Mr. Ledbetter's Math Class - Enduring Understandings:€¦ · Web viewThe solution of a linear equation must be reasonable to the situation it describes. Equations can be solved in

381 LessonLINEAR1 (4 instructional days)Solving Equations and Inequalities

Enduring Understandings: The student understands…

That student understands that certain patterns exist in nature and can be represented mathematically.

That functions can be used to model real-world situations. That data representing real-world situations can be collected, organized, and interpreted in order

to solve problems. That linear functions have unique properties and attributes that make them linear. That linear functions can be represented in a variety of ways. That slopes of linear functions can be found from various representations and that they have

meaning based on the related linear situation. The importance of the skills required to manipulate symbols in order to solve problems. That an equation or inequality is the comparison of two expressions such that the values of the

two expressions may or may not be equal.Vocabulary:function notation, arithmetic sequence, term, term value, nth term, recursion, common difference, function, independent, dependent, discrete, continuous, domain, range, input, output, mapping, scatterplot, regression, causation, association, correlation, correlation coefficient, linear, parent function, rate of change, coefficient, constant, slope, slope-intercept form, point-slope form, standard form, trend line, x- and y-intercept, x, y, solution, horizontal, vertical, proportional change, direct variation, directly proportional, zero of a function, constant of proportionality, parallel, perpendicular, inequality, solution set, between, inclusive, exclusive

A.5 Linear functions, equations, and inequalities. The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions.

(A) The student is expected to solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides.; Readiness

The student will know… The student will be able to… The solution of a linear equation must

be reasonable to the situation it describes.

Equations can be solved in a variety of ways.

A linear equation can be used to generate (a) solution(s) to a problem situation.

Solve one-variable equations in real-world and mathematical situations using a variety of methods involving:

Distributive property Variables on both sides

Interpret the solution to one-variable equations from a variety of representations.

Graph Table Algebraic methods

Verify possible solutions with and without technology (calculator).

Table Graph Determine the reasonableness of the solution to

a linear equation as it relates to the situation.

A.5 Linear functions, equations, and inequalities. The student applies the mathematical process standards to solve, with and without technology, linear equations and evaluate the reasonableness of their solutions.

(B) The student is expected to solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides.; Supporting

The student will know… The student will be able to… The solution of a linear inequality must

be reasonable to the situation it describes.

Inequalities can be solved in a variety of ways.

A linear inequality can be used to generate (a) solution(s) to a problem situation.

Solve one-variable inequalities in real-world and mathematical situations using a variety of methods involving: Distributive property Variables on both sides

Interpret the solution to one-variable inequalities from a variety of representations. Graph Table Algebraic methods

Verify possible solutions with and without technology (calculator). Table Graph

Determine the reasonableness of the solution to a linear inequality as it relates to the situation.

A.12 Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to write, solve, analyze, and evaluate equations, relations, and functions.

(E) The student is expected to solve mathematic and scientific formulas, and other literal equations, for a specified variable.; Supporting

The student will know… The student will be able to… Equivalent equations can be written in

various forms. Equations can be manipulated to

isolate different variables while maintaining equivalency.

LINEAR Given a two-variable equation, solve for y. Convert any given equation from one of the forms

listed. Point-slope Slope-intercept Standard

Solve literal equations such as:

Area (A=lw, A=bh, , ,

) Perimeter Circumference Surface Area Volume V=lwh (solve for l, w or h) (solve for h only) Hooke’s law (F=-kX) d=rt F=ma

Limit formulas to those that use operations familiar to students (add, subtract, multiply, divide, distribute, variables on both sides).

Technology TEKS:8(3) Research and information fluency. The student acquires, analyzes, and manages content from

digital resources. The student is expected to:(C) select and evaluate various types of digital resources for accuracy and validity; and(D) process data and communicate results.

8(4) Critical thinking, problem solving, and decision making. The student makes informed decisions by applying critical-thinking and problem-solving skills. The student is expected to:(C) collect and analyze data to identify solutions and make informed decisions;(E) make informed decisions and support reasoning;

ELPS:(2) Cross-curricular second language acquisition/listening. The student is expected to:

(C) learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions;

(D) monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed;

(3) Cross-curricular second language acquisition/speaking. The student is expected to:(D) speak using grade-level content area vocabulary in context to internalize new English

words and build academic language proficiency;(E) share information in cooperative learning interactions;

(4) Cross-curricular second language acquisition/reading. The student is expected to:(E) read linguistically accommodated content area material with a decreasing need for

linguistic accommodations as more English is learned;(5) Cross-curricular second language acquisition/writing. The student is expected to:

