Transcript Expressions (part 1) 2016

Chapter 5
Expressions
(Part 1)
Day…..
1. Order of Operations w/
Exponents
2. Solving Numerical Expressions
3. Writing Numerical Expressions
4. Algebraic Properties
Day 1
Bell Work
Please complete the
Provided Pages 111-112
In your bell ringer book.
Homework Check
Vocabulary
• Algebraic Expressions - A combination of variables, numbers, and at least
one operation.
• Equivalent Expressions- Expressions that have the same value.
• Evaluate- To find the value of an algebraic expression by replacing variables
with numbers.
• Exponent•
The shorthand way to represent repeated multiplication.
Numerical Expression - A combination of numbers and operations.
• 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
Today’s Standard
Write and evaluate
numerical expressions
involving whole-number
exponents.
Exponents
Essential Understanding:
•Exponents are a shorthand way to show how many
times a number, called the base, is multiplied times
itself.
•Example:
• 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 equation.
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
Law:
①x1 = x
②x0 = 1
③x-1 = 1/x
④xmxn = xm+n
⑤xm/xn = xm-n
⑥(xm)n = xmn
⑦(xy)n = xnyn
⑧(x/y)n = xn/yn
⑨x-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
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) =
1)14-8+5*5+102=
Your Turn
1. Orange Book pages 148-149
2. https://drive.google.com/open?id=0B39oLT9
Jr3WDVTM2am1CdlF5UTg
3. Green Book page 97
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 2
Bell Work
Please complete
pages 150- 151
in your orange book.
Homework Check
Vocabulary
• Algebraic Expressions - A combination of variables, numbers, and at least
one operation.
• Equivalent Expressions- Expressions that have the same value.
• Evaluate- To find the value of an algebraic expression by replacing variables
with numbers.
• Exponent•
The shorthand way to represent repeated multiplication.
Numerical Expression - A combination of numbers and operations.
• 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
Today’s Standard
Write and evaluate
numerical expressions
involving whole-number
exponents.
Numerical Expressions
Essential Understanding: When you look at a problem with
numbers, you are most likely looking at a numerical
expression.
• A numerical expression is a mathematical sentence
involving only numbers and one or more operation symbols.
• Examples of operation symbols are the ones for addition,
subtraction, multiplication, and division
• Numerical Expressions that have more than one operation
must be solved using the order of operations.
Group Work
As a group work together to
complete page 104 in the
Green Book.
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 3
Bell Work
Please complete pages 152-153
in your orange book.
Homework Check
Vocabulary
• Algebraic Expressions - A combination of variables, numbers, and at least
one operation.
• Equivalent Expressions- Expressions that have the same value.
• Evaluate- To find the value of an algebraic expression by replacing variables
with numbers.
• Exponent•
The shorthand way to represent repeated multiplication.
Numerical Expression - A combination of numbers and operations.
• 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
Today’s Standard
Write and evaluate
numerical expressions
involving whole-number
exponents.
Writing Numerical Expressions
Essential Understanding: word problems are just expressions written
in word form. They are used to describe real life situations and to solve
real life problems.
Example:
• The key to successfully solving an algebraic word problem is to
translate the expression from word form to numerical form. To do
this, we follow a few very simple steps.
Step 1: Know your vocabulary.
Step 2: Read the problem CAREFULLY.
Step 3: Code the problem.
Step 4: Determine what is known (what numbers are given)
Step 5: Determine what is unknown (what variables are given)
Step 6: Determine what operation(s) to used based on what the question
is asking/telling.
Step 7: Translate expression/equation
Step 8: Solve if necessary Examples:
Your Turn
https://drive.google.com/open?id=0
B39oLT9Jr3WDYldnOTE5clJpX0k
Math Menu
Directions: As a group you will work to complete
pages 7-9 of your math menu packet.
https://drive.google.com/open?id=0B39oLT9Jr3
WDUmJiUjlGRlFscGs
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 4
Bell Work
Homework Check
Vocabulary
• Algebraic Expressions - A combination of variables, numbers, and at least
one operation.
• Equivalent Expressions- Expressions that have the same value.
• Evaluate- To find the value of an algebraic expression by replacing variables
with numbers.
• Exponent•
The shorthand way to represent repeated multiplication.
Numerical Expression - A combination of numbers and operations.
• 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
Today’s Standard
Apply the properties of
operations to generate
equivalent expressions.
Algebraic Properties
Essential Understanding:
Algebraic properties can be used to rewrite
expressions/generate equivalent expressions. For
instance, the expression 3+4+2 can be rewritten as
4+3+2 using commutative property of addition to
rearrange the numbers.
Examples of other algebraic properties:
I.1 x 4 x 3 = 4 x 3 x 1 -_____________________
II.(6 + 3) +8 = (8 +3) + 6-____________________
III.9 x (3 x 2) = (9 x 3) x 2-____________________
IV.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)
Your Turn
Property Sort
https://drive.google.com/open?id=0B39
oLT9Jr3WDcm11eU9mYlBsZDg
Wrap it Up
• Review
• Questions
• Exit Tickets
Day 5
Bell Work
Please complete green book
page 98 in your bell ringer book.
pOp Quiz
Clear EVERYTHING from your desk
Homework Check
Vocabulary
• Algebraic Expressions - A combination of variables, numbers, and at least
one operation.
• Equivalent Expressions- Expressions that have the same value.
• Evaluate- To find the value of an algebraic expression by replacing variables
with numbers.
• Exponent•
The shorthand way to represent repeated multiplication.
Numerical Expression - A combination of numbers and operations.
• 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
Today’s Standard
Identify when two
expressions are equivalent
(i.e., when the two
expressions name the same
number regardless of which
value is substituted into
them).
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.Spend your tickets, if you have any.
2.Pack up everything else, except for a
pencil.
3.Sit quietly unit everyone is ready.
Wrap it Up
• Review
• Questions
• Exit Tickets