what are we going to learn?

CA 7th Grade Algebra and Functions 4.1 (3Q)Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from

which they arose, and verify the reasonableness of the results.Lesson to be used by EDI-trained teachers only.

READY TO TEACHSM EDI® Lessons©2012 All rights reserved.

What are we going to learn?What are we going to learn?

CFUCFU

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

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

Make ConnectionMake Connection

1 says or tells 1 says or tells

VocabularyVocabulary

Inverse Operations

+ and – and

Solve the one-step equations.

Learning ObjectiveLearning Objective

Activate Prior Knowledge

Activate Prior Knowledge

We will solve two-step equations.

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

Equation

x + 7 = 9expression expression

1. x + 7 = 9− 7 − 7

x = 2

2. x + 3 = 7− 3 − 3

x = 4

3. 4x = 164

x = 44

4. 2x = 42x = 2

2

CA 7th Grade Algebra and Functions 4.1 (3Q)Solve two-step equations.

Lesson to be used by EDI-trained teachers only. ©2012 All rights reserved.

A two-step equation contains2 two operations.

Solving Two-Step Equations

Concept DevelopmentConcept Development

2 has within it3 needs (synonym)

2 has within it3 needs (synonym)


5 14

x2x 3 7

addition

multiplication

subtraction

division

A 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.

2x 3 7− 3 − 3

2x 0 42 2

x 2

1 Inverse Operation Balance 1

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

Checking a Solution

2x 3 72(2) 3 7

Solution

?

True7 7

x 2 2x 3 72(4) 3 7

NOT a Solution

?

False11 7

x 42x 3 7

Flashcards:Inverse Operations

Inverse Operations

+ and –

and

CFU

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)?

Addition & Division

1 Inverse Operation Balance 1

2 Inverse Operation Balance 2Inverse Operation2 Balance 2

Animated



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

Isolate4 the term with the variable.Solve for the variable.Check and interpret the solution. Hint: Answer the question.

Solve two-step equations.1

234

a 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?

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?

CFUCFU

2

3

4

Skill Development/Guided Practice

Skill Development/Guided Practice

4 separate4 separate


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

Flashcards:Steps to Check a Solution

1. What is the unknown value of x in the two-step equation?

3 22

x

2. What is the unknown value of x in the two-step equation?

6 35

x

+3 +3

2x

12• •2

x 2

+6 +6

5x

35• •5

x 15

“x = 15 is the solution because it makes the equation true.”“x = 2 is the solution because it makes the equation true.”

?

?

?

?

Now Check! Now

Check!



Skill Development/Guided Practice (continued)



Isolate the term with the variable.Solve for the variable.Check and interpret the solution. Hint: Answer the question.


234

a How did I/you connect the problem to the given two-step 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?

How did I/you connect the problem to the given two-step 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?

CFUCFU

2

3

4

1a



Inverse Operations

+ and –

and

3. A gym membership charges a flat fee5 to sign up, as well as a monthly rate. Jessica paid $50 to sign up and $25 each month. If Jessica has paid $175 to the gym, how long has she been a member?

25m + 50 = 175−50 −5025m = 12525 25m = 5

If Jessica has paid $175 to the gym, she has been a member for five months.

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

125 + 50 = 175175 = 175

?

?

If Maurice has paid $36 to the book club, he has been a member for three years.

4. A book club membership charges a flat fee to sign up, as well as an annual6 rate. Maurice paid $15 to sign up and $7 each year. If Maurice has paid $36 to the book club, how long has he been a member?

7y + 15 = 36−15 −157y = 217 7y = 3

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

21 + 15 = 3636 = 36

?

?

5 one-time payment6 yearly

5 one-time payment6 yearly


Now Check!

Now Check!





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?

w

l = 20 cm

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

?

?

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?

l = 2 in

w

2w + 2l = P

2w + 4 = 10−4 −4

2w = 62 2w = 3

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

6 + 4 = 1010 = 10

?

?

The width of the cell phone screen is 3 in.

w = 16 cmw = 3 in

2w + 2(2) = 10

2w + 2l = P




234



CFUCFU

2

3

4

1a



Inverse Operations

+ and –

and

Now Check!

Now Check!





7. A middle school hosted a fall festival to raise money for both grades in the school. The seventh 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 altogether?

