Lesson 6.2.7 – Writing Equations and Inequalitiesimages.pcmac.org/SiSFiles/Schools/MS/DeSotoCounty/... · Lesson 6.2.7 – Writing Equations and Inequalities 9 | P a g e Section

Lesson 6.2.7 – Writing Equations and Inequalities

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Teacher Lesson Plan Lesson: 6.2.7 – Supplement Writing Equations and Inequalities CC Standards

7.EE.1 Apply properties of equations as strategies to add, subtract, factor, and expand linear equations with rational numbers.

7.EE.4 Use variables to represent quantities in the real world or mathematical problem, and construct

simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Fluently solve equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of real-world problems.

Objective Students will learn to write equations from word problem in the form of px + q = r or p(x + q) = r and inequalities in the form of px + q > r or px + q < r. Mathematical Practices #1 Make sense of problems and persevere in solving them #5 Look for and express regularity in repeated reasoning. Teacher Input Bellwork: Review bellwork. Homework: Review important problems assigned the previous night. Introduction: Ask: If you could visit any country in the world, which country would you choose and why? Display image of redheads. The two kids with red hair said, “Ireland”. When asked why, they said that in Ireland, people don’t think it’s strange to have red hair. Share some interesting facts about redheads. Then lead students into how equations can be used in the real world with the travel planning. Discuss the reading problem and how an equation can be written to find a solution. Lesson: Teach as directed in Student Notes. Practice Classwork: Page 11 Extra Practice: Page 13 (Algebra Mixed Review) Homework: Teacher selected Closure Teacher selected


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Over the past few days we have been solving equations and inequalities. Today, we will be given a real-world problem, and we’ll have to write an equation or inequality. Let’s start with equations…

Introduction to Writing Equations Writing equations from word problems can be quite challenging and the equations can get very long. In 7th grade, we will focus on two types of equation formats.

px + q = r p(x + q) = r

Let’s take a look at a real-world problem, and then we will write an equation in one of these formats.


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If you could choose any country in the world to visit, which country would you choose and why?

The two kids with red hair said, “Ireland”. When asked why, they said that in Ireland, people don’t think it’s strange to have red hair.

Where is Ireland?

Republic of Ireland


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Interesting facts about redheads:

Red hair is the rarest natural hair color in humans. Only 1-2% of the human population has red hair.

Countries with the most redheads: Scotland and Ireland

Red hair is caused by a variant of the MC1R gene, which is found on Chromosome 16.

The gene for red hair is a recessive gene, meaning it is weaker than other genes like the brown hair gene. Because of this, in order to have natural red hair, a person needs to have red haired ancestors present on both the mother's side and the father's side of the family.

It is associated with fair skin color, freckles, and sensitivity to ultraviolet light (more prone to skin cancer).

Redheads are often portrayed as “fiery-tempered”. It was noted that this fiery temper may have helped give them the aggression they needed to survive in the harsh northern climates where they originated from.

Redheads feel more pain than other people. 1) Red haired people need more anesthesia than other people. Studies show that redheads need 20% more anesthesia to knock them out during a surgery than others. 2) Red heads also are resistant to local anesthesia, so trips to the dentist are often feared. 3) Red heads also feel thermal pain much sooner than others.

Cultural reaction to redheads: Varies from ridicule to admiration.

http://simple.wikipedia.org/wiki/Ancestor

http://en.wikipedia.org/wiki/Freckle

http://en.wikipedia.org/wiki/Ultraviolet_light


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How does this relate to equations?

Travel Planning

The Davis Family wants to save $900 to

go to Ireland. They save $45 a week and

now have $180. To find how many

weeks “w” it will take to have $900, we

can write the following equation:

45w + 180 = 900

Notice the format in which the equation is written:


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Student Notes Section 1: Writing equations in the form of px + q = r.

Ryan is saving money to buy a skateboard that costs $85. He has already saved

$40. He plans to save the same amount each week for three weeks. How

much should Ryan save each week? Write an equation and solve.

Format: Write Equation: Solve: 3 3 x = $15 Section 2: Writing equations in the form of p(x + q) = r. Mr. Summer had three sheets of stickers. He gave 20 stickers from each sheet to his students and has 12 total stickers left. Write and solve an equation to find how many stickers, “s”, were originally on each sheet.

Format: Write Equation: Solve:

3 3 x = 24 stickers


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You Try!

px + q = r p (x + q) = r

1) 2)

3) How are equations in px + q= r form different from p(x+q) = r equations?

