Transcript Chapter 5 Expressions part 3 2015

Chapter 5
Expressions
Day…..
1.
Combining Like Terms (with Exponents)
2. Field Trip
3.
Combining Like Terms (with Distributive
Property)
4. Evaluating Algebraic Expressions
5. Translating Verbal Expressions
Day 1
Bell Work
1. What is the value of the expression 32 + 33?
2. Choose all the expressions equivalent to
4(9+3).
a.
b.
c.
d.
e.
4(12)
36+3
36+12
4+(9+3)
(9+3) + (9+3) + (9+3) + (9+3)
3. What is the value of 1500/ (62 + 43 ) * 37 ?
Homework Check
Please turn in your Facing Math projects.
Vocabulary
• Algebraic Expressions - A combination of variables, numbers, and at least one
operation.
• 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.
• Equivalent Expressions- Expressions that have the same value.
• Evaluate- To find the value of a mathematical statement. To solve or find a
solution.
• Exponent-
A small number written to the right and above a base.
Shorthand way to express repeated multiplication of the base.
• Numerical Expression - A combination of numbers and operations.
Vocabulary
• 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.
• Simplify-
To make smaller or easier.
• Substitution- To replace one thing with another.
• Term- Each part of an algebraic expression or equation separated by a positive (
+) or negative sign ( - ).
• Translate- To change from one form or place to another.
• 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….
combine like terms to
simplify algebraic
expressions.
Combining Like Terms
Essential Understandings: Expressions that can not be solved , can often be simplified by
combining the terms that are alike.
• 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 expressions before attempting to
combine the like terms. Remember the sign belongs to the term that follows.
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 in the next step.
Example:
•
Once you have rearranged the terms, you can simply combine (add) the 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 2
Homework Check
Vocabulary
• Algebraic Expressions - A combination of variables, numbers, and at least one
operation.
• 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.
• Equivalent Expressions- Expressions that have the same value.
• Evaluate- To find the value of a mathematical statement. To solve or find a
solution.
• Exponent-
A small number written to the right and above a base.
Shorthand way to express repeated multiplication of the base.
• Numerical Expression - A combination of numbers and operations.
Vocabulary
• 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.
• Simplify-
To make smaller or easier.
• Substitution- To replace one thing with another.
• Term- Each part of an algebraic expression or equation separated by a positive (
+) or negative sign ( - ).
• Translate- To change from one form or place to another.
• 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
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 3
Bell Work
1. Write a numerical expression that is equal to 10,
using at least four different numbers, parentheses,
exponents, division, multiplication, and addition.
1. Factor 6x – 9
a. 2(3x-9)
b. 3(2x-3)
c. 3(3x-2)
d. 6(x-9)
Homework Check
Vocabulary
• Algebraic Expressions - A combination of variables, numbers, and at least one
operation.
• 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.
• Equivalent Expressions- Expressions that have the same value.
• Evaluate- To find the value of a mathematical statement. To solve or find a
solution.
• Exponent-
A small number written to the right and above a base.
Shorthand way to express repeated multiplication of the base.
• Numerical Expression - A combination of numbers and operations.
Vocabulary
• 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.
• Simplify-
To make smaller or easier.
• Substitution- To replace one thing with another.
• Term- Each part of an algebraic expression or equation separated by a positive (
+) or negative sign ( - ).
• Translate- To change from one form or place to another.
• 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….
combine like terms to
simplify algebraic
expressions.
Combining Like Terms
Essential Understanding:
•You can simplify an expression by combining like terms.
Example:
•Only like terms can be combined (added). To be considered alike they must have
the exact same variable with the exact same exponent. Terms without variable are
called constants, and can be combined with other constants.
Example:
•Terms can be coded and rearranged using commutative property to make
simplifying easier. Remember to make a key.
Examples:
•When simplifying an expression you must follow the order of operations. PEMDAS
Examples:
•Unlike like terms cannot be combined, but they can be multiplied by other unlike
terms. Often this appears in the form of distributive property.
Example:
Distributive Property
Essential Understanding:
Distributive property can be used to rewrite algebraic expressions. This
is done by multiplying the term on the outside of the parenthesis by
Every term on the 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)
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 4
Bell Work
1.
What is the value of 6(x + 15) – 12 when x=12 ?
2.
Does n=3 make the following equations true? Yes or No
a.
b.
c.
d.
3.
