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382 LessonEQINEQ2 (6 instructional days)Representing and Using Equations and Inequalities in Problem Situations8(8)??Expressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations or inequalities in problem situations. The student is expected to:(A)??write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants; SupportingThe student will know…The student will be able to…symbols can be used to represent unknowns or variables.a linear equation or inequality can be used to generate answers to a problem situation.the difference between > and >, and between < and <.to recognize words that indicate constraints or conditions (ie at least, at most, no more than, etc.) that exist in the problem.the difference between the terms coefficient and constant in an equation.define what an unknown or variable represents in a problem situation.write a linear equation or inequality to represent a problem situation.8(8)??Expressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations or inequalities in problem situations. The student is expected to:(B)??write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants; SupportingThe student will know…The student will be able to…a linear equation or inequality describes a relationship between unknowns.to recognize words that indicate constraints or conditions (ie at least, at most, no more than, etc.) that exist in the problem.create a real-world problem from a one-variable equation or inequality.define what a variable represents in a problem situation.analyze a situation involving a one-variable equation or inequality.8(8)??Expressions, equations, and relationships. The student applies mathematical process standards to use one-variable equations or inequalities in problem situations. The student is expected to:(C)??model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants; Readiness The student will know…The student will be able to…symbols can be used to represent unknowns or variables.the connection between concrete and symbolic methods of solving equations.an equation can be solved using a variety of methods; concrete models, tables, algebraic methods.the concept of an equation means that the value of the expression on the left side is always equivalent to the value of the expression on the right side.to solve an equation or inequality means to determine the value(s) of the unknown which makes the number sentence a true statement.to keep an equation balanced, an operation performed on one side of the equation must also be performed on the other side of the equation.a linear equation can be used to generate answers to a problem situation.the solution of a linear equation must be reasonable to the situation it describes.substitute the appropriate value(s) in order to solve an equation in a problem situation.define what an unknown represents in a problem situation. solve one-variable equations with variables on both sides with models and algebraically. solve one-variable inequalities with variables on both sides algebraically.justify the solution to one-variable equations and inequalities with variables on both sides algebraically and with a graphing calculator.Technology TEKS:NoneELPS:(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;(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;Materials:Markers/Colored PencilsScissorsTape/Glue1 copy of What’s My Equation, Inequality, or Scenario? per student (Day 1)1 class set of Scenarios with Variables on Both Sides Match Up Cards (Day 2)1 copy of Scenarios with Variables on Both Sides Match Up Recording Sheet per student (Day 2)1 copy of More Equations, Inequalities, and Scenarios per student (Day 2)1 copy of Riddle Me This per student (Days 3 – 6)1 or 2 copies of Variables on Both Sides Math Lib Problems – on card stock (Days 3 – 6)MATH_0382_EQINEQ2_MAT_VOBMATHLIB_021 copy of Variables on Both Sides Math Lib Recording Sheet per student (Days 3 – 6)1 copy of The Choice Is Yours: Variables on Both Sides Choice Board per student (Days 3 – 6)MATH_0382_EQINEQ2_MAT_VOBCHOICEBOARD_02 (on legal)1 copy of The Choice Is Yours: Variables on Both Sides Recording Sheet per student (Days 3 – 6)1 copy of Analyzing and Authoring Real-World Problems Tiered Alternative Assessment per student (Days 3 – 6)EQINEQ2 Problem Bank – to be broken up for individual practice/homework (Days 3 – 6) Procedure:Day 1Use the MATH_0382_EQINEQ2_MAT_VOBSCENARIOPRESENT1_02 notebook file to guide this lesson.Slide 1: Title SlideUse this column to write your own notes:Slide 2: Students build the table for each pizzeria in this scenario. Pull the tabs to reveal the table for each pizzeria.Slide 3: Pull the pizza icons to reveal questions. Students may use the table to help them answer the questions.Mama Mia’s: 8p + 4Antonio’s: 6p + 108p + 4 = 6p + 10 Slide 4: Pull the pizza icons to reveal questions. Students may use the table to help them answer the questions.Mama Mia’s less than Antonio’s:8p + 4 < 6p + 10Mama Mia’s greater than or equal to Antonio’s:8p + 4 > 6p + 10 Slide 5: Have students explain to you how to solve each equation/inequality. You may write as students explain or have students come to the smartboard and solve.Pull out the question icon to reveal a question about what the answers mean.8p + 4 = 6p + 10p = 3; Both pizzerias cost the same when 3 pizzas are sold.8p + 4 < 6p + 10p < 3; Mama Mia’s costs less than Antonio’s when 1 or 2 pizzas are sold. 8p + 4 > 6p + 10p > 3; Mama Mia’s costs greater than or equal to Antonio’s when 3, 4, 5, … pizzas are sold. Slide 6: This slide shows each solution’s representation on a number line.Pull out the question icon to reveal possible solutions and have students determine which equation/inequality they belong to.4 pizzas: C12 pizzas: C2 pizzas: B5 pizzas: C1 pizza: B3 pizzas: A and C Slide 7: Students build the table for each pizzeria in this scenario. Pull the tabs to reveal the table for each pizzeriaSlide 8: Pull the pizza icons to reveal questions. Students may use the table to help them answer the questions.Marco’s: 5p + 9Marco’s: 5p + 65p + 9 = 5p + 6 Slide 9: Pull the pizza icons to reveal questions. Students may use the table to help them answer the questions.Marcos’s more than Romano’s:5p + 9 > 5p + 6Marcos’s no more than Romano’s:5p + 9 < 5p + 6 Slide 10: Have students explain to you how to solve each equation/inequality. You may write as students explain