Download Week 9 ,Solving Linear equations Algebriac

Rewrite these verbal expressions as algebraic
expressions.
1. Four less than a number
N-4
2. the product of 12 and some number
12n
3. 48 increased by twice a number
48+2a
Let’s make verbal expressions for these algebraic
expressions.
1.
2(5+n)
2.
5n -2
3.
x-4
•Prepare to
take Cornell
Notes
Performance Objective
I can translate a realworld situation into an
algebraic expression or
equation and express
my thinking in writing.
Definition of Algebraic Expression
•An Algebraic Expression is an
Expression that contains one or More
numbers, one or More variables, and
one or More Arithmetic operations.
Examples of Algebraic
Expression:
Daily Work
• Tell me what was
suggested on this
video clip would be a
good way to learn
how to solve
Algebraic equations.
Be prepared to share
what you write.
Math
Translating Algebraic Expressions
What do I represent?
What am I?
How did I
get here?
a
b
x
I am so
unknown
y
Variables are letters that represent unknown values.
Numerical Expressions
Numerical expressions include numbers and operation symbols.
Remember:
1. A variable is a letter used to represent an
unknown value.
2. A numerical expression includes numbers
and operations.
3. An algebraic expression contains
variables, numbers and operations.
Partner Work:
Make a 4 section
chart.
In each row put these
titles Add, Subtract,
Multiply, and Divide


With your partner come up
with as many words as you
can that mean the same as
these words. For example
under subtract I could put
decrease. You have 6
minutes.

Share your list with the
partners next to you, see if
the groups can come up
with more words. Make
sure you add these words
to your list.
Algebraic Expressions
An algebraic expression includes:
Numbers
Operations
and Variables
Let’s look at examples of a numerical expressions:
12 + 3
32
8
7(4)
Let’s look at examples of algebraic expressions.
x-4
2(5+n)
b
2
Equations
Algebraic expressions like phrases in English are incomplete.
An equation, like a sentence, is complete. You will notice the
inclusion of a very special symbol.
An equation is made up of numbers, variables,
and an equal sign.
3b + 5 = 26
Rewrite these verbal expressions as algebraic expressions.
1. I do:
the sum of s and 12
s+12
2. We do: the product of 15 and some number
15n
3.You do:
n7
n to the seventh power
4. 56 increased by twice a number
56+2a
5. Four less than a number
n-4
Let’s write equations for these sentences.
1. Forty-three less than n is equal to 35.
n – 43 = 35
2. Seven more than y is 13.
y + 7 = 13
Let’s make verbal expressions for these
algebraic expressions.
I do:
x-4
We do: 2(5+n)
You do: 12 + 3
Your friend eats at Taco Bell every week. This
week, he bought a crunchy taco and a bean
burrito for $1.78, then added a large Dr.
Pepper that brought the bill to $3.20. Which
equation will help solve how much the Dr.
Pepper cost?
A. $1.78 + $3.20 = d
B. $1.42 + $1.78 = d
C. $1.42 + d = $3.20
D. $1.78 + d = $3.20
You bought a $2.50 notebook and $
.89 dividers for each of your 4 core
classes. Write an equation to show,
t, how much you spent.
A. 4(2.50) + .89 = t
B. 4(2.50 + .89) = t
C. 4 + .89(2.50) = t
D. .89 + 2.50 x 4 = t
Ty rode his motorcycle in a 33 mile
race. He finished the race in 30
minutes. Which equation can find
his average speed?
A. 33/.5 = mph
B. 33(.5) = mph
C. 33/30 = mph
D. 33(30) = mph
Jonathan was paid $13.50 for
babysitting from 3:30 to 8:00. Write
an expression showing how to
calculate how much Jonathan
earned per hour of babysitting.
Kailey wants to beat the current
school record of 1324 autographs
collected in five days. On the first
day, she collected 243 autographs.
Write an expression showing how
she can calculate the approximate
number of autographs she must get
on each of the remaining days to
break the record.
AGENDA/ACTIVITIES
3-1 ( Algebraic Expressions)
•Ticket out the door: What operations does the
phrase below describe and which operation
should be performed first?
13 less pennies than twenty pennies
times 4
•2-3 questions put in left column of notes.
Day 2:Five minute
check 3 - 1
•Prepare to
take Cornell
Notes
Performance Objective
• I can translate a realworld situation into an
algebraic expression
or equation and
express my thinking in
writing.
•Review with your
partner the notes you
took on the Algebraic
Expressions. Be
prepared to share
them with the class!
Divide into
groups of 3 or
4. You have 1
minute.