(B) write using newly acquired basic vocabulary and content-based grade-level vocabulary;

Materials: Graphing Calculators Markers/Colored Pencils Scissors Glue/Tape Chart Paper 1 set of Find Someone Who per student (Day 1) 1 copy of Harder Equations Notes per student (Day 2) 1 copy of Think Dots per student – optional (Day 2) 1 copy of Equations vs Inequalities Notes per student – optional (Day 3) 1 copy of Equations vs Inequalities Foldable per student (Day 3) 1 copy of Equation vs Inequality Practice per student (Day 3) 1 copy of Literal Equations Notes per student (Day 4) 1 copy of Literal Equations Puzzle per student (Day 4) A Good Strategy,… (optional - one per student)

Procedure:Day 1Use the MATH_0381_LINEAR1_MAT_1EQINEQ_01 notebook file to guide this lesson.

Slide 1: Title Slide

Slide 2: Teacher guided example

Review solving equations with combining like terms, distributive, and variables on both sides using algebra tiles and algebraic steps.









.

Slide 7: Pass out Find Someone Who. Students will walk around the room and find someone to work each of the problems on their sheet. While someone is working on their paper, they in return are working on the other persons.

Each student should only work the same problem once! If they have already worked the problem in need, they must find another person to switch with.

Day 2Use the MATH_0381_LINEAR1_MAT_2EQINEQ_01 notebook file to guide this lesson.

Slide 1: Introduction

Click to play the theme song from “The Jeffersons”. This is to motivate students for solving harder equations. Click to the next slide to stop the music.

Slide 2: Give students a copy of Harder Equations Notes.

Allow students time to work with a partner on each problem before going over them. Select students to show their work on the Smartboard.

One student shows the solving.

One student shows the checking.

One student draws the graph on a number line.

Ask students “How can the answer be verified in the calculator?” Continue the process for the other problems. Slide 3: This slide is a continuation of slide 2.

Slide 4: This slide is a continuation of slides 2 and 3.

Slide 5: This slide is a continuation of slides 2 – 4.

Please do not skip this slide. It is different from the others.



Please do not skip this slide. It is different from the others.



Slide 10: Students will have a copy of the problems for notes. Students are still working with a partner. Have the class read the problem together. Ask students to highlight important information. Then have a few students share. Give them time to write the equation that represents the situation before asking for a volunteer. Select students to show their work on the Smartboard.

One student shows the solving.

One student shows the checking.

One student draws the graph on a number line.

Ask students, “How can the answer be verified in the calculator?” Continue the process for the other problems.Slide 11: This slide is a continuation of slide 10.

Slide 12: This slide is a continuation of slides 10 and 11.

Slide 13: Practice problems – Think Dots

Students should work with a partner.

Students should be able to use calculators to verify their answers.

You can require students to solve at least one word problem for part of their points.


Use the Equations vs Inequalities Foldable as this lessons ISN entry.Slide 1: Ask students to find some similarities and differences between the two characters. This will lead into the discussion on similarities and differences between equations and inequalities. Ask students to share their ideas.

Slide 2: Students will work with a partner. On dry erase boards have one person solve the equation and the other solve the inequality. Remind students that the inequality symbol changes when multiplying or dividing both sides by a negative. Ask students to find some similarities and differences between the two characters. This will lead into the discussion on similarities and differences between equations and inequalities. Ask students to share their ideas. Then compare their steps. Select a student to show their solving steps on the Smartboard. Ask students, “Did anyone use different steps, but got the same solution?”Ask students, “How can the answer be verified in the calculator?” Continue the process for the other problems. Hint tabs are provided if needed.Pull the tab (man pulling a handle) to have students do the following:

One student shows the checking. One student draws the graph on

a number line.Discuss the differences between the solution of an equation and an inequality. Follow these procedures with each slide.

Slide 3: Follow the same procedure on this slide as you did on slide 2.

Slide 4: Follow the same procedure on this slide as you did on slides 2 and 3.

Slide 5: This is a transition slide to help students understand the concepts will not change as the level of difficulty increases for equations and inequalities. Click to reveal.

Slide 6: Pull the shade to reveal a harder equation. Discuss the concepts to solve this equation. (Ex: distributing, combine like terms, etc.) Then reveal the comic.

Slide 7: This slide is a continuation of slide 6. Allow students 2 -3 minutes to solve the equation. After students have had time to solve have a volunteer come to the smartboard and to show their work.