or have students come to the smartboard and solve.Pull out the question icon to reveal a question about what the answers mean.8p + 4 = 6p + 10p = 3; Both pizzerias cost the same when 3 pizzas are sold.8p + 4 < 6p + 10p < 3; Mama Mia’s costs less than Antonio’s when 1 or 2 pizzas are sold. 8p + 4 > 6p + 10p > 3; Mama Mia’s costs greater than or equal to Antonio’s when 3, 4, 5, … pizzas are sold. Slide 11: This slide shows each solution’s representation on a number line.Pull out the question icon to reveal possible solutions and have students determine which equation/inequality they belong to. Assign students What’s My Equation, Inequality, or Scenario? as individual practice/homework.Day 2There is no notebook file for this lesson.Students work in partners to complete Scenarios with Variables on Both Sides Match Up.Directions: Pre-cut each set of cards and mix up before giving to students. Give each pair of students a set of Match Up Cards and a recording document.? Students match each scenario with its equation/inequality and its solution.? Students will then add the number line representation to their recording document. ELL Modification: A set of cards with equation/inequality hints has been included to help ELL students understand the scenarios as they read through them. These cards are after the 6th page of cards and denoted with ELL MODIFIED SCENARIOS at the top of the page.Assign students More Equations, Inequalities, and Scenarios as individual practice/homework.Day 3 – 6; Option 1 – RIDDLE ME THISThere is no notebook file for this lesson.Students will work individually to complete the Riddle Me This Worksheet. Assign students problems from the EQINEQ2 Problem Bank as individual practice/homework on any of the four days.Day 3 – 6; Option 2 – MATH LIBUse the MATH_0382_EQINEQ2_MAT_VOBMATHLIB_02 PowerPoint file for the math lib problems.Students will work individually to complete the Variables on Both Sides Scenario Math Lib. Two versions have been included in the Power Point File.*Add teachers’/administartors’ names to slide 1 before printing.*The recording document and PowerPoint are set up as “she”. If you are a male teacher, you will want to change this.Assign students problems from the EQINEQ2 Problem Bank as individual practice/homework on any of the four days.Day 3 – 6; Option 3 – THE CHOICE IS YOURSThe choice board is legal size paper. Use the MATH_0382_EQINEQ2_MAT_VOBCHOICEBOARD_02 Word file for this activity.Students will work individually to complete the The Choice is Yours Choice Board. It may benefit students to sit in small groups in order to have others to discuss the scenarios and to get help solving.Assign students problems from the EQINEQ2 Problem Bank as individual practice/homework on any of the four days.Day 3 – 6; Option 4 – Performance AssessmentStudents will complete the tiered alternative assessment, Analyzing and Authoring Real-World Problems, in partners. Assign partners based on like readiness levels. Version A is for students who struggle with writing equations, inequalities, and real-world problems. Version B is for those students who need some support from the teacher. Version C is for those students who struggle very little and need a challenge. Graphing calculators should be readily available, but will not necessarily help students complete the assessment. Answer keys and grading suggestions are located after each version of the alternative assessment.Assign students problems from the EQINEQ2 Problem Bank as individual practice/homework on any of the four days.Name _________________________________________ Date _______________________ Period _____What’s My Equation, Inequality or Scenario?1.At Work-It-Out, a gym membership is $50 per month with no registration fee. At Get Fit, the registration fee is $100 and membership costs $30 per month. Which equation could be used to find the number of months, m, for which the total cost of both gyms is the same?A.100 + 30m = 50mB.50m = 30 + 100mC.100 + 50m = 30mD.50m = 100 – 30m2.Which of the following real-world problems can be modeled with the inequality 384 + 2x < 6x?A.Marta charges a flat fee of $384 plus $2 per linear foot to decorate tables for a quinceanera. Carla charges $6 per linear foot to do the same. For what number of linear feet, x, will the cost of both decorators be the same?B.Shawna has made 384 campaign buttons for the student council election. She plans to make 2 more buttons each hour. Marguerite plans to make 6 campaign buttons per hour. For what number of hours, x, will Shawna have the same amount of campaign buttons as Marguerite?C.Super Clean house cleaning company charges $384 to power wash a house plus $2 per linear foot. Power Bright charges $6 per linear foot and no flat fee. For what number of linear feet, x, will the cost of Super Clean be more expensive than Power Bright?D.Mega Gym charges a $384 registration fee and $2 each time the gym is used. Super Gym charges a fee of $6 every time the gym is used. What number of times, x, will Super Gym need to be used to exceed the cost of Mega Gym?3.Jose and Maris work for different car dealerships. Jose earns a monthly salary of $3,500 plus a 6% commission on his sales, x. Maris earns a monthly salary of $4,000 plus a 4% commission on her sales, x. For what value of sales, x, will Jose’s earnings be greater than Maris’ earnings?Choose the inequality that could be used to solve this problem.A.3,500 + 6x > 4,000 + 4xB.3,500 + 0.06x > 4,000 + 0.04xC.3,500 + 0.6x > 4,000 + 0.4xD.3,500 + 0.06x < 4,000 + 0.04xWhat’s My Equation, Inequality or Scenario? - KEY1.A2.D3.BScenarios with Variables on Both Sides Match Up Cards – Page 1Bruno Mars has $108 and is spending $4 per day. Rihanna has $45 and is earning $5 per day. After how many days, x, will Rihanna have no less than Bruno Mars?A rubber tree is 108 inches tall and growing at a rate of 4 inches per year. A cactus is 45 inches tall and growing at a rate of 5 inches per year. After how many years, x, will the rubber tree be shorter than the cactus?A fish tank holds 108 gallons of water and is losing water at a rate of 5 gallons per day. A second fish tank contains 45 gallons of water and is having 4 gallons added per day.After how many days, x, will the two fish tanks have the same amount of water?Taylor spent $108 to build her lemonade stand and sells lemonade for $5 per cup. Kenny spent $45 to build his lemonade stand and sells