A company charges $2 for each balloon in an arrangement and a $3 delivery fee. You have $9 to spend. Write equation: Solve:

Four friends went to the movies. They originally had a total of $40. Each friend had the same amount of money and spent $7.50 on a ticket. How much money did each boy have left after buying their tickets? Write Equation: Solve:


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Introduction to Writing Inequalities For purposes of 7th grade our inequalities will be in the form of:

px + q > r px + q < r

These word phrases will help you choose the correct symbol to use when writing your Inequality today.


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Section 3: Writing inequalities in the form of px + q > r or px + q < r.

Debbie is going to the school fair. It costs $5 to enter and $0.50 for each ticket for

games. She wants to spend less than $20. Write and solve an inequality to find the

number of tickets she can buy.

Format: or Write Equation: Solve: . .50 .50 x < 30 Debbie must buy fewer than 30 tickets to stay within her budget.

Trey makes $8.50 an hour working part time. If he gets a $30 bonus this week, what

is the fewest number of hours he must work to make at least $200?

Format: or Write Equation: Solve: 8.50 8.50 x 20 Trey must 20 or more hours to make at least $200.


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You Try!

px + q > r or px + q < r

1) 2)

A cab company charges a flat fee of $2 plus $ 0.75 per mile. Samuel has not more than $20 to spend on a cab ride. Write and solve an inequality to show the number of miles Samuel can travel in the cab? Write Inequality: Solve:

Christy wants to make more than $25 at her annual poster sale. She has already made $15. If she sells each poster for $3, how many more posters does Christy need to sell to reach her goal? Write Inequality: Solve:


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Classwork Name__________________________ Date__________ Period: ____

Directions: Write an equation for each situation and solve.

1) Toya had her birthday party at the movies. It cost $27 for pizza and $8.50 per friend for the movie tickets. How many friends did Toya have at her party if she spent $78?

Write Equation: Solve: 2) Syreeta wants to buy some CDs that each cost $14, and a DVD that costs $23. She has $65. Write and solve an equation to find how many CDs she can buy.

Write Equation: Solve: 3) Crisitano is saving money to buy a bike that costs $189. He has saved $99 so far. He plans on saving $10 each week. In how many weeks will he have enough money to buy the bike? Use an equation to solve algebraically.

Write Equation: Solve: 4) Anne bought a necklace for each of her three sisters. She paid $7 for each necklace. Suppose she had $9 left. Write and solve an equation to find how much money Anne had initially to spend on each sister.

Write Equation: Solve: 5) Mrs. Sorenstam bought one ruler, one compass, and one mechanical pencil at the prices

shown in the table for each of her 12 students. Suppose Mrs. Sorenstam had 36 cents left after buying the school supplies. Write and equation to fine the amount of money Mrs. Sorenstam initially had to spend on each student.

Write Equation: Solve:


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Directions: Write an inequality for each situation and solve. 6) Abigail has $400 in her savings account. She wants to keep at least $160 in the account. She withdraws $40 each week for food. Write and solve an inequality to show how many weeks she can make withdrawals from her account.

Write Inequality: Solve:

7) The bowling alley charges a flat fee of $500 for a birthday party plus $5 for each person. Chantell wants to spend no more than $100 for a party. Write and solve an inequality to show how many people she can invite.

Write Inequality: Solve:

8) You want to purchase a necklace for $325. You have already saved $115 and can set aside $22 a week. Which inequality can be used to find the number of weeks it will take to save at least $325?

A. 22w + 115 325 C. 22 + 115 325 B. 22w + 115 325 D. 22s + 115 325 9)

10) Several vendors at the carnival sell products and advertise their businesses. Shane works for a recreational company that sells ATVs, dirt bikes, snowmobiles, and motorcycles. His boss paid him $ for working all of the days at the carnival plus % commission on all of the sales made at the carnival. What was the minimum amount of sales Shane needed to make if he earned more than $ , ?


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Extra Practice

Name: _________________ Algebra Mixed Review

Period: _______

Section 1: Solving equations

Directions: Solve each equation. Justify your answer by showing your work and check your solution.

1) 2) 3) – 4) Check: Check: Check: Check:

5) 6) 7)

8)

Check: Check: Check: Check: 9) 10) Check: Check:


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11)

12)

Check: Check: 13) 14) Check: Check: 15) 16) Check: Check:


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Section 2: More Practice Solving Equations

17) Which expressions are equivalent to ? (PARCC clone 7.EE.1) Select all that apply.