• Each group will have 5
minutes to complete the
task presented. Then
We will rotate the
groups.
Rewrite these verbal expressions as algebraic
expressions.
1. Four less than a number
2.
the product of 12 and some number
3. 48 increased by twice a number
Let’s make verbal expressions for these algebraic
expressions.
4.
2(5+n)
5.
5n -2
6.
x-4
•Take out your
Cornell Notes
on Algebraic
Expressions.
Objective
• I can translate a realworld situation into an
algebraic expression or
equation and express
my thinking in writing.
QuickTime™ and a
H.264 decompressor
are needed to see this picture.
Algebraic Expressions
An algebraic expression includes:
Numbers
Operations
and Variables
Show me....
The operation!
paper clips? really?
Lindsay had 67 old copies of Tiger Beat. She
traded in several of them at Bookman Used
Bookstore. If she has 23 copies left, which
expression can you use to find m, the number
of magazines she traded in?
a)67 + m = 23
b)23m = 67
c)67 - m = 23
d)67/m = 23
Plumbing job, anyone?
Brendan pays his plumber $22
per hour to replace his drain pipe.
He ends up paying the plumber
$99. Which equation can you use
to find h, the number of hours the
plumber worked?
a)22/h = 99
b)22h = 99
c)22 + 99 = h
d)22 - h = 99
Who wants a raise?
Sara was earning $6.35 per hour in her
old job. She changed jobs, and got a
raise, to $8.78 per hour. Which equation
can you use to find r, the amount her
hourly wage increased?
a)r/6.35 = 8.78
b)6.35r = 8.78
c)8.78 + r = 6.35
d)6.35 + r = 8.78
Video game champion?
Peter Wilkes set a record high score on Donkey Kong in
March of 2007. Then 3 months later, Colton Crabb beat that
record by 1,100 points. Colton’s new record was 1,050,200
points. Which equation can you use to find w, Peter
Wilkes’s score?
a)3w = 1,100
b)1,050,200 + w = 1,100
c)w - 1,100 = 1,050,200
d)w + 1,100 = 1,050,200
Slam Dunk!
Sierra scored 21 points in a basketball game.
Sierra scored 7 more points than Tanya.
Which equation can you use to find t, the
number of points scored by Tanya?
a)t - 7 = 21
b)7 + t = 21
c)21/7 = t
d)7t = 21
paper clips? really?
Ryan has three times as many paper clips as
Lydia. She is very jealous. Ryan has 168
paper clips. Which expression can you use
to find L, the number of paper clips Lydia
has?
3L = 168
L/3 = 168
L + 3 = 168
168 - L = 3
Write your Own!
Write a word problem like one
that you’ve seen today. Be
prepared to exchange with a
neighbor, so they can write out
the equation!
Your friend eats at Panda Express every week.
This week, he bought a Panda Bowl for $6.78,
then added a large Dr. Pepper that brought the
bill to $8.20. Which equation will help solve how
much the Dr. Pepper cost?
A. $6.78 + d = $8.20
B. $1.42 + d = $8.20
C. $1.42 + $6.78 = d
D. $6.78 + $3.20 = d
You bought a $1.70 notebook and $ .89 dividers
for each of your 4 core classes and your 2
electives. Write an equation to show, t, how
much you spent.
A. 6 + .89(1.70) = t
B. 6(1.70 + .89) = t
C. 6(1.70) + .89 = t
D. .89 + 1.70 x 6 = t
Derek rode his bike in a 17 mile
race. He finished the race in 90
minutes. Which equation can find
his average speed?
A. 17(1.5) = mph
B. 17/90 = mph
C. 17(90) = mph
D. 17/1.5 = mph
Jesus was paid $12.50 for
mowing the lawn from 2:00 to
4:30. Write an expression
showing how to calculate
how much Jesus earned per
mowing the lawn.
Sarah wants to beat the current
school record of 1424 texts sent in
four days. On the first day, she sent
189 texts. Write an expression
showing how she can calculate the
approximate number of texts she
must send on each of the remaining
days to break the record.
Summarize your notes with
these questions.
What are expressions?
Equations? How can you use
key words in a word problem
to create an algebraic
expression or equation?
AGENDA/ACTIVITIES
Test on Algebraic Expressions
Pretest on Two Step Equations
Crystal Ball: Next week we will be solving 2 step
equations such as 3x + 5 = 8, how do you think the two
step strategy will help you solve two – step equations?
2-3 questions put in left column of notes.
AGENDA/ACTIVITIES
3-2 ( Adding and Subtracting with Variables)
Crystal Ball : Tomorrow we will solve
Multiplication equations, how will today’s
lesson help you prepare for tomorrows
lesson.