lemonade for $4 per cup. After how many cups of lemonade, x, will Taylor have earned the same as Kenny?A pool has 36 cubic yards of water and is draining at a rate of 3 cubic yards per second. A second pool is empty and filling at a rate of 6 cubic yards per second. At how many seconds, x, will the first pool have less water than the second?The temperature in Australia is 81 degrees and decreasing at a rate of 6 degrees per day. The temperature in the US is 36 degrees and is increasing at a rate of 3 degrees per day. For how many days, x, will Australia be at least as warm as the US?Scenarios with Variables on Both Sides Match Up Cards – Page 2Nicholas’s sand castle is 81 cm tall but the wind is blowing away sand at a rate of 3 cm per minute. Nina’s sand castle is 36 cm tall and she is adding more sand to it at a rate of 6 cm per minute. After how many minutes, x, will Nina and Nicholas’s sand castles be the same height?Nicki’s bank account has a negative balance of $36 so she deposits $3 per day. Kelly’s bank account has a negative balance of $81 so she deposits $6 per day. How many days, x, will it take for Nicki and Kelly’s bank accounts to be equal?Beyonce has $135 and earns $2 for each dog she walks. Ariana Grande has no money but earns $7 for each dog she walks. How many dogs, x, would need to be walked for Ariana to have more money than Beyonce?Comcast charges a $135 start-up fee and $2 per week for internet. AT&T charges a $90 start-up fee and $7 per week for internet. How many weeks, x, will it take for Comcast to cost no more than AT&T?Paul’s Plumbing charges a $90 house call fee and $2 per hour. Perfect Plumbing charges no fee and $7 per hour. How many hours, x, will it be until Paul’s Plumbing is the same price as Perfect Plumbing?Drake has $135 and is spending money at a rate of $2 per day. Luke Bryan has $90 and is working for $7 per day. After how many days, x, will Drake and Luke have the same amount of money?Scenarios with Variables on Both Sides Match Up Cards – Page 3 Scenarios with Variables on Both Sides Match Up Cards – Page 4Scenarios with Variables on Both Sides Match Up Cards – Page 5 Scenarios with Variables on Both Sides Match Up Cards – Page 6Scenarios with Variables on Both Sides Match Up Cards – ELL MODIFIED SCENARIOS Page 1Bruno Mars has $108 and is spending $4 per day. Rihanna has $45 and is earning $5 per day. After how many days, x, will Rihanna have no less than Bruno Mars?Rihanna No less thanBruno_____ + 5x___108 - ____A rubber tree is 108 inches tall and growing at a rate of 4 inches per year. A cactus is 45 inches tall and growing at a rate of 5 inches per year. After how many years, x, will the rubber tree be shorter than the cactus?Rubber TreeShorterCactus____ __ 4x<45 __ _____A fish tank holds 108 gallons of water and is losing water at a rate of 5 gallons per day. A second fish tank contains 45 gallons of water and is having 4 gallons added per day.After how many days, x, will the two fish tanks have the same amount of water?Tank 1SameTank 2___ __ ____=45 __ ____Taylor spent $108 to build her lemonade stand and sells lemonade for $5 per cup. Kenny spent $45 to build his lemonade stand and sells lemonade for $4 per cup. After how many cups of lemonade, x, will Taylor have earned the same as Kenny?TaylorSameKenny___ __ ____ ______ __ ____A pool has 36 cubic yards of water and is draining at a rate of 3 cubic yards per second. A second pool is empty and filling at a rate of 6 cubic yards per second. At how many seconds, x, will the first pool have less water than the second?Pool 1LessPool 2___ __ ____ ______ The temperature in Australia is 81 degrees and decreasing at a rate of 6 degrees per day. The temperature in the US is 36 degrees and is increasing at a rate of 3 degrees per day. For how many days, x, will Australia be at least as warm as the US?AustraliaAt LeastU.S.___ - 6x ______ __ ____Scenarios with Variables on Both Sides Match Up Cards – ELL MODIFIED SCENARIOS Page 2Nicholas’s sand castle is 81 cm tall but the wind is blowing away sand at a rate of 3 cm per minute. Nina’s sand castle is 36 cm tall and she is adding more sand to it at a rate of 6 cm per minute. After how many minutes, x, will Nina and Nicholas’s sand castles be the same height?NicholasSameNina81 - ____ =___ + 6xNicki’s bank account has a negative balance of $36 so she deposits $3 per day. Kelly’s bank account has a negative balance of $81 so she deposits $6 per day. How many days, x, will it take for Nicki and Kelly’s bank accounts to be equal?NickiEqualKelly___ __ __________ __ ____Beyonce has $135 and earns $2 for each dog she walks. Ariana Grande has no money but earns $7 for each dog she walks. How many dogs, x, would need to be walked for Ariana to have more money than Beyonce?ArianaMore ThanBeyonce____ ______ __ 2xComcast charges a $135 start-up fee and $2 per week for internet. AT&T charges a $90 start-up fee and $7 per week for internet. How many weeks, x, will it take for Comcast to cost no more than AT&T?ComcastNo More ThanAT&T___ __ 135 ______ __ 90Paul’s Plumbing charges a $90 house call fee and $2 per hour. Perfect Plumbing charges no fee and $7 per hour. How many hours, x, will it be until Paul’s Plumbing is the same price as Perfect Plumbing?Paul’s SamePerfect___ __ _______7xDrake has $135 and is spending money at a rate of $2 per day. Luke Bryan has $90 and is working for $7 per day. After how many days, x, will Drake and Luke have the same amount of money?DrakeSameLuke___ __ __________ __ ____Name ________________________________________ Date ___________________ Period _____Scenarios with Variables on Both Sides Match UpBruno and RihannaEquation/Inequality (With Work):Solution:Interpret Solution/What does it mean?Number Line Representation:PoolsEquation/Inequality (With Work):Solution:Interpret Solution/What does it mean?Number Line Representation:Nicholas and NinaEquation/Inequality (With Work):Solution:Interpret Solution/What does it mean?Number Line Representation:Comcast and AT&TEquation/Inequality (With Work):Solution:Interpret Solution/What does it mean?Number Line Representation:Paul’s Plumbing and Perfect PlumbingEquation/Inequality (With Work):Solution:Interpret Solution/What does it mean?Number Line Representation:Fish TanksEquation/Inequality (With Work):Solution:Interpret Solution/What does it mean?Number Line Representation:Beyonce and Ariana GrandeEquation/Inequality (With