A.

B.

C.

D.

E.

18) Two equations are shown. (PARCC clone 7.EE.4a-2)

Equation 1: – –

Equation 2: – –

Select each statement that must be true.

A. represents a negative value in both equations.

B. represents a positive value in both equations.

C. represents a positive value in one equation and a negative value in the other equation.

D. The value represents Equation 1 is greater than the value “x” represents in Equation 2.


Equation 1:

Equation 2:

Solve each equation. Then enter a number in each box to make this statement true. The value of is , and the value of is .


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Section 3: Writing Equations from Word Problems

20) Samantha went to Abby’s Restaurant and ordered 1 meat and 3 sides of vegetables for a total cost of $7.50.

The meat cost $3.00.

The sides of vegetables were the same amount each.

Write and solve an equation to determine the amount Samantha had to pay for each side item. (PARCC clone 7.EE.4a-1)

21) Jewel works 5 days a week as a housekeeper at Holiday Inn Express.

Her responsibilities include cleaning rooms and doing laundry.

Each day she spends 3 hours doing laundry.

She worked for a total 55 hours last week.

What is the number of hours Jewel spent each day cleaning rooms? Write and solve an equation to determine how many hours Jewel spends each day cleaning rooms? (PARCC clone 7.EE.4a-1)

22) Janice wants to buy stock in a company. Each share of stock costs $12. She must pay a one-time fee of $50 to buy the stock. If she paid $530, how many shares of stock, , did she buy? Write an equation and solve the problem.


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Student Notes Section 1: Writing equations in the form of px + q = r.

Ryan is saving money to buy a skateboard that costs $85. He has already saved

$40. He plans to save the same amount each week for three weeks. How

much should Ryan save each week? Write an equation and solve.

Format: Write Equation: Solve: 3 3 x = $15 Section 2: Writing equations in the form of p(x + q) = r. Mr. Summer had three sheets of stickers. He gave 20 stickers from each sheet to his students and has 12 total stickers left. Write and solve an equation to find how many stickers, “s”, were originally on each sheet.

Format: Write Equation: Solve:

3 3 x = 24 stickers


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You Try!

px + q = r p (x + q) = r

1) 2)

3) How are equations in px + q= r form different from p(x+q) = r equations?

Possible response: In the first equation x is multiplied by the p. In the second equation both the x and the q are being multiplied by the p. The second form is the factored version of the first.

A company charges $2 for each balloon in an arrangement and a $3 delivery fee. You have $9 to spend.

Write equation: Solve: x = 3 balloons

Four friends went to the movies. They originally had a total of $40. Each friend had the same amount of money and spent $7.50 on a ticket. How much money did each boy have left after buying their tickets? Write Equation: Solve: x = $2.50


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Section 3: Writing inequalities in the form of px + q > r or px + q < r.

Debbie is going to the school fair. It costs $5 to enter and $0.50 for each ticket for

games. She wants to spend less than $20. Write and solve an inequality to find the

number of tickets she can buy.

Format: or Write Equation: Solve: . .50 .50 x < 30 Debbie must buy fewer than 30 tickets to stay within her budget.

Trey makes $8.50 an hour working part time. If he gets a $30 bonus this week, what

is the fewest number of hours he must work to make at least $200?

Format: or Write Equation: Solve: 8.50 8.50 x 20 Trey must 20 or more hours to make at least $200.


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You Try!

px + q > r or px + q < r

1) 2)

A cab company charges a flat fee of $2 plus $ 0.75 per mile. Samuel has not more than $20 to spend on a cab ride. Write and solve an inequality to show the number of miles Samuel can travel in the cab? Write Inequality: .75x + 2 20 Solve: 18 miles

Christy wants to make more than $25 at her annual poster sale. She has already made $15. If she sells each poster for $3, how many more posters does Christy need to sell to reach her goal? Write Inequality: 3x + 15 > 25

Solve: 3

She would need to sell 4 posters.


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Classwork

Name__________________________ Date__________ Period: ____

Directions: Write an equation for each situation and solve.

1) Toya had her birthday party at the movies. It cost $27 for pizza and $8.50 per friend for the movie tickets. How many friends did Toya have at her party if she spent $78?