Slide 8: Give each student a copy of Equations vs Inequalities Notes. Students will work with a partner. One person solving the equation and the other solving the inequality. Then compare their steps. Select a student to show their solving steps on the Smartboard.

One student shows the solving. One student shows the checking. One student draws the graph on

a number line.Ask students, “Did anyone use different steps, but got the same solution?” Ask students, “How can the answer be verified in the calculator?” Continue the process for the other problems. Discuss the differences between the solution of an equation and an inequality. Slide 9: Follow the same procedure on this slide as you did on slide 8.

Slide 10: Follow the same procedure on this slide as you did on slides 9 and 9.

Slide 11: Follow the same procedure on this slide as you did on slides 9 - 10.

Slide 12: Follow the same procedure on this slide as you did on slides 9 - 11.

Slide 13: Review these inequality words with the students. Some of these words are ones they struggle with and will need a reminder.

Slide 14: Continue the same procedures as previous slides, but include the discussion of graphing the solution of the inequality and reasonable solutions for the situation. Ask students, “Can you have zero or negative solutions for the situation?”

Slide 15: Continue the same procedures as previous slides, but include the discussion of graphing the solution of the inequality and reasonable solutions for the situation. Ask students, “Can you have fractional solutions for the situation?”

Slide 16: This slide shows students how to set up their ISN entry for this lesson.

Assign students Equation vs. Inequality Practice as individual practice/homework.


Slide 1: Introduction

Slide 2: Ask students, “What are literal equations?” After a few responses, pull the shade to reveal the definition. Ask students, "Based on the definition have they ever seen a literal equation?” “If yes, give some examples.” Pull the shade to reveal the question, “What is the purpose of literal equations?”

Slide 3: The purpose of this slide is for students to substitute the given length (click on example) and the perimeter so students should be able to solve for the width. Students should realize that after substituting in the length and perimeter, a two-step equation is created. Work through one example at a time.

Slide 4: This slide is a continuation of slide 3.

On this slide students are given the information in a table, but the process should be the same.

Slide 5: This slide is continuation of slides 3 and 4.

On this slide students will answer the questions by discussing the mathematical concepts that were used to solve for the width. (Ex: subtract __ from both sides, divide both sides by __, etc.)

Slide 6: This slide is continuation of slides 3 – 5.

This slide will help students discover that the same mathematical process could be applied to the formula to solve for w.


On this slide compare the steps of the first process (substituting in values for the length and perimeter, then solve for the width) to the second process (take the formula for w, then substitute the values for length and perimeter to solve for the width). Do the comparison for each length and perimeter in the table. Students should realize the new equation is more efficient to use to solve for the width.

Slide 8: Follow the same procedure as you did for the previous slide.

On this slide compare the steps of the first process (substituting in values for the length and perimeter, then solve for the width) to the second process (take the formula for w, then substitute the values for length and perimeter to solve for the width). Do the comparison for each length and perimeter in the table. Students should realize the new equation is more efficient to use to solve for the width.

Slide 9: This slide will help students to understand that the mathematical processes used to solve equations, are the same processes to solve literal equations.

Slide 10: Transition Slide

Slide 11: Give students a copy of Literal Equation Notes for students to use as the class goes through the processes to solve literal equations. Mathematical processes are infinitely cloned if needed to help with the understanding during the solving process. Encourage students to work on the Smartboard when going over each problem.

Slide 12: Follow the same procedure as you did for slide 11.

Slide 13: Follow the same procedure as you did for slides 11 and 12.

Slide 14: Just a fun clip to show students that all literal equations are not made of letters.

Slide 15: The problems from this slide are on the student copy. Give them time to work with a partner before going over the problems with the whole class. Students will solve for y, but you do not need to use the term “slope intercept form.” If students use the term acknowledge with a positive phrase for remembering from middle school. Just a reminder for the teacher that this is not the purpose of this slide.

Assign students Literal Equation Puzzle as individual practice/homework.

Extra Materials (if needed): Give students the worksheet A Good Strategy which includes all the concepts covered in this section of the unit. Students can work with a partner or independently. The purpose is for students to skip around on the worksheet working problems first based on their level of understanding. Students will write the problem numbers in the order they decided to work. As the teacher looks at the student’s work, check to see if they answered correctly the problems that were worked first correctly.

Name __________________________________________________

Find Someone WhoFind someone to solve each equation. Make sure they show all of their work before signing their name.

