5
4. 7y – 3p when y=7 and p =2
Write the Room
everything except for a
pencil.
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 5
Bell Work
Directions: simplify or evaluate the following expressions.
1. 3x + 4y + 7g – 2x + 11g
2. 4h – 2h when h=11
3. x(y – 7) + 15xy + 19y
4. 5p + 4r -3r when r=2
5. 3d + 4a +5b + 10a + 6d
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.
Vocabulary
• Term•
Each part of an algebraic expression or equation separated by a plus
or minus sign. ( ex. 2x, -3, y, +10 )
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
Mid-Unit Assessment