2-3 questions put in left column of notes.
Adding and Subtracting with Variables
Worksheet
Five minute
check 3 - 2
•Prepare to
take Cornell
Notes
I can create and
solve 2-step
equations using
inverse operations
and express my
thinking orally.
Performance Objective
•I will be able to write
and solve addition and
subtraction one-step
linear equations using
the additive inverse
operation.
One-Step Equations
A one-step equation is as
straight forward as it
sounds. You will only
need to perform one
step in order to solve
the equation.
To Solve a One step Equation:
Remember the goal is to have the variable by itself on one
side of the equation. In this problem, that means moving
the 5 to the other side of the equation. Since the 5 is
added to the variable, we move it to the other side of the
equation by subtracting 5. However, if we subtract 5 from
the left side of the equation, we MUST also subtract 5
from the right side.
• On your Do Now write
one way Variables
integers is
areused
used
in our daily lives. You
have 2 minutes. Share
with your partner. A’s go
first the B’s.
3 O'clock High
Watching this video clip, tell me why you
think this boy cheating and how you could
prevent this temptation from happening in
this Math class. Be prepared to share what
you write.
Solving Equations
Aim: How do we solve addition and subtraction equations?
Expressions
Equation
y+5
We can evaluate
an expression,
when given the
value of the
variable.
y + 5 = 20 We can solve an
equation to find
the value of the
variable.
Aim: How do we solve addition and subtraction equations?
1. The '=' sign divides
the equation into two
parts.
2. Whatever you do on
one side of the equal
sign, must be done to the
other side.
3. You must isolate the
variable by using the
inverse operation.
4. Check your answer!
y + 5 = 20
-5 -5
y
= 15
15 + 5 = 20
20 = 20
Aim: How do we solve addition and subtraction equations?
1. The '=' sign divides the
equation into two parts.
2. Whatever you do on
one side of the equal
sign, must be done to the
other side.
3. You must isolate the
variable by using the
inverse operation.
4. Check your answer!
m+6=8
-6 -6
m
= 2
2+6=8
8=8
Aim: How do we solve addition and subtraction equations?
1. The '=' sign divides the
equation into two parts.
2. Whatever you do on
one side of the equal
sign, must be done to the
other side.
3. You must isolate the
variable by using the
inverse operation.
4. Check your answer!
9 + w = 20
-9
-9
w = 11
9 + 11 = 20
20 = 20
Aim: How do we solve addition and subtraction equations?
1. The '=' sign divides the
equation into two parts.
2. Whatever you do on
one side of the equal
sign, must be done to the
other side.
3. You must isolate the
variable by using the
inverse operation.
4. Check your answer!
r+6=2
-6 -6
r
= -4
-4 + 6 = 2
2=2
Aim: How do we solve addition and subtraction equations?
Partner work - Solve each equation. Show all work.
3) c + 8 = 3
1) 12 + y = 20 2) 15 = 7 + r
-12
-12
y=8
-7
-7
8=r
-8 -8
c = -5
Aim: How do we solve addition and subtraction equations?
You Do - Solve each equation. Show all work.
1)
17 + m = 32
-17
-17
m = 15
2)
-9 = 7 + r
-7 -7
-16 = r
3)
c+8=1
-8 -8
c = -7
Aim: How do we solve addition and subtraction equations?
1. The '=' sign divides
the equation into two
parts.
2. Whatever you do on
one side of the equal
sign, must be done to the
other side.
3. You must isolate the
variable by using the
inverse operation.
r -7 = 2
+7+7
r
= 9
Aim: How do we solve addition and subtraction equations?
Solve each equation.
1) r - 9 = 4
+9
+9
r =13
2) -12 = y - 3
+3
-9 =y
+3
Aim: How do we solve addition and subtraction equations?
Solve each equation.
1) r - 8 = 2
2) -15 = y - 4
Aim: How do we solve addition and subtraction equations?
Partner do - Solve each equation. Show all work.
2) 32 = r + 12 3) w - 5 = - 3
1) t - 7 = 20
Aim: How do we solve addition and subtraction equations?
You do - Solve each equation. Show all work.
4) -8 + m = 20 5) y- (-5)= 10 6) e + (-6) = -12
AGENDA/ACTIVITIES
3-2 ( Adding and Subtracting with Variables)
Crystal Ball : Tomorrow we will solve
Multiplication equations, how will today’s
lesson help you prepare for tomorrows
lesson.
2-3 questions put in left column of notes.
Adding and Subtracting with Variables
Worksheet
Day 3:AGENDA/ACTIVITIES
2-3 questions put in left column of
notes.