Work):Solution:Interpret Solution/What does it mean?Number Line Representation:Drake and Luke BryanEquation/Inequality (With Work):Solution:Interpret Solution/What does it mean?Number Line Representation:Taylor and KennyEquation/Inequality (With Work):Solution:Interpret Solution/What does it mean?Number Line Representation:Nicki and KellyEquation/Inequality (With Work):Solution:Interpret Solution/What does it mean?Number Line Representation:Australia and U.S.Equation/Inequality (With Work):Solution:Interpret Solution/What does it mean?Number Line Representation:Rubber Tree and CactusEquation/Inequality (With Work):Solution:Interpret Solution/What does it mean?Number Line Representation:Scenarios with Variables on Both Sides Match Up - KEYBruno and RihannaEquation/Inequality (With Work):Solution: Interpret Solution/What does it mean?After 7 days Rihanna will have no less than (more than or equal to) the amount of money as Bruno MarsNumber Line Representation:PoolsEquation/Inequality (With Work):Solution: Interpret Solution/What does it mean?The first pool will have less water than the second pool after 4 or more seconds. Number Line Representation:Nicholas and NinaEquation/Inequality (With Work):Solution: Interpret Solution/What does it mean?Nina and Nicholas’s castles will be the same height after 5 minutes.Number Line Representation:Comcast and AT&TEquation/Inequality (With Work):Solution: Interpret Solution/What does it mean?It will take 9 or more weeks for Comcast to cost no more than AT&T.Number Line Representation:Paul’s Plumbing and Perfect PlumbingEquation/Inequality (With Work):Solution: Interpret Solution/What does it mean?The two plumbing companies will be the same price after 18 hours.Number Line Representation:Fish TanksEquation/Inequality (With Work):Solution: Interpret Solution/What does it mean?The fish tanks will have the same amount of water after 7 days.Number Line Representation:Beyonce and Ariana GrandeEquation/Inequality (With Work):Solution: Interpret Solution/What does it mean?Ariana Grande would need to walk more than 27 dogs in order to have more money than BeyonceNumber Line Representation:Drake and Luke BryanEquation/Inequality (With Work):Solution: Interpret Solution/What does it mean?Drake and Luke Bryan will have the same amount of money after 5 days.Number Line Representation:Taylor and KennyEquation/Inequality (With Work):Solution: Interpret Solution/What does it mean?Taylor and Kenny will have earned the same amount of money after 63 cups of lemonade.Number Line Representation:Nicki and KellyEquation/Inequality (With Work):Solution: Interpret Solution/What does it mean?After 15 days Nicki and Kelly’s bank accounts will be equal.Number Line Representation:Australia and U.S.Equation/Inequality (With Work):Solution: Interpret Solution/What does it mean?Australia will be at least as warm as the U.S. for 5 or less days. Number Line Representation:Rubber Tree and CactusEquation/Inequality (With Work):Solution: Interpret Solution/What does it mean?The cactus will be shorter than the rubber tree after more than 63 years.Number Line Representation:Name ________________________________________ Date __________________________ Period _____More Equations, Inequalities, and Scenarios1.Derrick’s Doggie Day Care charges a $12 registration fee plus $5 per hour for pet sitting. Pauline’s Pooch Park charges $3 per hour plus an $18 registration fee. Which inequality below can be used to find the number of hours, h, for which the cost of Derrick’s Doggie Day Care is at most the cost of Pauline’s Pooch Park? A.12 + 5h ≥ 3h + 18 B.5h + 12 > 18 + 3hC.12 + 5h < 3h + 18D.12 + 5h ≤ 18 + 3h2.Billie needs to have her refrigerator repaired. She contacts two appliance companies and is given the rates shown in the panyService Call ChargeCharge Per HourAcme Repair$4922.50Ace Repair$034.75Write an inequality that can be used to find the number of hours, n, for which Ace’s total charge is less than or the same as Acme’s total charge.3.In any triangle, the length of the longest side must be less than the sum of the lengths of the other two sides. Write an inequality that can be used to find the value of x for the triangle shown below.1609725152400 More Equations, Inequalities, and Scenarios – KEY1.D2. 3.Name ___________________________________________ Date ________________________ Period ____Riddle Me This…What Do You Call A Pig Who Plays Basketball?____________________________________________________________841759522836Write an equation or inequality to model the scenarios given below.1. UPS charges a $7 packaging fee and $0.20 per pound. FedEx charges a $5 packaging fee and $0.30 per pound. How many pounds, x, will it take for UPS and FedEx to cost the same?2. Pedro and Maria each opened savings accounts on the same day, intending to withdraw the money for weekly expenses. Pedro opened his account with $750 and withdrew $35 per week. Maria opened her account with $600 and withdrew $25 weekly. In how many weeks, x, will Pedro have less money than Maria?3. Kaitlin has two puppies. Puppy A weighs 12 pounds and is gaining 1.5 pounds each week. Puppy B weighs 18 pounds and is gaining 0.75 pounds each week. How many weeks, x, will it take for the two puppies to weight the same amount?4. The Magic Carpet charges $35 for installation and $0.25 per square yard of carpeting. The Carpeteria’s installation price is $27 but the store charges $0.40 for each square yard. What number of square yards of carpeting, x, will make Carpeteria cost more than Magic Carpet?5. A twelve inch candle and an 18 inch candle are lit at the same time. The 12-in. candle burns 0.75 inches every hour. The 18 inch candle burns 1.5 inches every hour. After how many hours, x, will the two candles be the same height?6. Shawn and Nick are both selling t-shirts to raise money for their school trip. Shawn spent $750 on supplies and charges $35 per shirt. Nick spent $600 in supplies and charges $25 per shirt. How many shirts, x, must be sold in order for Shawn to earn at least as much as Nick?7. Container A and container B have leaks. Container A has 600 ml of water, and is leaking 5 ml per minute. Container B has 750 ml, and is leaking 7 ml per minute. How many minutes, x, will it take for the two containers to have the same amount of water?8. At Trophies Plus a trophy costs $27 and engraving costs $0.40 per letter. At Total Trophies the same trophy costs $35 and engraving