what are we going to do? cfu students, you already know how to solve equations. now, we will solve...

What are we going to do?

CFU

Students, you already know how to solve equations. Now, we will solve two-step equations.

Make Connection

An equation states1 two expressions are equal.Inverse operations are operations that undo each other.

1 says or tells

Vocabulary

Inverse Operations

+ and –

● and ÷

Learning Objective

Activate Prior Knowledge

We will solve two-step equations.

Solve the one-step equations.

Equation

expression expression

x + 7 = 9

1. x + 7 = 9− 7 − 7

x = 2

2. x + 3 = 7− 3 − 3

x = 4

3. 4x = 16 4

x = 4

44. 2x = 4

2

x = 2

2

7.EE.4; 6.EE.7 Solve real-world and mathematical problems by writing and solving equations

Name: __________________Wednesday, February 19, 2014

Which of the following is an example of a two-step equation? How do you know?

A 5x = 6

B 5x - 4 = 6

C x - 4 = 6 Which two inverse operations

would be used to solve the two-step equation 5x - 4 = 6?

How do you know?

What is the difference between the solution (x = 2) and

non-solution (x = 4)?

CFU

2 has within it3 needs (synonym)

Vocabulary

Concept Development

A two-step equation contains2 two operations.

2x + 3 = 7

multiplication

addition

- 5 = 1x4

subtraction

division

Inverse Operations

+ and –

● and ÷

Solving Two-Step EquationsA two-step equation requires3 two inverse operations to solve for the variable.

• To keep an equation balanced, inverse operations must be done on both sides of the equation.

22

2x + 3 = 7- 3 - 32x = 4

x = 2

Inverse Operatio

n

Inverse Operati

on

Balance

Balance

Solution

Checking a SolutionThe solution is the value of the variable that makes the equation true.

Solution x = 22x + 3 = 7

2(2) + 3 = 74 + 3 = 7

7 = 7 True!

NOT aSolution

x = 42x + 3 = 7

2(4) + 3 = 78 + 3 = 7

11 = 7 False!

FlashcardsInverse Operations

Isolate2 the term with the variable. Hint: Use inverse operations.

Solve for the variable. Hint: Use inverse operations.

Check and interpret3 the solution. Hint: Answer the question.

Solve two-step equations.1

23

2 separate3 explain

Vocabulary

How did I/you isolate the term with the variable?How did I/you solve for the variable?How did I/you check the solution?

CFU

1

2

3

Skill Development/Guided Practice

1.

________________________________

________________________________

2.

________________________________

________________________________

- 3 = -2x2

+3 +3

2x 12• •2

x 2

x = 2 is the solution because it makes

the equation true.

- 6 = -3x5

+6 +6

5x 35• •5

x 15

x = 15 is the solution because it makes

the equation true.

A two-step equation contains two operations.A two-step equation requires two inverse operations to solve.• To keep an equation balanced, inverse operations must be done on both sides

of the equation.The solution is the value of the variable that makes the equation true.

Inverse Operations

+ and –

● and ÷

3. Jessica paid a $50 flat fee5 to sign up for a gym and $25 each month. If Jessica has paid $175 to the gym, how long has she been a member?

25m + 50 = 175

________________________________

________________________________

4. Maurice paid $15 to sign up for a book club and a $7 annual6 rate. If Maurice has paid $36 to the book club, how long has he been a member?

7y + 15 = 36

________________________________

________________________________

Skill Development/Guided Practice (continued)

Read the problem and identify (underline) important information. Connect the problem to the given equation.

Isolate the term with the variable. Hint: Use inverse operations.


Check and interpret the solution. Hint: Answer the question.


234

a



How did I/you connect the problem to the given equation.How did I/you isolate the term with the variable?How did I/you solve for the variable?How did I/you check the solution?

CFU

2

1a

3

4

Inverse Operations

+ and –

● and ÷

5 (flat fee) one-time payment6 yearly

Vocabulary

− 50 − 5025m = 12525 25

m = 5

25( ) + 50 = 17525(5) + 50 = 175

125 + 50 = 175

175 = 175

?

?

If Jessica has paid $175 to the gym, she has

been a member for five months.

− 15 − 157y = 217 7y = 3

7( ) + 15 = 367(3) + 15 = 3621 + 15 = 36

36 = 36

?

?

If Maurice has paid $36 to the book club, he has

been a member for three years.







234

a



How did I/you connect the problem to the given equation.How did I/you isolate the term with the variable?How did I/you solve for the variable?How did I/you check the solution?

CFU

2

1a

3

4

Inverse Operations

+ and –

● and ÷

5. The length of a rectangular computer monitor is 20 cm. The perimeter of the monitor is 72 cm. What is the width of the computer monitor?

2w + 2l = P

________________________________

________________________________

6. The length of a rectangular cell phone screen is 2 in. The perimeter of the cell phone screen is 10 in. What is the width of the cell phone screen?