Name _______________________________________ Name _______________________________________ Name _______________________________________

Name _______________________________________ Name _______________________________________ Name _______________________________________

Name _______________________________________ Name _______________________________________ Name _______________________________________

Find Someone Who - KEYFind someone to solve each equation. Make sure they show all of their work before signing their name.

Harder Equations NotesSolve and check each equation. Then graph the solution on a number line.

Solve the Equation Check Algebraically Represent Solution on Number Line

1.

2.

3.

4.

Solve the Equation Check Algebraically Represent Solution on Number Line

5.

6.

7.

8.

Solve the Equation Check Algebraically Represent Solution

on Number Line9. After an oil pipeline burst one morning, gas went up by $2.20 per gallon. If that afternoon you bought 10 gallons of gas for $53.90, what was the price per gallon before the oil pipeline burst that morning?

10. When Apple sells their iPads, they increase the price $50 from what it costs them to actually make the iPads. One Apple store sold 10 iPads one day which cost a total of $5000. How much does an iPad cost to actually make?

11. For Christmas, Samantha purchased subscriptions to Xbox Live for her four children. Each subscription cost $5 per month plus a $15 sign-up fee. If she received a bill for $120, for how many months did she purchase subscriptions for her children?

Harder Equations Notes – KEY Solve and check each equation. Then graph the solution on a number line.

Solve the Equation Check Graph1.

2.

3.

4.

or

5.

6.

7.

8.

9. After an oil pipeline burst one morning, gas went up by $2.20 per gallon. If that afternoon you bought 10 gallons of gas for $53.90, what was the price per gallon before the oil pipeline burst that morning?

10. When Apple sells their iPads, they increase the price $50 from what it costs them to actually make the iPads. One Apple store sold 10 iPads one day which cost a total of $5000. How much does an iPad cost to actually make?

11. For Christmas, Samantha purchased subscriptions to Xbox Live for her four children. Each subscription cost $5 per month plus a $15 sign-up fee. If she received a bill for $120, for how many months did she purchase subscriptions for her children?

Think DotsEach problem below is assigned a point value as indicated by the numbered cube to the left. Choose enough problems to total at least 10 points and work those for your assignment.

Solve and graph the equation. Use the calculator to verify the answer.

Solve: Represent Solution on Number Line:







386 students went on a field trip. Eight buses were filled and 10 students traveled in cars. How many students were in each bus?


Bill weighs 120 pounds and is gaining ten pounds each month. Phil weighs 150 pounds and is gaining 4 pounds each month. How many months, m, will it take for Bill to weigh the same as Phil?


Think Dots – KeyEach problem below is assigned a point value as indicated by the numbered cube to the left. Choose enough problems to total at least 10 points and work those for your assignment.





386 students went on a field trip. Eight buses were filled and 10 students traveled in cars. How many students were in each bus?

Bill weighs 120 pounds and is gaining ten pounds each month. Phil weighs 150 pounds and is gaining 4 pounds each month. How many months, m, will it take for Bill to weigh the same as Phil?

Equations vs Inequalities Notes PageSolve and check each equation and inequality. Then graph the solution.1.

2.

3.

4.

5.

6. You want to organize a group of friends to go to a karaoke studio this Friday night. You must pay $30 to reserve a private karaoke room plus $5 for each person in the group. You also want to have snacks for the group at a cost of $2 per person. How many people can be in the group in order for the total cost to be $65?

You want to organize a group of friends to go to a karaoke studio this Friday night. You must pay $30 to reserve a private karaoke room plus $5 for each person in the group. You also want to have snacks for the group at a cost of $2 per person. How many people can be in the group in order for the total cost to be at most $65?

Equations vs Inequalities Practice - KEYSolve and check each equation and inequality. Then graph the solution.

1.

2.

3.

4.

5.

6. You want to organize a group of friends to go to a karaoke studio this Friday night. You must pay $30 to reserve a private karaoke room plus $5 for each person in the group. You also want to have snacks for the group at a cost of $2 per person. How many people can be in the group in order for the total cost to be at most $65?

You want to organize a group of friends to go to a karaoke studio this Friday night. You must pay $30 to reserve a private karaoke room plus $5 for each person in the group. You also want to have snacks for the group at a cost of $2 per person. How many people can be in the group in order for the total cost to be $65?

Equations vs Inequalities Foldable

Solve each inequality.solution.

Solve each equation. Check your answer algebraically. Graph the solution.

Equation vs. Inequality PracticeSolve each equation or inequality, check your solution algebraically, and represent the solution on a number line.