costs $0.25. How many letters, x, must be engraved for the costs at Trophies Plus to be no more than Total Trophies?9. The cost to purchase a song from website 1 is $0.30 per song and a $7 membership fee. To purchase a song from website 2 there is a membership fee of $5 and each purchased song costs $0.20. How many downloaded songs, x, must be purchased for the two websites to be equal?ALMOPTEBHIGSRiddle Me This…What Do You Call A Pig Who Plays Basketball? (KEY)HEISABALLHOG841759522836Write an equation or inequality to model the scenarios given below.1. UPS charges a $7 packaging fee and $0.20 per pound. FedEx charges a $5 packaging fee and $0.30 per pound. How many pounds, x, will it take for UPS and FedEx to cost the same?2. Pedro and Maria each opened savings accounts on the same day, intending to withdraw the money for weekly expenses. Pedro opened his account with $750 and withdrew $35 per week. Maria opened her account with $600 and withdrew $25 weekly. In how many weeks, x, will Pedro have less money than Maria?3. Kaitlin has two puppies. Puppy A weighs 12 pounds and is gaining 1.5 pounds each week. Puppy B weighs 18 pounds and is gaining 0.75 pounds each week. How many weeks, x, will it take for the two puppies to weight the same amount?4. The Magic Carpet charges $35 for installation and $0.25 per square yard of carpeting. The Carpeteria’s installation price is $27 but the store charges $0.40 for each square yard. What number of square yards of carpeting, x, will make Carpeteria cost more than Magic Carpet?5. A twelve inch candle and an 18 inch candle are lit at the same time. The 12-in. candle burns 0.75 inches every hour. The 18 inch candle burns 1.5 inches every hour. After how many hours, x, will the two candles be the same height?6. Shawn and Nick are both selling t-shirts to raise money for their school trip. Shawn spent $750 on supplies and charges $35 per shirt. Nick spent $600 in supplies and charges $25 per shirt. How many shirts, x, must be sold in order for Shawn to earn at least as much as Nick?7. Container A and container B have leaks. Container A has 600 ml of water, and is leaking 5 ml per minute. Container B has 750 ml, and is leaking 7 ml per minute. How many minutes, x, will it take for the two containers to have the same amount of water?8. At Trophies Plus a trophy costs $27 and engraving costs $0.40 per letter. At Total Trophies the same trophy costs $35 and engraving costs $0.25. How many letters, x, must be engraved for the costs at Trophies Plus to be no more than Total Trophies?9. The cost to purchase a song from website 1 is $0.30 per song and a $7 membership fee. To purchase a song from website 2 there is a membership fee of $5 and each purchased song costs $0.20. How many downloaded songs, x, must be purchased for the two websites to be equal?ALMOPTEBHIGSName ____________________________________________ Date _________________________ Period ____Variables on Both Sides Scenario Math Lib(1) _________________ was (2) _____________________ to (3) _________________ when she saw (4) _________________being (5) _________________ by (6) ___________________. The only way to stop the (6) ___________________ was to quickly (7) _______________________ and (8) ____________________________. Luckily this strategy worked and (4) _________________was saved from the (6) ___________________. However, before (4) __________________ was safe a giant (9) ________________ hit the Earth! (1) ___________________ and (4) ___________________ were saved from near death though by their (10) ___________________________. Variables on Both Sides Scenario Math Lib – Version 1 KEY1.C2.D3.C4.B5.D6.A7.A8.B9.C10.B(1) YOUR NAME was (2) taking her/his jet pack to (3) Kroger when she saw (4) One Directionbeing (5) abducted by (6) polka-dotted pandas. The only way to stop the (6) polka-dotted pandas was to quickly (7) do the wobble and (8) recite the Pythagorean Theorem. Luckily this strategy worked and (4) One Direction was saved from the (6) polka-dotted pandas. However, before (4) One Direction was safe a giant (9) alien space ship hit the Earth! (1) YOUR NAME and (4) One Direction were saved from near death though by their (10) killer karate chop. Variables on Both Sides Scenario Math Lib – Version 2 KEY1.D2.C3.A4.A5.B6.D7.C8.C9.B10.A(1) YOUR NAME was (2) floating to (3) Walmart when she saw (4) Maroon 5being (5) sweat talked by (6) little green goblins. The only way to stop the (6) little green goblins was to quickly (7) spin rapidly in a circle and (8) wave goodbye. Luckily this strategy worked and (4) Maroon 5 was saved from the (6) little green goblins. However, before (4) Maroon 5 was safe a giant (9) meteor hit the Earth! (1) YOUR NAME and (4) Maroon 5 were saved from near death though by their (10) awesome math skills. Variables on Both Sides Scenario Math Lib – Version 3 KEY1.C2.D3.B4.B5.A6.D7.A8.C9.A10.D(1) YOUR NAME was (2) skipping to (3) Target when she saw (4) Beyoncebeing (5) run over by (6) stealthy sea lions. The only way to stop the (6) stealthy sea lions was to quickly (7) go home and take a nap and (8) do a backflip. Luckily this strategy worked and (4) Beyonce was saved from the (6) stealthy sea lions. However, before (4) Beyonce was safe a giant (9) piece of the moon hit the Earth! (1) YOUR NAME and (4) Beyonce were saved from near death though by their (10) beautiful smiles.The Choice Is Yours: Variables on Both SidesChoose one of the following arrangement for your choice board.The Choice Is Yours: Variables on Both Sides - KEYHealth Club 1 costs no more than Health Club 2 for 11 or less months. No SolutionThe containers have the same amount after 50 minutes.Awesome Wireless costs at least as much as Phones-R-Us for 200 texts or less.Infinitely Many SolutionsBailey’s number is -6.Rectangle 1 has a length of 6 and width of 2. Rectangle 2 has a length and width of 4.The two candles will be the same height at 11pm.No SolutionBill weighs less than Phil for anything less than 5 months.Infinitely Many SolutionsVista Bowl and Pinz cost the same amount when 12 games are bowled.Michigan’s population will be greater than Ohio’s after 15 years.Analyzing and Authoring Real-World ProblemsAlternative Assessment for Equations and Inequalities with Variables on Both Sides - APart 1: Students in Ms. McMath’s class were asked to write a real-world problem that could be solved with the inequality 35 + 0.75x ≥ 0.5x + 