550 253

m

750 3502

m

+ 750 + 750

11002

m

• 22 •

m = 2200

The fall festival at the middle school earned $2,200.

750 3502

2200750 350

2

?

1100 − 750 = 350?

350 = 350

+ 550 + 550

5 753

m

• 33 •

m = 1725

Maria’s grandmother gave Maria and her sisters $1,725 to share.

550 253

1725550 25

3

?

575 − 550 = 25?

25 = 25




234



CFUCFU

2

3

4

1a



Inverse Operations

+ and –

and

Now Check!

Now Check!



Solving two-step equations will help you solve problems in other classes.

Solving two-step equations will help you do well on tests.

1

Does anyone else have another reason why it is relevant to solve two-step equations? (Pair-Share) Why is it relevant to solve two-step equations? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why?

Does anyone else have another reason why it is relevant to solve two-step equations? (Pair-Share) Why is it relevant to solve two-step equations? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why?

CFUCFU3

RelevanceRelevance



In chemistry, we use equations to show chemical reactions. The equation below shows methane burning with oxygen.

CH4 + 2 O2 CO2 + 2 H2O

Sample Test Question:

43. Joan needs $60 for a class trip. She has $32. She can earn $4 an hour mowing lawns. If the equation shows this relationship, how many hours must Joan work to have the money she needs?

4h + 32 = 60

A 7 hours B 17 hours C 23 hours D 28 hours

Solving two-step equations will help you solve real-world problems.

2

B Street Bikes rents bicycles for $16 plus $4 per hour. Eduardo paid $36 to rent a bicycle. For how many hours did he rent the bicycle?

B Street Bikes rents bicycles for $16 plus $4 per hour. Eduardo paid $36 to rent a bicycle. For how many hours did he rent the bicycle?

4h 16 36



What did you learn today about solving two-step equations? (Pair-Share) Summary Closure

Summary Closure

Constructed Response Closure

Constructed Response Closure






234

a

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?

w

l = 2 m2w + 2(2) = 6

2w + 4 = 6− 4 − 42w = 22 2w = 1

The width of the basketball backboard is 1 m.

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

2 + 4 = 66 = 6

?

?w = 1 m

2w + 2l = P

Write an example of a two-step equation.How do you know it is an example of a two-step equation?

Inverse Operations

+ and –

and

Now Check!

Skill ClosureSkill Closure



Independent PracticeIndependent Practice




234

a



Inverse Operations

+ and –

and

3. A cell phone service charges a flat fee for activation1, as well as a monthly rate. Petra paid $145 to sign up and $50 each month. If Petra has paid $395, how long has she had her cell phone service?

1. What is the unknown value of x in the two-step equation? 2. What is the unknown value of x in the two-step equation?

“x = -12 is the solution because it makes the equation true.” “x = -3 is the solution because it makes the equation true.”

3x – 12 = 38 54x

-8 -8

4x

-34• •4

x -12

+12 +12

9

x -3

3x-3 -3

If Petra has paid $395, she has had her cell phone service for five months.50m + 145 = 395

− 145 − 14550m = 25050 50m = 5

50(5) + 145 = 395

250 + 145 = 395395 = 395

?

?

1 start1 start


Now Check! Now

Check!

Now Check!



Independent Practice (continued)

Independent Practice (continued)

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?

The width of the football field is 160 ft.

w

l = 360 ft2w + 2l = P

2w + 720 = 1040− 720 − 720

2w = 3202 2

w = 160

2(160) + 720 = 1040

320 + 720 = 10401040 = 1040

?

?

Hom

e

Vis

itor

w = 160 ft

2w + 2(360) = 1040

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?

15 205

m

+ 15 + 15

355

m

• 55 •

m = 175

Bill and his friends earned $175 doing chores.

1751 5 2 0

5?

35 − 15 = 20?

20 = 20




234

a



Inverse Operations

+ and –

and

Now Check!

Now Check!



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?

The width of the fence must be 30 m.

l = 55ft 2w + 2l = P

2w + 110 = 170− 110 − 110

2w = 602 2w = 30

2(30) + 110 = 170

60+ 110 = 170170 = 170

?

?

Hom

e

Vis

itor

w = 30ft

2w + 2(55) = 170

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

If Chandra made seven free throws and scored 23 points, she made eight baskets.




