Download Variables, Algebraic Expressions, and Simple Equations

Variables, Algebraic
Expressions, and Simple
Equations
1
Can you form your own definition of
a variable based on the following?
These are variables
A = # , C = #,
X = #,r = #, n = #
=#
=#
These are not
A,
C,
n
3, 10, 75, 8,
12, 1, 0
2
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
3
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
4
Parts of an Expression
Complete the
Algebraic
expression
graphic
organizer.
Identify the
parts.
5
Reading and Writing Algebraic Expressions
Directions: Fill in the words on your graphic organizer from this page.
+
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
Per
Other ways to show
multiplication :
5x6
5(6)
5·6

divided
quotient
divided by
Parts
Pieces
Other ways to show
division:
12 ÷ 6
12/6
6
Look at these examples of word problems translated
into Algebraic expressions.
7
Here are some more examples:
8
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.
10
Try to write these on your
own:
Add 3 to a number
3 + n or n + 3
Some number multiplied by 16
16b
11
Now, try to translate, or write the
following algebraic expressions into a
word phrase on your own.
1) n - 5
2) 9 + t
12
Now, try to translate, or write the
following algebraic expressions into a
word phrase on your own.
1) n - 5
Answers will vary…
1) Take 5 away from a
number
2) 9 + t
2) 9 added to a number
13
Directions: Write each phrase as an expression.
Write your answers on the back of your graphic
organizer.
14
Check your answers from the previous slide.
15
Complete the Translating
Expressions Assessment.
16
Equations
http://www.learnalberta.ca/content/mesg/html
/math6web/math6shell.html
(link to video)--- you will need to do the following:
Skip intro, Click on Lessons, Click on the 11th video.
17
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
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
19
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?
20
For Practice:
• Do pg. 41 #17-20
together
• Then, with a partner,
do #5-16 (using
beans, buttons, etc..)
21
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.