Summary using the vocabulary word
in it.
• 1. n – 5
• 2. 7d
• 3. a number increased
by eight
• 4. Find three less than a
number then double it.
•Prepare to
take Cornell
Notes
I can create and
solve 2-step
equations using
inverse operations
and express my
thinking orally.
Performance Objective
•I will be able to write
and solve addition and
subtraction one-step
linear equations using
one variable.
One-Step Equations
A one-step equation is as
straight forward as it
sounds. You will only
need to perform one
step in order to solve
the equation
October Sky
How did using variables help these
boys solve their dilemma and what
was it. Be prepared to share what
you write.
Take One Step at a Time !
Have you ever seen these?
Number
Date
Description of Transaction
Debit (-)
10-12
Previous balance
Deposit
10-13
Direct Deposit- paycheck from business you
own – Cutting Edge IT
Check #100
10-13
Car note- for your Maybach
Credit (+)
Balance
$1,000,000
?
$10,000
?
$5,5000
$1,010,000.00
$1,004,500.00
x + $10,000= $1,010,000
$1,000,000
$1,010,000 - x = $1,004,500
$5,5000
One Step
Equations
Part 1
ONE STEP EQUATIONS
Today we will learn how to complete one
step equations using addition and
subtraction.
ONE STEP EQUATIONS
An equation is like a balance scale
because it shows that two
quantities are equal.
What you do to one side of the
equation must also be done to the
other side to keep it balanced.
ONE STEP EQUATIONS
To solve one step equations, you need to
ask three questions about the equation:
• What is the variable?
• What operation is performed on the variable?
• What is the inverse operation?
ONE STEP EQUATIONS
A variable is a symbol (like x or y) that
is used in mathematical expressions to
represent an undetermined quantity
ONE STEP EQUATIONS
The inverse operation is the one that
will undo what is being done to the
variable
ONE STEP EQUATIONS
The operation performed by the
variable is addition, subtraction,
multiplication, or division.
ONE STEP EQUATIONS
Example 1 Solve x + 4 = 12
What is the variable? The variable is x.
What operation is being performed on the variable? Addition
What is the inverse operation (the one that will undo what is
being done to the variable)?
Subtraction
Subtract 4 from both sides of the equation.
ONE STEP EQUATIONS
x + 4 = 12
-4 -4
x= 8
ONE STEP EQUATIONS
Check your answer
x = 8
8 + 4 = 12
ONE STEP EQUATIONS
Example 2 Solve y - 8 = 17
What is the variable? The variable is y.
What operation is being performed on the variable? Subtraction
What is the inverse operation (the one that will undo what is
being done to the variable)?
Addition
Add 8 to both sides of the equation.
ONE STEP EQUATIONS
y - 8 = 17
+8 +8
y = 25
ONE STEP EQUATIONS
Check your answer
y = 25
25 - 8 = 17
ONE STEP EQUATIONS
Let’s work this together Solve a + 5 = 11
What is the variable? The variable is a.
What operation is being performed on the variable? Addition
What is the inverse operation (the one that will undo what is
being done to the variable)?
Subtraction
What should you do now?
Subtract 5 from both sides of the equation.
ONE STEP EQUATIONS
a + 5 = 11
-5 -5
a= 6
ONE STEP EQUATIONS
Check your answer
a= 6
6 + 5 = 11
ONE STEP EQUATIONS
Let’s work this together Solve x - 7 = 39
What is the variable? The variable is x.
What operation is being performed on the variable? Subtraction
What is the inverse operation (the one that will undo what is
being done to the variable)?
Addition
What should you do now?
Add 7 to both sides of the equation.
ONE STEP EQUATIONS
x - 7 = 39
+7 + 7
x = 46
ONE STEP EQUATIONS
Check your answer
x = 46
46 - 7 = 39
ONE STEP EQUATIONS
Try this on your own
69 + p = 117
-69
-69
p = 48
ONE STEP EQUATIONS
Try this on your own
102 = v - 66
+ 66
+ 66
168 = v
Tell me in your own words
what we covered today…
Make sure you use the vocabulary words.
Solve this real life situation using a
variable.
A repair service charges $25 to send a service person on a call
and $30 per hour for labor. If h stands for the number of hours of
labor, which expression below can the company use to compute
the charge for the service call?
a) 25h + 30
b) 55h
c) 30h
25
d) 25 + 30h
• A repair service charges $25 to send a service
person on a call and $30 per hour for labor. If h
stands for the number of hours of labor, which
expression below can the company use to
compute the charge for the service call?
• d) 25 + 30h
• Now say the problem is 25 + 30h = 115
• What is h ?
