CHAPTER TWO
Variables
Expressions
and
Properties
2-1 USING VARIABLES TO WRITE
EXPRESSIONS
Objective: write numerical
expressions with variables to
represent relations
How: take notes, think pair share,
read word phrases to convert to
algebraic expressions
VARIABLE
 a quantity (or
amount) that can
change, usually
represented with a
letter
Variable like the
word vary meaning it
changes or varies.
Example:
5a where a is a variable
Non-example:
4 2 there is no variable
COEFFICIENT
 A number multiplied by
a variable
 Example:
5a (5xA)
 Think of Co- like
sharing so coefficients
have to share
multiplication with a
variable
 Think of Efficient- like
achieving maximum
productivity with
minimum wasted effort
or expense
 Non-example:
5+a no multiplication
ALGEBRAIC EXPRESSION
Mathematical
phrase having at
least one variable
and one operation
Example:
5+T or w/7
Non-example:
w=8 or 6x8= 48
MEGAN BOUGHT SOCKS
ON EBAY FOR $10 A PAIR.
How
can you
represent
the total
cost of
the socks
bought?
Pairs of Socks Cost
1
$10 x 1
2
$10 x 2
3
$10 x 3
4
$10 x 4
A
$10 x A
When we
don’t know
how many
pairs of
socks
Megan
bought we
can use the
variable A to
represent
potential
socks
bought.
That amount
can change
which is why
we use a
VARIable.
Word Phrase
five minutes more than
time t
ten erasers decreased by a
number n
six times a width w
n nectarines divided by
three
eight more than four times
an amount x
Operation
Algebraic
Expression
Word Phrase
five minutes more than
time t
ten erasers decreased by a
number n
six times a width w
n nectarines divided by
three
Operation
addition
subtraction
multiplication
division
eight more than four times multiplication and addition
an amount x
Algebraic
Expression
Word Phrase
five minutes more than
time t
ten erasers decreased by a
number n
six times a width w
n nectarines divided by
three
Operation
Algebraic
Expression
addition
t+5
subtraction
10 - n
multiplication
6 x W or 6w
division
n ÷ 3 or n
3
eight more than four times multiplication and addition
an amount x
4x + 8
NOW LET’S TRY SOME TOGETHER
12 times a number g
The difference of a
number m and 18
P pennies added to
22 pennies
Yuri walk p poodles
and b bulldogs.
Write an algebraic
expression to
represent how many
dogs were walked.
EXIT TICKET
Keeshon bought packages of
pens. There are 4 pens in each
package. Keeshon gave 6 pens to
his friends. Write an expression
that show this situation.
 (Hint- there are 2 operations that take place)
STARTER FOR 2-2
Juanita sells homemade jam at the
farmers’ market. She sold 35 jars
during the first hour and 85 jars
during the second hour. Write an
algebraic expression to show the
number of jars Juanita has left to sell.
Explain how the expression relates to
the problem.
2-2 PROPERTIES OF OPERATIONS
Objective: give missing addends and
factors in equations and state the
property used
How: discuss properties of addition
and multiplication then use these
properties to label equations and
determine missing information
COMMUTATIVE PROPERT Y OF ADDITION
The order numbers
are added does not
change the sum.
Think about when
you commute you
can go different
ways and still get to
work.
a+b=b+a
8 + 18 = 18 + 8
6 + c = c + 6
COMMUTATIVE PROPERT Y OF
MULTIPLICATION
The order numbers
are multiplied does
not change the
product.
Think about when
you commute you
can go different
ways and still get to
work.
axb=bxa
8 x 18 = 18 x 8
6 x c = c x 6
ASSOCIATIVE PROPERT Y OF ADDITION
 The way numbers are
GROUPED does not
affect the sum
 Think my
associates/friends:
sometimes I hangout
with one group
sometimes another
and they are all my
friends
 a+(b+c)=(a+b)+c
 2+(3+4)=(2+3)+4
 3+(a+4)=(3+a)+4
ASSOCIATIVE PROPERT Y OF
MULTIPLICATION
The way numbers
are GROUPED does
not affect the
product
Think my
associates/friends:
sometimes I
hangout with one
group sometimes
another and they are
all my friends
 a(bxc)=(axb)c
 2(3x4)=(2x3)4
 3x(ax4)=(3xa)x4
IDENTIT Y PROPERT Y OF ADDITION
The sum of any
number and zero is
that number
Think about what
you can do to a
number that won’t
change it’s value.