2w + 2l = P

________________________________

________________________________

l = 20 cm

w

2w + 2(20) = 722w + 40 = 72

− 40 − 402w = 322 2w = 16

The width of the computer monitor is 16 cm.

2( ) + 40 = 722(16) + 40 = 72

32 + 40 = 7272 = 72

?

?

= 16 cm w2w + 2(2) = 10

2w + 4 = 10− 4 − 42w = 62 2w = 3

The width of the cell phone screen is 3 in.

2( ) + 4 = 102(3) + 4 = 10

6 + 4 = 1010 = 10

?

?

= 3 in

l = 2 in

Flash Cards (Inverse Operations)

Inverse Operations

+ and –

● and ÷

What two inverse operations would be used to solve the equation?

Addition & Multiplication

- 3 = 2x3




Inverse Operations

+ and –

● and ÷


3x - 4 = -13

Addition & Division




Inverse Operations

+ and –

● and ÷


6 + 4x = 14

Subtraction & Division




Inverse Operations

+ and –

● and ÷


Subtraction & Multiplication

3 + = 2x3

Back toConcept Dev




7. A middle school hosted a fall festival to raise money for both grades in the school. The 7th grade class used their half of the money to buy a $750 chemistry set. After buying the chemistry set, the 7th graders had $350 left over. How much money did the school earn at the fall festival?

________________________________

________________________________

8. Maria’s grandmother gave Maria money to share with her two sisters. The three girls split the money evenly and Maria used her share to buy a computer that cost $550. After buying the computer, she had $25 leftover. How much money did Maria’s grandmother give Maria and her sisters?

\

________________________________

________________________________

m2

- 750 = 350

+ 750 + 750m2

= 11002 • • 2

m = 2200

____ 2

- 750 = 3502200

1100 - 750 = 350

350 = 350

The fall festival at the middle school

earned $2,200.

m3

- 550 = 25

+ 550 + 550m3

= 5753 • • 3

m = 1725

____ 3

- 550 = 251725

575 - 550 = 25

25 = 25

Maria’s grandmother gave Maria and her

sisters $1,725 to share.

How did I/you determine what the question is asking?How did I/you determine the math concept required?How did I/you determine the relevant information?How did I/you solve and interpret the problem?How did I/you check the reasonableness of the answer?

CFU

2

1

3

4

5






234

a

What did you learn today about solving two-step equations? (Pair-Share)Use words from the word bank.

Skill Closure

Access Common Core

Summary Closure

Word Bank

two-stepequationinverse

operationsolutionisolate



Inverse Operations

+ and –

● and ÷

1. The length of the basketball backboard is 2 m. The perimeter of the backboard is 6 m. What is the width of the basketball backboard?

2w + 2l = P

_________________________

_________________________

l = 2 m

w= 1 m

2w + 2(2) = 62w + 4 = 6

− 4 − 42w = 22 2

w = 1The width of the basketball

backboard is 1 m.

2( ) + 4 = 62(1) + 4 = 6

2 + 4 = 66 = 6

?

?

Which two inverse operations would be used to solve the equation? Explain your answer.

6z - 36 = 60The two inverse operations used would be addition and division because they are the inverse of subtraction and multiplication.

Independent PracticeA two-step equation contains two operations.A two-step equation requires two inverse operations to solve.• To keep an equation balanced, inverse operations must be done on

both sides of the equation.The solution is the value of the variable that makes the equation true.

Inverse Operations

+ and –

● and ÷

1.

________________________________

________________________________

2.

________________________________

________________________________

8 54x

-8 -8

4x

-34• •4

x -12

x = -12 is the solution because it

makes the equation true.

-3x – 12 = -3+12 +12

9

x -3

-3x-3 -3

x = -3 is the solution because it

makes the equation true.





23






234

a



Inverse Operations

+ and –

● and ÷

3. Petra paid $145 for activation1 of a cell phone and pays $50 monthly. If Petra has paid $395, how long has she had her cell phone service?

50m + 145 = 395

________________________________

________________________________

4. The length of a football field is 360 ft. The perimeter of the football field is 1040 ft. What is the width of the football field?

2w + 2l = P

________________________________

________________________________

1 start

Vocabulary

− 145 − 14550m = 25050 50

m = 5

50(5) + 145 = 395

250 + 145 = 395

395 = 395

?

?

If Petra has paid $395, she has had her cell

phone service for 5 months.

w2w + 2(360) = 10402w + 720 = 1040

− 720 − 7202w = 3202 2w = 160

The width of a football field is 160 ft.

2( ) + 720 = 10402(160) + 720 = 1040320 + 720 = 1040

1040 = 1040

?

?

160 ft =

l = 360 feet

Independent Practice (continued)

Independent Practice (continued)

5. Bill and his four friends earned money doing chores for their neighbors. Bill spent $15 of his share on a new book and had $20 left. How much money did Bill and his friends earn doing chores?