Write Equation: Solve: friends 2) Syreeta wants to buy some CDs that each cost $14, and a DVD that costs $23. She has $65. Write and solve an equation to find how many CDs she can buy.

Write Equation: Solve: CDs 3) Crisitano is saving money to buy a bike that costs $189. He has saved $99 so far. He plans on saving $10 each week. In how many weeks will he have enough money to buy the bike? Use an equation to solve algebraically.

Write Equation: Solve: weeks 4) Anne bought a necklace for each of her three sisters. She paid $7 for each necklace. Suppose she had $9 left. Write and solve an equation to find how much money Anne had initially to spend on each sister.

Write Equation: Solve: 5) Mrs. Sorenstam bought one ruler, one compass, and one mechanical pencil at the prices

shown in the table for each of her 12 students. Suppose Mrs. Sorenstam had 36 cents left after buying the school supplies. Write and equation to fine the amount of money Mrs. Sorenstam initially had to spend on each student.



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Directions: Write an inequality for each situation and solve. 6) Abigail has $400 in her savings account. She wants to keep at least $160 in the account. She withdraws $40 each week for food. Write and solve an inequality to show how many weeks she can make withdrawals from her account.

Write Equation: Solve: 7) The bowling alley charges a flat fee of $50 for a birthday party plus $5 for each person. Chantell wants to spend no more than $100 for a party. Write and solve an inequality to show how many people she can invite.


8) You want to purchase a necklace for $325. You have already saved $115 and can set aside $22 a week. Which inequality can be used to find the number of weeks it will take to save at least $325? Answer: A A. 22w + 115 325 C. 22 + 115 325 B. 22w + 115 325 D. 22s + 115 325 9)

Extra Practice

10) Several vendors at the carnival sell products and advertise their businesses. Shane works

for a recreational company that sells ATVs, dirt bikes, snowmobiles, and motorcycles. His boss paid him $ for working all of the days at the carnival plus % commission on all of the sales made at the carnival. What was the minimum amount of sales Shane needed to make if he earned more than $ , ?

Inequality: .05s + 500 > 1500 Solve: s > 20,000 The sales had to be more than $ , for Shane to earn more than $ , .


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Name: _________________ Algebra Mixed Review

Period: _______

Section 1: Solving equations

Directions: Solve each equation. Justify your answer by showing your work and check your solution.

1) 2) 3) – 4) Check: Check: Check: Check:

5) 6) 7)

8)

Check: Check: Check: Check: 9) 10)

n =

Check: Check:


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11)

12)

Check: Check: 13) 14) Check: Check: 15) 16) Check: Check:


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Section 2: More Practice Solving Equations

17) Which expressions are equivalent to ? (PARCC clone 7.EE.1) Select all that apply.

A.

B.

C.

D.

E.


Equation 1: – –

Equation 2: – –

Select each statement that must be true.

A. represents a negative value in both equations.

B. represents a positive value in both equations.

C. represents a positive value in one equation and a negative value in the other equation.

D. The value represents Equation 1 is greater than the value “x” represents in Equation 2.


Equation 1:

Equation 2:

Solve each equation. Then enter a number in each box to make this statement true. The value of is , and the value of is .


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Section 3: Writing Equations from Word Problems

20) Samantha went to Abby’s Restaurant and ordered 1 meat and 3 sides of vegetables for a total cost of $7.50.

The meat cost $3.00.

The sides of vegetables were the same amount each.

Write and solve an equation to determine the amount Samantha had to pay for each side item. (PARCC clone 7.EE.4a-1)

Format per objective:

21) Jewel works 5 days a week as a housekeeper at Holiday Inn Express.

Her responsibilities include cleaning rooms and doing laundry.

Each day she spends 3 hours doing laundry.

She worked for a total 55 hours last week.

What is the number of hours Jewel spent each day cleaning rooms? Write and solve an equation to determine how many hours Jewel spends each day cleaning rooms? (PARCC clone 7.EE.4a-1)

Format per objective:

22) Janice wants to buy stock in a company. Each share of stock costs $12. She must pay a one-time fee of $50 to buy the stock. If she paid $530, how many shares of stock, , did she buy?

Write an equation and solve the problem. Format per objective:

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Lesson 6.2.7 – Writing Equations and Inequalitiesimages.pcmac.org/SiSFiles/Schools/MS/DeSotoCounty/... · Lesson 6.2.7 – Writing Equations and Inequalities 9 | P a g e Section