8n=512
0.5n = 1.25
2n = 6
4n – 30 = 34
At a bake sale, plates of cookies , p, are sold for $5 each. The
amount of money from the sale of cookies is expressed as dollars,
d. Which equation represents the earnings of the bake sale?
a.
b.
c.
d.
P =5d
d = p+5
d= p/5
d=5p
Homework Check
Vocabulary
• Algebraic Expressions - A combination of variables, numbers, and at least one
operation.
• 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.
• Equivalent Expressions- Expressions that have the same value.
• Evaluate- To find the value of a mathematical statement. To solve or find a
solution.
• Exponent-
A small number written to the right and above a base.
Shorthand way to express repeated multiplication of the base.
• Numerical Expression - A combination of numbers and operations.
Vocabulary
• 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.
• Simplify-
To make smaller or easier.
• Substitution- To replace one thing with another.
• Term- Each part of an algebraic expression or equation separated by a positive (
+) or negative sign ( - ).
• Translate- To change from one form or place to another.
• 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….
evaluate algebraic
expressions involving
substitution.
Evaluating Expressions
Essential Understanding: Substitution is used to evaluate an algebraic expression, when
the value of the variables is given.
•To do this, you simply replace the variable(s) with the given value.
Example:
•Then simply evaluate the expressions following the standard procedure. PEMDAS
Example:
Additional 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
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 5
Bell Work
1. Solve the expression if y=8.
((y3 – 212) *2) + (12 + 22 + 32)2
2. Which numerical expression is equivalent to
add seven and seven, then multiply by seven,
then divide by seven?
a.
b.
c.
d.
(7*7)+7/ 7
7*7+(7 / 7)
( 7*7*7)/ 7
7*(7+7)/ 7
Homework Check
Vocabulary
• Algebraic Expressions - A combination of variables, numbers, and at least one
operation.
• 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.
• Equivalent Expressions- Expressions that have the same value.
• Evaluate- To find the value of a mathematical statement. To solve or find a
solution.
• Exponent-
A small number written to the right and above a base.
Shorthand way to express repeated multiplication of the base.
• Numerical Expression - A combination of numbers and operations.
Vocabulary
• 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.
• Simplify-
To make smaller or easier.
• Substitution- To replace one thing with another.
• Term- Each part of an algebraic expression or equation separated by a positive (
+) or negative sign ( - ).
• Translate- To change from one form or place to another.
• 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….
Identify key terms for
addition, subtraction,
multiplication, division,
etc...
Key Terms for Addition
•
•
•
•
•
•
•
•
•
•
Increased +
Added +
Combine +
Plus +
And +
Climbed +
Rose +
Together +
Sum ( + )
Average ( + ) then ÷
Key Terms for Subtraction
•
•
•
•
•
•
•
•
Subtracted Decreased –
Reduced Minus Less Lower Dropped Difference ( - )
•
•
•
•
•
•
•
•
•
Key Terms for
Multiplication
Times x
Each x
Of x
Multiply x
Half x½
Double x2
Twice x2
Triple x3
Product ( x )
Key Terms for Division
Key Terms for Exponents
Key Terms for Order
•
•
•
•
•
•
•
•
•
Than
switch
Sum ( + )
Difference ( - )
Product ( x )
Quotient ( ÷ )
First
Then
Next
Last
Key Terms for Equations
• Is =
• Equals =
• Equivalent =
Key Terms for Inequalities
•Greater than ≥
•Less than ≤
•Is not equal to ≠
I Can….
Translate expressions
from written/verbal form
to numerical form.
Translating verbal/written expressions
Essential Understanding: Translating expressions is the process of changing expressions and
equations from one form to another.
•
•
•
This is made simpler by breaking apart the phrase/problem.
Try to think about the meaning of each individual word.
Then code the problem/expression to make translating quick and precise.
Examples:
•
The twenty six increased ten.
•
Eighteen minus four.
•
The product of nine and six.
•
The quotient of four and two.
•
Eight times the sum of four and x.
•
Three more than eleven.
Let’s Practice
Directions: Translate the following expressions to numerical form.
1. Four more that the difference of six and two.
2. Fifteen less than the product of nine and a number.
3. Eleven added to the quotient of thirty six and six.
4. A number reduced by seven.
5. The product of nine and number divided by two less than the
product ten and number.
Wrap it Up
• Review
• Questions
• Exit Tickets