Week 10 2-step equations 2012
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Transcript Week 10 2-step equations 2012
Day 1:Five
minute check
3-4
•Prepare
to take
Cornell
Notes
AGENDA/ACTIVITIES
Monday ( Work Backwards)
Crystal Ball: This week we will be solving 2 step
equations such as 3x + 5 = 8, how do you think the 0ne
step strategy will help you solve two – step equations?
2-3 questions put in left column of notes.
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 ?
We are going to party today, starting out doing the two step for a
bit! Everybody out of your seat and get ready to dance!
Just like the two step dance we do Math equations that have two
or more steps so lets learn how to do them now.
I can create and
solve 2-step
equations using
inverse operations
and express my
thinking orally.
A two Step
equation is simply
an equation that
requires two steps
to solve it.
Example
3h + 4 = 16
*Get the Variable by itself- when doing
that know that
addition and subtraction always come
before multiplication
and subtraction.
3h + 4 = 16
-4=-4
3h = 12
3h / 3 = 12 / 3
h = 4
Solving 2-Step Variable
Equations
What??? I just learned 1-step!
Relax. You’ll use what you already know
to solve 2-step equations.
So, what’s first?
You need to break up the equation into its
two steps.
STEP 1
The first step will always be either adding or
subtracting.
STEP 2
The second step will always be either
multiplying or dividing.
Let’s try a problem.
This
problem has
addition, so
we need to
subtract
first.
8x + 5 = 61
-5 -5
8x
= 56
Whatever
we do on
one side,
we have to
do on the
other.
Now, Step 2.
This problem
has
multiplication,
so we need to
divide now.
8x = 56
8
8
x = 7
Whatever we
do on one
side, we have
to do on the
other.
Let’s try another problem.
This
problem has
subtraction,
so we need
to add first.
3a - 8 = 4
+8 +8
3a
= 12
Whatever
we do on
one side,
we have to
do on the
other.
Now, Step 2.
This problem
has
multiplication,
so we need to
divide now.
3a = 12
3
3
a = 4
Whatever we
do on one
side, we have
to do on the
other.
Now you try some problems.
Copy these problems onto a piece of paper.
Break each problem into 2 parts to solve.
Show all your work!
7f + 5 = 40
12t – 6 = 90
5q – 7 = 13
4y + 8 = -12
Summarize with these questions.
1. What are equations? How can
you use key words in a word
problem to create an algebraic 2step equation?
2. What is a 2-step algebraic
equation? How do you solve
them?
2 STEP EQUATIONS
Bell Work
1. 2x + 4x – 3
2. 5n - 4 + 9n
3. -4j – 6 + 8
4. 7p + 3p + 4 + 10
5. -6 + 2w – 12 – 3w
Bell Work Answers
1. 2x + 4x – 3
2. 5n - 4 + 9n
3. -4j – 6 + 8
4. 7p + 3p + 4 + 10
5. -6 + 2w – 12 – 3w
6x – 3
14n – 4
-4j + 2
10p + 14
-w – 18
Objective
I can create and solve 2-step
equations using inverse
operations and express my
thinking orally.
Fill in the Blank Vocabulary
Equations are mathematical ____________ that contain an
_________ sign.
Addition and Subtraction are _____________ operations.
Multiplication and Division are ______________ operations.
A ___________ represents a number we don’t know.
______________ are numbers that don’t have variables stuck
to them that are added or subtracted in our equation.
Fill in the Blank Vocabulary
Equations are mathematical sentences that contain an equals
sign.
Addition and Subtraction are inverse operations.
Multiplication and Division are inverse operations.
A variable represents a number we don’t know.
Constants are numbers that don’t have variables stuck to
them that are added or subtracted in our equation.
Concept
2 step equations always follow a pattern.
Just like putting socks and shoes on.
Addition and Subtraction are ALWAYS undone
first!!
Then undo multiplication or division second.
Example 1
3x + 5 = 17
3x + 5 = 17
Example 1
3x + 5 = 17
3x + 5 = 17
Example 1
3x + 5 = 17
3x + 5 = 17
-5 -5
Example 1
3x + 5 = 17
3x + 5 = 17
-5 -5
3x
= 12
Example 1
3x + 5 = 17
3x + 5 = 17
-5 -5
3x
= 12
3
3
Example 1
3x + 5 = 17
3x + 5 = 17
-5 -5
3x
= 12
3
3
Example 1
3x + 5 = 17
3x + 5 = 17
-5 -5
3x
= 12
3
3
x
=4
Example 1
3x + 5 = 17
3x + 5 = 17
-5 -5
3x
= 12
3
3
x
=4
x=4
Check the answer
3x + 5 = 17
3(4) + 5 = 17
Check the answer
3x + 5 = 17
3(4) + 5 = 17
12 + 5 = 17
Check the answer
3x + 5 = 17
3(4) + 5 = 17
12 + 5 = 17
17
= 17
Check the answer
3x + 5 = 17
3(4) + 5 = 17
12 + 5 = 17
17
= 17
Our answer is correct!
