Download Variables, Algebraic Expressions, and Simple Equations

Variables, Algebraic Expressions,
and Simple Equations
1
Discuss and make a list of
similarities and differences
(compare and contrast)
These are variables
A = # , C = #,
X = #,r = #, n = #
=#
=#
How they’re the
same:
These are not
A,
How they’re different:
C,
n
3, 10, 75, 8,
12, 1, 0
Use interwrite board to fill in 3
See if your definition that you came
up with matches the definition of a
variable:
Variable is…. A letter or symbol that stands
for an unknown number.
Examples: a , C, x, N,
,
Copy this down in your notes
4
Algebraic Expressions
• An expression consists of a combination of numbers,
operation symbols, and grouping symbols such as
parentheses ( ). An algebraic expression is an
expression that contains one or more variables.
• Expressions:
Algebraic Expressions
3+4
3 (c + 8)
Notice that you
don’t see any
6–2
2a
equal signs
(6 + 3) -1
9–x
5
Equations
Equation

An equation is a SENTENCE.

One solves an equation.

An equation HAS a relation symbol.
Ex.
1. Ten is five less than a number.
10 = x – 5
2. A number is less than five.
x<5
More Ex.
2x-5= 5
x +5= 10
Reading and Writing Algebraic Expressions
+
plus
sum
more than
increased
by
total
in all
added to
minus
difference
less than
subtract
decreased
by
Take away
Subtracted
from
x

times
product
multiplied
each
of
divided
quotient
divided by
Other ways to
show
multiplication :
Other ways to show
division:
5n
5(6)
5·6
12 ÷ 6
12/6
7
Glue this in your notes and go over examples of how to read/write algebraic expressions
Now, that we know the components of this expression, let’s
try to write an algebraic expression for each word phrase
4 increased by a number
4+c
*it does not matter what
letter you use, just as
long as you include a
variable.
25 less than a number
n – 25
*just because we see
25 first in the word
phrase, doesn’t mean
that 25 is written first
in the expression.
9
Try to write these on your own:
Add 3 to a number
3 + n or n + 3
Some number multiplied by 16
16 x b or b x 16
10
Now, try to translate, or write the
following algebraic expressions into a
word phrase on your own.
1) n - 5
1) 9 + t
11
Now, try to translate, or write the
following algebraic expressions into a
word phrase on your own.
Answers will vary…
1) n - 5 1)Take 5 away from a
number
1) 9 + t 1)9 added to a number
12
When we evaluate algebraic expressions, we are
substituting a number in place of variable, then
solving for an answer
Evaluate each expression
when a = 12
1)a + 3
1)17 – a
13
When we evaluate algebraic expressions, we are
substituting a number in place of variable, then
solving for an answer
Evaluate each expression
when a = 12
1)a + 3
12 + 3
15
2) 17 – a
17 – 12
5
14
You try to evaluate the following
when n = 4
1) 9n
*(what operation does this mean when a
number is right beside a variable? Look at
your notes if you don’t know)
2) 40 / n
15
You try to evaluate the following
when n = 4
1) 9n
9x4
36
1) 40 / n
40 / 4
10
If several students had trouble with
the algebraic expressions today,
have them do WB 8 and save the partner
activity for Thursday.
Stop here for Tues.
16
An Equation is a complete
sentence that is either true or false
= shows that each side has the same value
examples:
x + 7 = 14
7 + 7 = 14
14 = 14
47 = 50 – 3
y – 6 = 13
17
Determine if the following are
expressions or equations:
1) 7x
2) (6-3) – 1 = 2
3) 14 = 7(2)
4) X + 9 = 13
5) 12 – 5
18
Determine if the following are
expressions or equations:
1) 7x
2) (6-3) – 1 = 2
3) 14 = 7(2)
4) X + 9 = 13
5) 12 – 5
•
•
•
•
•
1) expression
2) equation
3) equation
4) equation
5) expression
How could you tell the difference between the two?
19
For Practice:
• Do pg. 41 #17-20
together
• Then, with a partner,
do #5-16 (using
beans, buttons, etc..)
20
Mixed Review
for Quiz
• Each student needs a sheet of
paper
Directions:
The following questions are similar to the
types of questions that you will see on
tomorrow’s quiz.
Every student needs to answer or attempt to
answer each question.
If you find that you get several answers
wrong, please talk to the teacher at the
end of class or during content mastery for
additional help 
#1 - In your own words, tell me what a
variable is?
#2 - Write down at least 2 examples of
variables:
#1 - In your own words, tell me what a
variable is? A variable is a letter or symbol
that represents an unknown #
#2 - Write down at least 2 examples of
variables: C, x, n,
Answers may vary
Write an algebraic expression for
each word phrase:
#3) take 14 from a number
#4) 15 is decreased by a number
#5) add 8 to a number
Write an algebraic expression for
each word phrase:
#3) take 14 from a number
n – 14
#4) 15 is decreased by a number
15 – n
#5) add 8 to a number
n + 8 or 8 + n
Evaluate each expression when
x=9
#6) 7 + x _________
#7) x – 3 _________
Evaluate each expression when
x=9
#6) 7 + x _________
7 + 9 = 16
#7) x – 3 _________
9–3=6
Use mental math to solve the equations.
Rewrite the equation showing that both
sides are equal.
#8) 75 + t = 80
t = ____
___________
#9) b – 52 = 17
b= ____
__________
Use mental math to solve the equations.
Rewrite the equation showing that both
sides are equal.
#8) 75 + t = 80
t=5
75 + 5 = 80
80 = 80
#9) b – 52 = 17
b= _69_
69 – 52 = 17
17 = 17
Which number sentence is true if
x= 5
#10) a) 38 – x = 30
b) 33 + x = 38
c) 38 = x + 30
d) x – 38 = 33
The correct answer is ____
Explain how you know:
Which number sentence is true if
x= 5
#10) a) 38 – x = 30
b) 33 + x = 38
c) 38 = x + 30
d) x – 38 = 33
The correct answer is b
Explain how you know: 33 + 5 = 38
38 = 38
It was the only equation that was “true”
You decide what the following equation
represents.
$50.00 – x = $45.00
11) Write a word problem to fit the equation.
Then solve your problem.
You decide what the following equation
represents.
$50.00 – x = $45.00
11) Write a word problem to fit the equation.
(example: ) My grandparents gave me fifty
dollars for my birthday. I spent some of my
money on a toy, and now I have $45 left. How
much was the toy that I bought?
Then solve your problem.
$50 – $5 = $45
x = $5
• Evaluate means to substiture a value, then
solve the problem.