55. Four of her students’ responses are shown in the table below. Complete the table to analyze their responses. If you circle yes, there is no need for an explanation. (64 points)StudentReal-world ProblemCan 35 + 0.75x ≥ 0.5x + 55 be used to solve the real-world problem?Explain in detail what needs to be changed in the real-world problem so 35 + 0.75x ≥ 0.5x + 55 can be used to solve it.MaryRental car company A charges an initial fee of $35 plus $0.75 per mile. Rental car company B charges $0.50 per mile and an initial fee of $55. For what number of miles will the cost of both rental car companies be the same?NoYes JerryJose bought a pair of shoes for $35 and a number of pairs of socks for $0.75 per pair. Mena bought a pair of jeans that cost $55 and a number of pairs of socks that cost $0.50 per pair. How many pairs of socks will make the total cost of Jose’s purchases exceed the total cost of Mona’s purchases?NoYesLarryTodd earns $0.75 for every hour he babysits his younger brother. His mom also pays him $35 per month for an allowance. Caleb earns $0.55 for every hour he babysits his siblings, and his mom pays him $50 per month for an allowance. For what number of hours of babysitting will Todd’s earnings be no less than Caleb’s earnings per month?NoYesKerriAt Coffee-R-Us, Kyle’s salary is $35 per week. He also earns 75% of his weekly sales as a commission. Mona works at Coffee-4-U, and she earns $55 per week in addition to 50% of her weekly sales as a commission. For what amount of weekly sales will Kyle’s weekly earnings be at least as much as Mona’s weekly earnings?NoYesAlternative Assessment for Equations and Inequalities with Variables on Both Sides - APart 2: Write a real-world problem that can be solved with the inequality shown below. (36 points)30 + 2x < 5xSteps for Writing a Real-world Problem for an Equation or Inequality with Variables on Both Sides1. Define the variable.2. Write the situation for the left-hand side of the equation or inequality using the defined variable.3. Write the situation for the right-hand side of the equation or inequality using the same defined variable as the left- hand side.4. Determine what question to ask depending upon the symbol in the center of the equation or inequality.Analyzing and Authoring Real-World ProblemsAlternative Assessment for Equations and Inequalities with Variables on Both Sides - AAnswer KeyThis version is for those students who may struggle with writing real-world problems for inequalities with variables on both sides (VOBS) and may need some help from the teacher.Remember to read student responses carefully and give partial credit for correct thinking!Part 1 (64 points)Mary (16 points – 8 points for “no” and 8 points for correcting the problem)No, she forgot that an inequality was given. The question she wrote asks when the costs of both rental car companies will be the same, and that would mean the equation 35 + 0.75x = 0.5x + 55 would be used to model her problem. She should have written, “For what number of miles will the cost of rental car company A be no less than the cost of rental car company B.” Students may also use “at least as much as” or “greater than or equal to.”Jerry (16 points – 8 points for “no” and 8 points for correcting the problem)No, he knew that an inequality was given, but it says greater than or equal to, and not just greater than. He understood the greater than part when using the word “exceed,” but he should have written, “How many pairs of socks will make the total cost of Jose’s purchases no less than the total cost of Mona’s purchases?” Students may also use “at least as much as” or “greater than or equal to.”Larry (16 points – 8 points for “no” and 8 points for correcting the problem)No, he has the inequality symbol correct, but he switched the 55 and 0.50 for the right-hand side of the equation. He should have written, “Caleb earns $0.50 for every hour he babysits his siblings, and his mom pays him $55 per month for an allowance.”Kerri (16 points – 8 points for “yes” and 8 points for leaving the correction box blank)Yes, she is correct.Part 2 (36 points)Answers will vary for the real-world problem for 30 + 2x < 5x. Be sure that the description of the variable chosen for x on the left-hand side of the inequality is the same as the description of the variable chosen for x on the right-hand side of the inequality. For example, if x represents number of minutes on the left-hand side of the inequality, x has to represent number of minutes on the right-hand side of the inequality.If the student’s real-world problem matches the left-hand side of the inequality, award 12 points.If the student’s real-world problem matches the right-hand side of the inequality, award 12 points.If the inequality symbol is described correctly in terms of the real-world problem, award 12 points.All students will most likely earn at least 12 points.Analyzing and Authoring Real-World ProblemsAlternative Assessment for Equations and Inequalities with Variables on Both Sides - BPart 1: Students in Ms. McMath’s class were asked to write a real-world problem that could be solved with the inequality 35 + 0.75x ≥ 0.5x + 55. Four of her students’ responses are shown in the table below. Complete the table to analyze their responses. If you circle yes, there is no need for an explanation. (64 points)StudentReal-world ProblemCan 35 + 0.75x ≥ 0.5x + 55 be used to solve the real-world problem?Explain in detail what needs to be changed in the real-world problem so 35 + 0.75x ≥ 0.5x + 55 can be used to solve it.MaryRental car company A charges an initial fee of $35 plus $0.75 per mile. Rental car company B charges $0.50 per mile and an initial fee of $55. For what number of miles will the cost of both rental car companies be the same?NoYes KerriAt Coffee-R-Us, Kyle’s salary is $35 per week. He also earns 75% of his weekly sales as a commission. Mona works at Coffee-4-U, and she earns $55 per week in addition to 50% of her weekly sales as a commission. For what amount of weekly sales will Kyle’s weekly earnings be at least as much as Mona’s weekly earnings?NoYesLarryTodd earns $0.75 for every hour he babysits his younger brother. His mom also pays him $35 per month for an allowance. Caleb earns $0.55 for every hour he babysits his siblings, and his mom pays him $50 per month for an allowance. For what number of hours of babysitting will Todd’s earnings be no less than