Their “name tag”
a+0=a
24 + 0 = 24
IDENTIT Y PROPERT Y OF MULTIPLICATION
The product of any
number and one is
that number
Think about what
you can do to a
number that won’t
change it’s value.
Their “name tag”
ax1=a
24 x 1 = 24
NOW LET’S PRACTICE






__ x (14x32) = (5x14) x 32
5 + 23 + 4 = 23 + 4 + __
25 + 0 + 3 = 25 + __
(7 + 12) + 4 = 7 + (12+__)
(5 x 7) x (3 x 8) = (5 x 3) x (8 x __)
(43 x 1) x 4 = ___ x 4
 CHALLENGE
 (41 x 43) x (3 x 19) = (41 x __) x (19 x 43)
 (5 + 3) + __ = 5 + (8 + 3)
EXIT TICKET
 328 x 1
 8 + __ = 4 + 8
STARTER 2-3
Can you use Associative,
Commutative, or Identity
Properties with subtraction
or division? Explain.
2-3 ORDER OF OPERATIONS
Objective: Use the order of
operations to evaluate expressions
How: Watch a video, learn a song,
and evaluate numeric and algebraic
expressions.
THERE IS AN AGREED
UPON ORDER IN WHICH
OPERATIONS ARE
CARRIED OUT IN A
NUMERICAL
EXPRESSION.
ORDER OF
OPERATIONS
ORDER OF OPERATIONS
 The order to perform operations in calculations
 Compute inside parentheses.
 Evaluate terms with exponents.
 Multiply and Divide from left to right.
 Add and Subtract from left to right.
PEMDAS
NOW LET’S PRACTICE!
9 2 - 8 x 3
24 / 4 + 8 + 2
18 – 3 x 5 + 2
49 – 4 x (49 /7)
5 2 – 6 x 0
24 / (4+8) + 2
EXIT TICKET
Use parentheses to make each number
sentence true.
8 x 9 – 2 – 3 = 53
6 2 + 7 + 9 x 10 = 133
2 2 + 4 x 6 = 48
2-4 STARTER
Mrs. Nerren is decorating her
rectangular bulletin board by placing
stars along the edges. It is 5 feet
wide and 3 feet tall. She places stars
every 6 inches. How many stars does
she need? Explain your reasoning.
2-4 THE DISTRIBUTIVE PROPERT Y
Objective: use the distributive
property to evaluate expressions and
to compute mentally.
How: take notes, video clip, work
with a partner
DISTRIBUTIVE PROPERT Y
Multiplying a sum
(or difference) by a
number gives the
same result as
multiplying each
number in the sum
(or difference) by the
number and adding
(or subtracting)
products
 WHITE BOARD
2-6 STARTER
Provide the missing information,
then solve.
Aki must take turns with his sisters
mowing the lawn. One of them must
mow the lawn every week. How
many times in 12 weeks will Aki
mow the Lawn?
2-6 EVALUATING EXPRESSIONS
Objective: Evaluate algebraic
expressions using substitution.
How: take notes on how to replace
variables with given numbers and
solving the expression.
EVALUATE
Find the value
of an expression
EXAMPLES:
5 3 = 125
2+8 = 10
SOLVE!
NON-EXAMPLES:
5 3 = 5 x 5 x 5
2 + 8 = W
Get a number
for an answer!!!
SUBSTITUTION
Replace the variable
with a number
EXAMPLE:
y+9
 Y = 10
 10+9= 19
NON-EXAMPLE:
y+9
 Y = 10
 W+9 =9
LET’S PRACTICE
Evaluate each expression for 2, 5, and 8.
9x
3x+6
48 ÷ x
x(0)
1x
x(4) ÷ 2
X 2 + 1
EXIT TICKET
Evaluate the expression for the
values of n.
N
2+3n
3
5
8
12
25
2-7/2-8 STARTER
Max’s farm has 480 acres. His
farm is divided into fields of n
acres each. Write an expression
that shows the number of fields
on Max’s farm. EXPLAIN YOUR
THINKING.
2-7/2-8 USING EXPRESSIONS TO
DESCRIBE PATTERNS AND MAKING A
TABLE TO SOLVE PROBLEMS
Objective: identify missing numbers in a
pattern and write algebraic expressions
to describe the pattern, make and use
tables to solve word problems.
How: take notes, read and create tables,
discuss patterns with a partner, write
expressions.
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