234

a



Inverse Operations

+ and –

and

Now Check!

Periodic Review 1Periodic Review 1

− 7 − 72b = 162 2

b = 8

2(8) + 7 = 23

16 + 7 = 2323 = 23

?

?

2b + f = 232b + 7 = 23



1. A rental car charges an initial1 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?

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




234

a



Inverse Operations

+ and –

and


Charles rented the car for seven days.

34d + 125 = 363− 125 − 125

34d = 23834 34

d = 7

34(7) + 125 = 363

238 + 125 = 363363 = 363

?

?

1 beginning

If Troy made eleven free throws and scored 19 points, he made four baskets.

2b + 11 = 19− 11 − 11

2b = 82 2b = 4

2(4) + 11 = 19

8 + 11 = 1919 = 19

?

?

2b + f = 19



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?




234

a



Inverse Operations

+ and –

and


m 75 5

4+ 75 + 75

804

m

● 44 ●

m = 320

Janine and her brothers were given $320.

320 7 5 54

?

80 − 75 = 5?

5 = 5

The length of the flag must be 19 ft.

w = 10 ft

2w + 2l = P

20 + 2l = 58− 20 − 20

2l = 382 2l = 19

20 + 2(19) = 58

20 + 38 = 5858 = 58

?

?

l = 19 ft 2(10) + 2l = 58



Inverse Operations

+ and –

and



1. A rental car charges an initial1 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?

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

Which of the following statements is true? How do you know?

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

Subtraction (–) will be the first inverse operation to solve this problem.

The equation used to solve this problem is

The meaning of the solution to this problem is the amount of money he earned. Yes/No34d + 125 = 363. Yes/No

Yes/No

Yes/No


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



The meaning of the solution to this problem is the total number of points that Troy scored. Yes/NoYes/No

Yes/No

Yes/No

2b + 11 = 19.

2b + f = 19.

1 beginning1 beginning


Access Common CoreAccess Common Core





1. 4x 5 19

3. In your own words, describe why equations #1 and #2 have the same solution?

_____________________________________________________________

_

_____________________________________________________________

_

_____________________________________________________________

_

_____________________________________________________________

_

_____________________________________________________________

_

2. 4x 11 13

Inverse Operations

+ and –

and






1. An oversized American 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?


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

The length of the American flag will be 19 ft.


The meaning of the solution to this problem is the length in feet of the flag.

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

20 + 2l = 58.


The meaning of the solution to the problem is the distance around the fence.

The width of the fence will be 60 m.

The inverse operation addition (+) will be used to solve the problem.

The width of the fence will be 110 m.

Yes/NoYes/No

Yes/No

Yes/No

Yes/NoYes/No

Yes/No

Yes/No

Inverse Operations

+ and –

and




Flash Cards (Inverse Operations)


What are the two operations of the equation? What two inverse operations would be used to solve the equation? How do you know?

Subtraction Division Addition Multiplication

4 3 2xReturn to Concept

A two-step equation contains two operations.

A two-step equation requires two inverse operations to solve.





Return to Concept

3x 4 13What are the two operations of the equation? What two inverse operations would be used

to solve the equation? How do you know?

Subtraction Multiplication Addition Division







Return to Concept

6 4x 14What are the two operations of the equation? What two inverse operations would be used

to solve the equation? How do you know?

Addition Multiplication Subtraction Division







Return to Concept

What are the two operations of the equation? What two inverse operations would be used to solve the equation? How do you know?

Addition Division Subtraction Multiplication

27 8xA two-step equation contains two operations.




Flash Cards (Checking Solution)


3 24x

Check the solution to the two-step equations.


Is 20 the value of x that makes the equation true?

“20 _____ the value of x that makes the equation true because _________.”

Whiteboard

1 replace2 explain

1 replace2 explain


Substitue1 the given solution for the variable. Simplify the equation. Interpret2 the given solution. “___ is/is not the solution because __________.”

Solve two-step equations1

23








7 132x


Whiteboard

1 replace2 explain

1 replace2 explain




23





6 4x 14





Whiteboard

1 replace2 explain

1 replace2 explain




23








7x 6 24


Whiteboard

1 replace2 explain

1 replace2 explain




23

what are we going to learn?

Documents