________________________________

________________________________

m5

- 15 = 20+ 15 + 15

m5

= 355 • • 5

m = 175

____ 5

- 15 = 20175

35 - 15 = 20

20 = 20

Bill and his friends earned $175 doing chores.

Periodic Review 1

Access Common Core

1. To ensure a swimming pool is safe, a fence is being built to surround it. To surround the pool, the perimeter of the fence must be 170 m and the length 55 m. How wide does the fence need to be to surround the entire pool?

2w + 2l = P

_________________________________

_________________________________

__

2. In basketball, each basket scores two points and free throws one point. Chandra made 7 free throws. If she scored a total of 23 points, how many baskets did she make?

2b + f = 23

_______________________________________

_______________________________________The width of the fence must be 30 m. If Chandra made 7 free throws and scored 23 points, she

made 8 baskets.

Describe and correct the error each student made below.

Jami:331 students went on a field trip. Six buses were filled and 7 students traveled in cars. How many students were in each bus?

Julio:Imani bought a magazine for $5 and four erasers. She spent a total of $25. How much did each eraser cost?

Juliann:Jill sold half of her comic books and thenbought sixteen more. She now has 36. With how many did she begin?

Jami did not use the correct inverse operation. She should have subtracted 7 instead of adding.

Julio did not use the correct inverse operation. He should have divided by 4 instead of multiplying.

Juliann set up the equation incorrectly. The equation should be c2+ 16 = 36.

Periodic Review 2

Access Common Core

1. A rental car charges an initial payment of $125, plus $34 every day the car is rented. Charles rents a car and pays $363. How long did Charles rent the car?

34d + 125 = 363

_________________________________

_________________________________

__

2. In basketball, each basket scores two points and free throws one point. Troy made 11 free throws. If he scored a total of 19 points, how many baskets did he make?

_______________________________________

_______________________________________

Charles rented the car for seven days. If Troy made 11 free throws and scored 19 points, he

made four baskets.

1 beginning

Vocabulary

1. Malinda has a collection of 34 mugs. When packing to move, she put the same number of mugs in each of the first 5 boxes and 4 mugs in the last box. How many mugs were in each of the first 5 boxes?

Choose Yes or No to indicate whether each statement is true or false.

A The inverse operation of subtraction (-) will be used to solve this problem.

B The equation used to solve this problem is 5b + 4 = 34.

C The solution to the equation represents the number of mugs Malinda has.

D The solution to the equation is b = 6.

O Yes O No

O Yes O No

O Yes O No

O Yes O No

Access Common Core

3. It took Sharon 85 minutes to wash three cars. She spent the same amount of time on each car. She also spent 10 minutes putting everything away. How long was Sharon washing each car?

Choose Yes or No to indicate whether each statement is true or false.

A The inverse operation of addition (+) will be used to solve this problem.

B The equation used to solve this problem is 3m + 10 = 85.

C The solution to the equation represents the amount of time Sharon spent washing each car.

D The solution to the equation is m = 10.

O Yes O No

O Yes O No

O Yes O No

O Yes O No

2. Susan bought 7 reams of paper at the store. The tax on her purchase was $2. She paid a total of $30. How much did each ream of paper cost before tax?

A The equation used to solve this problem is 2r + 7 = 30.

B The inverse operation of subtraction (-) will be used to solve this problem.

C The solution to the equation represents the number of reams of paper Susan bought.

D The solution to the equation is r = 2.

O Yes O No

O Yes O No

O Yes O No

O Yes O No

Periodic Review 3

Access Common Core

1. Janine and her three brothers are given spending money to share. Janine sets $75 aside to save, and spends the other $5 on lunch that afternoon. How much money were Janine and her brothers given?

_________________________________

_________________________________

__

2. An oversized America flag is created to hang above the fence of a softball field. The flag must have a width of 10 ft. and a perimeter of 58 ft. What must the length of the American flag be?

______________________________

______________________________Janine and her brothers were given $320. The length of the flag must be 19 ft.

Match each word problem to the equation that can be used to solve it.

1. Carrie had $32 when she got to the carnival. After riding 6 rides, she had $20 left. What is the price of each ride?

32 - 6x = 20

6x + 32 = 202. Chuck jogged the same distance on Tuesday and Friday, and 8 miles on Sunday, for a total of 20 miles for the week. What is the distance Rick jogged on Tuesday and Friday?

2x + 8 = 20

2x + 20 = 8

3. Jenny wants to save $900 to go to Puerto Rico. She now has $180. If she saves $45 a week, how many more weeks will it take to have $900 saved?

45x + 180 = 900

45x - 180 = 900

4. Brian had $26 when he went to the fair. After playing 7 games, he had $5 left. Find the price for each game.

26 - 7x = 5

26 - 5x = 7

what are we going to do? cfu students, you already know how to solve equations. now, we will solve...

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