Solution Solution

Check Algebraically Check Algebraically

Represent Solution on Number Line Represent Solution on Number Line

Solution Solution



Solution Solution



Solve each equation or inequality, check your solution algebraically, and represent the solution on a number line.Solution Solution



Solution Solution



A family wants to hold a dinner party at a restaurant. The restaurant charges $150 to rent space for the party. The food cost for each person at the party is $18. How many people will be able to attend the party if the family spends $420?

Solution A family wants to hold a dinner party at a restaurant. The restaurant charges $150 to rent space for the party. The food cost for each person at the party is $18. How many people can come to the party if the family spends no more than $420?

Solution



Solve each equation or inequality, check your solution algebraically, and represent the solution on a number line.

Solution Solution



Solution Solution



Solution Solution



6

KEY

6

2.8 2

0.5 0.5

Solve each equation or inequality, check your solution algebraically, and represent the solution on a number line.

Solution Solution



Solution Solution



A family wants to hold a dinner party at a restaurant. The restaurant charges $150 to rent space for the party. The food cost for each person at the party is $18. How many people will be able to attend the party if the family spends $420?

Solution A family wants to hold a dinner party at a restaurant. The restaurant charges $150 to rent space for the party. The food cost for each person at the party is $18. How many people can come to the party if the family spends no more than $420?

Solution



-5

-4

15

-4

15

-5

Literal Equations Notes

1. The formula for potential energy is , where P is potential energy, m is mass, g is gravity, and h is height. Write an equation to represent g.

2. Johnny’s teacher asked him to write a more efficient formula for the base of a triangle by rewriting its area formula. He wrote the verbal descriptions instead. Find the formula by filling in the steps based on his verbal descriptions.

3. An oil company’s employee was asked to find the height of a cylindrical tank. Rewrite the formula to represent the height.

Solve each literal equation for the indicated variable.

1. ; for y 2. ; for y 3. ; for y

Literal Equations Notes KEY

1. The formula for potential energy is , where P is potential energy, m is mass, g is gravity, and h is height. Write an equation to represent g.

2. Johnny’s teacher asked him to write a more efficient formula for the base of a triangle by rewriting its area formula. He wrote the verbal descriptions instead. Find the formula by filling in the steps based on his verbal descriptions.

3. An oil company’s employee was asked to find the height of a cylindrical tank. Rewrite the formula to represent the height.

Solve each literal equation for the indicated variable.

1. ; for y 2. ; for y

3. ; for y

Literal Equations Puzzle Name __________________________________________ Period ____

What Do You Call a Wristwatch to be Worn in the 23rd Century?Solve each formula below for the indicated letter. Circle the letter next to your answer. Write this letter in the box at the bottom of the page that contains the number of that exercise.

, for r

(E)

(L)

, for h

(H)

(U)

, for b2

(A)

(U)

, for r

(N)

(S) , for p

(N)

(T)

, for b

(A)

(I)

, for F

(S)

(F)

, for S

(K)

(E) , for d

(S)

(R)

, for w

(I)

(P)

, for t

(N)

(W)

, for v

(T)

(S) , for h

(I)

(V)

, for y

(N)

(C)

, for C

(T)

(S)

, for e

(C)

(R)

6 10 5 12 9 3 1 11 16 7 13 2 15 4 8 14

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

What Do You Call a Wristwatch to be Worn in the 23rd Century?Solve each formula below for the indicated letter. Circle the letter next to your answer. Write this letter in the box at the bottom of the page that contains the number of that exercise.

, for r

(E)

(L)

, for h

(H)

(U)

, for b2

(A)

(U)

, for r

(N)

(S) , for p

(N)

(T)

, for b

(A)

(I)

, for F

(S)

(F)

, for S

(K)

(E) , for d

(S)

(R)

, for w

(I)

(P)

, for t

(N)

(W)

, for v

(T)

(S)

, for h

(I)

(V)

, for y

(N)

(C)

, for C

(T)

(S)

, for e

(C)

(R)

6

A10

f5

u12

t9

u3

r1

e11

w16

r7

i13

s2

t15

t4

i8

c14

k

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

KEY

Name ___________________________________________ Date _____________________ Period ____

A Good Strategy…work what you know first!Write in the blanks the problem number based on the order that you choose to work.

____, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____

1. Write an equation for the situation below. Write the answer in a complete sentence. Verify the answer in the calculator. Then graph the solution.

On Saturday, you bowl at Mar Vista Bowl, where renting shoes costs $2 and each game is $3.50. On Sunday, you bowl at Pinz where the shoe rental is $5 and each game bowled is $3.25. If you spent the same amount each day, how many games, g, were bowled?