2 step equations with
combining
2g + 4 + 3g = 29
2g + 3g + 4 = 29
5g + 4 = 29
2 step equations with
combining
2g + 4 + 3g = 29
2g + 3g + 4 = 29
5g + 4 = 29
2 step equations with
combining
2g + 4 + 3g = 29
2g + 3g + 4 = 29
5g + 4 = 29
-4 -4
2 step equations with
combining
2g + 4 + 3g = 29
2g + 3g + 4 = 29
5g + 4 = 29
-4 -4
5g
= 25
2 step equations with
combining
2g + 4 + 3g = 29
2g + 3g + 4 = 29
5g + 4 = 29
-4 -4
5g
= 25
5
5
g
=5
2 step equations with
combining
2g + 4 + 3g = 29
2g + 3g + 4 = 29
5g + 4 = 29
-4 -4
5g
= 25
5
5
g
=5
2 step equations with
combining
2g + 4 + 3g = 29
2g + 3g + 4 = 29
5g + 4 = 29
-4 -4
5g
= 25
5
5
g
=5
20 Questions
Step 1: Get out a piece of paper
Step 2: Fold the paper in half
Step 3: Fold the paper in half again
Step 4: Fold the paper again
Step 5: Fold the paper one more time.
20 Questions
On these cards are 36 questions.
I will put one on each desk. Start by doing the
problem on your desk. LEAVE this card at
your desk!
After 1 minute, everyone needs to switch desks
and find a new card and do that problem.
20 Questions
When an entire side of your paper is full, turn
your paper over and continue doing problems
NO CHEATING!
Now you try some problems.
Copy these problems onto your board.
Break each problem into 2 parts to solve.
Show all your work!
2f + 4 = 60
4t – 5 = 35
6q – 2 = 10
-3y + 7 = -14
I can create and
solve 2-step
equations using
inverse operations
and express my
thinking orally.
A two Step
equation is simply
an equation that
requires two steps
to solve it.
Solving Linear Equations Activity
• You will be in groups of 3-4 .
• Read as a group the rules for the activity.
• You will have 15 minutes to find the correct
steps for each equation.
• Work as a team!
• Every one is required to participate!
Daily Quiz
I can create and
solve 2-step
equations using
inverse operations
and express my
thinking orally.
A two Step
equation is simply
an equation that
requires two steps
to solve it.
•Students review
solving basic twostep equations by
playing a class game
of football.
On the board is a football field
and a football magnet to keep
score. The class will divide into
two teams and take turns
answering questions from the
PowerPoint.
The football starts in the
middle of the field. If the
team gets their question
right, the ball advances
toward their goal. If they get
their question wrong, the ball
advances toward the other
team's goal.
• First one to their goal wins!
• All students will work out the
problems on their white boards if
both partners agree then flip your
boards.
MATH FOOTBALL
Algebra Review
Solve for the variable!
0.5x 1 15
Solve for the variable!
5.5 = -.5x + .5
Solve for the variable!
y
50
4
Solve for the variable!
14x 23 5
Solve for the variable!
y
3
14
Solve for the variable!
11x 143
Solve for the variable!
4/5y + (-25) = 105
Solve for the variable!
2x 3 13
Solve for the variable!
2a 1 501
Solve for the variable!
Because you are a Red
Cross certified babysitter
you charge $6 per hour,
plus an additional $5 to
reserve the date. Friday
night, you earned $41 for
babysitting. How many
hours did you
work?
Solve for the variable!
w
49
18
Solve for the variable!
6x 66
Solve for the variable!
8/3x - 3 = 15
Solve for the variable!
Birdie saved $39 so she
could take her friends to the
movies. It cost $8 for a
ticket, plus she spent $7 for
popcorn and candy. How
many tickets did she buy?
Solve for the variable!
12x 120 0
Solve for the variable!
3x 5 25
Give me an example of
a CONSTANT that
LOOKS LIKE a
VARIABLE
Solve for the variable!
y
110
8
Solve for the variable!
3x 9
Combine like terms!
3x 4x 8x 10
Solve for the variable!
4x 48
Solve for the variable!
10a 21 51
Solve for the variable!
y
3
5
Solve for the variable!
w
4 4
9
Solve for the variable!
4a 3 7
What is the definition of
a variable?
Solve for the variable!
2x 322
What is the
coefficient of 3m ?
Solve for the variable!
8a 12 156
Solve for the variable!
w
5 1
2
Solve for the variable!
2a 4 8
Solve for the variable!
w
3 11
2
Solve for the variable!
w
59
10
Combine like terms!
x 5x
2 2
Solve for the variable!
y
2 .5
4
Solve for the variable!
w
4 11
5
Combine like terms!
3c 2b 4
Solve for the variable!
w
1 3
3
Solve for the variable!
w
1 2
3
Solve for the variable!
w
25
2
How many TERMS are
in the expression
2 x 3 y 4a 2b
Solve for the variable!
w
20
15
Combine like terms!
2 x 4 y 8x 5 y x
Combine like terms!
3x 4x 8x
What is the
coefficient of x ?
Glencoe Main
Idea 3 – 5
Review
I can create and
solve 2-step
equations using
inverse operations
and express my
thinking orally.
A two Step
equation is simply
an equation that
requires two steps
to solve it.
• You charge $8 per hour to mow
the golf course, plus an additional
$7 for gas. Monday, you earned
$63. How many hours did you
work?
Solve for x.
4/5x - 5 = 20
Karla saved $577 so she could take her
friends to the One Directions’ concert in
L.A.. It cost $122 for a ticket, plus she
spent $89 for the motel room to stay the
night. How many tickets did she buy?
Solve for y.
2/3 + (-12) = 106
Solve for x.
6.6 = -.6x + .6
Assessment time!