Solve this real life situation using a
variable.
A car repair shop charges a service charge of
$150 to go to your vehicle to get it started. The
service person on the call charges an additional
$60 per hour for labor. If h stands for the number
of hours of labor, which expression below can the
company use to compute the charge for the
service call?
a) 150 h + 60
b) 150 + 60h
c) 150h
60
d) 90h
• A car repair shop charges a service charge of
$150 to go to your vehicle to get it started. The
service person on the call charges an additional
$30 per hour for labor. If h stands for the number
of hours of labor, which expression below can
the company use to compute the charge for the
service call?
• b) 150 + 60h
• Now say the problem is 150 + 60h = 450
• What is h ?
AGENDA/ACTIVITIES
3-2 ( Adding and Subtracting with
Variables)
2-3 questions put in left column of
notes.
Adding and Subtracting with
Variables Worksheet 2
Summary using the vocabulary word
in it.
Day 4:Five
minute check
3-3
•Prepare to
take Cornell
Notes
I can create and
solve 2-step
equations using
inverse operations
and express my
thinking orally.
Performance Objective
• I will be able to write and
solve multiplication and
division one-step linear
equations using one
variable and solve problems
involving rates, average
speed, distance, and time.
One-Step Equations
A one-step equation is as
_____ __________ as
it sounds. You will only
need to perform
___________in order to
solve the equation.
Write this in your notes filling in
the blanks.
Dglearn
How were variables used in this
situation? Also give me another real
life situation that variables could be
used in. Be prepared to share what
you write.
One step equations
Add
Subtract
Multiply
Divide
• Addition Rule for solving 1 step
equations:
• You must subtract the same
number from both sides that is
being added. The idea is get
the variable alone by doing the
opposite.
• X + 5 = -9
• X + 5 - 5 = -9 -5
• X = -14
• -6 + X = -4
• -6 + 6 + X = -4 + 6
• X=2
Try the following on your paper.
• 10 = X + 3
• 5+X=9
• 6=3+X
Answers!!!
• X=7
• X=4
• X=3
• Subtraction Rule for solving 1 step
equations:
• You must add the same number
(that is subtracted) from both sides.
The idea is get the variable alone
by doing the opposite.
Equations with subtraction
• X-5=8
• X - 5 + 5 = 8+5
• X = 13
•
•
•
•
•
5-X=6
5 - 5 -X = 6 - 5
-X = 1
(-1)-X = (-1)1
X = -1
Try the following on your paper.
• X - 7 = -1
• X - 4 = 66
• 8=X-2
• -8 = X - 2
Answers!!!
• X=6
• X = 70
• X = 10
• X = -6
• When solving
multiplication
equations, you divide
both sides by the
number attached to
the variable. Be sure
to use the same sign.
Multiplication of Equations
• 3X = -9
3X/3 = -9/3
• X = -3
• -5X = -40
• -5X/-5 = -40/-5
• X=8
3(-3)= -9
-9 = -9
-5(8) = -40
-40 = -40
Try these on your paper.
• 4X = -16
• -1X = 9
• 6 = 5X
• 12X = 3
Answers!!!
• X = -4
• X = -9
• X = 6/5
• X = 1/4
• When
solving division
equations, multiply
both sides by the
reciprocal. You
must keep the sign
of the number with
the number.
Division of Equations
• X/2 = 4
• (2) X = 4(2)
• X=8
• -3/4X = 6
• (-4/3)(-3/4)X = 6(-4/3)
• X = -8
8/2 = 4
4=4
•-3/4(-8) = 6
6=6
Try these on your paper.
– X/3 = 9
– -X/.4 = 7
– 1/3X = -1
– 4 = X/4
Answers!!!
• X = 27
• X = -2.8
• X = -3
• X = 16
One Step Equations
Assessment
1)
2)
-4X = 15
x
2
6) X + 5 = 5
= -8
7) X - 4 = 4
3)
9 - X = -1
8) -X = 5
4)
5)
-12 + X = 0
x
3
=4
9) =-50
10)
x
5 = -55
1)
x
4
2)
x
2
3)
1
3
4)
12
3
5)
x
3
One Step Equations
Assessment
= 15
= -8
6)
1
4
X=5
7) -
7
8
X =4
X = -1
8)
X=0
9)
=4
10)
x
- 2X
3
4
=5
x =-60
x
= -55
5
AGENDA/ACTIVITIES
3-3( Multiplying with Variables)
Ticket out the door:
d = rt.
Using the formula above write your own
rate problem
2-3 questions put in left column of
notes.
Multiplying with Variables worksheet
Five minute
check 3 - 4