2. Which literal equation represents solving for F correctly?

A. C.

B. D.

3. Solve and check the inequality. Then graph the solution.

4. Write an inequality for the situation below. Write the answer in a complete sentence. Then graph the solution.Erica has $50 to spend for food for a birthday party. The birthday cake will cost $22, and she also wants to buy 4 bags of mixed nuts. How much could she spend on each bag of nuts?

5. Solve the literal equation for y.

6. Max is solving the equation . Which of the following are the correct steps in finding the solution?

A. Divide both sides by 4. Then add 5 to both sides.B. Add 4 plus 4. Then subtract x from both sides.C. Subtract 4 from both sides. Then divide both sides by 8.D. Distribute 4 across the parenthesis. Then combine like terms.

7. The solution of this equation has an error. Identify at which step the error occurred.

Step 1Step 2Step 3 Step 4

A. Step 1 C. Step 3

B. Step 2 D. Step 4

8. The length of a rectangle is 50 centimeters longer than the width. If the perimeter of the rectangle is 220 centimeters, find the width and length.

9. Which equations are equivalent?

I. II. III.

A. I & II C. I & III

B. II & III D. None of the equations are equivalent

10. Solve and check the equation. Then graph the solution.

11. A store had homemade quilts on sale for $20 off the original price. Grandmother Ethel jumped at the bargain and bought a quilt for 5 members of her family. If Grandmother Ethel paid $375 for all the quilts, what was the original price of each quilt?

12. Which inequality has a solution represented by the graph below?

A. C.

B. D.

13. Which is equivalent to ?

A. C.

B. D.


15. A student worked the inequality showing the steps below.

Step 1 Step 2 Step 3 Step 4

Which statement is correct?

A. There is an error in Step 2. C. There is an error in Step 4.

B. There is an error in Step 3. D. No errors were made. The problem was worked correctly.

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A Good Strategy, work what you know first! (KEY)Write in the blanks the problem number based on the order that you choose to work.

____, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____, ____

1. Write an equation for the situation below. Write the answer in a complete sentence. Verify the answer in the calculator. Then graph the solution.

On Saturday, you bowl at Mar Vista Bowl, where renting shoes costs $2 and each game is $3.50. On Sunday, you bowl at Pinz where the shoe rental is $5 and each game bowled is $3.25. If you spent the same amount each day, how many games, g, were bowled?

2. Which literal equation represents solving for F correctly?

A. C.

B. D.

3. Solve and check the inequality. Then graph the solution.

4. Write an inequality for the situation below. Write the answer in a complete sentence. Then graph the solution.Erica has $50 to spend for food for a birthday party. The birthday cake will cost $22, and she also wants to buy 4 bags of mixed nuts. How much could she spend on each bag of nuts?


6. Max is solving the equation . Which of the following are the correct steps in finding the solution?

A. Divide both sides by 4. Then add 5 to both sides.B. Add 4 plus 4. Then subtract x from both sides.C. Subtract 4 from both sides. Then divide both sides by 8.D. Distribute 4 across the parenthesis. Then combine like terms.

7. The solution of this equation has an error. Identify at which step the error occurred.

Step 1Step 2Step 3 Step 4

A. Step 1 C. Step 3

B. Step 2 D. Step 4

8. The length of a rectangle is 50 centimeters longer than the width. If the perimeter of the rectangle is 220 centimeters, find the width and length.

The length is 80 cenitmeters and the width is 30 centimeters.

9. Which equations are equivalent?

I. II. III.

A. I & II C. I & III

B. II & III D. None of the equations are equivalent

10. Solve and check the equation. Then graph the solution.

x

x+50

11. A store had homemade quilts on sale for $20 off the original price. Grandmother Ethel jumped at the bargain and bought a quilt for 5 members of her family. If Grandmother Ethel paid $375 for all the quilts, what was the original price of each quilt?

12. Which inequality has a solution represented by the graph below?

A. C.B. D.

13. Which is equivalent to ?

A. C.

B. D.


15. A student worked the inequality showing the steps below.

Step 1 Step 2 Step 3 Step 4

Which statement is correct?

A. There is an error in Step 2. C. There is an error in Step 4.

B. There is an error in Step 3. D. No errors were made. The problem was worked correctly.

2-2 0

Documents

Mr. Ledbetter's Math Class - Enduring Understandings:€¦ · Web viewThe solution of a linear equation must be reasonable to the situation it describes. Equations can be solved in