Download Terms and addition and subtraction

Warm up
1.
5 word prediction. Guess the
meanings of the following words:
Variable, expression, base, constant,
& factor.
Standards

MGSE9-12.A.SSE.1 Interpret expressions that
represent a quantity in terms of its context.

MGSE9-12.A.SSE.1a Interpret parts of an
expression, such as terms, factors, and
coefficients, in context.

MGSE9-12.A.SSE.1b Given situations which
utilize formulas or expressions with multiple
terms and/or factors, interpret the meaning (in
context) of individual terms or factors.
Learning Target
 Identify
the different parts of the
expression and explain their
meaning within the context of a
problem.
 Simplify
and/or use the
operations of addition,
subtraction.
Definitions
IDENTIFYING PARTS
GUIDED NOTES
Algebraic Expression
 Can
have variables, numbers, addition,
subtraction, multiplication, division,
parenthesis, square roots, exponents…
 Examples:
x2
3  x  2
5b  7c  d
5 xy
Variable
 Symbols
or letters used to represent an
unknown
 Examples:
x



Term
 How
many items are being added,
subtracted, divided
 Examples:
2
5a  2 xy  3
3
P  2x
2
a b
4
Like Terms
 Same
variable raised to the same
power
 Examples:
2
2
5 x y and 8 x y
2
7y and 22y
2
Coefficient
 The
number in front of a variable
 Examples:
123 xy
3 2
9xy z
x
123
9
1
Exponent
 The
number up in the air next to a
base
 The number of times you multiply
something times itself
 Examples:
3
3
12
12
2
x
4
3y  7 4
Base
 What
the exponent sits on
 The part that has been raised to a
power
 Examples:
3
2
12
x
2
x
4
3y  7 y
Constant
A
number that has no variable
 It
can be positive or negative
 Examples:
42
3x  5
2
-42
5
4
5 x  3y  8
-8
Factors

Items that are being multiplied together

Can be numbers, variables, parenthesis

Examples:
6
9xy
1 and 6…. Or 2 and 3
9 and x and y
 x  2  y  3  (x + 2) and (y – 3)
3  z  9
3 and (z – 9)
Order of Operations
 Simplify
inside parenthesis
 Take care of exponents
 In order from left to right, multiplication or
division
 In order from left to right, addition or
subtraction
 Examples:
5  3  2  1  4
2
-18
Which is it?
Translations
ADDITION
Sum
Plus
Add
More
Than
Increased
Together
SUBTRACTION
Difference
Minus
Decreased
Less
Than (swaps the
order)
Take away
DIVISION
Quotient
Half
Divide
by
MULTIPLICATION
Product
Twice
Double
Triple
Times
EXPONENTS
Square
Cubed
To
the power of
Raised to a power
Translate
The sum of a number and 10
x + 10
Translate
The product of 9 and x
squared
2
9x
Translate
9 less than g to the fourth
power
4
g –
9
Translate
8 + 3x
Eight increased by
three times x
Translate and Solve
1. Five times a number increased by 5 is the
same as 3 times the same number
decreased by 7.
2. Four times a number plus 10 minus two
times the same number is 6.
Unit 1
Operations &
Rules
Degree of the Polynomial
Highest (largest)
exponent of the
polynomial
Standard Form
Terms are placed in
descending order by the
DEGREE.
Answers will always be
written in this form.
Degree
(largest exponent)
Name by
degree
0
Constant
1
Linear
2
Quadratic
3
Cubic
1. What is the degree name?
 2y  9
Linear
2. What is the degree name?
34x
3
Cubic
Adding
Polynomials
Drop the parenthesis &
combine like terms
3.
 2x
2
 
2

 4x  3  x  5x  1
2
3x
+x+2
4.
6  x    2 x  8 
2
2
x
+ 2x – 2
5. Find the perimeter of the rectangle.
3x  7
2x  1
10x + 12
Subtracting
Polynomials
Distribute the negative
& combine like terms
6.
 3a
2
2
3a
2
 

2
8a
+a
 10a  8a  a
+ 10a –
–
2
5a
+ 11a
7.
 3x
2
2
3x
2
 

2
2x
–x+1
 2x  4  2x  x  1
+ 2x – 4 –
2
x
+x–3
Classwork
Writing an Expression Practice
Worksheet