Caleb’s earnings per month?NoYesJerryJose bought a pair of shoes for $35 and a number of pairs of socks for $0.75 per pair. Mena bought a pair of jeans that cost $55 and a number of pairs of socks that cost $0.50 per pair. How many pairs of socks will make the total cost of Jose’s purchases exceed the total cost of Mona’s purchases?NoYesAlternative Assessment for Equations and Inequalities with Variables on Both Sides - BPart 2: Write a real-world problem that can be solved with the inequality shown below. (36 points)50 – 3x < 30 – 2xSteps for Writing a Real-world Problem for an Equation or Inequality with Variables on Both Sides1. Define the variable.2. Write the situation for the left-hand side.3. Write the situation for the right-hand side. 4. Determine what question to ask.Analyzing and Authoring Real-World ProblemsAlternative Assessment for Equations and Inequalities with Variables on Both Sides - BAnswer KeyThis version is for those students who may need some support with writing real-world problems for inequalities with variables on both sides (VOBS), but will most likely do so with little help from the teacher.Remember to read student responses carefully and give partial credit for correct thinking!Part 1 (64 points)Mary (16 points – 8 points for “no” and 8 points for correcting the problem)No, she forgot that an inequality was given. The question she wrote asks when the costs of both rental car companies will be the same, and that would mean the equation 35 + 0.75x = 0.5x + 55 would be used to model her problem. She should have written, “For what number of miles will the cost of rental car company A be no less than the cost of rental car company B.” Students may also use “at least as much as” or “greater than or equal to.”Kerri (16 points – 8 points for “yes” and 8 points for leaving the correction box blank)Yes, she is correct.Larry (16 points – 8 points for “no” and 8 points for correcting the problem)No, he has the inequality symbol correct, but he switched the 55 and 0.50 for the right-hand side of the equation. He should have written, “Caleb earns $0.50 for every hour he babysits his siblings, and his mom pays him $55 per month for an allowance.”Jerry (16 points – 8 points for “no” and 8 points for correcting the problem)No, he knew that an inequality was given, but it says greater than or equal to, and not just greater than. He understood the greater than part when using the word “exceed,” but he should have written, “How many pairs of socks will make the total cost of Jose’s purchases no less than the total cost of Mona’s purchases?” Students may also use “at least as much as” or “greater than or equal to.”Part 2 (36 points)Answers will vary for the real-world problem for 50 – 3x < 30 – 2x. Be sure that the description of the variable chosen for x on the left-hand side of the inequality is the same as the description of the variable chosen for x on the right-hand side of the inequality. For example, if x represents number of minutes on the left-hand side of the inequality, x has to represent number of minutes on the right-hand side of the inequality.If the student’s real-world problem matches the left-hand side of the inequality, award 12 points.If the student’s real-world problem matches the right-hand side of the inequality, award 12 points.If the inequality symbol is described correctly in terms of the real-world problem, award 12 points.All students will most likely earn at least 12 points.Analyzing and Authoring Real-World ProblemsAlternative Assessment for Equations and Inequalities with Variables on Both Sides - CPart 1: Students in Ms. McMath’s class were asked to write a real-world problem that could be solved with the inequality 35 + 0.75x ≥ 0.5x + 55. Four of her students’ responses are shown in the table below. Complete the table to analyze their responses. If you circle yes, there is no need for an explanation. (64 points)StudentReal-world ProblemCan 35 + 0.75x ≥ 0.5x + 55 be used to solve the real-world problem?Explain in detail what needs to be changed in the real-world problem so 35 + 0.75x ≥ 0.5x + 55 can be used to solve it.MaryRental car company A charges an initial fee of $35 plus $0.75 per mile. Rental car company B charges $0.50 per mile and an initial fee of $55. For what number of miles will the cost of both rental car companies be the same?NoYes JerryJose bought a pair of shoes for $35 and a number of pairs of socks for $0.75 per pair. Mena bought a pair of jeans that cost $55 and a number of pairs of socks that cost $0.50 per pair. How many pairs of socks will make the total cost of Jose’s purchases exceed the total cost of Mona’s purchases?NoYesKerriAt Coffee-R-Us, Kyle’s salary is $35 per week. He also earns 75% of his weekly sales as a commission. Mona works at Coffee-4-U, and she earns $55 per week in addition to 50% of her weekly sales as a commission. For what amount of weekly sales will Kyle’s weekly earnings be at least as much as Mona’s weekly earnings?NoYesLarryTodd earns $0.75 for every hour he babysits his younger brother. His mom also pays him $35 per month for an allowance. Caleb earns $0.55 for every hour he babysits his siblings, and his mom pays him $50 per month for an allowance. For what number of hours of babysitting will Todd’s earnings be no less than Caleb’s earnings per month?NoYesAlternative Assessment for Equations and Inequalities with Variables on Both Sides - CPart 2: Write a real-world problem that can be solved with the inequality shown below. (36 points)2.5x + 20.5 < 4x +14Analyzing and Authoring Real-World ProblemsAlternative Assessment for Equations and Inequalities with Variables on Both Sides - CAnswer KeyThis version is for those students who may need very little to no support with writing real-world problems for inequalities with variables on both sides (VOBS).Remember to read student responses carefully and give partial credit for correct thinking!Part 1 (64 points)Mary (16 points – 8 points for “no” and 8 points for correcting the problem)No, she forgot that an inequality was given. The question she wrote asks when the costs of both rental car companies will be the same, and that would mean the equation 35 + 0.75x = 0.5x + 55 would be used to model her problem. She should have written, “For what number of miles will the cost of rental car company A be no less than the cost of rental car company B.” Students may also use “at least as much as” or “greater than or equal to.”Jerry (16 points – 8 points for “no” and 8 points for correcting the problem)No, he knew that an inequality was given, but it says greater than or equal to, and not just greater than. He understood the greater than part when using the word “exceed,” but he should have written, “How many pairs of socks will make the total cost of Jose’s purchases no less than the total cost of Mona’s purchases?” Students may also use “at least as much as” or “greater than or equal to.”Kerri (16 points – 8 points for “yes” and 8 points for leaving the correction box blank)Yes, she is correct.Larry (16 points – 8 points for “no” and 8 points for correcting the problem)No, he has the inequality symbol correct, but he switched the 55 and 0.50 for the right-hand side of the equation. He should have written, “Caleb earns $0.50 for every hour he babysits his siblings, and his mom pays him $55 per month for an allowance.”Part 2 (36 points)Answers will vary for the real-world problem for 2.5x + 20.5 < 4x +14. Be sure that the description of the variable chosen for x on the left-hand side of the inequality is the same as the description of the variable chosen for x on the right-hand side of the inequality. For example, if x represents number of minutes on the left-hand side of the inequality, x has to represent number of minutes on the right-hand side of the inequality.If the student’s real-world problem matches the left-hand side of the inequality, award 12 points.If the student’s real-world problem matches the right-hand side of the inequality, award 12 points.If the inequality symbol is described correctly in terms of the real-world problem, award 12 points.All students will most likely earn at least 12 points.EQINEQ2 Problem Bank1.Purple Taxi has no pick-up fee, but charges $0.25 per mile. ABC Taxi charges $3 for pick-up and $0.15 per mile. Which inequality can be used to find the number of miles, n, for which the cost of a cab ride with Purple Taxi exceeds the cost of a cab ride with ABC Taxi?A.0.25n ≥ 3 + 0.15nB.0.25n + 3 < 0.15nC.0.25n > 0.15n + 3D.3 + 0.15n > 0.25n2.A handyman charges a flat rate of $150, plus $25 per hour for house painting. A painter charges $55 per hour for house painting. Which equation could be used to determine, h, the number of hours each would have to work for their fees to be the same?A.150 – 25h = 55hB.150 + 25h = 55hC.150 – 55h = 25hD.55h + 150 = 25h3.Which of the following scenarios can be modeled with the equation 365 +125x = 175 + 250x?A.Rent-a-Tent rents party tents for a flat fee of $365 plus a daily fee of $125. Superior Rentals rents party tents for $175 per day plus a flat fee of $250. For what number of days, x, will the cost of Rent-a-Tent be equal to the cost of Superior Rentals?B.Rent-a-Tent rents party tents for a flat fee of $365 plus a daily fee of $125. Superior Rentals rents party tents for $250 per day plus a flat fee of $175. For what number of days, x, will the cost of Rent-a-Tent be equal to the cost of Superior Rentals?C.Rent-a-Tent rents party tents for a flat fee of $365 plus a daily fee of $125. Superior Rentals rents party tents for $250 per day plus a flat fee of $175. For what number of days, x, will the cost of Rent-a-Tent exceed the cost of Superior Rentals?D.Rent-a-Tent rents party tents for a flat fee of $125 plus a daily fee of $365. Superior Rentals rents party tents for $175 per day plus a flat fee of $250. For what number of days, x, will the cost of Rent-a-Tent be equal to the cost of Superior Rentals?4.D. J. plans to earn money for an electric guitar. He has two options:Option 1: His grandmother will pay him $250 to paint her tool shed, and he can work for his dad for $10 per hour. He will save 80% of the money he earns.Option 2: He can work for his uncle for $16 per hour. He will save 75% of the money he earns. Which equation below can be used to find the number of hours, h, that D. J. will need to work in order for the money he saves from each option to be the same? A. C.B. D.5.Which of the following scenarios can be represented with the inequality 31.2 – 0.12y < 28.62 – 0.08y?A.Juan has $31.20 in his lunch account. He spends $0.12 per day on snacks in the school cafeteria. Juanita has $28.62 in her lunch account. She spends $0.08 per day on snacks. For how many days, y, will the amount in Juan’s lunch account be more than the amount in Juanita’s lunch account?B.Megan has $31.20 and she saves $0.12 per day by collecting coins she finds on the floor at school and on the bus. Molly has $28.62 and she saves $0.08 per day by collecting coins she finds. In how many days, y, will the total amount of money Megan has saved be less than the total amount of money Molly has saved?C.A tank holds 28.62 gallons of water and a larger tank holds 31.2 gallons of water. The larger tank is leaking at a rate of 0.12 gallon per hour. The smaller tank is leaking at a rate of 0.08 gallon per hour. After how many hours, y, will there be less water in the larger tank than in the smaller tank? D.A commercial coffee pot holds 28.62 ounces of coffee and a larger commercial coffee pot holds 31.2 ounces of coffee. The larger coffee pot is leaking at a rate of 0.08 ounce per hour. The smaller coffee pot is leaking at a rate of 0.12 ounce per hour. After how many hours, y, will the larger coffee pot have less coffee than the smaller coffee pot?6.Scoops Ice Cream Shop sells a large bowl of ice cream for $5.00 plus $1.25 per topping. They also sell a medium bowl of ice cream for $3.50 plus $1.50 per topping. For how many toppings will a medium bowl of ice cream cost more than a large bowl of ice cream?7.A swimming pool containing 23,000 gallons of water loses water due to evaporation at a rate of 600 gallons per week. A swimming pool containing 15,000 gallons of water loses water due to evaporation at a rate of 200 gallons per week. After how many weeks, w, will the smaller pool have at least as much water as the larger pool?8.A home builder wants to hire a painter to paint the inside of a home he is building. Ace painting Services charges a flat rate of $37.50 per hour. Acme Painters charges $25.00 per hour plus $75.00 for supplies. For how many hours, h, will Ace Painting Services charge less than Acme Painters?EQINEQ2 Problem Bank – KEY1.C2.B3.B4.B5.C6.more than 6 toppings7.20 or more weeks8.less than 6 hours ................
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